Charles Sanders Peirce's Harvard Lectures

Charles Sanders Peirce and William James
Charles Sanders Peirce and William James
The one who did the most to help Peirce in his desperate times was his old friend William James, dedicating his "Will to Believe" (1897) to Peirce, and arranging for Peirce to be paid to give two series of lectures at or near Harvard (1898 and 1903)
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This a series of seven lectures, delivered at Harvard from March through May, 1903, in which Peirce sought to build a case for pragmatism by examining its pros and cons. He also wanted to distinguish his pragmatism from other, more popular, versions. These are the lectures that William James characterized as "flashes of brilliant light relieved against Cimmerian darkness!" (Head Notes for the EP 2, Chapter 10)

Charles Sanders Peirce's Harvard Lectures
Pragmatism As a Principle and Method of Right Thinking: The 1903 Harvard Lectures on Pragmatism by Charles Sanders Peirce (Author), Patricia Ann Turrisi (Contributor)
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The seven Harvard Lectures that Charles S. Peirce presented in 1903 on pragmatism.
Peirce is known as the founder of the philosophy of pragmatism and these lectures, given near the end of his life, represent his mature thoughts on the philosophy. Peirce’s decomposition of thinking into abduction,deduction, and induction is among the important points in the lectures.

1 Lecture One: Introduction (Pragmatism: The Normative Sciences)
2 Lecture Two: Phenomenology (The Doctrine of Categories)
3 Lecture Three: The Categories Defended
4 Lecture Four: The Reality of Thirdness (The Seven Systems of Metaphysics)
5 Lecture Five: The Normative Sciences
6 Lecture Six: The Nature of Meaning
7 Lecture Seven: Three Cotary Propositions of Pragmatism

Pragmatism is a practical approach. The value of an idea is its "cash-value", a term coined by William James. In philosophical terms, pragmatism states that practicality precedes dogma.
As Peirce puts it, in several places, pragmatism is the doctrine that every conception is a conception of conceivable practical effects. (Lecture VII, page 250)

Pragmatism allows any flight of imagination, provided this imagination ultimately alights upon a possible practical effect. (Lecture VII, page 249 (page 57 herein))

Any hypothesis, therefore, may be admissible, in the absence of any special reasons to the contrary, provided it be capable of experimental verification and only in so far as it is capable of such verification. This is approximately the doctrine of pragmatism. (Lecture VII, page 250 (page 58 herein))

Burch explains Peirce’s pragmatism as follows: “When [Peirce] said that the whole meaning of a (clear) conception consists in the entire set of its practical consequences, he had in mind that a meaningful conception must have some experiential ‘cash value’, capable of being specified as some sort of collection of possible empirical observations under specifiable conditions”.

Atkins notes that pragmatism is intended to enable us to “see what difference the truth of certain concepts would make to our lives”.

Webster’s Dictionary describes pragmatism as the proposition that “the meaning of conceptions is to be sought in their practical bearings, that the function of thought is to guide action, and that truth is preeminently to be tested by the practical consequences of belief”.

Thayer explains that “Because the emphasis is upon method, Peirce often remarked that pragmatism is not a philosophy, a metaphysic, or a theory of truth; it is not a solution or answer to anything but a technique to help us find solutions to problems of a philosophical or scientific nature”.

I save for last in this section what I believe to be the most abstruse of Peirce’s definitions of pragmatism. I believe it is also the most famous. It is often referred to as the Maxim (i.e., principle) of Pragmatism:
"Consider what effects that might conceivably have practical bearings we conceive the object of our conception to have; then, our conception of those effects is the whole of our conception of the object". (Lecture VI, page 231 (page 50 herein))

With all due respect, I believe that the nuts and bolts of pragmatism is the admonition to cultivate the use of abduction -an unconscious process -and the conscious application of deduction and induction. I believe that Peirce would agree that this is the “right way of thinking”.

Pragmatism is the proposal that the value and meaning of any concept is the set of its possible effects (Lecture VI, page 231 (page 50 herein)). If a concept has no possible effects, then it has no value and no meaning. If two concepts have the same set of possible effects, then the two concepts are the same. Pragmatism is utilitarianism with long-range goals (Lecture VI, page 224 (page 49 herein)).

In his Harvard Lectures, Peirce built his case for pragmatism on a new theory of perception, grounded in his theory of categories and on results from phenomenology, esthetics, and ethics (sel. 10).
He argued that there is a realm of reality associated with each category and that the reality of thirdness is necessary to explain a mode of influence on external facts that cannot be explained by mechanical action alone (sel. 11).
He argued that pragmatism is a logical, or semiotic, thesis concerning the meaning of a particular kind of symbol, the proposition, and explained that propositions are signs that must refer to their objects in two ways: indexically, by means of subjects, and iconically, by means of predicates (sel. 12).
The crucial element of Peirce's argument, from the standpoint of his realism, involved the connection between propositional thought and perception. To preserve his realism, Peirce distinguished percepts, which are not propositional, from perceptual judgments, which are propositional, and which are, furthermore, the "first premisses" of all our reasonings.
The process by which perceptual judgments arise from percepts became a key factor in Peirce's case (sel. 13). But if perceptual judgments are the starting points for all intellectual development, then we must be able to perceive generality (sel. 14).
Peirce next argued that abduction shades into perception, so that pragmatism may be regarded as the logic of abduction, and, finally, isolated three key points: that nothing is in the intellect that is not first in the senses; that perceptual judgments contain general elements; and that abductive inference shades into perceptual judgment without any sharp line of demarcation (sel. 15). Pragmatism, Peirce showed, follows from these propositions (sel. 16).

It was in the Harvard Lectures that Peirce, for the first time, made it clear that his realism was opposed to idealism as well as to nominalism. Peirce's new theory of perception embraced the doctrine of immediate perception, to deny which, according to Peirce, "cuts off all possibility of ever cognizing a relation." That idea was carried forward into the Lowell Lectures, where Peirce continued with his effort to prove pragmatism. In "What Makes a Reasoning Sound" (sel. 17), Peirce made a strong case for objective grounds for evaluating reasonings and argued that with the right method even "a slight tendency to guess correctly" will assure progress toward the truth.


Lecture One: Introduction (Pragmatism: The Normative Sciences)

In Lecture One, Peirce describes the goal of the lecture series, namely to provide formal support (as opposed to empirical support) for pragmatism. Yes, pragmatism is certainly valuable, but this does not mean that it is “true.” Peirce believed in an architectonic arrangement of science, namely, mathematics supports phenomenology, and phenomenology supports esthetics, and esthetics supports ethics, and ethics supports logic, and so on.

Logic is where pragmatism fits. This hierarchical notion is similar to the notion that physics supports chemistry, and chemistry supports biology.
Peirce intended to establish pragmatism by first establishing phenomenology, then building on that to establish esthetics, and then building on that to establish ethics, and finally building on that to establish logic.

*Peirce described these lectures as a “philosophical system” that applied to science, philosophy, and the “conduct of life.” Peirce intended in these lectures to provide a proof of pragmatism.
*Pragmatism is conceived to be a principle in logic. That is, it is a rule of how we should think. It is valuable in practical terms, but there are objections to it. There are many definitions of pragmatism, all moderately acceptable, but none of them describe pragmatism with a satisfying precision.
*Because the emphasis is upon method, Peirce often remarked that pragmatism is not a philosophy, a metaphysic, or a theory of truth; it is not a solution or answer to anything but a technique to help us find solutions to problems of a philosophical or scientific nature.
*There is an association between “successful” and “efficient” people and those who understand probabilities and use pragmatism. (There is no certainty in life. A pragmatist is someone who believes the rules of probability and acts accordingly,)
*Because pragmatism is valuable, we should determine if it will always lead us aright. Logic describes what we should think and is dependent upon ethics, which describes what we should do and is dependent upon esthetics, which describes what we should admire.
*Peirce argued that just because something has practical value does not imply that it is “true,” hence the need for a proof of pragmatism. Also, like other scientific theories, pragmatism is simple and may need adjustment over time to fit in practice. Peirce thinks that we humans want to be consistent, so we want to act according to what we reason out. Pragmatism is a fundamental principle of logic. That is, it is a rule of how we should think.
*What is the proof of pragmatic maxim that the possible practical consequences of a concept constitute the sum total of the concept? How do we know that belief is nothing but the deliberate preparedness to act according to the formula believed?

In Lecture I, Peirce considers the utility of the pragmatic maxim and claims that its usefulness does not constitute a proof of its truth--it must pass "through the fire of drastic analysis." Peirce outlines the steps he will take to support his version of pragmatism. He rejects his earlier appeal to facts of psychology and points out that if pragmatism teaches that what we think is to be understood in terms of what we are prepared to do, then the doctrine of how we ought to think (logic) must be a branch of the doctrine of what we deliberately choose to do (ethics). But what we choose to do depends on what we are prepared to admire, which brings us to esthetics. An examination of pragmatism, therefore, involves all three of the normative sciences: logic, ethics, and esthetics. But first we must consider phenomenology, the science that deals with phenomena objectively and isolates the universal categories that pervade all our experience. (Head Notes for the EP 2, Chapter 10)


Pragmatism is a fundamental principle of logic. That is, it is a rule of how we should think. It is valuable in practical terms, but there are objections to it. There are many definitions of pragmatism, all moderately acceptable, but none of them describe pragmatism with a satisfying precision.

The initial definition of pragmatism for these lectures is the one from January 1878 (Lecture I, page 24 (page 17 herein)). Many have people have built on this definition, all without acknowledging the author (Peirce). Perhaps those other writers have thought the author too pedestrian.

Imagine people who are “infinitely” rich, gambling. Whether each person continues to play depends upon whether or not they are winning. But no matter how many times they win, the winners are no richer than before because they were already “infinitely” rich.

So probabilities involve “paradoxes” and “puzzles.” An insurance company uses probabilities so that the company’s income will be greater than its claims.

Probabilities, at least for insurance companies, reflect what happens in the world and is not simply a mental construct.

Probabilities are intended to reflect ratios involving events for an unbounded number of events. Imagine tossing a coin—we win if it is heads; we lose if it is tails—an indefinite number of times. In this case it is impossible to determine whether we end up winning or losing.

A probability of 1 does not mean certainty, oddly enough.

There is an association between “successful” and “efficient” people and those who use pragmatism. Pragmatism solves many questions. But this does not mean that pragmatism is “true”: it might need embellishment.

The argument in the “original paper” is that the proof of pragmatism rests on “belief,” which is a willingness to put into action one’s cognitive conclusions. Perhaps belief is a manifestation of people’s desire to act “consistently.” Can we attribute this desire for consistency to evolution? Can we understand a concept independently of our belief in it (i.e., our willingness to adapt our behavior based on the concept)?

An “assertion” is different than “laying a wager.” Can belief have any effect besides upon behavior? What difference in behavior is there if we do or do not believe that we can state the precise value of an irrational number, say? One of the values of pragmatism is that it can accept or discard theories based on their practical effects.

Because pragmatism is valuable, we should determine if it will always lead us aright. Logic describes what we should think and is dependent upon ethics, which describes what we should do and is dependent upon esthetics, which describes what we should admire.

Esthetics is dependent upon phenomenology, which describes what is. The goal of phenomenology is to describe the “categories” or “fundamental modes” by which we describe a phenomenon. Hegel thought there were two types of categories, namely (1) Universal and (2) a sequence of categories that are a function of evolutionary stages.

There are three categories in Hegel’s Universal type. Hegel did not call them “categories” but rather called them, accurately, “stages of thinking.” Because esthetics, ethics, and logic all depend upon phenomenology, phenomenology should be studied prior to the others.

Phenomenology is based on mathematics. Mathematics is concerned with how things could be, not how they are. Hegel’s phenomenology depended upon an immature mathematics and as a consequence is a “pitiful clubfooted affair.”

Perhaps Williams James was the one who described these lectures as philosophy as it pertains to the “practical bearing upon life.” At any rate, Peirce described these lectures as a “philosophical system” that applied to science, philosophy, and the “conduct of life.” Peirce intended in these lectures to provide a proof of pragmatism, preceded by a definition.

Pragmatism as a Logical Maxim
Peirce in 1878 presented his “pragmatic maxim”: “Consider what effects that might conceivably have practical bearings we conceive the object of our conception to have; then, our conception of those effects is the whole of our conception of the object” (Lecture VI, page 231 (page 50 herein)).

Peirce wanted to reclaim the definition of the term.

Turrisi states that Peirce wanted to base his proof on the “ladder” or hierarchy of the sciences. This hierarchy is an “architectonic” view.

Solutions in one science should be derived from building on knowledge developed by sciences below it in the hierarchy. Within philosophy, logic is based on ethics, and logic, in turn, is based on esthetics.

Turrisi says that this set of lectures provides Peirce’s most detailed description of the hierarchy.

Pragmatism’s Efficacy versus Pragmatism’s Truth: The Need for a Proof
Pragmatism “works,” as evidenced by people who use it.

Peirce argued that just because something has practical value does not imply that it is “true,” hence the need for a proof of pragmatism. Also, like other scientific theories, pragmatism is simple and may need adjustment over time to fit in practice. Peirce thinks that we humans want to be consistent, so we want to act according to what we reason out.

We humans want to reduce what Peirce called “doubt.”

Peirce placed pragmatism within logic. He thought that humans were disposed to think pragmatically. Perhaps this was no more than the result of evolution, which could include logical forces.

The Role of Pragmatism in Logic and the Role of Logic in the Architectonic of Science
Is “doubt” and its motivation logical? Turrisi explains that Peirce considered logic to be a way to determine how to reason.

If pragmatism is part of logic, then it should help further the goal of logic. A proof should rely upon the sciences below logic in the hierarchy.

Logic corresponds to thought; ethics corresponds to reactions; and esthetics corresponds to feeling. These are the three “normative” sciences: they describe what ought to be. These rest on phenomenology, the intent of which is to consider things “as they are.”

[Note: Of course we are unable to determine if we ever see things as they are. “Out of the great cake of life, each species cuts a slice,” as Üexkull puts it (page 227), meaning that each species has sensors for only a limited range of input. Dogs, for example, hear more frequencies than humans, but humans see more frequencies—color vs. only black & white—than dogs. What we do know is that if we are able to survive, our perception has some correspondence to reality.
Meanwhile, we “see” things (i.e., we perceive meaning) only within a context. It is the context that provides the meaning. In the split-second occasions when we are without context— when we are awoken from a deep sleep, sometimes—we work frantically to establish context.]

Peirce uses mathematical examples in these lectures because of his belief in the architectonic nature of science.

Peirce considered these lectures to present a complete arrangement in support of pragmatism and that he was the only one to have provided such a complete arrangement.



14. A certain maxim of Logic which I have called Pragmatism has recommended itself to me for divers reasons and on sundry considerations. Having taken it as my guide in most of my thought, I find that as the years of my knowledge of it lengthen, my sense of the importance of it presses upon me more and more. If it is only true, it is certainly a wonderfully efficient instrument. It is not to philosophy only that it is applicable. I have found it of signal service in every branch of science that I have studied. My want of skill in practical affairs does not prevent me from perceiving the advantage of being well imbued with pragmatism in the conduct of life.

15. ... I propose, then, to submit to your judgment in half a dozen lectures an examination of the pros and cons of pragmatism by means of which I hope to show you the result of allowing to both pros and cons their full legitimate values.

16. I suppose I may take it for granted that you all know what pragmatism is. I have met with a number of definitions of it lately, against none of which I am much disposed to raise any violent protest. Yet to say exactly what pragmatism is describes pretty well what you and I have to puzzle out together.

We must start with some rough approximation of it, and I am inclined to think that the shape in which I first stated [it] will be the most useful one to adopt as matter to work upon, chiefly because it is the form most personal to your lecturer, and [upon] which for that reason he can discourse most intelligently. Besides pragmatism and personality are more or less of the same kidney.

17. I sent forth my statement in January 1878; and for about twenty years never heard from it again. I let fly my dove; and that dove has never come back to me to this very day. But of late quite a brood of young ones have been fluttering about, from the feathers of which I might fancy that mine had found a brood. To speak plainly, a considerable number of philosophers have lately written as they might have written in case they had been reading either what I wrote but were ashamed to confess it, or had been reading something that some reader of mine had read. For they seem quite disposed to adopt my term pragmatism. I shouldn't wonder if they were ashamed of me. What could be more humiliating than to confess that one has learned anything of a logician? But for my part I am delighted to find myself sharing the opinions of so brilliant a company. The new pragmatists seem to be distinguished for their terse, vivid and concrete style of expression together with a certain buoyancy of tone as if they were conscious of carrying about them the master key to all the secrets of metaphysics.

Every metaphysician is supposed to have some radical fault to find with every other, and I cannot find any direr fault to find with the new pragmatists than that they are lively. In order to be deep it is requisite to be dull.

18. On their side, one of the faults that I think they might find with me is that I make pragmatism to be a mere maxim of logic instead of a sublime principle of speculative philosophy. In order to be admitted to better philosophical standing I have endeavored to put pragmatism as I understand it into the same form of a philosophical theorem. I have not succeeded any better than this:
Pragmatism is the principle that every theoretical judgment expressible in a sentence in the indicative mood is a confused form of thought whose only meaning, if it has any, lies in its tendency to enforce a corresponding practical maxim expressible as a conditional sentence having its apodosis in the imperative mood.

But the Maxim of Pragmatism, as I originally stated it, Revue philosophique VII, is as follows:
Considérer quels sont les effets pratiques que nous pensons pouvoir être produits par l'objet de notre conception. La conception de tous ces effets est la conception complète de l'objet. [p. 48.]
Pour développer le sens d'une pensée, il faut donc simplement déterminer quelles habitudes elle produit, car le sens d'une chose consiste simplement dans les habitudes qu'elle implique. Le caractère d'une habitude dépend de la façon dont elle peut nous faire agir non pas seulement dans telle circonstance probable, mais dans toute circonstance possible, si improbable qu'elle puisse être. Ce qu'est une habitude dépend de ces deux points: quand et comment elle fait agir. Pour le premier point: quand? tout stimulant à l'action dérive d'une perception; pour le second point: comment? le but de toute action est d'amener au résultat sensible. Nous atteignons ainsi le tangible et le pratique comme base de toute différence de pensée, si subtile qu'elle puisse être. [p. 47.]

19. The utility of the maxim, provided it is only true, appears in a sufficient light in the original article. I will here add a few examples which were not given in that paper.

There are many problems connected with probabilities which are subject to doubt. One of them, for example, is this: Suppose an infinitely large company of infinitely rich men sit down to play against an infinitely rich bank at a game of chance, at which neither side has any advantage, each one betting a franc against a franc at each bet. Suppose that each player continues to play until he has netted a gain of one franc and then retires, surrendering his place to a new player.

The chance that a player will ultimately net a gain of a franc may be calculated as follows:

Let XL be a player's chance, if he were to continue playing indefinitely, of ever netting a gain of 1 franc.

But after he has netted a gain of 1 franc, his chance of doing which is X[1], he is no richer than before, since he is infinitely rich. Consequently his chance of winning the second franc, after he has won the first, is the same as his chance of winning the first franc. That is, it is X[1] and his chance of winning both is X[2] = (X[1])2. And so in general, X[L] = (X[1])L.

Now his chance of netting a gain of 1 franc, X[1], is the sum of the chances of the two ways in which it may come about; namely by first winning the first bet of which the chance is 1/2, and by first losing the first bet and then netting a gain of 2 francs of which the chance is 1/2 X[1]2. Therefore

X[1] = 1/2 + 1/2 X[1]2
or X[1]2 - 2X[1] + 1 = 0
or (X[1] - 1)2 = 0.

But if the square of a number is zero, the number itself is zero. Therefore

X[1] - 1 = 0
or X[1] = 1.

Consequently, the books would say it was dead certain that any player will ultimately net his winning of a franc and retire. If so it must be certain that every player would win his franc and would retire.

Consequently there would be a continual outflow of money from the bank. And yet, since the game is an even one, the banker would not net any loss. How is this paradox to be explained?

20. The theory of probabilities is full of paradoxes and puzzles. Let us, then, apply the maxim of pragmatism to the solution of them.

In order to do this, we must ask What is meant by saying that the probability of an event has a certain value, p? According to the maxim of pragmatism, then, we must ask what practical difference it can make whether the value is p or something else. Then we must ask how are probabilities applied to practical affairs. The answer is that the great business of insurance depends upon it. Probability is used in insurance to determine how much must be paid on a certain risk to make it safe to pay a certain sum if the event insured against should occur. Then, we must ask how can it be safe to engage to pay a large sum if an uncertain event occurs. The answer is that the insurance company does a very large business and is able to ascertain pretty closely out of a thousand risks of a given description how many in any one year will be losses. The business problem is this. The number of policies of a certain description that can be sold in a year will depend on the price set upon them. Let p be that price, and let n be the number that can be sold at that price, so that the larger p is, the smaller n will be. Now n being a large number a certain proportion q of these policies, qn in all, will be losses during the year; and if I be the loss on each, qnl will be the total loss. Then what the insurance company has to do is to set p at such a figure that pn-qln or (p-ql)n shall reach its maximum possible value.

The solution of this equation is:


p = q l + ((δp/δn)(n))

where δp/δn is the amount by which the price would have to be lowered in order to sell one policy more. Of course if the price were raised instead of lowered just one policy fewer would be sold.

For then by so lowering the profit from being

(p - ql)n

[it] would be changed to

(p - ql - δp/δn)(n + 1)

that is to

(p - ql)n + p - ql - δp/δn(n + 1)

and this being less than before ql + δp/δn(n + 1) > p

and by raising it, the change would be to

(p - ql + δp/δn)(n - 1)

that is to

(p - ql)(n - p + ql + δp/δn(n - 1)

and this being less than before

p > ql + δp/δn(n-1)

so since p is intermediate between

ql + (δp/δn)n + δp/δn


ql + (δp/δn)n - δp/δn

and δp/δn is very small, it must be close to the truth to write

p = ql + δp/δn(n).

21. This is the problem of insurance. Now in order that probability may have any bearing on this problem, it is obvious that it must be of the nature of a real fact and not a mere state of mind. For facts only enter into the solution of the problem of insurance. And this fact must evidently be a fact of statistics.

Without now going into certain reasons of detail that I should enter into if I were lecturing on probabilities, it must be that probability is a statistical ratio; and further, in order to satisfy still more special conditions, it is convenient, for the class of problems to which insurance belongs, to make it the statistical ratio of the number of experiential occurrences of a specific kind to the number of experiential occurrences of a generic kind, in the long run.

In order, then, that probability should mean anything, it will be requisite to specify to what species of event it refers and to what genus of event it refers.

It also refers to a long run, that is, to an indefinitely long series of occurrences taken together in the order of their occurrence in possible experience.

In this view of the matter, we note, to begin with, that a given species of event considered as belonging to a given genus of events does not necessarily have any definite probability. Because [it may be the case that] the probability is the ratio of one infinite multitude to another. Now infinity divided by infinity is altogether indeterminate, except in special cases.

22. It is very easy to give examples of events that have no definite probability. If a person agrees to toss up a cent again and again forever and beginning as soon as the first head turns up whenever two heads are separated by any odd number of tails in the succession of throws, to pay 2 to that power in cents, provided that whenever the two successive heads are separated by any even number of throws he receives 2 to that power in cents, it is impossible to say what the probability will be that he comes out a winner. In half of the cases after the first head the next throw will be a head and he will receive (-2)0 = 1 cent. Which since it happens half the time will be in the long run a winning of 1/2 a cent per head thrown.

But in half of the other half the cases, that is in 1/4 of all the cases, one tail will intervene and he will have to receive (-2)1 = -2 cents, i.e., he will have to pay 2 cents, which happening 1/4 of the time will make an average loss of 1/2 a cent per head thrown.

But in half the remaining quarter of the cases, i.e., of all the cases, two tails will intervene and he will receive (-2)2 = 4 cents which happening one every eight times will be worth 1/2 a cent per head thrown and so on; so that his account in the long run will be 1/2-1/2+1/2-1/2+1/2-1/2+1/2-1/2 ad infinitum, the sum of which may be 1/2 or may be zero. Or rather it is quite indeterminate.

If instead of being paid (-2)n when n is the number of intervening tails, he were paid (-2)n2 the result would be he would probably either win or lose enormously without there being any definite probability that it would be winning rather than losing.

I think I may recommend this game with confidence to gamblers as being the most frightful ruin yet invented; and a little cheating would do everything in it.

23. Now let us revert to our original problem and consider the state of things after every other bet. After the second, 1/4 of the players will have gained, gone out, and been replaced by players who have gained and gone out, so that a number of francs equal to half the number of seats will have been paid out by the bank, 1/4 of the players will have gained and gone out and been replaced by players who have lost, making the bank even; 1/4 of the players will have lost and then gained, making the bank and them even; 1/4 of the players will have lost twice, making a gain to the bank of half as many francs as there are seats at the table. The bank then will be where it was. Players to the number of three-quarters of the seats will have netted their franc each; but players to the number of a quarter of the seats will have lost two francs each and another equal number one franc each, just paying for the gains of those who have retired. That is the way it will happen every time.

Just before the fifth bet of the players at the table, 3/8 will have lost nothing, 1/4 will have lost one franc, 1/4 two francs, 1/16 three francs and 1/16 four francs. Thus some will always have lost a good deal. Those who sit at the table will among them always have paid just what those who have gone out have carried away.

24. But it will be asked: How then can it happen that all gain? I reply that I never said that all would gain, I only said that the probability was 1 that anyone would ultimately gain his franc. But does not probability 1 mean certainty? Not at all, it only means that the ratio of the number of those who ultimately gain to the total number is 1. Since the number of seats at the table is infinite the ratio of the number of those who never gain to the number of seats may be zero and yet they may be infinitely numerous. So that probabilities 1 and 0 are very far from corresponding to certainty pro and con.

25. If I were to go into practical matters, the advantage of pragmatism, of looking at the substantial practical issue, would be still more apparent. But here pragmatism is generally practised by successful men. In fact, the genus of efficient men [is] mainly distinguished from inefficient precisely by this.

26. There is no doubt, then, that pragmatism opens a very easy road to the solution of an immense variety of questions. But it does not at all follow from that, that it is true. On the contrary, one may very properly entertain a suspicion of any method which so resolves the most difficult questions into easy problems. No doubt Ockham's razor is logically sound. A hypothesis should be stripped of every feature which is in no wise called for to furnish an explanation of observed facts. Entia non sunt multiplicanda praeter necessitatem; only we may very well doubt whether a very simple hypothesis can contain every factor that is necessary. Certain it is that most hypotheses which at first seemed to unite great simplicity with entire sufficiency have had to be greatly complicated in the further progress of science.

27. What is the proof that the possible practical consequences of a concept constitute the sum total of the concept? The argument upon which I rested the maxim in my original paper was that belief consists mainly in being deliberately prepared to adopt the formula believed in as the guide to action. If this be in truth the nature of belief, then undoubtedly the proposition believed in can itself be nothing but a maxim of conduct. That I believe is quite evident.

28. But how do we know that belief is nothing but the deliberate preparedness to act according to the formula believed?

My original article carried this back to a psychological principle. The conception of truth, according to me, was developed out of an original impulse to act consistently, to have a definite intention. But in the first place, this was not very clearly made out, and in the second place, I do not think it satisfactory to reduce such fundamental things to facts of psychology. For man could alter his nature, or his environment would alter it if he did not voluntarily do so, if the impulse were not what was advantageous or fitting. Why has evolution made man's mind to be so constructed? That is the question we must nowadays ask, and all attempts to ground the fundamentals of logic on psychology are seen to be essentially shallow.

29. The question of the nature of belief, or in other words the question of what the true logical analysis of the act of judgment is, is the question upon which logicians of late years have chiefly concentrated their energies. Is the pragmatistic answer satisfactory?

Do we not all perceive that judgment is something closely allied to assertion? That is the view that ordinary speech entertains. A man or woman will be heard to use the phrase, "I says to myself." That is, judgment is held to be either no more than an assertion to oneself or at any rate something very like that.

30. Now it is a fairly easy problem to analyze the nature of assertion. To find an easily dissected example, we shall naturally take a case where the assertive element is magnified -- a very formal assertion, such as an affidavit. Here a man goes before a notary or magistrate and takes such action that if what he says is not true, evil consequences will be visited upon him, and this he does with a view to thus causing other men to be affected just as they would be if the proposition sworn to had presented itself to them as a perceptual fact.

We thus see that the act of assertion is an act of a totally different nature from the act of apprehending the meaning of the proposition and we cannot expect that any analysis of what assertion is (or any analysis of what judgment or belief is, if that act is at all allied to assertion), should throw any light at all on the widely different question of what the apprehension of the meaning of a proposition is.

31. What is the difference between making an assertion and laying a wager? Both are acts whereby the agent deliberately subjects himself to evil consequences if a certain proposition is not true. Only when he offers to bet he hopes the other man will make himself responsible in the same way for the truth of the contrary proposition; while when he makes an assertion he always (or almost always) wishes the man to whom he makes it to be led to do what he does. Accordingly in our vernacular "I will bet" so and so, is the phrase expressive of a private opinion which one does not expect others to share, while "You bet" is a form of assertion intended to cause another to follow suit.

32. Such then seems at least in a preliminary glance at the matter to be a satisfactory account of assertion. Now let us pass to judgment and belief. There can, of course, be no question that a man will act in accordance with his belief so far as his belief has any practical consequences. The only doubt is whether this is all that belief is, whether belief is a mere nullity so far as it does not influence conduct. What possible effect upon conduct can it have, for example, to believe that the diagonal of a square is incommensurable with the side? Name a discrepancy e no matter how small, and the diagonal differs from a rational quantity by much less than that. Professor Newcomb in his calculus and all mathematicians of his rather antiquated fashion think that they have proved two quantities to be equal when they have proved that they differ by less than any assignable quantity. I once tried hard to make Newcomb say whether the diagonal of the square differed from a rational fraction of the side or not; but he saw what I was driving at and would not answer. The proposition that the diagonal is incommensurable has stood in the textbooks from time immemorial without ever being assailed and I am sure that the most modern type of mathematician holds to it most decidedly. Yet it seems quite absurd to say that there is any objective practical difference between commensurable and incommensurable.

33. Of course you can say if you like that the act of expressing a quantity as a rational fraction is a piece of conduct and that it is in itself a practical difference that one kind of quantity can be so expressed and the other not. But a thinker must be shallow indeed if he does not see that to admit a species of practicality that consists in one's conduct about words and modes of expression is at once to break down all the bars against the nonsense that pragmatism is designed to exclude.

What the pragmatist has his pragmatism for is to be able to say: here is a definition and it does not differ at all from your confusedly apprehended conception because there is no practical difference. But what is to prevent his opponent from replying that there is a practical difference which consists in his recognizing one as his conception and not the other? That is, one is expressible in a way in which the other is not expressible.

Pragmatism is completely volatilized if you admit that sort of practicality.


Source: Christopher Hookway's The Pragmatist Maxim and the Proof of Pragmatism  Copy

Peirce observes that “the act of assertion is an act of a totally different nature from the act of apprehending a proposition” so we should not expect an analysis of the former to cast any light on the latter.

One thing he says here is clear. We can do many things with propositions: we can believe them, assert them, doubt them, put them as questions, reflect on their meanings, and so on. An analysis of assertion is an explanation of just one thing we can do with propositions, and it is clear that we can assert propositions of which whose meaning we have a very poor grasp. The analysis of assertion is not itself an explanation of what is involved in clarifying a proposition. But it does not follow from this that the former can cast no light on the latter at all. …

Assertion is one thing we do with propositions, but there are others too. Perhaps the pragmatic maxim would be valuable as a guide to the practice of assertion even if it does not provide a clarification that meets all of our cognitive needs. …There can be no doubt that someone will act in the light of their beliefs “so far as his belief has any practical consequences”. The matter for doubt is “whether this is all that belief is, whether belief is a mere nullity so far as it does not influence conduct”. We may do more with propositions than assert or believe them; and we may do more with beliefs than act on them.

We should therefore leap forward to lecture five when he announces that he is now beginning “to get upon the trail of pragmatism, after a long and apparently aimless beating about the bush. (EP2: 200). The ensuring discussion yields the conclusion that “logical goodness is simply the excellence of argument”. … And when we then ask “what the soundness of an argument consists in”, we have to begin by recognizing “three radically different kinds of arguments”, Abduction, Induction, and Deduction (EP2: 205). It is natural to take from this that the key to establishing the correctness of pragmatism lies in paying attention to the role of propositions, not in belief or assertion, but in formulating and defending good arguments.

By the final lecture, Peirce claims that “the question of pragmatism […] is nothing else than the question of the logic of abduction”. … Once this is established, the only other roles we need to take account of are those in inductive and deductive arguments. The next stage is clear:
1. That pragmatism cannot interfere with induction is evident: because induction simply teaches us what we have to expect as a result of experimentation and it is plain that such expectation may conceivably concern practical conduct. (EP2: 235)
2. While the pragmatist maxim will affect the results that can be achieved by deductive reasoning, it does so only by influencing the range of propositions that are available through abduction as premises for deductions. But, first, this does not affect the logic of deduction; and, second, since this effect of pragmatism is “consequent upon its effects on abduction”, this does not alter the general claim that the normative impact of pragmatism lies in abduction. (EP2: 235)

So it is only in connection with abduction that we can see how pragmatism can have a normative impact, only in connection with abduction that pragmatism makes a difference. In that case, it seems, once we have shown that abduction conforms to the pragmatist maxim, the correctness of pragmatism has been proved. There is no possibility that there are other areas of the intellectual life where pragmatism would be an obstacle on the road to truth.

So the overall structure of the proof seems clear:
1. In order to defend pragmatism we have to show that it is a correct norm to use in exercising logical self-control.
2. Logical norms are fundamentally concerned with determining which arguments are good.
3. There are just three kinds of arguments: deduction, induction and abduction.
4. The pragmatic maxim is the fundamental norm that determines whether abductions are good.
5. Whether pragmatism is correct makes no difference to the soundness of deductive or inductive arguments that is not a consequence of its effects on abductive ones.
So: the pragmatist maxim is correct.

34. It must be understood that all I am now attempting to show is that Pragmatism is apparently a matter of such great probable concern, and at the same time so much doubt hangs over its legitimacy, that it will be well worth our while to make a methodical, scientific, and thorough examination of the whole question, so as to make sure of our ground, and obtain some secure method for such a preliminary filtration of questions as pragmatism professes to furnish.

Let us, then, enter upon this inquiry. But before doing so let us mark out the proposed course of it. That should always be done in such cases, even if circumstances subsequently require the plan to be modified, as they usually will.

Although our inquiry is to be an inquiry into truth, whatever the truth may turn out to be, and therefore, of course, is not to be influenced by any liking for pragmatism or any pride in it as an American doctrine, yet still we do not come to this inquiry, any more than anybody comes to any inquiry, in that blank state that the lawyers pretend to insist upon as desirable, though I give them credit for enough common-sense to know better.

35. We have some reason already to think there is some truth in pragmatism although we also have some reason to think that there is something wrong with it. For unless both branches of this statement were true we should do wrong to waste time and energy upon the inquiry we are undertaking.

I will, therefore, presume that there is enough truth in it to render a preliminary glance at ethics desirable. For if, as pragmatism teaches us, what we think is to be interpreted in terms of what we are prepared to do, then surely logic, or the doctrine of what we ought to think, must be an application of the doctrine of what we deliberately choose to do, which is Ethics.

36. But we cannot get any clue to the secret of Ethics -- a most entrancing field of thought but soon broadcast with pitfalls -- until we have first made up our formula for what it is that we are prepared to admire. I do not care what doctrine of ethics be embraced, it will always be so. Suppose, for example, our maxim of ethics to be Pearson's that all our action ought to be directed toward the perpetuation of the biological stock to which we belong. Then the question will arise, On what principle should it be deemed such a fine thing for this stock to survive -- or a fine thing at all? Is there nothing in the world or in posse that would be admirable per se except copulation and swarming? Is swarming a fine thing at all, apart from any results that it may lead to? The course of thought will follow a parallel line if we consider Marshall's ethical maxim: Act to restrain the impulses which demand immediate reaction, in order that the impulse-order determined by the existence of impulses of less strength, but of wider significance, may have full weight in the guidance of your life. Although I have not as clear an apprehension as I could wish of the philosophy of this very close, but too technical, thinker, yet I presume that he would not be among those who would object to making Ethics dependent upon Esthetics. Certainly, the maxim which I have just read to you from his latest book supposes that it is a fine thing for an impulse to have its way, but yet not an equally fine thing for one impulse to have its way and for another impulse to have its way. There is a preference which depends upon the significance of impulses, whatever that may mean. It supposes that there is some ideal state of things which, regardless of how it should be brought about and independently of any ulterior reason whatsoever, is held to be good or fine. In short, ethics must rest upon a doctrine which, without at all considering what our conduct is to be, divides ideally possible states of things into two classes, those that would be admirable and those that would be unadmirable, and undertakes to define precisely what it is that constitutes the admirableness of an ideal. Its problem is to determine by analysis what it is that one ought deliberately to admire per se in itself regardless of what it may lead to and regardless of its bearings upon human conduct. I call that inquiry Esthetics, because it is generally said that the three normative sciences are logic, ethics, and esthetics, being the three doctrines that distinguish good and bad; Logic in regard to representations of truth, Ethics in regard to efforts of will, and Esthetics in objects considered simply in their presentation. Now that third Normative science can, I think, be no other than that which I have described. It is evidently the basic normative science upon which as a foundation, the doctrine of ethics must be reared to be surmounted in its turn by the doctrine of logic.

37. But before we can attack any normative science, any science which proposes to separate the sheep from the goats, it is plain that there must be a preliminary inquiry which shall justify the attempt to establish such dualism. This must be a science that does not draw any distinction of good and bad in any sense whatever, but just contemplates phenomena as they are, simply opens its eyes and describes what it sees; not what it sees in the real as distinguished from figment -- not regarding any such dichotomy -- but simply describing the object, as a phenomenon, and stating what it finds in all phenomena alike. This is the science which Hegel made his starting-point, under the name of the Phänomenologie des Geistes -- although he considered it in a fatally narrow spirit, since he restricted himself to what actually forces itself on the mind and so colored his whole philosophy with the ignoration of the distinction of essence and existence and so gave it the nominalistic and I might say in a certain sense the pragmatoidal character in which the worst of the Hegelian errors have their origin. I will so far follow Hegel as to call this science Phenomenology although I will not restrict it to the observation and analysis of experience but extend it to describing all the features that are common to whatever is experienced or might conceivably be experienced or become an object of study in any way direct or indirect.

38. Hegel was quite right in holding that it was the business of this science to bring out and make clear the Categories or fundamental modes. He was also right in holding that these Categories are of two kinds; the Universal Categories all of which apply to everything, and the series of categories consisting of phases of evolution.

As to these latter, I am satisfied that Hegel has not approximated to any correct catalogue of them. It may be that here and there, in the long wanderings of his Encyclopædia he has been a little warmed by the truth. But in all its main features his catalogue is utterly wrong, according to me. I have made long and arduous studies of this matter, but I have not been able to draw up any catalogue that satisfies me. My studies, if they are ever published, will I believe be found helpful to future students of this most difficult problem, but in these lectures I shall have little to say on that subject. The case is quite different with the three Universal Categories, which Hegel, by the way, does not look upon as Categories at all, or at least he does not call them so, but as three stages of thinking. In regard to these, it appears to me that Hegel is so nearly right that my own doctrine might very well be taken for a variety of Hegelianism, although in point of fact it was determined in my mind by considerations entirely foreign to Hegel, at a time when my attitude toward Hegelianism was one of contempt. There was no influence upon me from Hegel unless it was of so occult a kind as to entirely escape my ken; and if there was such an occult influence, it strikes me as about as good an argument for the essential truth of the doctrine, as is the coincidence that Hegel and I arrived in quite independent ways substantially to the same result.

39. This science of Phenomenology, then, must be taken as the basis upon which normative science is to be erected, and accordingly must claim our first attention.

This science of Phenomenology is in my view the most primal of all the positive sciences. That is, it is not based, as to its principles, upon any other positive science. By a positive science I mean an inquiry which seeks for positive knowledge; that is, for such knowledge as may conveniently be expressed in a categorical proposition. Logic and the other normative sciences, although they ask, not what is but what ought to be, nevertheless are positive sciences since it is by asserting positive, categorical truth that they are able to show that what they call good really is so; and the right reason, right effort, and right being, of which they treat, derive that character from positive categorical fact.

40. Perhaps you will ask me whether it is possible to conceive of a science which should not aim to declare that something is positively or categorically true. I reply that it is not only possible to conceive of such a science, but that such science exists and flourishes, and Phenomenology, which does not depend upon any other positive science, nevertheless must, if it is to be properly grounded, be made to depend upon the Conditional or Hypothetical Science of Pure Mathematics, whose only aim is to discover not how things actually are, but how they might be supposed to be, if not in our universe, then in some other.†1 A Phenomenology which does not reckon with pure mathematics, a science hardly come to years of discretion when Hegel wrote, will be the same pitiful club-footed affair that Hegel produced.



Lecture Two: Phenomenology (The Doctrine of Categories)

In Lecture Two, Peirce argues that (1) Phenomenology is the basis of normative science and that mathematics is the basis of phenomenology.
(2)There are three categories of phenomena -- Firstness, Secondness, and Thirdness.
(3) Mathematics consists of hypotheses that have at least one, two, or three terms.
(4) The three categories of Phenomenology, Firstness, Secondness, and Thirdness, correspond to mathematical expressions of one, two, and three terms, respectively.

*Firstness - When anything is present to the mind, the very first and simplest character to be noted in it, is its presentness. The present is just what it is regardless of the absent, regardless of past and future. It is such as it is, utterly ignoring anything else. Consequently, it cannot be abstracted for the abstracted is what the concrete. It is nothing but a simple positive character. Such a consciousness might be just an odour, say a smell of attar; or it might be one infinite dead ache; it might be the hearing of a piercing eternal whistle. In short, any simple and positive quality of feeling would be something which our description fits that it is such as it is quite regardless of anything else. The quality of feeling is the true psychical representative of the first category of the immediate as it is in its immediacy, of the present in its direct positive presentness.
Firstness is a qualitative possibility. The quality of being white would be a first. As Hume suggests, white in itself tells no tales about anything else: It is just what it is.
*Secondness - The next simplest feature that is common to all that comes before the mind, and consequently, the second category, is the element of Struggle.
The second category, the Struggle, requires two parties, each exerting force - action and reaction.
Secondness is an actuality. It is factual objects and events in the world around us; and it is our experience and we learn by experience.
*Thirdness - This third category is the “category of representation or thought”; it is the category of “Thirdness” or “mediation”. Thirdness is law, habit, or custom.

In his second Harvard lecture on 2 April 1903, Peirce remarks near the beginning of this lecture that "my purpose this evening is to call your attention to certain questions of phenomenology upon the answers to which, whatever they may be, our final conclusion concerning pragmatism must repose at last." He goes on to clarify the nature of phenomenology (later called phaneroscopy), whose goal is to isolate the universal categories of experience. Peirce has found these to be, first, the quality of feeling, second, the element of struggle or reaction in experience or consciousness, and third, an intellectual element that seems much like representation or a sense of learning. He believes that this third element is necessary to explain a mode of influence on external facts that cannot be explained by mechanical action alone and he thinks that the idea of evolution requires this element. Near the end of this lecture Peirce remarks that "what the true definition of Pragmatism may be, I find it very hard to say; but in my nature it is a sort of instinctive attraction for living facts." (Head Notes for the EP 2, Chapter 11)

One of the questions that preoccupied Peirce was, What is there to be investigated? or, What is before the mind? In answer to this, he developed what he called phaneroscopy, or phenomenology, that is, a theory of phaneron, “the collective total of all that is in any way or in any sense present to the mind”. His answer is that what is before the mind exemplifies of three categories: Firstness, Secondness, or Thirdness.
Firstness is a qualitative possibilities. It is monadic in that it has no essential relationship to anything else. The quality of being white would be a first. As Hume suggests, white in itself tells no tales about anything else: It is just what it is.
Secondness is actual fact that it is diadic; to be that particular actuality, it has to have certain relations to some other thing – spatial and temporal relations, for example, or causal relations.
Thirdness is law, habit, or custom and, according to Peirce, it is triadic.

One thing that makes Peirce’s phaneroscopy exciting is the way in which he characterizes mental activity. All mental activity is sign activity and all thoughts are signs. Now, a sugn is something that stands for object for some interpreter; that is, the sign by virtue of some habit, law, or custom gives rise to some interpretant. Thus all sign activity is triadic, involving a sign, an object of the sign, and an interpretant of the sign; that is, the way in which the interpreter interprets the sign as standing from that object. The interpretant is itself another sign of that same object.

At the end of Lecture One, Peirce explains that before we can attack any normative science, any science which proposes to separate the sheep from the goats, it is plain that there must be a preliminary inquiry which shall justify the attempt to establish such dualism. This must be a science that does not draw any distinction of good and bad in any sense whatever, but just contemplates phenomena as they are, simply opens its eyes and describes what it sees; not what it sees in the real as distinguished from figment -not regarding any such dichotomy --but simply describing the object, as a phenomenon, and stating what it finds in all phenomena alike.
This is the science which Hegel made his starting-point, under the name of the Phänomenologie des Geistes --although he considered it in a fatally narrow spirit, since he restricted himself to what actually forces itself on the mind and so colored his whole philosophy with the ignoration of the distinction of essence and existence and so gave it the nominalistic and I might say in a certain sense the pragmatoidal character in which the worst of the Hegelian errors have their origin. I will so far follow Hegel as to call this science Phenomenology although I will not restrict it to the observation and analysis of experience but extend it to describing all the features that are common to whatever is experienced or might conceivably be experienced or become an object of study in any way direct or indirect. (CP5-37)

This science of Phenomenology, then, must be taken as the basis upon which normative science is to be erected, and accordingly must claim our first attention. This science of Phenomenology is in my view the most primal of all the positive sciences. That is, it is not based, as to its principles, upon any other positive science. By a positive science I mean an inquiry which seeks for positive knowledge; that is, for such knowledge as may conveniently be expressed in a categorical proposition. Logic and the other normative sciences, although they ask, not what is but what ought to be, nevertheless are positive sciences since it is by asserting positive, categorical truth that they are able to show that what they call good really is so; and the right reason, right effort, and right being, of which they treat, derive that character from positive categorical fact. (CP5-39)

Perhaps you will ask me whether it is possible to conceive of a science which should not aim to declare that something is positively or categorically true. I reply that it is not only possible to conceive of such a science, but that such science exists and flourishes, and Phenomenology, which does not depend upon any other positive science, nevertheless must, if it is to be properly grounded, be made to depend upon the Conditional or Hypothetical Science of Pure Mathematics, whose only aim is to discover not how things actually are, but how they might be supposed to be, if not in our universe, then in some other. (CP5-40)


Note: This lecture contains two drafts of “Part A: Mathematics as a Basis of Logic” and three drafts of “Part B: On Phenomenology”.

Part A: Mathematics as a Basis of Logic (Draft One)
The first job of education is thoroughness. The second job is logic (i.e., how to think). The significantly-less-important third job is the detail of various topics such as mathematics, history, and geography.

Mathematics studies hypotheses. Hypotheses can be categorized based on the number of terms they use. The simplest hypotheses consist of a single term. Such hypotheses provide no information. The next simplest hypotheses consist of two terms. These hypotheses bifurcate the world. Boolean algebra fits here (because all Boolean variables are constrained to hold one of only two values).
Two-term hypotheses constitute .Dichotomic Mathematics,. which includes linear algebra.

If there are three terms, then we have “trichotomic mathematics”. Three terms can be arranged in only one way, as points of a triangle, so that each relates to the other two.

Similarly, four objects can be arranged in only one way. This is self-evident, like all mathematics.

An arrangement is a relation. A “relation” itself can be thought of as an object in its own right, though an unusual one. The objects and their arrangements can be likened to atoms and chemical bonds, respectively.

Part A: Mathematics as a Basis of Logic (Draft Two)
Mathematics is the study of abstract hypotheses. The field depends on diagrams or pictures of some kind.
Mathematics enables generalizations that apply in all cases, unlike natural science. But no one has ever described the steps of how to think mathematically.
Mathematical thinking usually includes a particular type of logical step. “Hard” is an example of a “concrete” type of description, and “hardness” is an example of an “abstract” type of description.
The logical step involves moving from the concrete to the abstract. Or, more simply, presuming that there is an explanation, it involves detecting something more fundamental.
This logical step is demonstrated in geometry. Let “filament” be the part of a line occupied by a particle at any instant. Filament is abstract and the particle is concrete.
A “film” is an abstraction of a filament, and a “solid body” is an abstraction of a film, and so on. Another abstraction is a “collection” and its constituting members.

The branches of mathematics derive from the different number of terms in their hypotheses. Hypotheses with a single term are the simplest but because these hypotheses apply to everything (or nothing), they provide no description. Hypotheses with two terms dichotomize the universe.
Hypotheses with three terms describe triadic relations.

Peirce's three phenomenological categories
Notes of Peirce's three phenomenological categories
Peirce's three phenomenological categories
Table source: Sandia Report/Philip L. Campbell Peirce, Pragmatism, and The Right Way of Thinking. (pp 13-14)  

Part B: On Phenomenology (Draft One)
What it means to say that something is in our minds? Peirce said he had been at work on this problem for forty years. The first thing we notice, he says, is “presentness”.
Presentness is the first category, named “Quality”. The second category is “Struggle”, implying interaction between at least two things. There would be no “struggle” if the two things were not reacting in some way.
Struggle is the fundamental aspect of experience, and that is almost self-evident.

Experience is the only way we learn. Experience teaches by “surprises”. An example of a surprise is a ship unexpectedly hitting a rock. Experiments increase the number of surprises.

Surprise forces two, separate items before our minds: “ego” and “non-ego”. At the moment of surprise they are both present. The production of these two items is not under our control (i.e., they arise from the subconscious) so there is no sense in judging them to be either good or bad.
(Note: Philip L. Campbell would define “ego” as Peirce uses the term, to mean “what we were thinking was how the world worked” and “non-ego” to mean “how the world really works (perhaps)”. )

How do we recognize it when we are surprised? It cannot be that we infer the surprise because the surprise is forced upon us: our consciousness is split and there is a struggle.
Do we surprise ourselves or do we infer the surprise? Neither path is reasonable. Rather, non-ego - the world around us - surprises us.

Surprise sets off a struggle, a Reaction. If, in this struggle, the non-ego side collapses, then we attribute the experience to Perception. That is, we say that we correctly understood what the world was saying to us. If, on the other hand, the ego side collapses, then we attribute the experience to Imagination. That is, we say we only imagined what we thought the world was saying. In between these extremes, the struggle is more energetic.

A “genuine” form of struggle involves two items that are different; a “degenerate” form involves two items that only appear to be different. The genuine/degenerate dichotomy is sometimes expressed as objective/subjective, outward/inward, true/false, good/bad dichotomies.

The third category -the first two being Quality and Surprise -involves a sign. We judge what we see, whereby we associate it with signs.
This third category is the “category of representation or thought”; it is the category of “Thirdness” or “mediation”.

Part B: On Phenomenology (Draft Two)
Lecture One described pragmatism, noting its worth and the importance of verifying its truth. There are points in mathematics in which pragmatism seems to have no bearing, because the points seem to have no practical bearing. This lecture is intended to determine the “meaning or significance of any phrase or conception”.

Mathematics does not concern itself with the correspondence between its theories and reality. Philosophy is unique in that it does not generate experiments but uses everyday experience. Metaphysics provides a Weltanschauung; phenomenology provides an understanding of “appearance”; and the normative part of philosophy distinguishes between good and bad.

There are certain phenomenological questions, the answers for which will concern pragmatism. To answers these questions, one needs to be able to do the following: (1) to see things as they are, (2) to follow an intellectual path, and (3) to generalize away inessentials. Phenomenology’s goal is the establishment of “categories” that are the building blocks of phenomena in a manner that is similar to the way that the chemical elements are the building blocks of material. There are two types of categories: “particular” and “universal”. Hegel’s “three stages of thought” [presumably, thesis, antithesis, and synthesis] are the correct universal categories, though Hegel does not call them categories.

The three categories are both necessary and sufficient. Other philosophers err by ignoring one or more of the categories. If we name the three categories A, B, and C, and if a given metaphysics can accept any combination of those three categories, then there are exactly seven types of metaphysics, characterized by the categories accepted, namely, A, B, C, AB, AC, BC, and ABC.

The first category is “Quality of Feeling”. It is independent of anything else, in the sense, I believe, that it does not require a context. It is “presentness”. The blue of the sky is an example.

The second category is Struggle. It requires two parties, each exerting force. This is true of objects in the world around us, such as half-open doors that we might choose to push upon, and also true of the world within us, such as constructing mental images that we might choose to rotate or otherwise manipulate.
This “struggle” is not a special phenomenon particular to humans, and it is not reducible to other phenomenon but is a result of two conflicting parties.

Humans are able to hypothesize scientific laws because we are part of the universe. So the struggle we perceive is a function of our integration with all that is around us.
Law implies active force, just as a legal court is of no value unless there is a sheriff ready to enforce the findings of the court. The struggle is more than just two parties in conflict: it is representative of law.

We learn by experience. We are able to generate many hypotheses, some true, but most of them false. It is “surprise” that winnows out the false ones: “A ship is sailing along in a smooth sea, the navigator having no other expectation than that of the usual monotonous voyage, when suddenly she strikes upon a rock”. Experiments increase the number of surprises.

Oddly enough, we humans do not teach each other as experience does. No one advocates teaching via surprise, which involves, “practical jokes, mostly cruel”. The surprise consists of Ego - what we expected - suddenly confronted by Non-Ego - a “Strange intruder” - something at odds with what we expected. We should be able to confirm this description from our own experience. The surprise is not a conscious activity.

The Ego and Non-Ego react to each other. This is the “doctrine of Immediate Perception”, accepted by dualists and rejected by idealists.

Part B: On Phenomenology, or the Categories (Draft Three)
The categories are based on common sense.
Testing the simplest hypothesis first (i.e., Ockham’s razor) is a principle of scientific research. However, it is of no help in our everyday lives. Philosophy is based on Ockham’s razor: it is all nominalistic (as opposed to realistic). Hegel’s philosophy is especially nominalistic.

Nominalism is the basis of everyday thought for the “average modern mind”. Mechanics, it is presumed, can explain everything (i.e., Cartesianism). But ideas have an effect upon matter. Darwin’s notion of evolution will eventually show the error of the mechanistic view.

Physicists, who delve into mechanics and thus should be the ones to know, are apt to deny Cartesianism.
As a refutation of Cartesianism, Peirce suggests that there is no mechanical explanation for the effect of molecules that twist light to the left vs. to the right.


The focus of this lecture is phenomenology. This is equated with the “categories”, i.e., the mental bins that we have and by which we mentally organize our world. Peirce felt he did not have enough time in the lectures to present the material that he considered that his audience required. A book is not so constrained, so Turrisi presents in this lecture several draft versions of the lecture to give the reader some of the added material that Peirce wanted to include.

A Method of Work and its Application
There are five drafts extant of parts of Lecture Two. Turrisi includes this material in the lecture. In her commentary Turrisi also includes manuscripts on Peirce’s approach to developing philosophy, which is an example of pragmatism in action, so to speak. Turrisi considers Peirce’s early drafts to show what Peirce thought. Later drafts are an adaptation of that material for a particular audience, hence the value of the earlier drafts.

Peirce wanted to explain and justify his architectonic view of the sciences.
Like Descartes and Leibniz, Peirce described his method for developing philosophy. His method required such detail that he felt he could do little more in the lectures than give conclusions.
Turrisi provides Peirce’s description of his philosophical method, from MS 311 and MS 312, which was explicit and intended to be exhaustive. His method was iterative, examining a question from as many sides as he deemed reasonable, periodically starting anew and comparing those results with previous results. Peirce compares his method of addressing a philosophical question to the process of a seedling growing into a tree: both require nurturing and both proceeding slowly (see also Lecture V, pages 205-7 (page 42 herein)).

Turrisi notes that Peirce’s approach can be a description of how to think pragmatically. Such thought is methodical above all else.

Some Pedagogical Considerations
Peirce considered that his audience needed preliminary instruction to understand his message. Turrisi views the early drafts of Peirce’s lectures to be independent of his audience, the later drafts adapted to this particular audience.
Peirce had a lifelong interest in pedagogy. He believed that we understand only what we derive ourselves and that thought requires method and attention to detail.


Excerpt and condensation from LECTURE II. THE UNIVERSAL CATEGORIES

Be it understood that what we have to do, as students of phenomenology, is simply to open our mental eyes and look well at the phenomenon and say what are the characteristics that are never wanting in it, whether that phenomenon be something that outward experience forces upon our attention, or whether it be the wildest of dreams, or whether it be the most abstract and general of the conclusions of science. (CP5-41)

The faculties which we must endeavor to gather for this work are three.
The first and foremost is that rare faculty, the faculty of seeing what stares one in the face, just as it presents itself, unreplaced by any interpretation, unsophisticated by any allowance for this or for that supposed modifying circumstance. This is the faculty of the artist who sees for example the apparent colors of nature as they appear. When the ground is covered by snow on which the sun shines brightly except where shadows fall, if you ask any ordinary man what its color appears to be, he will tell you white, pure white, whiter in the sunlight, a little greyish in the shadow. But that is not what is before his eyes that he is describing; it is his theory of what ought to be seen. The artist will tell him that the shadows are not grey but a dull blue and that the snow in the sunshine is of a rich yellow. That artist's observational power is what is most wanted in the study of phenomenology.
The second faculty we must strive to arm ourselves with is a resolute discrimination which fastens itself like a bulldog upon the particular feature that we are studying, follows it wherever it may lurk, and detects it beneath all its disguises.
The third faculty we shall need is the generalizing power of the mathematician who produces the abstract formula that comprehends the very essence of the feature under examination purified from all admixture of extraneous and irrelevant accompaniments. (CP5-42)

A very moderate exercise of this third faculty suffices to show us that the word Category bears substantially the same meaning with all philosophers. For Aristotle, for Kant, and for Hegel, a category is an element of phenomena of the first rank of generality. It naturally follows that the categories are few in number, just as the chemical elements are. The business of phenomenology is to draw up a catalogue of categories and prove its sufficiency and freedom from redundancies, to make out the characteristics of each category, and to show the relations of each to the others. I find that there are at least two distinct orders of categories, which I call the particular and the universal. The particular categories form a series, or set of series, only one of each series being present, or at least predominant, in any one phenomenon. The universal categories, on the other hand, belong to every phenomenon, one being perhaps more prominent in one aspect of that phenomenon than another but all of them belonging to every phenomenon. I am not very well satisfied with this description of the two orders of categories, but I am pretty well satisfied that there are two orders. I do not recognize them in Aristotle, unless the predicaments and the predicables are the two orders. But in Kant we have Unity, Plurality, and Totality not all present at once; Reality, Negation, and Limitation not all present at once; Inherence, Causation, and Reaction not all present at once; Possibility, Necessity, and Actuality not all present at once. On the other hand Kant's four greater categories, Quantity, Quality, Relation, and Modality, form what I should recognize as Kant's Universal Categories. In Hegel his long list which gives the divisions of his Encyclopædia are his Particular Categories. His three stages of thought, although he does not apply the word Category to them, are what I should call Hegel's Universal Categories. My intention this evening is to limit myself to the Universal, or Short List of Categories, and I may say, at once, that I consider Hegel's three stages as being, roughly speaking, the correct list of Universal Categories. . . . (CP5-43)

When anything is present to the mind, what is the very first and simplest character to be noted in it, in every case, no matter how little elevated the object may be? Certainly, it is its presentness. So far Hegel is quite right. Immediacy is his word. To say, however, that presentness, presentness as it is present, present presentness, is abstract, is Pure Being, is a falsity so glaring, that one can only say that Hegel's theory that the abstract is more primitive than the concrete blinded his eyes to what stood before them. Go out under the blue dome of heaven and look at what is present as it appears to the artist's eye. The poetic mood approaches the state in which the present appears as it is present. Is poetry so abstract and colorless? The present is just what it is regardless of the absent, regardless of past and future. It is such as it is, utterly ignoring anything else. Consequently, it cannot be abstracted (which is what Hegel means by the abstract) for the abstracted is what the concrete, which gives it whatever being it has, makes it to be. The present, being such as it is while utterly ignoring everything else, is positively such as it is. Imagine, if you please, a consciousness in which there is no comparison, no relation, no recognized multiplicity (since parts would be other than the whole), no change, no imagination of any modification of what is positively there, no reflexion -- nothing but a simple positive character. Such a consciousness might be just an odour, say a smell of attar; or it might be one infinite dead ache; it might be the hearing of a piercing eternal whistle. In short, any simple and positive quality of feeling would be something which our description fits that it is such as it is quite regardless of anything else. The quality of feeling is the true psychical representative of the first category of the immediate as it is in its immediacy, of the present in its direct positive presentness. Qualities of feeling show myriad-fold variety, far beyond what the psychologists admit. This variety however is in them only insofar as they are compared and gathered into collections. But as they are in their presentness, each is sole and unique; and all the others are absolute nothingness to it -- or rather much less than nothingness, for not even a recognition as absent things or as fictions is accorded to them. The first category, then, is Quality of Feeling, or whatever is such as it is positively and regardless of aught else. (CP5-44)

The next simplest feature that is common to all that comes before the mind, and consequently, the second category, is the element of Struggle. It is convenient enough, although by no means necessary, to study this, at first, in a psychological instance. Imagine yourself making a strong muscular effort, say that of pressing with all your might against a half-open door. Obviously, there is a sense of resistance. There could not be effort without an equal resistance any more than there could be a resistance without an equal effort that it resists. Action and reaction are equal. If you find that the door is pushed open in spite of you, you will say that it was the person on the other side that acted and you that resisted, while if you succeed in pushing the door to, you will say that it was you who acted and the other person that resisted. In general, we call the one that succeeds by means of his effort the agent and the one that fails the patient. But as far as the element of Struggle is concerned, there is no difference between being an agent and being a patient. It is the result that decides; but what it is that is deemed to be the result for the purpose of this distinction is a detail into which we need not enter.
If while you are walking quietly along the sidewalk a man carrying a ladder suddenly pokes you violently with it in the back of the head and walks on without noticing what he has done, your impression probably will be that he struck you with great violence and that you made not the slightest resistance; although in fact you must have resisted with a force equal to that of the blow. Of course, it will be understood that I am not using force in the modern sense of a moving force but in the sense of Newton's actio; but I must warn you that I have not time to notice such trifles.
In like manner, if in pitch darkness a tremendous flash of lightning suddenly comes, you are ready to admit having received a shock and being acted upon, but that you reacted you may be inclined to deny. You certainly did so, however, and are conscious of having done so. The sense of shock is as much a sense of resisting as of being acted upon.
So it is when anything strikes the senses. The outward excitation succeeds in producing its effect on you, while you in turn produce no discernible effect on it; and therefore you call it the agent, and overlook your own part in the reaction. On the other hand, in reading a geometrical demonstration, if you draw the figure in your imagination instead of on paper, it is so easy to add to your image whatever subsidiary line is wanted, that it seems to you that you have acted on the image without the image having offered any resistance. That it is not so, however, is easily shown. For unless that image had a certain power of persisting such as it is and resisting metamorphosis, and if you were not sensible of its strength of persistence, you never could be sure that the construction you are dealing with at one stage of the demonstration was the same that you had before your mind at an earlier stage. The main distinction between the Inner and the Outer Worlds is that inner objects promptly take any modifications we wish, while outer objects are hard facts that no man can make to be other than they are. Yet tremendous as this distinction is, it is after all only relative. Inner objects do offer a certain degree of resistance and outer objects are susceptible of being modified in some measure by sufficient exertion intelligently directed. (CP5-45)

Experience is our only teacher. Far be it from me to enunciate any doctrine of a tabula rasa. There manifestly is not one drop of principle in the whole vast reservoir of established scientific theory that has sprung from any other source than the power of the human mind to originate ideas that are true. But this power, for all it has accomplished, is so feeble that as ideas flow from their springs in the soul, the truths are almost drowned in a flood of false notions; and that which experience does is gradually, and by a sort of fractionation, to precipitate and filter off the false ideas, eliminating them and letting the truth pour on in its mighty current. (CP5-50)
[Note: Peirce asserted quite emphatically that "experience is our only teacher," and thus embraced a fundamental tenet of classical empiricism. Yet he rejected the doctrine of a tabula rasa, claiming that there "is not one drop of principle in the whole vast reservoir of established scientific theory that has sprung from any other source than the power of the human mind to originate ideas that are true." But this power to originate ideas is feeble, Peirce said, and "the truths are almost drowned in a flood of false notions." Experience enables us to "filter off" the false ideas, "letting the truth pour on in its mighty current". ] (the Essential Peirce - Introduction to EP Volume 1 )

But precisely how does this action of experience take place? It takes place by a series of surprises. There is no need of going into details. At one time a ship is sailing along in the trades over a smooth sea, the navigator having no more positive expectation than that of the usual monotony of such a voyage, when suddenly she strikes upon a rock. The majority of discoveries, however, have been the result of experimentation. Now no man makes an experiment without being more or less inclined to think that an interesting result will ensue; for experiments are much too costly of physical and psychical energy to be undertaken at random and aimlessly. And naturally nothing can possibly be learned from an experiment that turns out just as was anticipated. It is by surprises that experience teaches all she deigns to teach us. (CP5-51)

The phenomenon of surprise in itself is highly instructive in reference to this category because of the emphasis it puts upon a mode of consciousness which can be detected in all perception, namely, a double consciousness at once of an ego and a non-ego, directly acting upon each other. Understand me well. My appeal is to observation -- observation that each of you must make for himself. (CP5-52)

The question is what the phenomenon is. We make no vain pretense of going beneath phenomena. We merely ask, what is the content of the Percept? Everybody should be competent to answer that of himself. Examine the Percept in the particularly marked case in which it comes as a surprise. Your mind was filled [with] an imaginary object that was expected. At the moment when it was expected the vividness of the representation is exalted, and suddenly, when it should come, something quite different comes instead. I ask you whether at that instant of surprise there is not a double consciousness, on the one hand of an Ego, which is simply the expected idea suddenly broken off, on the other hand of the Non-Ego, which is the strange intruder, in his abrupt entrance. (CP5-53)

The whole question is what the perceptual facts are, as given in direct perceptual judgments. By a perceptual judgment, I mean a judgment asserting in propositional form what a character of a percept directly present to the mind is. The percept of course is not itself a judgment, nor can a judgment in any degree resemble a percept. It is as unlike it as the printed letters in a book, where a Madonna of Murillo is described, are unlike the picture itself. (CP5-54)

If, therefore, our careful direct interpretation of perception, and more emphatically of such perception as involves surprise, is that the perception represents two objects reacting upon one another, that is not only a decision from which there is no appeal, but it is downright nonsense to dispute the fact that in perception two objects really do so react upon one another. (CP5-55)

That, of course, is the doctrine of Immediate Perception which is upheld by Reid, Kant, and all dualists who understand the true nature of dualism, and the denial of which led Cartesians to the utterly absurd theory of divine assistance upon which the preestablished harmony of Leibniz is but a slight improvement. Every philosopher who denies the doctrine of Immediate Perception -- including idealists of every stripe -- by that denial cuts off all possibility of ever cognizing a relation. Nor will he better his position by declaring that all relations are illusive appearances, since it is not merely true knowledge of them that he has cut off, but every mode of cognitive representation of them. (CP5-55)

When a man is surprised he knows that he is surprised. Now comes a dilemma. Does he know he is surprised by direct perception or by inference?
First try the hypothesis that it is by inference. This theory would be that a person (who must be supposed old enough to have acquired self-consciousness) on becoming conscious of that peculiar quality of feeling which unquestionably belongs to all surprise, is induced by some reason to attribute this feeling to himself. It is, however, a patent fact that we never, in the first instance, attribute a Quality of Feeling to ourselves. We first attribute it to a Non-Ego and only come to attribute it to ourselves when irrefragable reasons compel us to do so. Therefore, the theory would have to be that the man first pronounces the surprising object a wonder, and upon reflection convinces himself that it is only a wonder in the sense that he is surprised. That would have to be the theory. But it is in conflict with the facts which are that a man is more or less placidly expecting one result, and suddenly finds something in contrast to that forcing itself upon his recognition. A duality is thus forced upon him: on the one hand, his expectation which he had been attributing to Nature, but which he is now compelled to attribute to some mere inner world, and on the other hand, a strong new phenomenon which shoves that expectation into the background and occupies its place. The old expectation, which is what he was familiar with, is his inner world, or Ego. The new phenomenon, the stranger, is from the exterior world or Non- Ego. He does not conclude that he must be surprised because the object is so marvellous. But on the contrary, it is because of the duality presenting itself as such that he [is] led by generalization to a conception of a quality of marvellousness. (CP5-57)

Try, then, the other alternative that it is by direct perception, that is, in a direct perceptual judgment, that a man knows that he is surprised. The perceptual judgment, however, certainly does not represent that it is he himself who has played a little trick upon himself. A man cannot startle himself by jumping up with an exclamation of Boo! Nor could the perceptual judgment have represented anything so out of nature. The perceptual judgment, then, can only be that it is the Non-Ego, something over against the Ego and bearing it down, is what has surprised him. But if that be so, this direct perception presents an Ego to which the smashed expectation belonged, and the Non-Ego, the sadder and wiser man, to which the new phenomenon belongs. . . . (CP5-58)

There never was a sounder logical maxim of scientific procedure than Ockham's razor: Entia non sunt multiplicanda praeter necessitatem. That is to say; before you try a complicated hypothesis, you should make quite sure that no simplification of it will explain the facts equally well. No matter if it takes fifty generations of arduous experimentation to explode the simpler hypothesis, and no matter how incredible it may seem that that simpler hypothesis should suffice, still fifty generations are nothing in the life of science, which has all time before it; and in the long run, say in some thousands of generations, time will be economized by proceeding in an orderly manner, and by making it an invariable rule to try the simpler hypothesis first. Indeed, one can never be sure that the simpler hypothesis is not the true one, after all, until its cause has been fought out to the bitter end. But you will mark the limitation of my approval of Ockham's razor. It is a sound maxim of scientific procedure. If the question be what one ought to believe, the logic of the situation must take other factors into account. Speaking strictly, belief is out of place in pure theoretical science, which has nothing nearer to it than the establishment of doctrines, and only the provisional establishment of them, at that. Compared with living belief it is nothing but a ghost. If the captain of a vessel on a lee shore in a terrific storm finds himself in a critical position in which he must instantly either put his wheel to port acting on one hypothesis, or put his wheel to starboard acting on the contrary hypothesis, and his vessel will infallibly be dashed to pieces if he decides the question wrongly, Ockham's razor is not worth the stout belief of any common seaman. For stout belief may happen to save the ship, while Entia non sunt multiplicanda praeter necessitatem would be only a stupid way of spelling Shipwreck. Now in matters of real practical concern we are all in something like the situation of that sea-captain. (CP5-60)

Philosophy, as I understand the word, is a positive theoretical science, and a science in an early stage of development. As such it has no more to do with belief than any other science. Indeed, I am bound to confess that it is at present in so unsettled a condition, that if the ordinary theorems of molecular physics and of archaeology are but the ghosts of beliefs, then to my mind, the doctrines of the philosophers are little better than the ghosts of ghosts. I know this is an extremely heretical opinion. The followers of Haeckel are completely in accord with the followers of Hegel in holding that what they call philosophy is a practical science and the best of guides in the formation of what they take to be Religious Beliefs. I simply note the divergence, and pass on to an unquestionable fact; namely, the fact that all modern philosophy is built upon Ockhamism; by which I mean that it is all nominalistic and that it adopts nominalism because of Ockham's razor. And there is no form of modern philosophy of which this is more essentially true than the philosophy of Hegel. But it is not modern philosophers only who are nominalists. The nominalistic Weltanschauung has become incorporated into what I will venture to call the very flesh and blood of the average modern mind. (CP5-61)

The third category of which I come now to speak is precisely that whose reality is denied by nominalism. For although nominalism is not credited with any extraordinarily lofty appreciation of the powers of the human soul, yet it attributes to it a power of originating a kind of ideas the like of which Omnipotence has failed to create as real objects, and those general conceptions which men will never cease to consider the glory of the human intellect must, according to any consistent nominalism, be entirely wanting in the mind of Deity. Leibniz, the modern nominalist par excellence, will not admit that God has the faculty of Reason; and it seems impossible to avoid that conclusion upon nominalistic principles. (CP5-62)

But it is not in Nominalism alone that modern thought has attributed to the human mind the miraculous power of originating a category of thought that has no counterpart at all in Heaven or Earth. Already in that strangely influential hodge-podge, the salad of Cartesianism, the doctrine stands out very emphatically that the only force is the force of impact, which clearly belongs to the category of Reaction; and ever since Newton's Principia began to affect the general thought of Europe through the sympathetic spirit of Voltaire, there has been a disposition to deny any kind of action except purely mechanical action. The Corpuscular Philosophy of Boyle -- although the pious Boyle did not himself recognize its character -- was bound to come to that in the last resort; and the idea constantly gained strength throughout the eighteenth century and the nineteenth until the doctrine of the Conservation of Energy, generalized rather loosely by philosophers, led to the theory of psycho-physical parallelism, against which there has, only of recent years, been any very sensible and widespread revolt. Psychophysical parallelism is merely the doctrine that mechanical action explains all the real facts, except that these facts have an internal aspect which is a little obscure and a little shadowy. (CP5-63)

To my way of regarding philosophy, all this movement was perfectly good scientific procedure. For the simpler hypothesis which excluded the influence of ideas upon matter had to be tried and persevered in until it was thoroughly exploded. But I believe that now at last, at any time for the last thirty years, it has been apparent, to every man who sufficiently considered the subject, that there is a mode of influence upon external facts which cannot be resolved into mere mechanical action, so that henceforward it will be a grave error of scientific philosophy to overlook the universal presence in the phenomenon of this third category. Indeed, from the moment that the Idea of Evolution took possession of the minds of men the pure Corpuscular Philosophy together with nominalism had had their doom pronounced. I grew up in Cambridge, [Massachusetts] and was about 21 when the Origin of Species appeared. There was then living here a thinker who left no remains from which one could now gather what an educative influence his was upon the minds of all of us who enjoyed his intimacy, Mr. Chauncey Wright. He had at first been a Hamiltonian but had early passed over into the warmest advocacy of the nominalism of John Stuart Mill; and being a mathematician at a time when dynamics was regarded as the loftiest branch of mathematics, he was also inclined to regard nature from a strictly mechanical point of view. But his interests were wide and he was also a student of Gray. I was away surveying in the wilds of Louisiana when Darwin's great work appeared, and though I learned by letters of the immense sensation it had created, I did not return until early in the following summer when I found Wright all enthusiasm for Darwin, whose doctrines appeared to him as a sort of supplement to those of Mill. I remember well that I then made a remark to him which although he did not assent to it, evidently impressed him enough to perplex him. The remark was that these ideas of development had more vitality by far than any of his other favorite conceptions and that though they might at that moment be in his mind like a little vine clinging to the tree of Associationalism, yet after a time that vine would inevitably kill the tree. He asked me why I said that and I replied that the reason was that Mill's doctrine was nothing but a metaphysical point of view to which Darwin's, which was nourished by positive observation, must be deadly. Ten or fifteen years later, when Agnosticism was all the go, I prognosticated a short life for it, as philosophies run, for a similar reason. What the true definition of Pragmatism may be, I find it very hard to say; but in my nature it is a sort of instinctive attraction for living facts. (CP5-64)

All nature abounds in proofs of other influences than merely mechanical action, even in the physical world. They crowd in upon us at the rate of several every minute. And my observation of men has led me to this little generalization. Speaking only of men who really think for themselves and not of mere reporters, I have not found that it is the men whose lives are mostly passed within the four walls of a physical laboratory who are most inclined to be satisfied with a purely mechanical metaphysics. On the contrary, the more clearly they understand how physical forces work the more incredible it seems to them that such action should explain what happens out of doors. A larger proportion of materialists and agnostics is to be found among the thinking physiologists and other naturalists, and the largest proportion of all among those who derive their ideas of physical science from reading popular books. These last, the Spencers, the Youmanses, and the like, seem to be possessed with the idea that science has got the universe pretty well ciphered down to a fine point; while the Faradays and Newtons seem to themselves like children who have picked up a few pretty pebbles upon the ocean beach. But most of us seem to find it difficult to recognize the greatness and wonder of things familiar to us. As the prophet is not without honor save [in his own country] so it is also with phenomena. Point out to the ordinary man evidence, however conclusive, of other influence than physical action in things he sees every day, and he will say: "Well, I don't see as that frog has got any points about him that's any different from any other frog." For that reason we welcome instances perhaps of less real cogency but which have the merit of being rare and strange. Such, for example, are the right-handed and lefthanded screw-structures of the molecules of those bodies which are said to be "optically active." Of every such substance there are two varieties, or as the chemists call them, two modifications, one of which twists a ray of light that passes through it to the right, and the other, by an exactly equal amount, to the left. All the ordinary physical properties of the right-handed and left-handed modifications are identical. Only certain faces of their crystals, often very minute, are differently placed. No chemical process can ever transmute the one modification into the other. And their ordinary chemical behaviour is absolutely the same, so that no strictly chemical process can separate them if they are once mixed. Only the chemical action of one optically active substance upon another is different if they both twist the ray the same way from what it is if they twist the ray different ways. There are certain living organisms which feed on one modification and destroy it while leaving the other one untouched. This is presumably due to such organisms containing in their substance, possibly in very minute proportion, some optically active body. Now I maintain that the original segregation of levo-molecules, or molecules with a left-handed twist, from dextromolecules, or molecules with a right-handed twist, is absolutely incapable of mechanical explanation. Of course you may suppose that in the original nebula at the very formation of the world right-handed quartz was collected into one place, while left-handed quartz was collected into another place. But to suppose that, is ipso facto to suppose that that segregation was a phenomenon without any mechanical explanation. The three laws of motion draw no dynamical distinction between right-handed and left-handed screws, and a mechanical explanation is an explanation founded on the three laws of motion. There, then, is a physical phenomenon absolutely inexplicable by mechanical action. This single instance suffices to overthrow the Corpuscular Philosophy. (CP5-65)



Lecture Three: The Categories Defended (The Categories Continued)

In Lecture Three, Peirce argues that his three categories - Firstness, Secondness, and Thirdness - are both necessary and sufficient. Peirce explains the meaning of “icon”, “index”, and “symbol”, each an element of the three categories, respectively.

This is the third Harvard lecture, delivered on 9 April 1903. In this lecture Peirce goes into more detail concerning the nature of his categories and uses them to distinguish three kinds of signs: icons, indices, and symbols. He analyzes in particular one type of symbol, the proposition, which always refers to its object in two ways: indexically, by means of its subject, and iconically, by means of its predicate. Peirce defends his categories against the view he attributes to A. B. Kempe that Thirdness is not required to express the relations of mathematics, and he argues for the independence of Firstness, Secondness, and Thirdness. (Head Notes for the EP 2, Chapter 12)


Note: This lecture consists of six sections.

There are three fundamental categories: “Firstness”, “Secondness”, and “Thirdness”. Firstness is independent of anything else. It is a “Quality of Feeling”. Secondness is a “reaction”. Thirdness is a “representation”.

Firstness has no “degenerate” (or “weakened”) form. Secondness has a degenerate form, for “example: “Psychological Reaction”. This can be “Willing” or “Sensation”. The former is a stronger form of Secondness; the latter is a weaker form.

Thirdness has two forms of degeneracy: “Irrational Plurality” and a “dark instinct of being a germ of thought”.

A set of recursive maps can represent “pure self-consciousness”.

Thirdness has three types, one relatively genuine, a second somewhat like Secondness, and a third somewhat like Firstness, corresponding to the three types of signs: “symbol”, “index”, and “icon”, respectively. A word, perhaps “centaur”, is an example of a symbol; a hygrometer (for measuring humidity) is an example of an index; a statue of a centaur is an example of an icon.

An index has a degenerate form, such as a landmark, whose relationship to the item is based on convention, for example, and a genuine form, such as the example of the hygrometer, in which the index has some integral relationship to the item.

Symbols are of three types: Term, Proposition, and Argument, which require one, two, or three parameters, respectively.

The three categories define the seven, possible types of metaphysics.those that accept/reject each of the three categories. So if we name the categories F, S, T, the seven sets are {{F}, {S}, {T}, {FS}, {FT}, {ST}, {FST}}, where “{FS}” means that the metaphysic acknowledges the existence of Firstness and Secondness but denies the existence of Thirdness.

Condillac’s metaphysic, for example, accepts only Firstness and is thus an example of {F}.

Helmholtz’s corpuscularian metaphysics accepted reaction only, it appears, and is thus an example of {S}. Hegel.s metaphysics is an example of {T}.

The metaphysics that accepts only two categories include the nominalists ({FS}), Berkeleyans ({FT}), and Cartesian metaphysics, along with Spinoza and Kant ({ST}). These different combinations are shown in Table 3 below.

Table 3 Combinations of Categories
 Combinations of Categories
Combinations of Categories

All three categories exist. They are independent of each other and, together, they can account for all thought. Enough was said in Lecture Two about Firstness. The “logic of relations” implies Secondness.

Schroder, like the hedonists, wrongly assumed that logic (Secondness) is based on feelings (Firstness).

But a feeling cannot feel anything about the feeling.

Propositions (i.e., logical statements) use a symbol that represents an object. The symbol and object are distinct. …
… and thus propositions are elements of Secondness.

If feeling were based on feeling, as Sigwart held, then there would be no distinction between truth and falsehood. But Sigwart’s position can be trivially refuted by anyone claiming to feel good about their refutation of Sigwart’s position.

While Secondness involves two parameters, Thirdness necessarily involves a third. For example, if we say that X reacts to Y, we can also say that Y reacts to X. The description differs only in the viewpoint that it represents because the reality is that X and Y react to each other - the relationship is symmetric. However, “giving” is an example of Thirdness because not only does it involve some X and some Y, but it also involves some Z that represents “ownership”.

Or, to put it another way, “X gives Z to Y” is materially different than “Y gives Z to X”.

A genuine index could be a photograph, for example. By comparison, an icon could be a drawing that represents the object photographed.

A degenerate index is related to an object by agreement. A proper name is an example of a degenerate index. It provides no information in and of itself.

Formal fallacies in logic are due to misuse of .Anything. (i.e., for all) and .Something. (i.e. there exists).
        Peirce notes that “All men are mortal” should be written “Anything is mortal or else not a man”.

Mathematics is almost free of this problem because it confines itself to relations between “single objects” (a set of objects is also a single object).

Kempe argues that Thirdness can be reduced to Secondness because a (mathematical) graph, which consists of nodes and edges, can represent mathematical relationships. The ten-ray theorem supports this position. Kempe can be refuted via three arguments.
*The first argument is that a graph is written on a surface, which represents the third category.
*The second argument, which seems specific to the nine-point theorem, is that the important relation is a triple - the three rays share a common point (i.e., copunctual) - which requires a new type of edge.

The third argument is that Kempe does not deal with “infinite collections”. But consider a graphical system in which (a) nodes represent predicates, (b) arcs represent relations, (c) the page upon which the system is written represents the “Universe of Truth”, and (d) circles represent negations (circles enclose predicates and relations that are outside of the Universe of Truth (the default is to be connected)).

This graphical system is the simplest possible.

Thirdness represents an idea that is “unanalyzable” (and hence Thirdness is not reducible to any combination of Firstness and Secondness). The reader is encouraged to explain the concept of representation without introducing Thirdness, and then explain “A gives B to C”.

And finally the reader is challenged to explain the idea of some convolvement of two items -- i.e., explain Z = XY -- without Thirdness.

Hegel argued that Thirdness alone is sufficient. But actually the concept of Thirdness assumes (but does not subsume) the concepts of Firstness and Secondness.

Thirdness could be pure reason. The following is an example of Secondness (a.k.a. Reaction): “Yet if while you are walking in the street reflecting upon how everything is the pure distillate of Reason a man carrying a heavy pole suddenly pokes you in the small of back …. “You and the pole react. An example of Firstness (a.k.a. Quality) is seeing the color red.

The next lecture (Lecture Four) will consider the sufficiency of the three categories and their reality (i.e., that they exist independent of the mind).

Turrisi: Commentary
The categories to which Peirce refers in the title of this lecture are “sensation, perception, and thought” (a.k.a. Firstness, Secondness, and Thirdness), and his “defense” consists in arguing that the three are each fundamental and none of them can be reduced to any of the others.

Peirce explained the “genuine” forms of the categories by describing their “degenerate” forms. The fundamental nature of the categories is intended to help us understand what it means to know something. Peirce presented an analogy that compares consciousness to maps.

A General Theory of Modeling Applied to Thought
Not all of thought is conscious, so we view only part of the territory. Unlike other philosophers of the time, Peirce considered both subjects (i.e., thinkers) and objects (i.e., what thinkers think about). Peirce did not separate “noumena” from “phenomena”, as Kant did, but he considered all things before the mind to be phenomena.

Peirce was most concerned with a subset of phenomena, namely thoughts. Peirce used a model to explain thought. A model imitates an object by imitating relationships.

Of the many types of models possible, Peirce favored the mathematical ones that represent relationships logically.

Peirce’s term “representamen” is what we would today call a model. It is a representation and thus a form of Thirdness. Turrisi argues that Peirce’s text is itself a model of thought.
(Note: Using Peirce’s terms, Lecture Three is a representation of thought. )
(Note: Kant “asserted that things of our experience, called phenomena, may be known, but that themind could never practically know things-in-themselves, or noumena, which cannot be sensuously perceived. Phenomena, which can be perceived in the pure forms of sensibility, space, and time, must be understood to possess those characteristics which constitute our categories of understanding”.)

The Definitions and Value of Degenerate Forms of Thirdness
A symbol, for Peirce, succeeds only because of how it is interpreted.

There are “genuine” representations and “degenerate” (also called “partial or reduced”) representations. The problem is not with the symbol but with the object: the object cannot be fully represented. A non-genuine symbol is an “icon”. For example, a statue of a centaur is an icon: it cannot fully represent a centaur because centaurs do not exist.

An “index” has its own relationship to the object and exists independently of interpretation. However, interpretation connects the index to the object. The example that Peirce gives is of a hygrometer. The hygrometer represents humidity, even if no one is aware of that, but interpretation makes the connection.

The play Hamlet is itself a symbol of Shakespeare’s thought, but the play within Hamlet, The Mouse-trap in Act III, is not a symbol but rather an icon: the inner play exists and relates to the action it portrays, but the players within Hamlet give the play an added interpretation.

The degenerate forms of Thirdness represent (1) things about which we can think and (2) models of thought as well. Both of these are models to which pragmatism can be applied.

Peirce presented a recursive map as a model of consciousness.

The map shows a certain territory. Imagine that within that map there is a second map of the same territory, and that within that second map there is a third map, “and so to infinity”. If such a map were faithful to the territory, then it would have to be the territory, and no longer a map. Representations are thus by definition “degenerate”. Every object is a mixture of the three categories.

Are all representations thus degenerate? But a “symbol”, independent of Peirce’s use of the word, can represent more than the object it symbolizes. A national flag is an example of such a symbol. How does Peirce account for this?


Excerpt and condensation from LECTURE III. THE CATEGORIES CONTINUED

66. Category the First is the Idea of that which is such as it is regardless of anything else. That is to say, it is a Quality of Feeling.

Category the Second is the Idea of that which is such as it is as being Second to some First, regardless of anything else, and in particular regardless of any Law, although it may conform to a law. That is to say, it is Reaction as an element of the Phenomenon.

Category the Third is the Idea of that which is such as it is as being a Third, or Medium, between a Second and its First. That is to say, it is Representation as an element of the Phenomenon.

67. A mere complication of Category the Third, involving no idea essentially different, will give the idea of something which is such as it is by virtue of its relations to any multitude, enumerable, denumeral, or abnumerable or even to any supermultitude of correlates; so that this Category suffices of itself to give the conception of True Continuity, than which no conception yet discovered is higher.

68. Category the First owing to its Extremely Rudimentary character is not susceptible of any degenerate or weakened modification.

69. Category the Second has a Degenerate Form, in which there is Secondness indeed, but a weak or secondary Secondness that is not in the pair in its own quality, but belongs to it only in a certain respect. Moreover, this degeneracy need not be absolute but may be only approximative. Thus a genus characterized by Reaction will by the determination of its essential character split into two species, one a species where the secondness is strong, the other a species where the secondness is weak, and the strong species will subdivide into two that will be similarly related, without any corresponding subdivision of the weak species. For example, Psychological Reaction splits into Willing, where the Secondness is strong, and Sensation, where it is weak; and Willing again subdivides into Active Willing and Inhibitive Willing, to which last dichotomy nothing in Sensation corresponds. But it must be confessed that subdivision, as such, involves something more than the second category.

70. Category the Third exhibits two different ways of Degeneracy, where the irreducible idea of Plurality, as distinguished from Duality, is present indeed but in maimed conditions. The First degree of Degeneracy is found in an Irrational Plurality which, as it exists, in contradistinction [to] the form of its representation, is a mere complication of duality. We have just had an example of this in the idea of Subdivision. In pure Secondness, the reacting correlates are Singulars, and as such are Individuals, not capable of further division. Consequently, the conception of Subdivision, say by repeated dichotomy, certainly involves a sort of Thirdness, but it is a thirdness that is conceived to consist in a second secondness.

71. The most degenerate Thirdness is where we conceive a mere Quality of Feeling, or Firstness, to represent itself to itself as Representation. Such, for example, would be Pure Self-Consciousness, which might be roughly described as a mere feeling that has a dark instinct of being a germ of thought. This sounds nonsensical, I grant. Yet something can be done toward rendering it comprehensible.

I remember a lady's averring that her father had heard a minister, of what complexion she did not say, open a prayer as follows: "O Thou, All-Sufficient, Self-Sufficient, Insufficient God." Now pure Self-consciousness is Self-sufficient, and if it is also regarded as All-sufficient, it would seem to follow that it must be Insufficient. I ought to apologize for introducing such Buffoonery into serious lectures. I do so because I seriously believe that a bit of fun helps thought and tends to keep it pragmatical.

Imagine that upon the soil of a country, that has a single boundary line thus country boundary line, there lies a map of that same country. This map may distort the different provinces of the country to any extent. But I shall suppose that it represents every part of the country that has a single boundary, by a part of the map that has a single boundary, that every part is represented as bounded by such parts as it really is bounded by, that every point of the country is represented by a single point of the map, and that every point of the map represents a single point in the country. Let us further suppose that this map is infinitely minute in its representation so that there is no speck on any grain of sand in the country that could not be seen represented upon the map if we were to examine it under a sufficiently high magnifying power. Since, then, everything on the soil of the country is shown on the map, and since the map lies on the soil of the country, the map itself will be portrayed in the map, and in this map of the map everything on the soil of the country can be discerned, including the map itself with the map of the map within its boundary. Thus there will be within the map, a map of the map, and within that, a map of the map of the map, and so on ad infinitum. These maps being each within the preceding ones of the series, there will be a point contained in all of them, and this will be the map of itself. Each map which directly or indirectly represents the country is itself mapped in the next; i.e., in the next [it] is represented to be a map of the country. In other words each map is interpreted as such in the next. We may therefore say that each is a representation of the country to the next map; and that point that is in all the maps is in itself the representation of nothing but itself and to nothing but itself. It is therefore the precise analogue of pure self-consciousness. As such it is self-sufficient. It is saved from being insufficient, that is as no representation at all, by the circumstance that it is not all-sufficient, that is, is not a complete representation but is only a point upon a continuous map. I dare say you may have heard something like this before from Professor Royce, but if so, you will remark an important divergency. The idea itself belongs neither to him nor to me, and was used by me in this connection thirty years ago.

72. The relatively degenerate forms of the Third category do not fall into a catena, like those of the Second. What we find is this. Taking any class in whose essential idea the predominant element is Thirdness, or Representation, the selfdevelopment of that essential idea -- which development, let me say, is not to be compassed by any amount of mere "hard thinking," but only by an elaborate process founded upon experience and reason combined -- results in a trichotomy giving rise to three sub-classes, or genera, involving respectively a relatively genuine thirdness, a relatively reactional thirdness or thirdness of the lesser degree of degeneracy, and a relatively qualitative thirdness or thirdness of the last degeneracy. This last may subdivide, and its species may even be governed by the three categories, but it will not subdivide, in the manner which we are considering, by the essential determinations of its conception. The genus corresponding to the lesser degree of degeneracy, the reactionally degenerate genus, will subdivide after the manner of the Second category, forming a catena; while the genus of relatively genuine Thirdness will subdivide by Trichotomy just like that from which it resulted. Only as the division proceeds, the subdivisions become harder and harder to discern.

73. The representamen, for example, divides by trichotomy into the general sign or symbol, the index, and the icon. An icon is a representamen which fulfills the function of a representamen by virtue of a character which it possesses in itself, and would possess just the same though its object did not exist. Thus, the statue of a centaur is not, it is true, a representamen if there be no such thing as a centaur. Still, if it represents a centaur, it is by virtue of its shape; and this shape it will have, just as much, whether there be a centaur or not. An index is a representamen which fulfills the function of a representamen by virtue of a character which it could not have if its object did not exist, but which it will continue to have just the same whether it be interpreted as a representamen or not. For instance, an old-fashioned hygrometer is an index. For it is so contrived as to have a physical reaction with dryness and moisture in the air, so that the little man will come out if it is wet, and this would happen just the same if the use of the instrument should be entirely forgotten, so that it ceased actually to convey any information. A symbol is a representamen which fulfills its function regardless of any similarity or analogy with its object and equally regardless of any factual connection therewith, but solely and simply because it will be interpreted to be a representamen. Such for example is any general word, sentence, or book.

Of these three genera of representamens, the Icon is the Qualitatively degenerate, the Index the Reactionally degenerate, while the Symbol is the relatively genuine genus.

74. Now the Icon may undoubtedly be divided according to the categories; but the mere completeness of the notion of the icon does not imperatively call for any such division. For a pure icon does not draw any distinction between itself and its object. It represents whatever it may represent, and whatever it is like, it in so far is. It is an affair of suchness only.

75. It is quite otherwise with the Index. Here is a reactional sign, which is such by virtue of a real connection with its object. Then the question arises is this dual character in the Index, so that it has two elements, by virtue of the one serving as a substitute for the particular object it does, while the other is an involved icon that represents the representamen itself regarded as a quality of the object -- or is there really no such dual character in the index, so that it merely denotes whatever object it happens to be really connected with just as the icon represents whatever object it happens really to resemble? Of the former, the relatively genuine form of Index, the hygrometer, is an example. Its connection with the weather is dualistic, so that by an involved icon, it actually conveys information. On the other hand any mere land-mark by which a particular thing may be recognized because it is as a matter of fact associated with that thing, a proper name without signification, a pointing finger, is a degenerate index. Horatio Greenough, who designed Bunker Hill Monument, tells us in his book that he meant it to say simply "Here!" It just stands on that ground and plainly is not movable. So if we are looking for the battle-field, it will tell us whither to direct our steps.

76. The Symbol, or relatively genuine form of Representamen, divides by Trichotomy into the Term, the Proposition, and the Argument. The Term corresponds to the Icon and to the degenerate Index. It does excite an icon in the imagination. The proposition conveys definite information like the genuine index, by having two parts of which the function of the one is to indicate the object meant, while that of the other is to represent the representamen by exciting an icon of its quality. The argument is a representamen which does not leave the interpretant to be determined as it may by the person to whom the symbol is addressed, but separately represents what is the interpreting representation that it is intended to determine. This interpreting representation is, of course, the conclusion. It would be interesting to push these illustrations further; but I can linger nowhere. As soon as a subject begins to be interesting I am obliged to pass on to another.

77. The three categories furnish an artificial classification of all possible systems of metaphysics which is certainly not without its utility. The scheme is shown in this figure. It depends upon what ones of the three categories each system admits as important metaphysico-cosmical elements.

The Seven Systems of Metaphysics The Seven Systems of Metaphysics
The Seven Systems of Metaphysics

78. One very naturally and properly endeavors to give an account of the universe with the fewest and simplest possible categories. Praedicamenta non sunt multiplicanda praeter necessitatem.

79. We ought therefore to admire and extol the efforts of Condillac and the Associationalists to explain everything by means of qualities of feeling [i]. If, however, this turns out to be a failure, the next most admirable hypothesis is that of the corpuscularians, Helmholtz and the like, who would like to explain everything by means of mechanical force, which they do not distinguish from individual reaction [ii]. That again failing, the doctrine of Hegel is to be commended who regards Category the Third as the only true one [iii]. For in the Hegelian system the other two are only introduced in order to be aufgehoben. All the categories of Hegel's list, from Pure Being up, appear to me very manifestly to involve Thirdness, although he does not appear to recognize it, so immersed is he in this category.

80. All three of these simplest systems having worked themselves out into absurdity, it is natural next in accordance with the maxim of Parsimony to try explanations of the Universe based on the recognition of two only of the Categories.

81. The more moderate nominalists who nevertheless apply the epithet mere to thought and to representamens may be said to admit Categories First and Second and to deny the third [i ii]. The Berkeleyans, for whom there are but two kinds of entities, souls, or centres of determinable thought, and ideas in the souls, these ideas being regarded as pure statical entities, little or nothing else than Qualities of Feeling, seem to admit Categories First and Third and to deny Secondness, which they wish to replace by Divine Creative Influence, which certainly has all the flavor of Thirdness [i iii]. So far as one can make out any intelligible aim in that singular hodge-podge, the Cartesian metaphysics, it seems to have been to admit Categories Second and Third as fundamental and to deny the First [ii iii]. Otherwise, I do not know to whom we can attribute this opinion which certainly does not seem to be less acceptable and attractive than several others. But there are other philosophies which seem to do full justice to Categories Second and Third and to minimize the first, and among these perhaps Spinoza and Kant are to be included.

82. We must begin by asking whether the three categories can be admitted as simple and irreducible conceptions; and afterward go on to ask whether they cannot all be supposed to be real constituents of the universe. For when I say that certain metaphysical schools do not admit them, I do not mean to say that they do not admit them as mere conceptions but that they do not admit them as real constituents of the universe.

I do not know that I could add anything material to what I said in my last lecture to show that Category the First must be admitted as an irreducible constituent of the phenomenon.

83. There would be no question that Category the Second is an irreducible conception were it not for the deplorable condition of the science of logic. This is illustrated by the fact that so flippant and wildly theorizing work as Prantl's Geschichte der Logik should be accepted, as it generally is, even among learned men, as a marvel of patient research. It is true that one or two chapters of it are relatively well done. The account of Aristotle's logic, though not good upon any high standard of completeness or of thorough comprehension, is nevertheless the best account of its subject that we have. But Prantl, to begin with, does not himself understand logic, meaning by logic the science of which those works treated, of which he gives or he professes to give an account; and yet with the shallowest ideas, he is so puffed up with his own views that he disdains to take the trouble to penetrate their meaning. The crude expressions of contempt in which he continually indulges toward great thinkers ought to put readers on their guard against him. In the next place he belongs to that too well-known class of German critics who get bitten with theories deduced from general conceptions, and who fall in love with these theories because they are their own offspring and treat them as absolute certainties although the complete refutation of them is near at hand. You will understand, of course, that I do not say these things without having read all the chief contributions to the questions on both sides and without having subjected them to careful study and criticism. Prantl's opinions about the Megarian philosophers, about what he calls the Byzantine logic, about the Latin medieval logic, about the Parva Logicalia, are wild theories, utterly untenable, and in several cases easily refuted by an easy examination of the MSS. Moreover, it is not a history of logic but mostly of the most trivial parts of logic. But I shall be asked whether I do not think his reading marvellously extensive. No, I do not. He had the Munich library at his hand. He had only to look into the books, and for the most part he has done little more than merely to look into them. He really often has no idea of what the real substance of the books is; and nothing is more common than to find in his notes passages copied out of one book which are nothing but textual copies of celebrated passages in much older works. I do not deny that the book is useful, because the rest of us haven't access to such a library; but I do not consider it a work of respectable erudition. There is no need of mincing words because he himself not only refers most disrespectfully to such solid students of medieval writings as Charles Thurot, Haureau and others, but frequently descends to what in English we should call the language of Billingsgate in characterising ancient opinions which he may or may not be aware are identical with those held today by analysts of logical forms whose studies are so much more exact than his that they are not to be named in the same day.

84. Nevertheless, bad as Prantl's history is, it is the best we have, and any person who reads it critically, as every book ought to be read, will easily be able to see that the ancient students of logic, Democritus, Plato, Aristotle, Epicurus, Philoponus, even Chrysippus, were thinkers of the highest order, and that St. Augustine, Abelard, Aquinas, Duns Scotus, Ockham, Paulus Venetus, even Laurentius Valla, were logicians of the most painstaking and subtle types. But when the revival of learning came, the finest minds had their attention turned in quite another direction, and modern mathematics and modern physics drew away still more. The result of all this has been that during the centuries that have elapsed since the appearance of the De Revolutionibus [1543] -- and remember, if you please, that the work of Copernicus was the fruit of the scientific nourishment that he had imbibed in Italy in his youth -- throughout these ages, the chairs of Logic in the Universities have been turned over to a class of men, of whom we should be speaking far too euphemistically if we were to say that they have in no wise represented the Intellectual Level of their age. No, no; let us speak the plain truth -- modern logicians as a class have been distinctly puerile minds, the kind of minds that never mature, and yet never have the élan and originality of youth. First cast your eyes over the pages of a dozen average treatises, dismissing all preconceived estimates of their authors, and see if that is not the impression you derive from them. Why, in the majority of them, the greatest contribution to reasoning that has been generally applied during these centuries -- the Calculus of Probabilities -- is almost entirely ignored. If it were only the common run of logics that were affected by this state of things, it would not much matter; for if only one per cent of works on the subject were what they should be, we should still be in possession of a splendid and extensive literature. But unfortunately the general standard has been so terribly lowered that even the treatises written by men of real ability have been but half thought out things. Arnauld, for example, was a thinker of considerable force, and yet L'Art de penser, or the Port Royal Logic, is a shameful exhibit of what the two and a half centuries of man's greatest achievements could consider as a good account of how to think. You may retort that the past three centuries seem to have got on nicely without the aid of logic. Yes, I reply, they have, because there is one thing even more vital to science than intelligent methods; and that is, the sincere desire to find out the truth, whatever it may be; and that those centuries have been blessed with. But according to such estimate -- not exactly mere guess-work, although rough enough, no doubt -- as I have been able to form, if logic during those centuries had been studied with half the zeal and genius that has been bestowed upon mathematics, the twentieth century might have opened with the special sciences generally -- particularly such vitally important sciences as molecular physics, chemistry, physiology, psychology, linguistics, and ancient historical criticism -- in a decidedly more advanced condition than there is much promise that they will have reached at the end of 1950. I shouldn't say that human lives were the most precious things in the world; but after all they have their value; and only think how many lives might thus have been saved. We can mention individuals who might probably have done more work; say Abel, Steiner, Gaulois, Sadi Carnot. Think of the labor of a generation of Germany being allowed to flow off into Hegelianism! Think of the extravagant admiration that half a generation of English -- decidedly the best average reasoners of any modern people, bestowed on that silly thing, Hamilton's New Analytic. Look through Vaihinger's commentary to see what an army of students have been entrapped by Kant's view of the relation between his Analytic and Synthetic Judgments -- a view that a study of the logic of relatives would at once have exploded.

85. Had logic not been sunk since the time of Copernicus into a condition of semi-idiocy, the Logic of Relatives would by this time have been pursued for three centuries by hundreds of students, among whom there would have been no small number who in this direction or in that would have surpassed in ability any of the poor handful of students who have been at work upon it for the last generation or so. And let me tell you that this study would have completely revolutionized men's most general notions about logic -- the very ideas that are today current in the market-place and on the boulevards. One of the early results of such wide study of the logic of relatives must have been to cause the idea of reaction to be solidly fixed in the minds of all men as an irreducible category of Thought -- whatever place might have been accorded to it in metaphysics as a cosmical category. This I venture to say, notwithstanding that the lamented Schröder did not seem to see it so. Schröder followed Sigwart in his most fundamental ideas of logic. Now I entertain a high respect for Sigwart -- the kind of respect that I feel for Rollin as a historian, for Buffon as a zoölogist, for Priestley as a chemist, for Biot as a physicist -- a class of men whom {ohi polloi} always place too high, and scientific specialists too low. He is one of the most critical and least inexact of the inexact logicians. Sigwart, like almost all the stronger logicians of today, present company excepted, makes the fundamental mistake of confounding the logical question with the psychological question.†3 The psychological question is what processes the mind goes through. But the logical question is whether the conclusion that will be reached, by applying this or that maxim, will or will not accord with the fact. It may be that the mind is so constituted that that which our intellectual instinct approves will be true to the extent to which that instinct approves of it. If so, that is an interesting fact about the human mind; but it has no relevancy for logic whatsoever. Sigwart says that the question of what is good logic and what bad must in the last resort come down to a question of how we feel; it is a matter of Gefühl, that is, a Quality of Feeling. And this he undertakes to demonstrate. For he says if any other criterion be employed, the correctness of this criterion has to be established by reasoning, and in this reasoning antecedent to the establishment of any rational criterion we must rely upon Gefühl; so that Gefühl is that to which any other criterion must ultimately be referred. Good! This is good intelligent work, such as advances philosophy -- a good, square, explicit fallacy that can be squarely met and definitively refuted. It is the more valuable because it is a form of argument of very wide applicability. It is precisely analogous to the reasoning by which the hedonist in ethics, the subjectivist in esthetics, the idealist in metaphysics, attacks the category of reaction. You perceive the analogy between their arguments. The hedonist says that the question of what is good morals and what bad must ultimately come down to a question of pleasure. For, he says, suppose we desire anything but our own pleasure. Then whatever it may be that we desire, we take satisfaction in; and if we did not take satisfaction in it we should not desire it. But this satisfaction is that very Quality of Feeling that we call pleasure; and thus the only thing we ever can desire is pleasure, and all deliberate action must be performed for the sake of our own pleasure.

Every idealist, too, begins with an analogous argument, though he very likely may not remain consistently on the ground it leads to, so far as it leads anywhere. He says: When I perceive anything I am conscious; and when I am conscious of anything, I am immediately conscious and aught else I may be conscious of, I am conscious of through that immediate consciousness. Consequently whatever I learn from perception is merely that I have a feeling together with whatever I infer from that immediate consciousness.

86. The answer to all such arguments is that no desire can possibly desire its own satisfaction, no judgment can judge itself to be true, and no reasoning can conclude that it is itself sound. For all these propositions stand on the same footing and must stand or fall together. If any judgment judges itself to be true, all judgments -- or at least all assertory judgments -- do so likewise; for there is no ground of discrimination between assertory judgments in this respect. Either therefore the judgment, J, and the judgment "I say that J is true" are the same for all judgments or for none. But if they are identical, their denials are identical. But their denials are respectively "J is not true" and "I do not say that J is true," which are very different. Consequently no judgment judges itself to be true. All that J does is to furnish a premiss which is complete evidence warranting my assertion in another judgment that J is true. It is important to draw this distinction. The judgment J may, for example, be that "Sirius is white." That is a judgment about Sirius. To myself who perceive myself making this judgment, or to another who hears me assert it and admits my veracity, the evidence is complete that I believe Sirius to be white. But the two propositions "Sirius is white" "I judge that Sirius is white" are two distinct propositions.

There are precisely analogous distinctions in the other cases. I may desire that my sick child should recover, and afterwards reflecting upon the intensity of that desire, I probably shall be unable to refrain from desiring that that desire should be gratified. But I cannot desire that a desire of mine should be gratified unless I already have such a desire; and I have no such desire as long as I am yet in the act of forming the desire, so that the desire is not yet complete. I dare say that some people's psychical disposition is such that they have no sooner formed a strong desire than their thoughts take a subjective turn and they forthwith begin to think what satisfaction it would give them if that desire were gratified, and such people find it difficult to conceive that there are other people whose thoughts follow a train of objective suggestions and who think very little about themselves and their gratifications. That is just one of those respects in which different people may be expected to differ widely. But in no case is the desire absolutely the same as the desire of the satisfaction of that desire.

87. To return, then, to Sigwart's argument, I not only deny what he asserts that when I make an inference I can only do so because of a certain feeling of logical satisfaction that is connected with doing so, but I maintain that I never can draw an inference because of such a feeling. On the contrary, I never know the inference will afford me any such satisfaction except by a subsequent reflexion after I have already drawn it. It may be that on recognizing the satisfaction the inference gives me I shall consider that as an additional reason for believing in it. But this is another inference which in its turn will afford a new gratification if I stop to reflect about it.

In point of fact it is a serious error of reasoning to regard the sense of logicality as anything more than a tolerably strong argument in favor of the soundness of an inference. For although no doubt the sense of logicality carries men right in the main, yet it very frequently deceives them.

But Sigwart's argument is plainly either wholly fallacious or else what it proves is that which he himself distinctly maintains that it proves, namely, that the soundness of an argument consists in nothing but the Gefühl of logicality. Yet this is a downright absurd position for a logician to take; since, if it were true, there could be no such thing as sincere reasoning that was illogical, and logic, as the criticism of arguments and discrimination of the good from the bad, would have no existence at all; and my sincere argument that Sigwart is wholly in the wrong would be a decision from which there would be no appeal.

If the Holy Father by virtue of his infallibility were to command the faithful to believe that everything that any protestant had ever said was ipso facto necessarily true, it could hardly strain one's assent more.

88. It is certainly hard to believe, until one is forced to the belief, that a conception, so obtrusively complex as Thirdness is, should be an irreducible unanalyzable conception. What, one naturally exclaims, does this man think to convince us that a conception is complex and simple, at the same time! I might answer this by drawing a distinction. It is complex in the sense that different features may be discriminated in it, but the peculiar idea of complexity that it contains, although it has complexity as its object, is an unanalyzable idea. Of what is the conception of complexity built up? Produce it by construction without using any idea which involves it if you can.

89. The best way of satisfying oneself whether Thirdness is elementary or not -- at least, it would be the best way for me, who had in the first place a natural aptitude for logical analysis which has been in constant training all my life long (and I rather think it would be the best way for anybody provided he ruminates over his analysis, returns to it again and again, and criticizes it severely and sincerely, until he reaches a complete insight into the analysis) -- the best way, I say, is to take the idea of representation, say the idea of the fact that the object, A, is represented in the representation, B, so as to determine the interpretation, C: to take this idea and endeavor to state what it consists in without introducing the idea of Thirdness at all if possible, or, if you find that impossible, to see what is the minimum or most degenerate form of Thirdness which will answer the purpose.

Then, having exercised yourself on that problem, take another idea in which, according to my views, Thirdness takes a more degenerate form. Try your hand at a logical analysis of the Fact that A gives B to C.

Then pass to a case in which Thirdness takes a still more degenerate form, as for example the idea of "A and B." What is at once A and B involves the idea of three variables. Putting it mathematically, it is Z = XY, which is the equation of the simpler of the two hyperboloids, the two-sheeted one, as it is called.

Whoever wishes to train his logical powers will find those problems furnish capital exercise; and whoever wishes to get a just conception of the universe will find that the solutions of those problems have a more intimate connection with that conception than he could suspect in advance.

90. I have thus far been intent on repelling attacks upon the categories which should consist in maintaining that the idea of Reaction can be reduced to that of Quality of Feeling, and the idea of Representation to those of Reaction and Quality of Feeling taken together. But meantime may not the enemy have stolen upon my rear, and shall I not suddenly find myself exposed to an attack which shall run as follows:

We fully admit that you have proved, until we begin to doubt it, that Secondness is not involved in Firstness nor Thirdness in Secondness and Firstness. But you have entirely failed to prove that Firstness, Secondness, and Thirdness are independent ideas for the obvious reason that it is as plain as the nose on your face that the idea of a triplet involves the idea of pairs, and the idea of a pair the idea of units. Consequently, Thirdness is the one and sole category. This is substantially the idea of Hegel; and unquestionably it contains a truth.

Not only does Thirdness suppose and involve the ideas of Secondness and Firstness, but never will it be possible to find any Secondness or Firstness in the phenomenon that is not accompanied by Thirdness.

91. If the Hegelians confined themselves to that position they would find a hearty friend in my doctrine.

But they do not. Hegel is possessed with the idea that the Absolute is One. Three absolutes he would regard as a ludicrous contradiction in adjecto Consequently, he wishes to make out that the three categories have not their several independent and irrefutable standings in thought. Firstness and Secondness must somehow be aufgehoben. But it is not true. They are in no way refuted nor refutable. Thirdness it is true involves Secondness and Firstness, in a sense. That is to say, if you have the idea of Thirdness you must have had the ideas of Secondness and Firstness to build upon. But what is required for the idea of a genuine Thirdness is an independent solid Secondness and not a Secondness that is a mere corollary of an unfounded and inconceivable Thirdness; and a similar remark may be made in reference to Firstness.

92. Let the Universe be an evolution of Pure Reason if you will. Yet if, while you are walking in the street reflecting upon how everything is the pure distillate of Reason, a man carrying a heavy pole suddenly pokes you in the small of the back, you may think there is something in the Universe that Pure Reason fails to account for; and when you look at the color red and ask yourself how Pure Reason could make red to have that utterly inexpressible and irrational positive quality it has, you will be perhaps disposed to think that Quality and Reaction have their independent standing in the Universe.



Lecture Four: The Reality of Thirdness (The Seven Systems of Metaphysics)

In Lecture Four, Peirce establishes the existence of Thirdness, then Firstness, and then Secondness. The order is significant: it represents a decreasing order with which we can accept existence. That is, we find it hardest to accept the existence of Thirdness and easiest to accept the existence of Secondness.

This is the fourth Harvard lecture, delivered on 16 April 1903. Here Peirce uses his doctrine of categories to characterize seven systems of metaphysics: Nihilism, Individualism, Hegelianism, Cartesianism, Berkeleyanism, Nominalism, and Kantianism. The systems are distinguished by which categories are admitted "as important metaphysico-cosmical elements." Peirce regards these seven systems, and variants of them, as exemplifying the full scope of metaphysics. Peirce aligns himself with the seventh system, arguing for the reality of all three categories and claiming that each is really operative in nature. He argues that perceptual judgements are the first premisses of all our reasonings, that symbols influence events in the way natural laws do, and that the universe is a great symbol "working out its conclusions in living realities." He strongly recommends a version of the fundamental "ethical" maxim: never say die. (Head Notes for the EP 2, Chapter 13)


Firstness is associated with “Quality,” Secondness with “Reaction,” and Thirdness with “Representation.” There are a number of combinations of these three categories, most of them associated with a form of metaphysics, as shown in Table 4.

Combinations of Categories
Combinations of Categories

Table 4 is slightly different than Table 3 on page 32 from Lecture III. The {F} class includes Nihilism and Idealistic Sensualism, the {S} class includes “strict individualism” and Lutaslawski, the {FS} class includes “ordinary nominalism,” and the {ST} class includes “the metaphysics of the Physicists today.”

Peirce considered himself an Aristotelian of the “scholastic wing, approaching Scotism, but going much further in the direction of scholastic realism.”

Thirdness is more than a product of the mind. Consider a “silly experiment” of letting go a stone to see if it will fall.

We all know that the stone will fall, based on experience.

The theory of falling objects is a type of representation. That does not in and of itself make the theory real, i.e., give it existence outside our minds. A reaction, on the other hand, is evidence of something real outside our minds. A theory, a Thirdness, “corresponds” to reality and can cover future events.

Hypotheses are based on some perceived regularity. The regularity is attributable either to chance or to some cause.

“Scholastic realism” argues that the regularity we experience around us is not due to chance, that there is some cause. That cause is a set of “general principles.”

Peirce explicitly subscribed to the Scholastic realism school.

A generality, such as a theory, is a representation but it circumscribes more than all possible instances. Thirdness describes the aspect of “Betweenness or Mediation” of an object.

Thirdness is a “synonym” for “Representation” (hence the meaning of “Betweenness or Mediation”). A “general principle” operates in the world the way a Representation (or a symbol) does. Words, for example, are Representations, and words, such as Patrick Henry’s, have an effect on the world. Words can have an effect independently of who spoke them. But we do not know how words effect the world. We know that thoughts affect and are affected by the world—perhaps words affect thoughts. In the same way the “laws of nature” effect the world. A law is only a symbol. Perhaps these laws are God’s thoughts, “ideas or resolutions in the mind of some vast consciousness.”

The Reality of Firstness
People think that Quality (i.e., Firstness) exists only in the mind. The “older” physicists believe that the interaction of molecules was due to a law, in particular the law of force, implying a belief in Thirdness. These physicists also believe in Secondness because they believe in reactions. But they think Firstness exists in the mind only.

The process of inference is a conscious activity and thus subject to the critique of logic which weeds the good from the bad. The subconscious uses a similar process but it is not “inference” because it is outside of conscious control: it does not make sense to judge whether this process is good or bad.

There are two objections to this train of thought. First, that logic has been reduced to psychology. But, logic is independent of psychology. Second, that logic has been reduced to morals, which are esthetics, which reduces to hedonism. The reply to this objection is based on a point made in the next lecture (Lecture V, page 210 (page 43 herein)).

Humans want to avoid pain. The reason for this, it is supposed, is that there is a commonality to different types of pain. But there does not appear to be any commonality. Thus the second objection is answered.

First a precept is formed, then, sometime later in the process, a judgment about the precept is formed, and then, sometime later, cognition begins. The activity prior to cognition is subconscious and uncontrollable. Thus there is no sense in criticizing the goodness or badness of this part of that activity but only in judging its consistency. Precept formation and perceptual judgment generate the premises of our reasoning. Physicists dismiss this activity as illusory because it is outside of their theoretical structure. This dismissal is infantile.

Both illusions and hallucinations (and, it appears, delusions) are real experiences, but that is not sufficient grounds to doubt the truth of what our senses report.

The universe is a “vast representamen.” It is an “argument,” perhaps as all art (e.g. poetry, painting, music) is an argument. The premises of Nature are “all the independent uncaused elements of fact.”

The Reality of Secondness
One objection to the claim that the three categories are independent is that Firstness and Thirdness can explain Secondness, that Secondness is a “succession of feelings.”

The “easiest” reply to this objection is to use the experience of surprise. When we are surprised we know that we are surprised. How do we come to this knowledge? If Secondness can be reduced to Thirdness and/or Firstness, then we come to the knowledge either by inference (a Thirdness) or by perception (a Firstness). If it is by inference, then we run counter to what happens in surprise, because the surprise forces itself upon us. If, on the other hand, we argue that it is by perception that we know we are surprised, then how do we explain the ego/non-ego conflict inherent in surprise?

Because perceptual facts arise from the subconscious there is no sense in judging them either good or bad. There is sense only in judging their consistency.

Turrisi: Commentary On Lecture Four
The title notwithstanding, the topic of this lecture is the existence of the three categories. Of the three, it is most important to establish the existence of Thirdness, followed by Firstness, and then finally by Secondness.

The Reality of Thirdness: A Condition for the Possibility of Science
We can abstract a similarity (or regularity), given a set of events. This similarity is due either to chance only (i.e., randomness) or to law.

Chance can account for any behavior. Theories based on chance are thus not falsifiable, implying that they can not provide us with any information.

Theories developed under the assumption that there is chance cannot be proven but theories developed under the assumption that there are laws can be proven.

Science is based on the assumption that there are laws. There would be no reason to run experiments if there were no laws (“some active general principle”).

The Reality of Firstness and Secondness: The Universe as an Argument
Firstness involves both a “perception” and a “perceptual judgment.” Firstness is a type of inference—because it draws conclusions based on premises—over which the conscious mind has no control. As a result value judgments (i.e., “good” and “bad”) are inappropriate. In this way, Turrisi claims that Peirce addressed illusions and delusions.

Humans are integral with the universe. The premises and process of Firstness are natural, as we would use the word today. The universe can thus be seen as an “argument,” i.e., of some logical form such as deduction: given A and B, we can conclude C. The “mind of God” established the relations; we perceive them as phenomena; their order enables meaning. Meanwhile, the world impinges on us via Secondness: it is more than simply feelings. For example, surprise (a feeling) is a reaction (a Secondness) to the world.

Surprise is an inference, because one thing was expected but another thing occurred, but surprise is not consciously generated. The universe itself, both biological and non-biological parts, is developing.


Excerpt and condensation from LECTURE IV. THE REALITY OF THIRDNESS (Seven Systems of Metaphysics)

93. I proceed to argue that Thirdness is operative in Nature. Suppose we attack the question experimentally. Here is a stone. Now I place that stone where there will be no obstacle between it and the floor, and I will predict with confidence that as soon as I let go my hold upon the stone it will fall to the floor. I will prove that I can make a correct prediction by actual trial if you like. But I see by your faces that you all think it will be a very silly experiment. Why so? Because you all know very well that I can predict what will happen, and that the fact will verify my prediction.

94. But how can I know what is going to happen? You certainly do not think that it is by clairvoyance, as if the future event by its existential reactiveness could affect me directly, as in an experience of it, as an event scarcely past might affect me. You know very well that there is nothing of the sort in this case. Still, it remains true that I do know that that stone will drop, as a fact, as soon as I let go my hold. If I truly know anything, that which I know must be real. It would be quite absurd to say that I could be enabled to know how events are going to be determined over which I can exercise no more control than I shall be able to exercise over this stone after it shall have left my hand, that I can so peer in the future merely on the strength of any acquaintance with any pure fiction.

95. I know that this stone will fall if it is let go, because experience has convinced me that objects of this kind always do fall; and if anyone present has any doubt on the subject, I should be happy to try the experiment, and I will bet him a hundred to one on the result.

96. But the general proposition that all solid bodies fall in the absence of any upward forces or pressure, this formula I say, is of the nature of a representation. Our nominalistic friends would be the last to dispute that. They will go so far as to say that it is a mere representation -- the word mere meaning that to be represented and really to be are two very different things; and that this formula has no being except a being represented. It certainly is of the nature of a representation. That is undeniable, I grant. And it is equally undeniable that that which is of the nature of a representation is not ipso facto real. In that respect there is a great contrast between an object of reaction and an object of representation. Whatever reacts is ipso facto real. But an object of representation is not ipso facto real. If I were to predict that on my letting go of the stone it would fly up in the air, that would be mere fiction; and the proof that it was so would be obtained by simply trying the experiment. That is clear. On the other hand, and by the same token, the fact that I know that this stone will fall to the floor when I let it go, as you all must confess, if you are not blinded by theory, that I do know -- and you none of you care to take up my bet, I notice -- is the proof that the formula, or uniformity, as furnishing a safe basis for prediction, is, or if you like it better, corresponds to, a reality.

97. Possibly at this point somebody may raise an objection and say: You admit, that is one thing really to be and another to be represented; and you further admit that it is of the nature of the law of nature to be represented. Then it follows that it has not the mode of being of a reality. My answer to this would be that it rests upon an ambiguity. When I say that the general proposition as to what will happen, whenever a certain condition may be fulfilled, is of the nature of a representation, I mean that it refers to experiences in futuro, which I do not know are all of them experienced and never can know have been all experienced. But when I say that really to be is different from being represented, I mean that what really is, ultimately consists in what shall be forced upon us in experience, that there is an element of brute compulsion in fact and that fact is not a mere question of reasonableness. Thus, if I say, "I shall wind up my watch every day as long as I live," I never can have a positive experience which certainly covers all that is here promised, because I never shall know for certain that my last day has come. But what the real fact will be does not depend upon what I represent, but upon what the experiential reactions shall be. My assertion that I shall wind up my watch every day of my life may turn out to accord with facts, even though I be the most irregular of persons, by my dying before nightfall.

If we call that being true by chance, here is a case of a general proposition being entirely true in all its generality by chance.

98. Every general proposition is limited to a finite number of occasions in which it might conceivably be falsified, supposing that it is an assertion confined to what human beings may experience; and consequently it is conceivable that, although it should be true without exception, it should still only be by chance that it turns out true.

99. But if I see a man who is very regular in his habits and am led to offer to wager that that man will not miss winding his watch for the next month, you have your choice between two alternative hypotheses only:

1. You may suppose that some principle or cause is really operative to make him wind his watch daily, which active principle may have more or less strength; or

2. You may suppose that it is mere chance that his actions have hitherto been regular; and in that case, that regularity in the past affords you not the slightest reason for expecting its continuance in the future, any more than, if he had thrown sixes three times running, that event would render it either more or less likely that his next throw would show sixes.

100. It is the same with the operations of nature. With overwhelming uniformity, in our past experience, direct and indirect, stones left free to fall have fallen. Thereupon two hypotheses only are open to us. Either

1. the uniformity with which those stones have fallen has been due to mere chance and affords no ground whatever, not the slightest for any expectation that the next stone that shall be let go will fall; or

2. the uniformity with which stones have fallen has been due to some active general principle, in which case it would be a strange coincidence that it should cease to act at the moment my prediction was based upon it.

That position, gentlemen, will sustain criticism. It is irrefragable.

101. Of course, every sane man will adopt the latter hypothesis. If he could doubt it in the case of the stone -- which he can't -- and I may as well drop the stone once for all -- I told you so! -- if anybody doubts this still, a thousand other such inductive predictions are getting verified every day, and he will have to suppose every one of them to be merely fortuitous in order reasonably to escape the conclusion that general principles are really operative in nature. That is the doctrine of scholastic realism.

102. You may, perhaps, ask me how I connect generality with Thirdness. Various different replies, each fully satisfactory, may be made to that inquiry. The old definition of a general is Generale est quod natum aptum est dici de multis. This recognizes that the general is essentially predicative and therefore of the nature of a representamen. And by following out that path of suggestion we should obtain a good reply to the inquiry.

103. In another respect, however, the definition represents a very degenerate sort of generality. None of the scholastic logics fails to explain that sol is a general term; because although there happens to be but one sun yet the term sol aptum natum est dici de multis. But that is most inadequately expressed. If sol is apt to be predicated of many, it is apt to be predicated of any multitude however great, and since there is no maximum multitude, those objects, of which it is fit to be predicated, form an aggregate that exceeds all multitude. Take any two possible objects that might be called suns and, however much alike they may be, any multitude whatsoever of intermediate suns are alternatively possible, and therefore as before these intermediate possible suns transcend all multitude. In short, the idea of a general involves the idea of possible variations which no multitude of existent things could exhaust but would leave between any two not merely many possibilities, but possibilities absolutely beyond all multitude.

104. Now Thirdness is nothing but the character of an object which embodies Betweenness or Mediation in its simplest and most rudimentary form; and I use it as the name of that element of the phenomenon which is predominant wherever Mediation is predominant, and which reaches its fullness in Representation.

105. Thirdness, as I use the term, is only a synonym for Representation, to which I prefer the less colored term because its suggestions are not so narrow and special as those of the word Representation. Now it is proper to say that a general principle that is operative in the real world is of the essential nature of a Representation and of a Symbol because its modus operandi is the same as that by which words produce physical effects. Nobody can deny that words do produce such effects. Take, for example, that sentence of Patrick Henry which, at the time of our Revolution, was repeated by every man to his neighbor:

"Three millions of people, armed in the holy cause of Liberty, and in such a country as we possess, are invincible against any force that the enemy can bring against us."

Those words present this character of the general law of nature. They might have produced effects indefinitely transcending any that circumstances allowed them to produce. It might, for example, have happened that some American schoolboy, sailing as a passenger in the Pacific Ocean, should have idly written down those words on a slip of paper. The paper might have been tossed overboard and might have been picked up by some Jagala on a beach of the island of Luzon; and if he had had them translated to him, they might easily have passed from mouth to mouth there as they did in this country, and with similar effect.

106. Words then do produce physical effects. It is madness to deny it. The very denial of it involves a belief in it; and nobody can consistently fail to acknowledge it until he sinks to a complete mental paresis.

But how do they produce their effect? They certainly do not, in their character as symbols, directly react upon matter. Such action as they have is merely logical. It is not even psychological. It is merely that one symbol would justify another. However, suppose that first difficulty to have been surmounted, and that they do act upon actual thoughts. That thoughts act on the physical world and conversely, is one of the most familiar of facts. Those who deny it are persons with whom theories are stronger than facts. But how thoughts act on things it is impossible for us, in the present state of our knowledge, so much as to make any very promising guess; although, as I will show you presently, a guess can be made which suffices to show that the problem is not beyond all hope of ultimate solution.

107. All this is equally true of the manner in which the laws of nature influence matter. A law is in itself nothing but a general formula or symbol. An existing thing is simply a blind reacting thing, to which not merely all generality, but even all representation, is utterly foreign. The general formula may logically determine another, less broadly general. But it will be of its essential nature general, and its being narrower does not in the least constitute any participation in the reacting character of the thing. Here we have that great problem of the principle of individuation which the scholastic doctors after a century of the closest possible analysis were obliged to confess was quite incomprehensible to them. Analogy suggests that the laws of nature are ideas or resolutions in the mind of some vast consciousness, who, whether supreme or subordinate, is a Deity relatively to us. I do not approve of mixing up Religion and Philosophy; but as a purely philosophical hypothesis, that has the advantage of being supported by analogy. Yet I cannot clearly see that beyond that support to the imagination it is of any particular scientific service. . . .

108. Reasoning cannot possibly be divorced from logic; because, whenever a man reasons, he thinks that he is drawing a conclusion such as would be justified in every analogous case. He therefore cannot really infer without having a notion of a class of possible inferences, all of which are logically good. That distinction of good and bad he always has in mind when he infers. Logic proper is the critic of arguments, the pronouncing them to be good or bad. There are, as I am prepared to maintain, operations of the mind which are logically exactly analogous to inferences excepting only that they are unconscious and therefore uncontrollable and therefore not subject to criticism. But that makes all the difference in the world; for inference is essentially deliberate, and selfcontrolled. Any operation which cannot be controlled, any conclusion which is not abandoned, not merely as soon as criticism has pronounced against it, but in the very act of pronouncing that decree, is not of the nature of rational inference -- is not reasoning. Reasoning as deliberate is essentially critical, and it is idle to criticize as good or bad that which cannot be controlled. Reasoning essentially involves self-control; so that the logica utens is a particular species of morality. Logical goodness and badness, which we shall find is simply the distinction of Truth and Falsity in general, amounts, in the last analysis, to nothing but a particular application of the more general distinction of Moral Goodness and Badness, or Righteousness and Wickedness.

109. To criticize as logically sound or unsound an operation of thought that cannot be controlled is not less ridiculous than it would be to pronounce the growth of your hair to be morally good or bad. The ridiculousness in both cases consists in the fact that such a critical judgment may be pretended but cannot really be performed in clear thought, for on analysis it will be found absurd.

110. I am quite aware that this position is open to two serious objections, which I have not time to discuss, but which I have carefully considered and refuted. The first is that this is making logic a question of psychology. But this I deny. Logic does rest on certain facts of experience among which are facts about men, but not upon any theory about the human mind or any theory to explain facts. The other objection is that if the distinction [between] Good and Bad Logic is a special case [of the distinction between] Good and Bad Morals, by the same token the distinction of Good and Bad Morals is a special case of the distinction [between] esthetic Goodness and Badness. Now to admit this is not only to admit hedonism, which no man in his senses, and not blinded by theory or something worse, can admit, but also, having to do with the essentially Dualistic distinction of Good and Bad -- which is manifestly an affair of Category the Second -- it seeks the origin of this distinction in Esthetic Feeling, which belongs to Category the First.

111. This last objection deceived me for many years. The reply to it involves a very important point which I shall have to postpone to the next lecture. When it first presented itself to me, all I knew of ethics was derived from the study of Jouffroy †1 under Dr. Walker, of Kant, and of a wooden treatise by Whewell;†3 and I was led by this objection to a line of thought which brought me to regard ethics as a mere art, or applied science, and not a pure normative science at all. But when, beginning in 1883, I came to read the works of the great moralists, whose great fertility of thought I found in wonderful contrast to the sterility of the logicians -- I was forced to recognize the dependence of Logic upon Ethics; and then took refuge in the idea that there was no science of esthetics, that, because de gustibus non est disputandum, therefore there is no esthetic truth and falsity or generally valid goodness and badness. But I did not remain of this opinion long. I soon came to see that this whole objection rests upon a fundamental misconception. To say that morality, in the last resort, comes to an esthetic judgment is not hedonism -- but is directly opposed to hedonism. In the next place, every pronouncement between Good and Bad certainly comes under Category the Second; and for that reason such pronouncement comes out in the voice of conscience with an absoluteness of duality which we do not find even in logic; and although I am still a perfect ignoramus in esthetics, I venture to think that the esthetic state of mind is purest when perfectly naive without any critical pronouncement, and that the esthetic critic founds his judgments upon the result of throwing himself back into such a pure naive state -- and the best critic is the man who has trained himself to do this the most perfectly.

112. It is a great mistake to suppose that the phenomena of pleasure and pain are mainly phenomena of feeling. Examine pain, which would seem to be a good deal more positive than pleasure. I am unable to recognize with confidence any quality of feeling common to all pains; and if I cannot I am sure it cannot be an easy thing for anybody. For I have gone through a systematic course of training in recognizing my feelings. I have worked with intensity for so many hours a day every day for long years to train myself to this; and it is a training which I would recommend to all of you. The artist has such a training; but most of his effort goes to reproducing in one form or another what he sees or hears, which is in every art a very complicated trade; while I have striven simply to see what it is that I see. That this limitation of the task is a great advantage is proved to me by finding that the great majority of artists are extremely narrow. Their esthetic appreciations are narrow; and this comes from their only having the power of recognizing the qualities of their percepts in certain directions.

But the majority of those who opine that pain is a quality of feeling are not even artists; and even among those who are artists there are extremely few who are artists in pain. But the truth is that there are certain states of mind, especially among states of mind in which Feeling has a large share, which we have an impulse to get rid of. That is the obvious phenomenon; and the ordinary theory is that this impulse is excited by a quality of feeling common to all these states -- a theory which is supported by the fact that this impulse is particularly energetic in regard to states in which Feeling is the predominant element. Now whether this be true or false, it is a theory. It is not the fact that any such common quality in all pains is readily to be recognized.

113. At any rate, while the whole phenomenon of pain and the whole phenomenon of pleasure are phenomena that arise within the universe of states of mind and attain no great prominence except when they concern states of mind in which Feeling is predominant, yet these phenomena themselves do not mainly consist in any common Feeling-quality of Pleasure and any common Feelingquality of Pain, even if there are such Qualities of Feeling; but they mainly consist [in a] Pain [which lies] in a Struggle to give a state of mind its quietus, and [in a] Pleasure in a peculiar mode of consciousness allied to the consciousness of making a generalization, in which not Feeling, but rather Cognition is the principal constituent. This may be hard to make out as regards the lower pleasures, but they do not concern the argument we are considering. It is esthetic enjoyment which concerns us; and ignorant as I am of Art, I have a fair share of capacity for esthetic enjoyment; and it seems to me that while in esthetic enjoyment we attend to the totality of Feeling -- and especially to the total resultant Quality of Feeling presented in the work of art we are contemplating -- yet it is a sort of intellectual sympathy, a sense that here is a Feeling that one can comprehend, a reasonable Feeling. I do not succeed in saying exactly what it is, but it is a consciousness belonging to the category of Representation, though representing something in the Category of Quality of Feeling.

In that view of the matter, the objection to the doctrine that the distinction Moral approval and disapproval is ultimately only a species of the distinction Esthetic approval and disapproval seems to be answered.

114. It appears, then, that Logica utens consisting in self-control, the distinction of logical goodness and badness must begin where control of the processes of cognition begins; and any object that antecedes the distinction, if it has to be named either good or bad, must be named good. For since no fault can be found with it, it must be taken at its own valuation.

115. Where then in the process of cognition does the possibility of controlling it begin? Certainly not before the percept is formed.

Even after the percept is formed there is an operation which seems to me to be quite uncontrollable. It is that of judging what it is that the person perceives. A judgment is an act of formation of a mental proposition combined with an adoption of it or act of assent to it. A percept on the other hand is an image or moving picture or other exhibition. The perceptual judgment, that is, the first judgment of a person as to what is before his senses, bears no more resemblance to the percept than the figure I am going to draw is like a man.


I do not see that it is possible to exercize any control over that operation or to subject it to criticism. If we can criticize it at all, as far as I can see, that criticism would be limited to performing it again and seeing whether, with closer attention, we get the same result. But when we so perform it again, paying now closer attention, the percept is presumably not such as it was before. I do not see what other means we have of knowing whether it is the same as it was before or not, except by comparing the former perceptual judgment and the later one. I should utterly distrust any other method of ascertaining what the character of the percept was. Consequently, until I am better advised, I shall consider the perceptual judgment to be utterly beyond control. Should I be wrong in this, the Percept, at all events, would seem to be so.

116. It follows, then, that our perceptual judgments are the first premisses of all our reasonings and that they cannot be called in question. All our other judgments are so many theories whose only justification is that they have been and will be borne out by perceptual judgments. But the perceptual judgments declare one thing to be blue, another yellow -- one sound to be that of A, another that of U, another that of I. These are the Qualities of Feeling which the physicists say are mere illusions because there is no room for them in their theories. If the facts won't agree with the Theory, so much the worse for them. They are bad facts. This sounds to me childish, I confess. It is like an infant that beats an inanimate object that hurts it. Indeed this is true of all fault-finding with others than oneself, and those for whose conduct one is responsible. Reprobation is a silly [business].

117. But peradventure I shall be asked whether I do not admit that there is any such thing as an illusion or hallucination. Oh, yes; among artists I have known more than one case of downright hallucinatory imaginations at the beck and call of these {poietai}. Of course, the man knows that such obedient spectres are not real experiences, because experience is that which forces itself upon him, will-he nill-he.

Hallucinations proper -- obsessional hallucinations -- will not down at one's bidding, and people who are subject to them are accustomed to sound the people who are with them in order to ascertain whether the object before them has a being independent of their disease or not. There are also social hallucinations.

In such a case, a photographic camera or other instrument might be of service.

118. Of course, everybody admits and must admit that these apparitions are entities -- entia; the question is whether these entia belong to the class of realities or not, that is, whether they are such as they are independently of any collection of singular representations that they are so, or whether their mode of being depends upon abnormal conditions. But as for the entire universe of Qualities which the physicist would pronounce Illusory, there is not the smallest shade of just suspicion resting upon their normality. On the contrary, there is considerable evidence that colors, for example, and sounds have the same character for all mankind.

Well, I will skip this. Suffice it to say that there is no reason for suspecting the veracity of the senses, and the presumption is that the physics of the future will find out that they are more real than the present state of scientific theory admits of their being represented as being.

119. Therefore, if you ask me what part Qualities can play in the economy of the universe, I shall reply that the universe is a vast representamen, a great symbol of God's purpose, working out its conclusions in living realities. Now every symbol must have, organically attached to it, its Indices of Reactions and its Icons of Qualities; and such part as these reactions and these qualities play in an argument that, they of course, play in the universe -- that Universe being precisely an argument. In the little bit that you or I can make out of this huge demonstration, our perceptual judgments are the premisses for us and these perceptual judgments have icons as their predicates, in which icons Qualities are immediately presented. But what is first for us is not first in nature. The premisses of Nature's own process are all the independent uncaused elements of facts that go to make up the variety of nature which the necessitarian supposes to have been all in existence from the foundation of the world, but which the Tychist supposes are continually receiving new accretions. These premisses of nature, however, though they are not the perceptual facts that are premisses to us, nevertheless must resemble them in being premisses. We can only imagine what they are by comparing them with the premisses for us. As premisses they must involve Qualities.

Now as to their function in the economy of the Universe. The Universe as an argument is necessarily a great work of art, a great poem -- for every fine argument is a poem and a symphony -- just as every true poem is a sound argument. But let us compare it rather with a painting -- with an impressionist seashore piece -- then every Quality in a Premiss is one of the elementary colored particles of the Painting; they are all meant to go together to make up the intended Quality that belongs to the whole as whole. That total effect is beyond our ken; but we can appreciate in some measure the resultant Quality of parts of the whole -- which Qualities result from the combinations of elementary Qualities that belong to the premisses.

But I shall endeavor to make this clearer in the next lecture.



Lecture Five: The Normative Sciences (The Three Kinds of Goodness)

In Lecture Five, Peirce reviews his classification of sciences, especially normative sciences. Peirce describes the normatives sciences.esthetics, ethics, and logic; the goal for each is to determine possibilities, not standards of conduct. At the end of the lecture, Peirce describes the three kinds of arguments, namely abduction, induction, and deduction.
*Philosophy is divided into three parts: phenomenology, the normative sciences, and metaphysics.
These parts correspond to the categories of Firstness, Secondness, and Thirdness, respectively,
*All three parts of philosophy deal with phenomena. Phenomenology focuses on their direct nature, thus phenomenology deals with Firstness. The normative sciences focus on how phenomena relate, via laws, to purposes, thus the normative sciences deal with Secondness. And metaphysics focuses on the lawful nature of that law, thus metaphysics deals with Thirdness.
*Normative science divides into esthetics, ethics, and logic.
*For Normative Science in general being the science of the laws of conformity of things to ends, esthetics considers those things whose ends are to embody qualities of feeling, ethics those things whose ends lie in action, and logic those things whose end is to represent something.
*Peirce argues that reasoning (logic) is a form of action and is thus subject to ethical considerations; in particular, it is subject to the need for self-control.
*The logically good is simply a particular species of the morally good. The morally good appears as a particular species of the esthetically good.
*The esthetically good involves the choice of aims or purposes and pragmatism involves the conception of actions relative to aims.
*Peirce continues his lecture by considering different types of reasoning or argumentation with respect to their logical goodness.
*He claims that although we have neither immediate consciousness nor direct experience of generality, nevertheless we perceive generality: it “pours in” upon us in our very perceptual judgments.

This fifth Harvard lecture was delivered on 30 April 1903. Peirce reviews his classification of the sciences, especially the normative sciences: esthetics, ethics, and logic. He argues that reasoning is a form of action and is thus subject to ethical considerations; in particular, it is subject to the need for self-control. The logically good, Peirce says, is a species of the morally good, and the morally good is itself a species of the esthetically good. Now the esthetically good involves the choice of aims, or purposes. Pragmatism comes back in at this point, for pragmatism involves the conception of actions relative to aims. Peirce continues his lecture by considering different types of reasoning or argumentation with respect to their logical goodness, and concludes by claiming that although we have neither immediate consciousness nor direct experience of generality, nevertheless we perceive generality: it "pours in" with our perceptual judgments. (Head Notes for the EP 2, Chapter 14)


Division of Philosophy
Division of Philosophy

In this lecture Peirce intends to use the relationship between the three normative sciences (i.e., esthetics, ethics, and logic) to explain how we figure out what anything means.
That is, logic is a proper subset of ethics, which, in turn, is a proper subset of esthetics.

But pragmatism also needs an understanding of the larger question of the purpose of philosophy. Peirce considered that his view of phenomenology would help.

Peirce considered that esthetics is a proper subset of phenomenology, which is where Peirce's three categories come in.

The Proper Division of Philosophy
Philosophy is a science that, unlike other sciences, does not generate facts but confines itself to those facts that are already available to all of us. The first question is: What are the building blocks of those facts?

The three divisions of philosophy are (1) phenomenology, (2) the normative sciences, and (3) metaphysics. Phenomenology is the study of the Firstness of phenomena. That is, the phenomena themselves. The normative sciences are the study of our interaction with phenomena, which is a Secondness. Metaphysics is outside of the scope of these lectures. The normative sciences study the purpose of our interaction with phenomena.
Philosophy is based on mathematics.

The Foundation of the Normative Sciences in Esthetics
Peirce never developed a significant esthetics, though he noted its role as the foundation of the normative sciences.

Pragmatism cannot be understood without first understanding the more fundamental normative sciences, namely esthetics and ethics. Esthetics, ethics, and logic correspond to Firstness, Secondness, and Thirdness, as well as to Feeling, Reaction, and Thought.
Consciousness exists in Feeling, Reaction, and Thought.
Good and bad can be judged by logica docens and logica utens.

Peirce provided a classification system for esthetics. He equated esthetic goodness with suitability and with clarity of reaction.

The extent of an item’s esthetic goodness can be gauged by the strength of the reaction that it engenders in us. That is, we respond to something that is esthetically good, even if it sickens, frightens, or otherwise unsettles us. Note that esthetic goodness is independent of pleasure. We do not respond to something that is esthetically bad. We can train ourselves to be more esthetically aware.

Esthetics deals with our reaction (i.e., Secondness) to phenomena.

The normative sciences deal with ends (i.e., purposes). Esthetics, ethics, and logic deal with ends based on feelings, action (and reaction), and representation, respectively. Ethics is built on esthetics because ethics uses a proper subset of feelings - only those that are “deliberate” - upon which to direct action.

We make ethical choices to conform to a pattern we feel to be admirable (i.e., esthetically worthwhile). The purpose of the normative sciences is not to provide guidance on how to live but rather on how to understand what is possible in the focus areas of the normative sciences.

The Role of Ethics in the Determination of Ultimate Aims
Ethics, as a normative science, focuses on what is possible. Ethics requires choice. A bad ethic is one that presents no choice. This only applies if the ethic has no final goal, when all roads are deemed the same, because only then is there no basis for decision. The “special sciences”, such as psychology, cannot help here. In fact, what people naturally do has no bearing on the efficacy of esthetics, ethics, or logic.

The reason that what people naturally do is of no bearing is that the purpose of the normative sciences is to determine what purposes are possible, what rules would always apply, given an unbounded extent of time. A candidate purpose is one that meets two conditions: (1) we think it is right and (2) it is in harmony with the world around us in the sense that it does not force us up against laws that would prevent its fulfillment.

People in their everyday lives are inherently short-sighted, from Peirce’s perspective, and thus not in a position to speak about absolute purposes. But even if we were sufficiently farsighted, do we know enough about the laws that would constrain such purposes to enable us to be in a position to separate the possible from the impossible?

The Good of Logic
According to other philosophers, logical goodness consists of two parts: “logical” truth, such as the results of formal arguments, and “material” truth, such as is inherent in propositions. In terms of logical goodness, the propositions are more important than the conclusions for two reasons. First, the propositions are accepted as true, by their nature as propositions. Second, the propositions are pregnant with more conclusions than we have been able to derive.
The logical goodness of a conclusion depends upon the type of argument by which it was derived. There are three types of arguments: abduction, induction, and deduction.

Philosophy is a “Positive Science, or Science of Fact”, meaning that philosophy does not generate facts but uses what is everyday before us. Philosophy does not generate facts because philosophy does not need to generate facts: Peirce argues that “nobody doubts or can doubt” what Pierce calls “common experience”.

Philosophy is divided into three parts: phenomenology, the normative sciences, and metaphysics. These parts correspond to the categories of Firstness, Secondness, and Thirdness, respectively, which correspondence lends credence, in Peirce’s mind, to the efficacy of those categories.
The normative sciences are themselves divided into three parts: esthetics (which pursues “Beauty”), ethics (which pursues “Right”), and logic (which pursues “Truth”).

All three parts of philosophy deal with phenomena. Phenomenology focuses on their direct nature, thus phenomenology deals with Firstness. The normative sciences focus on how phenomena relate, via laws, to purposes, thus the normative sciences deal with Secondness. And metaphysics focuses on the lawful nature of that law, thus metaphysics deals with Thirdness.

The normative sciences are theory. It is not their purpose to provide practical guidance. It just so happens that people feel, act, and think in accord with the results of the normative sciences, but that lends no weight to those results.

The normative sciences are distinct from mathematics for three reasons. First, the hypotheses of the normative sciences are facts; in mathematics they are ideals. Second, the process that normative science uses is not deduction, as it is for mathematics. And third, the normative sciences study the purposes to which phenomena serve, whereas there is no concept of purpose in mathematics.

It is a mistake to think that the purpose of the normative sciences is to separate the good from the bad logically, ethically, or even esthetically. If that were not a mistake, then the normative sciences would be concerned with quantity, i.e., how much good or bad. But the normative sciences are interested in quality, i.e., the type or kinds of truth, right, and beauty.

What is the goodness that is free from error, as opposed to the goodness that achieves some end? One of the problems of traditional philosophy is that it confines the normative sciences to human activity, as though mind existed in human pineal glands only, as Cartesians suppose. Meanwhile, few logicians acknowledge that esthetics and ethics are normative sciences. However, the division shown above is based on the three categories. The purpose of the three normative sciences is the study of what leads to feelings (esthetics), what leads to actions (ethics), and what leads to representations (logic).

The normative sciences assume both volition and an ideal. Esthetics is the study of what ideals we can admire (and thus what ideals we have the opportunity of choosing); ethics is the study of what ideals to which we can conform our action; and logic is the study of what ideals to which we can conform our arguments (i.e., what arguments we accept as valid). Logic is based on ethics, which, in turn, is based on esthetics.

Because pragmatism is an element of logic, we must understand logical goodness, which implies that we understand ethical goodness, which, in turn, implies that we understand esthetic goodness. Something is esthetically good to the degree that its parts serve the same end. Something is esthetically bad to the degree that its parts conflict.

(Philip L. Campbell’s Note: Another way of describing Peirce’s notion of esthetic goodness/badness is the clarity of our response. Something that is esthetically good will evoke a precise, focused response; something that is esthetically bad might not evoke any response (see Lecture V, page 70 (page 41 herein)).)

Ethical goodness implies some goal, some maxim of behavior that both (a) applies in all circumstances, and (b) we can choose to ignore. If the goal does not apply in some circumstances, then there is some other maxim that does, and that other maxim is actually the goal. If we are not able to avoid conforming our action to the goal, then the goal has no ethical nature to it. Only if we have no goal are we ethically bad.

Ethics studies possible goals. The special sciences such as psychology are of no help here.

Pragmatism, an element of logic, is intended to help us act. Possible actions can be evaluated only in light of goals. Goals are the purview of ethics. Thus the study of ethics is required to understand the significance of pragmatism.

A goal is a rule that applies in all circumstances and is something that can be achieved. Because we are limited in our ability to discern what can be achieved and what cannot, we have to assume that the goals that interest us can be achieved.

Logic is Thirdness, so an element of logic is a representation. A representation, such as a proverb, must be repeatable and must be related to some object.

Truth derived from logic – “logical truth” - is not superior to truth inherent in propositions – “material truth”. The former is one instance of what can be gleaned from the latter, but the latter embodies all that can be gleaned from the propositions.

There are at least two aspects of arguments, their soundness (i.e., the efficacy of the process of the argument) and the extent to which they teach us about the world. There are three kinds of arguments: abduction, induction, and deduction. Only deduction is “necessary”, meaning that given the premises, there is no choice but to arrive at the conclusion. Mathematics uses deduction. Induction is used to test a theory via experiment. Abduction alone generates theories. Science depends fundamentally upon abduction because abduction is fundamental to understanding.

It is not clear how these three kinds of arguments relate to the three categories.

(footnote 3) Perhaps abduction, induction, and deduction relate to Firstness, Secondness, and Thirdness, respectively.

Mathematical reasoning uses diagrams, each of which is by necessity a special case from which the viewer is to infer the general case, which is a Thirdness.

We do not derive generality. Rather, generality comes to our consciousness as part of perceptual judgments.


Excerpt and condensation from LECTURE V. THREE KINDS OF GOODNESS

I have already explained that by Philosophy I mean that department of Positive Science, or Science of Fact, which does not busy itself with gathering facts, but merely with learning what can be learned from that experience which presses in upon every one of us daily and hourly. It does not gather new facts, because it does not need them, and also because new general facts cannot be firmly established without the assumption of a metaphysical doctrine; and this, in turn, requires the coöperation of every department of philosophy; so that such new facts, however striking they may be, afford weaker support to philosophy by far than that common experience which nobody doubts or can doubt, and which nobody ever even pretended to doubt except as a consequence of belief in that experience so entire and perfect that it failed to be conscious of itself; just as an American who has never been abroad fails to perceive the characteristics of Americans; just as a writer is unaware of the peculiarities of his own style; just as none of us can see himself as others see him. (CP 5-120)

Philosophy has three grand divisions.
The first is Phenomenology, which simply contemplates the Universal Phenomenon and discerns its ubiquitous elements, Firstness, Secondness, and Thirdness, together perhaps with other series of categories.
The second grand division is Normative Science, which investigates the universal and necessary laws of the relation of Phenomena to Ends, that is, perhaps, to Truth, Right, and Beauty.
The third grand division is Metaphysics, which endeavors to comprehend the Reality of Phenomena.

Now Reality is an affair of Thirdness as Thirdness, that is, in its mediation between Secondness and Firstness. Most, if not all of you, are, I doubt not, Nominalists; and I beg you will not take offence at a truth which is just as plain and undeniable to me as is the truth that children do not understand human life. To be a nominalist consists in the undeveloped state in one's mind of the apprehension of Thirdness as Thirdness. The remedy for it consists in allowing ideas of human life to play a greater part in one's philosophy. Metaphysics is the science of Reality. Reality consists in regularity. Real regularity is active law. Active law is efficient reasonableness, or in other words is truly reasonable reasonableness. Reasonable reasonableness is Thirdness as Thirdness.

So then the division of Philosophy into these three grand departments, whose distinctness can be established without stopping to consider the contents of Phenomenology (that is, without asking what the true categories may be), turns out to be a division according to Firstness, Secondness, and Thirdness, and is thus one of the very numerous phenomena I have met with which confirm this list of categories. (CP 5-121)

Phenomenology treats of the universal Qualities of Phenomena in their immediate phenomenal character, in themselves as phenomena. It, thus, treats of Phenomena in their Firstness. (CP 5-122)

Normative Science treats of the laws of the relation of phenomena to ends; that is, it treats of Phenomena in their Secondness. (CP 5-123)

Metaphysics treats of Phenomena in their Thirdness. (CP 5-124)

Normative Science is not a skill, nor is it an investigation conducted with a view to the production of skill. … It is purely theoretical. Of course there are practical sciences of reasoning and investigation, of the conduct of life, and of the production of works of art. They correspond to the Normative Sciences, and may be probably expected to receive aid from them. But they are not integrant parts of these sciences. … Nor again is Normative Science a special science, that is, one of those sciences that discover new phenomena. It is not even aided in any appreciable degree by any such science. … The fact that men for the most part show a natural disposition to approve nearly the same arguments that logic approves, nearly the same acts that ethics approves, and nearly the same works of art that esthetics approves, may be regarded as tending to support the conclusions of logic, ethics, and esthetics. But such support is perfectly insignificant; and when it comes to a particular case, to urge that anything is sound and good logically, morally, or esthetically, for no better reason than that men have a natural tendency to think so, I care not how strong and imperious that tendency may be, is as pernicious a fallacy as ever was. (CP 5-125)

In one of the ways I have indicated, Normative Science is by the majority of writers of the present day ranked too low in the scale of the sciences. On the other hand, some students of exact logic rank that normative science, at least, too high, by virtually treating it as on a par with pure mathematics. There are three excellent reasons any one of which ought to rescue them from the error of this opinion. In the first place, the hypotheses from which the deductions of normative science proceed are intended to conform to positive truth of fact and those deductions derive their interest from that circumstance almost exclusively; while the hypotheses of pure mathematics are purely ideal in intention, and their interest is purely intellectual. But in the second place, the procedure of the normative sciences is not purely deductive, as that of mathematics is, nor even principally so. Their peculiar analyses of familiar phenomena, analyses which ought to be guided by the facts of phenomenology in a manner in which mathematics is not at all guided, separate Normative Science from mathematics quite radically. In the third place, there is a most intimate and essential element of Normative Science which is still more proper to it, and that is its peculiar appreciations, to which nothing at all in the phenomena, in themselves, corresponds. These appreciations relate to the conformity of phenomena to ends which are not immanent within those phenomena. (CP 5-126)

There are sundry other widely spread misconceptions of the nature of Normative Science. One of these is that the chief, if not the only, problem of Normative Science is to say what is good and what bad, logically, ethically, and esthetically; or what degree of goodness a given description of phenomenon attains. Were this the case, normative science would be, in a certain sense, mathematical, since it would deal entirely with a question of quantity. But I am strongly inclined to think that this view will not sustain critical examination. Logic classifies arguments, and in doing so recognizes different kinds of truth. In ethics, too, qualities of good are admitted by the great majority of moralists. As for esthetics, in that field qualitative differences appear to be so prominent that, abstracted from them, it is impossible to say that there is any appearance which is not esthetically good. Vulgarity and pretension, themselves, may appear quite delicious in their perfection, if we can once conquer our squeamishness about them, a squeamishness which results from a contemplation of them as possible qualities of our own handiwork --but that is a moral and not an esthetic way of considering them. I hardly need remind you that goodness, whether esthetic, moral, or logical, may either be negative --consisting in freedom from fault --or quantitative --consisting in the degree to which it attains. But in an inquiry, such as we are now engaged upon, negative goodness is the important thing. (CP 5-127)

A subtle and almost ineradicable narrowness in the conception of Normative Science runs through almost all modern philosophy in making it relate exclusively to the human mind. The beautiful is conceived to be relative to human taste, right and wrong concern human conduct alone, logic deals with human reasoning. Now in the truest sense these sciences certainly are indeed sciences of mind. Only, modern philosophy has never been able quite to shake off the Cartesian idea of the mind, as something that "resides" in the pineal gland. (CP 5-128)

I cannot linger more upon the general conception of Normative Science. I must come down to the particular Normative Sciences. These are now commonly said to be logic, ethics, and esthetics. Formerly only logic and ethics were reckoned as such. A few logicians refuse to recognize any other normative science than their own. My own opinions of ethics and esthetics are far less matured than my logical opinions. It is only since 1883 that I have numbered ethics among my special studies; and until about four years ago, I was not prepared to affirm that ethics was a normative science. As for esthetics, although the first year of my study of philosophy was devoted to this branch exclusively, yet I have since then so completely neglected it that I do not feel entitled to have any confident opinions about it. I am inclined to think that there is such a Normative Science; but I feel by no means sure even of that.

Supposing, however, that normative science divides into esthetics, ethics, and logic, then it is easily perceived, from my standpoint, that this division is governed by the three categories. For Normative Science in general being the science of the laws of conformity of things to ends, esthetics considers those things whose ends are to embody qualities of feeling, ethics those things whose ends lie in action, and logic those things whose end is to represent something. (CP 5-129)

The act of inference consists in the thought that the inferred conclusion is true because in any analogous case an analogous conclusion would be true. Thus, logic is coeval with reasoning. ... It essentially involves an approval of it --a qualitative approval. Now such self-approval supposes self-control. Not that we regard our approval as itself a voluntary act, but that we hold the act of inference, which we approve, to be voluntary. That is, if we did not approve, we should not infer.
There are mental operations which are as completely beyond our control as the growth of our hair. But when we institute an experiment to test a theory, or when we imagine an extra line to be inserted in a geometrical diagram in order to determine a question in geometry, these are voluntary acts which our logic, whether it be of the natural or the scientific sort, approves.
Now, the approval of a voluntary act is a moral approval.
Ethics is the study of what ends of action we are deliberately prepared to adopt. That is right action which is in conformity to ends which we are prepared deliberately to adopt. That is all there can be in the notion of righteousness, as it seems to me. The righteous man is the man who controls his passions, and makes them conform to such ends as he is prepared deliberately to adopt as ultimate. If it were in the nature of a man to be perfectly satisfied to make his personal comfort his ultimate aim, no more blame would attach to him for doing so than attaches to a hog for behaving in the same way.
A logical reasoner is a reasoner who exercises great self-control in his intellectual operations; and therefore the logically good is simply a particular species of the morally good.
Ethics --the genuine normative science of ethics, as contradistinguished from the branch of anthropology which in our day often passes under the name of ethics --this genuine ethics is the normative science par excellence, because an end --the essential object of normative science --is germane to a voluntary act in a primary way in which it is germane to nothing else.
For that reason I have some lingering doubt as to there being any true normative science of the beautiful. On the other hand, an ultimate end of action deliberately adopted --that is to say, reasonably adopted --must be a state of things that reasonably recommends itself in itself aside from any ulterior consideration. It must be an admirable ideal, having the only kind of goodness that such an ideal can have; namely, esthetic goodness. From this point of view the morally good appears as a particular species of the esthetically good. (CP 5-130)

If this line of thought be sound, the morally good will be the esthetically good specially determined by a peculiar superadded element; and the logically good will be the morally good specially determined by a special superadded element. (CP 5-131)

This suggestion must go for what it may be worth, which I dare say may be very little. If it be correct, it will follow that there is no such thing as positive esthetic badness; and since by goodness we chiefly in this discussion mean merely the absence of badness, or faultlessness, there will be no such thing as esthetic goodness. All there will be will be various esthetic qualities; that is, simple qualities of totalities not capable of full embodiment in the parts, which qualities may be more decided and strong in one case than in another. But the very reduction of the intensity may be an esthetic quality; nay, it will be so; and I am seriously inclined to doubt there being any distinction of pure esthetic betterness and worseness. My notion would be that there are innumerable varieties of esthetic quality, but no purely esthetic grade of excellence. (CP 5-132)

But the instant that an esthetic ideal is proposed as an ultimate end of action, at that instant a categorical imperative pronounces for or against it. Kant, as you know, proposes to allow that categorical imperative to stand unchallenged --an eternal pronouncement. His position is in extreme disfavor now, and not without reason. Yet I cannot think very highly of the logic of the ordinary attempts at refuting it. The whole question is whether or not this categorical imperative be beyond control. If this voice of conscience is unsupported by ulterior reasons, is it not simply an insistent irrational howl, the hooting of an owl which we may disregard if we can? Why should we pay any more attention to it than we would to the barking of a cur? If we cannot disregard conscience, all homilies and moral maxims are perfectly idle. But if it can be disregarded, it is, in one sense, not beyond control. It leaves us free to control ourselves. So then, it appears to me that any aim whatever which can be consistently pursued becomes, as soon as it is unfalteringly adopted, beyond all possible criticism, except the quite impertinent criticism of outsiders. An aim which cannot be adopted and consistently pursued is a bad aim. It cannot properly be called an ultimate aim at all. The only moral evil is not to have an ultimate aim. (CP 5-133)

Accordingly the problem of ethics is to ascertain what end is possible. It might be thoughtlessly supposed that special science could aid in this ascertainment. But that would rest on a misconception of the nature of an absolute aim, which is what would be pursued under all possible circumstances --that is, even though the contingent facts ascertained by special sciences were entirely different from what they are. Nor, on the other hand, must the definition of such aim be reduced to a mere formalism. (CP 5-134)

The importance of the matter for pragmatism is obvious. For if the meaning of a symbol consists in how it might cause us to act, it is plain that this "how" cannot refer to the description of mechanical motions that it might cause, but must intend to refer to a description of the action as having this or that aim. In order to understand pragmatism, therefore, well enough to subject it to intelligent criticism, it is incumbent upon us to inquire what an ultimate aim, capable of being pursued in an indefinitely prolonged course of action, can be. (CP 5-135)

The deduction of this is somewhat intricate, on account of the number of points which have to be taken into account; and of course I cannot go into details. In order that the aim should be immutable under all circumstances, without which it will not be an ultimate aim, it is requisite that it should accord with a free development of the agent's own esthetic quality. At the same time it is requisite that it should not ultimately tend to be disturbed by the reactions upon the agent of that outward world which is supposed in the very idea of action. It is plain that these two conditions can be fulfilled at once only if it happens that the esthetic quality toward which the agent's free development tends and that of the ultimate action of experience upon him are parts of one esthetic total. Whether or not this is really so, is a metaphysical question which it does not fall within the scope of Normative Science to answer. If it is not so, the aim is essentially unattainable. But just as in playing a hand of whist, when only three tricks remain to be played, the rule is to assume that the cards are so distributed that the odd trick can be made, so the rule of ethics will be to adhere to the only possible absolute aim, and to hope that it will prove attainable. Meantime, it is comforting to know that all experience is favorable to that assumption. (CP 5-136)

The ground is now cleared for the analysis of logical goodness, or the goodness of representation. There is a special variety of esthetic goodness that may belong to a representamen, namely, expressiveness. There is also a special moral goodness of representations, namely, veracity. But besides this there is a peculiar mode of goodness which is logical. What this consists in we have to inquire. (CP 5-137)

The mode of being of a representamen is such that it is capable of repetition. Take, for example, any proverb. "Evil communications corrupt good manners." Every time this is written or spoken in English, Greek, or any other language, and every time it is thought of it is one and the same representamen. Itis the same with a diagram or picture. It is the same with a physical sign or symptom. If two weathercocks are different signs, it is only in so far as they referto different parts of the air. A representamen which should have a unique embodiment, incapable of repetition, would not be a representamen, but a part of the very fact represented. This repetitory character of the representamen involves as a consequence that it is essential to a representamen that it should contribute to the determination of another representamen distinct from itself. ... I call a representamen which is determined by another representamen, an interpretant of the latter. Every representamen is related or is capable of being related to a reacting thing, its object, and every representamen embodies, in some sense, some quality, which may be called its signification. (CP 5-138)

A representamen [as symbol] is either a rhema, a proposition, or an argument. An argument is a representamen which separately shows what interpretant it is intended to determine. A proposition is a representamen which is not an argument, but which separately indicates what object it is intended to represent. A rhema is a simple representation without such separate parts. (CP 5-139)

Esthetic goodness, or expressiveness, may be possessed, and in some degree must be possessed, by any kind of representamen -- rhema, proposition, or argument. (CP 5-140)

Moral goodness, or veracity, may be possessed by a proposition or by an argument, but cannot be possessed by a rhema. A mental judgment or inference must possess some degree of veracity. (CP 5-141)

As to logical goodness, or truth, the statements in the books are faulty; and it is highly important for our inquiry that they should be corrected. The books distinguish between logical truth, which some of them rightly confine to arguments that do not promise more than they perform, and material truth which belongs to propositions, being that which veracity aims to be; and this is conceived to be a higher grade of truth than mere logical truth.
I would correct this conception as follows. In the first place, all our knowledge rests upon perceptual judgments. These are necessarily veracious in greater or less degree according to the effort made, but there is no meaning in saying that they have any other truth than veracity, since a perceptual judgment can never be repeated. At most we can say of a perceptual judgment that its relation to other perceptual judgments is such as to permit a simple theory of the facts. Thus I may judge that I see a clean white surface. But a moment later I may question whether the surface really was clean, and may look again more sharply. If this second more veracious judgment still asserts that I see a clean surface, the theory of the facts will be simpler than if, at my second look, I discern that the surface is soiled. Still, even in this last case, I have no right to say that my first percept was that of a soiled surface. I absolutely have no testimony concerning it, except my perceptual judgment, and although that was careless and had no high degree of veracity, still have to accept the only evidence in my possession.
Now consider any other judgment I may make. That is a conclusion of inferences ultimately based on perceptual judgments, and since these are indisputable, all the truth which my judgment can have must consist in the logical correctness of those inferences. Or I may argue the matter in another way. To say that a proposition is false is not veracious unless the speaker has found out that it is false. Confining ourselves, therefore, to veracious propositions, to say that a proposition is false and that it has been found to be false are equivalent, in the sense of being necessarily either both true or both false. Consequently, to say that a proposition is perhaps false is the same as to say that it will perhaps be found out to be false. Hence to deny one of these is to deny the other. To say that a proposition is certainly true means simply that it never can be found out to be false, or in other words, that it is derived by logically correct arguments from veracious perceptual judgments. Consequently, the only difference between material truth and the logical correctness of argumentation is that the latter refers to a single line of argument and the former to all the arguments which could have a given proposition or its denial as their conclusion.
Let me say to you that this reasoning needs to be scrutinized with the severest and minutest logical criticism, because pragmatism largely depends upon it. (CP 5-142)

It appears, then, that logical goodness is simply the excellence of argument -- its negative, and more fundamental, goodness being its soundness and weight, its really having the force that it pretends to have and that force being great, while its quantitative goodness consists in the degree in which it advances our knowledge. In what then does the soundness of argument consist? (CP 5-143)

In order to answer that question it is necessary to recognize three radically different kinds of arguments which I signalized in 1867 and which had been recognized by the logicians of the eighteenth century, although [those] logicians quite pardonably failed to recognize the inferential character of one of them. Indeed, I suppose that the three were given by Aristotle in the Prior Analytics, although the unfortunate illegibility of a single word in his MS. and its replacement by a wrong word by his first editor, the stupid [Apellicon], has completely altered the sense of the chapter on Abduction. At any rate, even if my conjecture is wrong, and the text must stand as it is, still Aristotle, in that chapter on Abduction, was even in that case evidently groping for that mode of inference which I call by the otherwise quite useless name of Abduction -- a word which is only employed in logic to translate the [{apagoge}] of that chapter. (CP 5-144)

These three kinds of reasoning are Abduction, Induction, and Deduction. Deduction is the only necessary reasoning. It is the reasoning of mathematics. It starts from a hypothesis, the truth or falsity of which has nothing to do with the reasoning; and of course its conclusions are equally ideal. The ordinary use of the doctrine of chances is necessary reasoning, although it is reasoning concerning probabilities. Induction is the experimental testing of a theory. The justification of it is that, although the conclusion at any stage of the investigation may be more or less erroneous, yet the further application of the same method must correct the error. The only thing that induction accomplishes is to determine the value of a quantity. It sets out with a theory and it measures the degree of concordance of that theory with fact. It never can originate any idea whatever. No more can deduction. All the ideas of science come to it by the way of Abduction. Abduction consists in studying facts and devising a theory to explain them. Its only justification is that if we are ever to understand things at all, it must be in that way. (CP 5-145)

Concerning the relations of these three modes of inference to the categories and concerning certain other details, my opinions, I confess, have wavered. ... This perhaps ought to give a slight additional weight to those opinions in which I have never wavered. Among these opinions which I have constantly maintained is this, that while Abductive and Inductive reasoning are utterly irreducible, either to the other or to Deduction, or Deduction to either of them, yet the only rationale of these methods is essentially Deductive or Necessary. If then we can state wherein the validity of Deductive reasoning lies, we shall have defined the foundation of logical goodness of whatever kind. (CP 5-146)

Now all necessary reasoning, whether it be good or bad, is of the nature of mathematical reasoning.
My analyses of reasoning surpass in thoroughness all that has ever been done in print, whether in words or in symbols. (CP 5-147)

It is on the basis of such analysis that I declare that all necessary reasoning, be it the merest verbiage of the theologians, so far as there is any semblance of necessity in it, is mathematical reasoning. Now mathematical reasoning is diagrammatic. This is as true of algebra as of geometry. But in order to discern the features of diagrammatic reasoning, it is requisite to begin with examples that are not too simple. In simple cases, the essential features are so nearly obliterated that they can only be discerned when one knows what to look for. But beginning with suitable examples and thence proceeding to others, one finds that the diagram itself, in its individuality, is not what the reasoning is concerned with. I will take an example which recommends itself only by its consideration requiring but a moment. A line abuts upon an ordinary point of another line forming two angles. The sum of these angles is proved by Legendre to be equal to the sum of two right angles by erecting a perpendicular to the second line in the plane of the two and through the point of abuttal. This perpendicular must lie in the one angle or the other. The pupil is supposed to see that. He sees it only in a special case, but he is supposed to perceive that it will be so in any case. The more careful logician may demonstrate that it must fall in one angle or the other; but this demonstration will only consist in substituting a different diagram in place of Legendre's figure. But in any case, either in the new diagram or else, and more usually, in passing from one diagram to the other, the interpreter of the argumentation will be supposed to see something, which will present this little difficulty for the theory of vision, that it is of a general nature. (CP 5-148)

Mr. Mill's disciples will say that this proves that geometrical reasoning is inductive. I do not wish to speak disparagingly of Mill's treatment of the Pons Asinorum because it penetrates further into the logic of the subject than anybody had penetrated before. Only it does not quite touch bottom. As for such general perceptions being inductive, I might treat the question from a technical standpoint and show that the essential characters of induction are wanting. But besides the interminable length, such a way of dealing with the matter would hardly meet the point. It is better to remark that the "uniformity of nature" is not in question, and that there is no way of applying that principle to supporting the mathematical reasoning that will not enable me to give a precisely analogous instance in every essential particular, except that it will be a fallacy that no good mathematician could overlook. If you admit the principle that logic stops where self-control stops, you will find yourself obliged to admit that a perceptual fact, a logical origin, may involve generality. This can be shown for ordinary generality. But if you have already convinced yourself that continuity is generality, it will be somewhat easier to show that a perceptual fact may involve continuity than that it can involve non-relative generality. (CP 5-149)

If you object that there can be no immediate consciousness of generality, I grant that. If you add that one can have no direct experience of the general, I grant that as well. Generality, Thirdness, pours in upon us in our very perceptual judgments, and all reasoning, so far as it depends on necessary reasoning, that is to say, mathematical reasoning, turns upon the perception of generality and continuity at every step. (CP 5-150)



Lecture Six: The Nature of Meaning

In Lecture Six, Peirce argues that abduction is the process used by the subconscious mind to generate instances of Thirdness. Abduction is the basis for science. Deduction, on the other hand, generates conclusions, based on the results of abduction, and induction tests those conclusions against the world.
*Perceptual judgments involve generality.
*Discussion of three types of reasoning: Deduction, Induction, and Abduction.
*Peirce argues that abduction is the process used by the subconscious mind to generate instances of Thirdness. Abduction is the basis for science. Deduction, on the other hand, generates conclusions, based on the results of abduction, and induction tests those conclusions against the world.
*He claims that “every single item” of scientific theory which stands established today has been due to Abduction and that however man may have acquired his faculty of “divining the ways of Nature”, it has certainly not been by a self-controlled and critical logic.
*The validity of induction depends upon the necessary relation between the general and the singular. It is precisely this which is the support of Pragmatism.
*The idea of meaningis such as to involve some reference to a purpose. But Meaning is attributed to representamens alone, and the only kind of representamen which has a definite professed purpose is an "argument." The professed purpose of an argument is to determine an acceptance of its conclusion, and it quite accords with general usage to call the conclusion of an argument its meaning.
*It seems natural to use the word meaning to denote the intended interpretant of a symbol.

This is the sixth Harvard lecture, delivered on 7 May 1903. Peirce sets out from his concluding claim in Lecture V, that perceptual judgments involve generality. He gives a sustained discussion of the different kinds of reasoning--deduction, induction, and abduction--and discusses other logical conceptions relevant to the question of the nature of meaning. He will use "meaning" technically, he says, to "denote the intended interpretant of a symbol." He then considers the role of perception in the acquisition of knowledge and the relation of perception to reasoning. Peirce claims that "every single item" of established scientific theory is the result of abduction but that the human faculty of "divining the ways of nature" is not subject to self-control. He argues that perception and abduction shade into one another and claims that pragmatism is the logic of abduction. (Head Notes for the EP 2, Chapter 15)


Perceptual judgments involve a generality. Even expository judgments involve a generality. For example, the expository judgment “Tully is Cicero” involves the generality of identity.
A singular interacts with the mind in forming a perceptual judgment that makes use of a generality.
That is, the mind understands a singular based on the singular conforming to some generality. If there is no generality available, then the singular has no meaning.

Every perceptual judgment refers to single objects. Perceptual judgments are understood because they refer to single objects with which we are already familiar. When we read the remark “a flying-machine, however successful, could be of no advantage to commerce”, we understand its meaning by relying upon our familiarity with the concepts of (1) objects that fly, (2) machines, and (3) commerce, independent of whether a flying-machine exists or could exist, and independent of whether we can articulate what constitutes a machine and what commerce is.

Perceptual judgments can only assert existence because perceptual judgments are developed in reaction to the world (and they are outside the control of consciousness). Perceptual judgments have the capacity to reveal facts but they do not do so necessarily. If I perceive (by perceptual judgment) that event A precedes event C because (1) event A precedes event B and (2) event B precedes event C, then from this I can infer a universal proposition, labeled “transitivity”, namely “If A precedes B, and B precedes C, then A precedes C”.

Turrisi’s commentary:
Generality in Perceptual Judgments
A general concept or proposition is one that describes a class and is in this sense universal. On the other hand, a singular concept or proposition is one that describes an individual. All singular concepts or propositions depend upon general concepts or propositions for their meaning. For example, the proposition “Tully is Cicero”, which is a singular, depends upon the general concept of identity.
The same parallelism applies to perceptual judgments: they are based on generalities, which are Thirdness. So Peirce says, “Thirdness pours in upon us through every avenue of sense”. That is, perceptual judgment is Thirdness.
But how can a proposition about single things involve generality? Consider the proposition that event A precedes event B. This proposition implies that A precedes any event C - a generality - that follows B. In addition, the concept of precedence - a second generality - is transitive - a third generality.
Logical Goodness and Logical Soundness
Logical soundness means not only that the premises are true and the conclusion valid but also that the conclusion corresponds to fact, to how things really are. Each of us by ourselves cannot determine facts. Facts are determined by a community, not individuals.
On the other hand, a popular theory that does not correspond to what might happen “in this universe or in any universe” is still false.
The End of Thought [i.e., the goal or purpose of thought]
Goodness is measured by how well something serves a purpose. Utilitarianism is pragmatism inasmuch as it serves true or long-term ends, as opposed to short-term ends.
Logic serves the ends defined by ethics, which, in turn, serves the ends defined by esthetics. Logic is not confirmed by a feeling or by noting what most people think. After all, mistakes in Euclid have come to light only after thousands of years of most people feeling good about it, all the while overlooking mistakes.
In addition, people do not have an instinct for correct logic. However, experience can teach us better logic if we are careful. We can use experience to develop predictive hypotheses that can be tested against future experience. This presumes that there is law-like behavior in the world around us.

There are three types of reasoning: deduction, induction, and abduction. Of the three, deduction alone is necessary. That is, given the premises, the conclusion must follow. The validity of the argument is independent of the truth of the premises.
Deduction is “diagrammatic”, meaning that when we think deductively we construct a model via abstractions which we refine, augment, and combine in an artful way to ferret out conclusions from the abstractions.
For example, if we say that “A is a bay horse, Therefore A is a horse”, we believe this to be true because it remains true under any circumstances we consider, such as the size of the horse, its age, its health, and so on. This is a perception.
Meaning is what can be deduced, so the meaning of a set of premises is the set of possible conclusions. Note that if deduction is done properly, we affirm the truth of the conclusions to the same extent that we affirm the truth of the premises.

Induction is a way to test a theory via investigation that asks a question of nature. A negative answer shows the theory to be in error. An affirmative answer can provide support for the theory. We cannot use probability here because probability is the ratio of the number of particular occurrences over time to the number of possible occurrences, and in general we do not know the number of possible occurrences. For example, it is reasonable to ask the probability of an object being red if we know the possible colors for the object, but it is not reasonable to ask the probability of a color being red, because we do not know the number of colors.
Induction presumes that with each additional test that we apply, we learn more. There is no end to the tests we can apply. The effect is similar to trying to determine the rule that generates a bit string by observing each bit as it is generated. The more bits we have, the greater our opportunity for inferring the rule. … Induction presumes that there is regularity (in the form of a law) that describes the generation of the bit string.

Abduction creates hypotheses to be tested by induction. Abduction is the only way we can understand anything. All of science has been built by abduction.
Deduction “provides that something must be”. It “merely evolves the necessary consequences of a pure hypothesis”. Induction “shows that something actually is operative”. Abduction “merely suggests that something may be”. It is the “process of forming an explanatory hypothesis”. It is “the only logical operation that introduces a new idea”.
Science has progressed too rapidly for chance to be the engine of abduction. There are trillions of possible hypothesis, including the alignment of the planets, or words spoken by the dowager empress of China, or the action of an invisible Jinni.

Psychologists are unable to explain the rate of progress of science, and there has not been enough time for it to be attributable to evolution. Man seems to have an “Insight” into the Thirdness of Nature, into its “general elements”. This Insight is similar to instinct in that it gives Man the appearance of knowing more than we do. This Insight is more often incorrect than correct but it is correct enough of the time to produce the results we have seen. This Insight originates outside consciousness, the way perceptual judgments do. We reveal our use of it when we justify the pursuit of a theory on the grounds that the theory is “reasonable”.
Another explanation is that every world view is self-supporting. The support or justification for each world view is generated by standards established by the world view itself. We in the Occident point to the advances of science to support our claim that we are the latest (i.e., most advanced) step in evolution. Note that evolution is one of the elements of our world view. We think that technological advance is incontrovertible evidence of the supremacy of our world view. But I am not convinced that other societies could not be just as convinced that their world view is best, even in light of a full understanding of ours. They could point to the unsustainability of our way of life, for example, to pollution and to prisons.

Meaning is connected with purpose. Traditionally, “meaning” has been used to refer to the conclusions of an argument.

Turrisi’s commentary:
There are three kinds of predictive hypotheses.
The first, deduction, is necessary reasoning: the conclusion must be true - it is necessary - if the premises are true. The second, induction, tests a theory by experiment, the name for an activity that is based on observation. [The third is abduction.]
Deductive reasoning involves the relationship between premises and conclusion. It does not involve the relationship between reality and premises. Deductive reasoning is “diagrammatic”: we build an icon (or model) by developing abstractions based on our focus of attention; we then manipulate the abstractions by refinement, augmentation, and combination.
This abstract reasoning is arduous, hence many people avoid it.
Induction investigates how closely a theory aligns with facts (reality). The soundness of an inductive argument can be measured by the difference between the integer one and the ratio of predictions to reality. The soundness of an abductive argument can be measured by the soundness of the theories it generates.
Arguments are generative. The set of things that an argument can generate is its meaning.
It is sufficient to say that the ultimate meaning of an element of an argument is what it contributes to what the argument generates. But this is not enough; it is not necessary; that is, we need more to be able to weed out nonsense.

Abduction and Perceptual Judgments
Pragmatism is based on three truths:
(a) our conceptions are based on perceptual judgments;
(b) perceptual judgments contain generality, implying that we perceive Thirdness;
(c) abduction is similar to perception. Perceptual judgments serve cognition by populating propositions.

The process (beyond conscious control) by which perceptions generate perceptual judgments is abductive. Pragmatism appears to be a similar abductive process, based on concepts. Thus the logic of abduction is the basis of pragmatism.

Our conceptions are based on perceptual judgments.
Perceptual judgments serve cognition by populating propositions.
Abduction is similar to perception. The process (beyond conscious control) by which perceptions generate perceptual judgments is abductive.
Pragmatism is based on concepts. Pragmatism appears to be a similar abductive process.
Thus the logic of abduction is the basis of pragmatism.

Comte argued that the only hypotheses that should be considered are those that are verifiable, which must mean verifiable by induction because that is the only possible way to verify an hypothesis. This implies that a conception is a candidate member of a proposition if and only if its consequences are perceptual. Otherwise the conception is not amenable to induction. This is the essence of pragmatism.
I think Popper’s argument is clearer: only falsifiable hypotheses are of value.


Excerpt and condensation from LECTURE VI. THREE TYPES OF REASONING

Perceptual judgments involve generality.
What is the general? The Aristotelian definition is good enough. It is quod aptum natum est praedicari de pluribus; {legö de katholou men ho epi pleionön pephyke katégoreisthai}. De Interp.
When logic was studied in a scientific spirit of exactitude it was recognized on all hands that all ordinary judgments contain a predicate and that this predicate is general. There seemed to be some exceptions, of which the only noticeable ones were expository judgments, such as "Tully is Cicero." But the Logic of Relations has now reduced logic to order, and it is seen that a proposition may have any number of subjects but can have but one predicate which is invariably general. Such a proposition as "Tully is Cicero" predicates the general relation of identity of Tully and Cicero.
Consequently, it is now clear that if there be any perceptual judgment, or proposition directly expressive of and resulting from the quality of a present percept, or sense-image, that judgment must involve generality in its predicate. (CP5-151)

In saying that perceptual judgments involve general elements I certainly never intended to be understood as enunciating any proposition in psychology. For my principles absolutely debar me from making the least use of psychology in logic. I am confined entirely to the unquestionable facts of everyday experience, together with what can be deduced from them. All that I can mean by a perceptual judgment is a judgment absolutely forced upon my acceptance, and that by a process which I am utterly unable to control and consequently am unable to criticize. Nor can I pretend to absolute certainty about any matter of fact.
Now consider the judgment that one event C appears to be subsequent to another event A. Certainly, I may have inferred this; because I may have remarked that C was subsequent to a third event B which was itself subsequent to A. But then these premisses are judgments of the same description. It does not seem possible that I can have performed an infinite series of acts of criticism each of which must require a distinct effort. The case is quite different from that of Achilles and the tortoise because Achilles does not require to make an infinite series of distinct efforts. It therefore appears that I must have made some judgment that one event appeared to be subsequent to another without that judgment having been inferred from any premiss [i.e.] without any controlled and criticized action of reasoning. If this be so, it is a perceptual judgment in the only sense that the logician can recognize. But from that proposition that one event, Z, is subsequent to another event, J, I can at once deduce by necessary reasoning a universal proposition. Namely, the definition of the relation of apparent subsequence is well known, or sufficiently so for our purpose. Z will appear to be subsequent to Y if and only if Z appears to stand in a peculiar relation, R, to Y such that nothing can stand in the relation R to itself, and if, furthermore, whatever event, X, there may be to which Y stands in the relation R, to that same X, Z also stands in the relation R. This being implied in the meaning of subsequence, concerning which there is no room for doubt, it easily follows that whatever is subsequent to C is subsequent to anything, A, to which C is subsequent --which is a universal proposition.
Thus my assertion at the end of the last lecture appears to be most amply justified. Thirdness pours in upon us through every avenue of sense. (CP5-157)

We may now profitably ask ourselves what logical goodness is. We have seen that any kind of goodness consists in the adaptation of its subject to its end. … If you call this utilitarianism, I shall not be ashamed of the title. For I do not know what other system of philosophy has wrought so much good in the world as that same utilitarianism. Bentham may be a shallow logician; but such truths as he saw, he saw most nobly. As for the vulgar utilitarian, his fault does not lie in his pressing too much the question of what would be the good of this or that. On the contrary his fault is that he never presses the question half far enough, or rather he never really raises the question at all. He simply rests in his present desires as if desire were beyond all dialectic. He wants, perhaps, to go to heaven. But he forgets to ask what would be the good of his going to heaven. He would be happy, there, he thinks. But that is a mere word. It is no real answer to the question. (CP5-158)

Our question is, What is the use of thinking? We have already remarked that it is the argument alone which is the primary and direct subject of logical goodness and badness. We have therefore to ask what the end of argumentation is, what it ultimately leads to. (CP5-159)

Reasoning is of three types, Deduction, Induction, and Abduction.
In deduction, or necessary reasoning, we set out from a hypothetical state of things which we define in certain abstracted respects. …. We consider this hypothetical state of things and are led to conclude that … something else not explicitly supposed in that hypothesis will be true invariably. Our inference is valid if and only if there really is such a relation between the state of things supposed in the premisses and the state of things stated in the conclusion. (CP5-161)

All necessary reasoning without exception is diagrammatic. That is, we construct an icon of our hypothetical state of things and proceed to observe it. This observation leads us to suspect that something is true, which we may or may not be able to formulate with precision, and we proceed to inquire whether it is true or not.
For this purpose it is necessary to form a plan of investigation and this is the most difficult part of the whole operation. We not only have to select the features of the diagram which it will be pertinent to pay attention to, but it is also of great importance to return again and again to certain features. Otherwise, although our conclusions may be correct, they will not be the particular conclusions at which we are aiming. (CP5-162)

Having thus determined the plan of the reasoning, we proceed to the reasoning itself, and this I have ascertained can be reduced to three kinds of steps. The first consists in copulating separate propositions into one compound proposition. The second consists in omitting something from a proposition without possibility of introducing error. The third consists in inserting something into a proposition without introducing error. (CP5-163)

Somebody may answer that the copulative proposition contains the conjunction "and" or something equivalent, and that the very meaning of this "and" is that the entire copulation is true if and only if each of the members is singly true; so that it is involved in the very meaning of the copulative proposition that any member may be dropped.
It is another way of saying that what we call the meaning of a proposition embraces every obvious necessary deduction from it.
But how it helps us to understand our passing from an accepted judgment A to another judgment C of which we not only feel equally confident but in point of fact are equally sure?
To this the advocate of the explanation by the conception of "meaning" may reply: that is meant which is intended or purposed; that a judgment is a voluntary act, and our intention is not to employ the form of the judgment A, except to the interpretation of images to which judgments, corresponding in form to C, can be applied. (CP5-165)

Perhaps it may reconcile the psychologist to the admission of perceptual judgments involving generality to be told that they are perceptual judgments concerning our own purposes. I certainly think that the certainty of pure mathematics and of all necessary reasoning is due to the circumstance that it relates to objects which are the creations of our own minds, and that mathematical knowledge is to be classed along with knowledge of our own purposes. When we meet with a surprising result in pure mathematics, as we so often do, because a loose reasoning had led us to suppose it impossible, this is essentially the same sort of phenomenon as when in pursuing a purpose we are led to do something that we are quite surprised to find ourselves doing, as being contrary, or apparently contrary, to some weaker purpose.(CP5-166)

Induction consists in starting from a theory, deducing from it predictions of phenomena, and observing those phenomena in order to see how nearly they agree with the theory. The justification for believing that an experiential theory which has been subjected to a number of experimental tests will be in the near future sustained about as well by further such tests as it has hitherto been, is that by steadily pursuing that method we must in the long run find out how the matter really stands. The reason that we must do so is that our theory, if it be admissible even as a theory, simply consists in supposing that such experiments will in the long run have results of a certain character. But I must not be understood as meaning that experience can be exhausted, or that any approach to exhaustion can be made. What I mean is that if there be a series of objects, say crosses and circles, this series having a beginning but no end, then whatever may be the arrangement or want of arrangement of these crosses and circles in the entire endless series must be discoverable to an indefinite degree of approximation by examining a sufficient finite number of successive ones beginning at the beginning of the series. This is a theorem capable of strict demonstration. The principle of the demonstration is that whatever has no end can have no mode of being other than that of a law, and therefore whatever general character it may have must be describable, but the only way of describing an endless series is by stating explicitly or implicitly the law of the succession of one term upon another. But every such term has a finite ordinal place from the beginning and therefore, if it presents any regularity for all finite successions from the beginning, it presents the same regularity throughout. Thus the validity of induction depends upon the necessary relation between the general and the singular. It is precisely this which is the support of Pragmatism.(CP5-170)

Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea; for induction does nothing but determine a value, and deduction merely evolves the necessary consequences of a pure hypothesis.
Deduction proves that something must be; Induction shows that something actually is operative; Abduction merely suggests that something may be.
Its only justification is that from its suggestion deduction can draw a prediction which can be tested by induction, and that, if we are ever to learn anything or to understand phenomena at all, it must be by abduction that this is to be brought about.
No reason whatsoever can be given for it, as far as I can discover; and it needs no reason, since it merely offers suggestions. (CP5-171)

A man must be downright crazy to deny that science has made many true discoveries. But every single item of scientific theory which stands established today has been due to Abduction.
But how is it that all this truth has ever been lit up by a process in which there is no compulsiveness nor tendency toward compulsiveness? Is it by chance? Consider the multitude of theories that might have been suggested. A physicist comes across some new phenomenon in his laboratory. How does he know but the conjunctions of the planets have something to do with it or that it is not perhaps because the dowager empress of China has at that same time a year ago chanced to pronounce some word of mystical power or some invisible jinnee may be present. Think of what trillions of trillions of hypotheses might be made of which one only is true; and yet after two or three or at the very most a dozen guesses, the physicist hits pretty nearly on the correct hypothesis. By chance he would not have been likely to do so in the whole time that has elapsed since the earth was solidified. You may tell me that astrological and magical hypotheses were resorted to at first and that it is only by degrees that we have learned certain general laws of nature in consequence of which the physicist seeks for the explanation of his phenomenon within the four walls of his laboratory. But when you look at the matter more narrowly, the matter is not to be accounted for in any considerable measure in that way. Take a broad view of the matter. Man has not been engaged upon scientific problems for over twenty thousand years or so. But put it at ten times that if you like. But that is not a hundred thousandth part of the time that he might have been expected to have been searching for his first scientific theory. (CP5-172)

However man may have acquired his faculty of divining the ways of Nature, it has certainly not been by a self-controlled and critical logic. Even now he cannot give any exact reason for his best guesses. It appears to me that the clearest statement we can make of the logical situation --the freest from all questionable admixture --is to say that man has a certain Insight, not strong enough to be oftener right than wrong, but strong enough not to be overwhelmingly more often wrong than right, into the Thirdnesses, the general elements, of Nature. An Insight, I call it, because it is to be referred to the same general class of operations to which Perceptive Judgments belong. This Faculty is at the same time of the general nature of Instinct, resembling the instinct s of the animals in its so far surpassing the general powers of our reason and for its directing us as if we were in possession of facts that are entirely beyond the reach of our senses. It resembles instinct too in its small liability to error; for though it goes wrong oftener than right, yet the relative frequency with which it is right is on the whole the most wonderful thing in our constitution. (CP5-173)

If you ask an investigator why he does not try this or that wild theory, he will say, "It does not seem reasonable." It is curious that we seldom use this word where the strict logic of our procedure is clearly seen. We do [not] say that a mathematical error is not reasonable. We call that opinion reasonable whose only support is instinct. . . . (CP5-174)

We have already seen some reason to hold that the idea of meaning is such as to involve some reference to a purpose. But Meaning is attributed to representamens alone, and the only kind of representamen which has a definite professed purpose is an "argument." The professed purpose of an argument is to determine an acceptance of its conclusion, and it quite accords with general usage to call the conclusion of an argument its meaning. But I may remark that the word meaning has not hitherto been recognized as a technical term of logic, and in proposing it as such (which I have a right to do since I have a new conception to express, that of the conclusion of an argument as its intended interpretant) I should have a recognized right slightly to warp the acceptation of the word "meaning," so as to fit it for the expression of a scientific conception. It seems natural to use the word meaning to denote the intended interpretant of a symbol. (CP5-175)

On the whole, then, if by the meaning of a term, proposition, or argument, we understand the entire general intended interpretant, then the meaning of an argument is explicit. It is its conclusion; while the meaning of a proposition or term is all that that proposition or term could contribute to the conclusion of a demonstrative argument. But while this analysis will be found useful, it is by no means sufficient to cut off all nonsense or to enable us to judge of the maxim of pragmatism. What we need is an account of the ultimate meaning of a term. To this problem we have to address ourselves. (CP5-179)



Lecture Seven: The Three Cotary Propositions of Pragmatism (Pragmatism and Abduction)

In Lecture Seven, Peirce argues that pragmatism uses abduction. The process by which perceptual judgments are generated is also abductive.
Peirce elaborates on the three key points mentioned at the end of Lecture Six. They are the “cotary” propositions of pragmatism. The word “cotary” is a neologism from the Latin for “whetstone”: the propositions sharpen, so to speak, the concept of pragmatism.

1: Everything in our minds is based on something generated by our senses.
Perceptual judgment is the starting point or first premise of all critical and controlled thinking.
2: Perceptual judgments include generality, so that universal propositions are deducible from them.
Perceptual judgments contain general statements, implying that we perceive Thirdness.
3: That abductive inference shades into perceptual judgment without any sharp line of demarcation between them. The subconscious uses abduction to produce perceptual judgments; the conscious mind does not criticize those perceptual judgments.
The perceptual judgments are our first premises and are to be regarded as an extreme case of abductive inferences.

Pragmatism follows from these propositions.
The process (beyond conscious control) by which perceptions generate perceptual judgments is abductive. Pragmatism appears to be a similar abductive process, based on concepts. Thus the logic of abduction is the basis of pragmatism.
Our conceptions are based on perceptual judgments.
Perceptual judgments serve cognition by populating propositions.
Abduction is similar to perception. The process (beyond conscious control) by which perceptions generate perceptual judgments is abductive.
Pragmatism is based on concepts. Pragmatism appears to be a similar abductive process.
Thus the logic of abduction is the basis of pragmatism.

This is the last of the seven Harvard lectures, delivered on 14 May 1903. This lecture was added so that Peirce could extend his remarks about the relation of pragmatism to abduction. He elaborates in particular on three key points raised in the sixth lecture: (1) that nothing is in the intellect that is not first in the senses, (2) that perceptual judgments contain general elements, and (3) that abductive inference shades into perceptual judgment without any sharp line of demarcation between them. Pragmatism follows from these propositions. Peirce reiterates that the function of pragmatism is to help us identify unclear ideas and comprehend difficult ones. It is in this lecture that Peirce delivers his famous dictum: "The elements of every concept enter into logical thought at the gate of perception and make their exit at the gate of purposive action; and whatever cannot show its passports at both those two gates is to be arrested as unauthorized by reason." In developing these ideas, Peirce emphasizes that in making every conception equivalent to a conception of "conceivable practical effects," the maxim of pragmatism reaches far beyond the merely practical and allows for any "flight of imagination," provided only that this imagination "ultimately alights upon a possible practical effect." (Head Notes for the EP 2, Chapter 16)

Peirce pragmatic maxim:
“Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have.
Then, our conception of these effects is the whole of our conception of the object”.

The first sentence of the maxim advises us to think about the ends of the object of our conception. What are its effects, in terms of Firstness, Secondness and Thirdness? There are all sorts of objects of conceptions that have all sorts of conceivable effects and “practical bearings” or ends. How can these be best characterized?
Piece’s lecture seven concerns the second sentence of the maxim and treats the manner in which “our conception of these effects” is possible.
How does the object of our conception come to be an object that we can consider its effect? The answer to this is provided by an anatomy of cognition. Sections 1 and 2 define and defend the cotary propositions. Sections 3, 4 and 5 reflect upon the proposal that pragmatism is the logic of abduction.

The perceptual judgments are our first premises and are to be regarded as an extreme case of abductive inferences.
The perceptual judgment is the result of a process and the process is like that of abductive inference. The similarity lies in their both proceeding from the unknown to the known or from the unapprehended to the apprehended. Also, each has a set of premises. In abduction, the premises consist of 1) the observation of a given fact and 2) a general notion as to the nature of the association of that fact with others. These are elements of a hypothesis that explains the fact. The conclusion of an abduction is the hypothesis that the fact is explicable by that notion. The “idea of putting together what we had never before dreamed of putting together” is responsible for the inference. In the case of perception, the premise is the generality insofar as it is available by means of the senses.

All three cotary propositions ought to be considered together, for the first hold that nothing enters the intellect except through the perception, and the third says that perception, from which general elements are deduced (so says the second), is the same species as abduction.

While it may be agreed that perception does introduce new concepts to the intellect, it may not be the only source of such concepts. It is then reasonable to suppose the sort of inference that does initiate hypotheses for consideration - that is, abductive inference – is a candidate for introducing new concepts as well. Peirce argued that noting new arises in the conclusion of an abduction that was not first in its premises. The conclusion of an abduction merely puts forward the suggestion that a plausible condition of a fact that would explain that fact is, indeed, an explanation of the fact.
The general elements, acknowledged to be deducible from perceptual judgment in a separate proof, in an abduction, are, likewise, implicit in the perceptual judgments. In other words, the premises for the premises of an abductive inference are real generalities or Thirdnesses. So there is no other possible source of new conceptions.

Turrisi’s commentary:
Psychological versus Logical Determinations of the Ultimate End of Reasoning
The purpose of reasoning is to find out something we do not know, based on something that we do. In 1877 Peirce thought that reasoning - what Peirce called “Inquiry” - was motivated by psychology. That is, we find ourselves irritated by doubt, so we change our beliefs until the doubt dissolves. However, by 1903, when he delivered these lectures, Peirce had changed his mind: he then thought that Inquiry was motivated by logic, by the question, Is this belief that I have true or false? A logical motivation suggests a logical criterion to resolution.

Kant argued that Inquiry is resolved by opinions.more firmly held opinions, but opinions just the same. These more firmly held opinions are supported by even more firmly held opinions. In 1877 Peirce suggested that there were three ways to reach resolution: (1) accept the first available hypothesis; (2) accept what culture or those in authority preach; or (3) accept the hypothesis that seems the best. By 1903 Peirce noted that these approaches are limited by the initial set of hypotheses. So we need to understand how hypotheses are generated.

The Cotary Propositions of Pragmatism:
Peirce"s three "cotary" propositions describe aspects of the mind.
1: Everything in our minds is based on something generated by our senses.
2: Perceptual judgments include generality, which enables us to generate general statements based on them.
3: The subconscious uses abduction to generate perceptual judgments; the conscious mind does not criticize those perceptual judgments.

If we think of perceptual judgments as abductions, which are based on premises, then we are led to search for the premises of perceptual judgments, and, in turn, for the premises of those premises. There is no logical end to this reduction and thus it does not explain perceptual judgments. The fault lies in the assumption that there are discrete premises. Just as Achilles overcomes the tortoise not by a series of discontinuous steps but rather as one continuous movement, so perceptual judgments proceed in “one continuous process”.
Abduction comes to us in a “flash”, like an “insight”. The pieces were there in our minds before; what is new is their connection.
Thus abduction is, at root, a connection, a relationship.


Turrisi’s commentary:
We experience the world based on context. Without context we would be unable to experience the world. Visual illusions demonstrate the presence of a context that provides meaning: for example, we interpret Peirce's serpentine line, a drawing of which is included in the text, as a stone wall, and, after repeated exposures, as just as serpentine line possibly, but never as a book or a chair, say. It is difficult for the conscious mind to influence the selection of a context.

Perception and abduction are both inferences in that they find out something we do not know, based on something that we do. They both explain something by generating perceptual judgments and hypotheses, respectively.
Perceptual judgments are the basis for abduction. An abduction, like a perceptual judgment, is an explanation. However, the explanation is already in the premises.
An abduction is unlike a perceptual judgment in that it can be questioned and denied. Proof as Enumeration

Included in the text is a drawing, consisting of a single, serpentine line, that looks like a stone wall. This drawing will help in understanding the second proposition.
The line can be classified (i.e., viewed) as either a line or as a stone wall. Our perception can move from one classification to the other, and then back again, which we observe as a change in the drawing itself somehow, as though it (not our perception of it) jumped from being a line to a stone wall, and then back again. But after a time, the illusion can dissipate: we somehow see the line as both a line and as a stone wall. However, note that the classification is embedded in the perception. The classification is an interpretation.
[Turrisi: Peirce’s illustrations demonstrate that 1) there are classifications under which we experience perceptions and we would not even be able to experience these perceptions without them, and 2) the classifications are (in qualified sense) beyond our control and thereby are contained within the perception itself.]
With some visual illusions we can consciously change the perception. We can say, .Now I am going to look at this drawing not as a stone wall but only as a serpentine line,. and then, with mental effort, we can do so. (Sometimes it requires visually occluding parts of the scene.) When we do this we usually laugh. We feel giddy, I believe, because we feel a superhuman power, that by mere force of will we are able to change reality. That is, we are under the illusion that we are changing what is out there. This is evidence of how closely bound are perceptual judgment and interpretation.
Can we see the line, after a time, as both a line and as a stone wall because we have formed a new perception? This suggests to me that the conscious mind can influence the formation of perceptions by the subconscious mind.

Other areas of perception reveal the same structure. For example, we can activate a subconscious alarm clock to wake us; if we are accustomed to some regular sound, such as the striking of a clock, then we can become aware of the absence of the sound even while we are unaware of its presence; proof-readers depend for their employment upon their ability to see letters as opposed to meaning; we can remember the meaning of a conversation even if we do not remember the words; politicians can suggest words without saying them.

This establishes the third cotary proposition.
Also, In order for the abduction implied by perceptual judgments to be possible, perceptual judgments must contain generality. And this establishes the second cotary proposition.

The process the conscious mind uses - abductive judgment - and the process the subconscious mind uses - perceptual judgment - are different only in that the results of the latter are unquestioned.

The unquestioned nature of perceptual judgment is the "test of inconceivability". if it appears to us inconceivable that a concept could be questioned, then the concept is the result of perceptual judgment; otherwise, it is the result of abductive judgment.

Abduction (also known as .adopting an explanatory hypothesis.) is an inference. It has a logical form:
“The surprising fact, C, is observed;
“But if A were true, C would be a matter of course.
“Hence, there is reason to suspect that A is true.”

Note that the conclusion – “A is true” - is in one of the premises – “But if A were true … “
There are three objections to the argument that all conceptions are based in perception.
First, conceptions might arise outside of logic.
Second, how could every hypothesis, even fanciful ones, be rooted in perceptual judgments?
And third, the conclusion is in the premises in the form of abduction, as shown above, but “common knowledge” suggests that there is some other origin for some hypotheses.

The first objection is an objection about logic, not about perceptual judgments.
In response to the first objection, suppose that some part of an argument’s conclusion is unconnected with any of the premises of the argument. This unconnected part arrives as a perceptual judgment and its inclusion in the argument is an inference we make consciously.
In response to the second objection, deduction is able to derive conclusions from premises, and this objection is due to ignorance of the “logic of relations”.
In response to the third objection, inference is a conscious activity consisting of a series of steps, of which there must be a first step, which must be based on something outside of consciousness. This activity is finally a winnowing process, not a generative one.
Continuing with the rebuttal of the third objection, when we first encounter the concept of an inference, for example, such as deduction, we encounter it as a type of inference. If the concept of “inference” means nothing to us, then we must understand how mental objects can be related. If that, in turn, means nothing to us, then we must understand the “world of ideas”. The point is that we must already have in mind a type within which we can consider deduction in order to understand deduction. The context for that type is based finally on perceptual judgment.
Inference, otherness, and character are “obviously” forms of Firstness, Secondness, and Thirdness. (Details in CP5 192-194)

There are three fundamental ways of reasoning: deduction, induction, and abduction. Induction is intended to be a process of testing hypotheses, or, less formally, testing expectations.

Pragmatism is “nothing else than the logic of abduction”. For example, suppose we are in the midst of our work, considering a number of facts but not able to see any general principles. However, it suddenly comes to us that if a certain principle were true, then it would explain these facts. This process is abduction. Mendeleev.s development of the Periodic Table is an example of abduction. He sought the general principle that would explain the facts of inorganic chemistry. He noticed that if atomic weights were the general principle, then it would explain the facts.

The purpose of induction is to generate theories which, by deduction, can develop expectations that can be tested by induction. This agrees with Comte’s argument that theories must be verifiable, meaning tested against experience.
Unfortunately Comte seemed to confine himself to Secondness, which confines him to hypotheses about physical things, as opposed to mental attitudes, for example.

Logic presumes a distinction between truth and falsehood, that those concepts apply independent of our being, and that we seek to align our notions of truth and falsehood of a given item based on the item’s actual truth and falsehood. This alignment is to the representation of the item, hence Thirdness. But the color red is not a representation; it is simply red, a Firstness. And taking action - a Secondness - is independent of the other two. The three categories are necessary for an understanding of abduction.

Pragmatism provides a way to judge hypotheses. If two conceptions lead to the same practical conduct - what we can expect if the conceptions are true - then the conceptions are identical. Pragmatism neither includes bad hypotheses nor excludes good ones: it exactly characterizes the set of good abductions. Pragmatism cannot impinge upon induction, though it can reduce some deductive premises, but these premises would lead to conclusions that we would not want to consider anyway.

Turrisi’s commentary:
When people use pragmatism, they include in the purpose of a concept all of the ends or purposes to which the concept can contribute. We generate that set of ends or purposes by abduction.
Abduction generates hypotheses; deduction makes predictions; induction tests the predictions. This process “approximates” experience and it is an “explanation” of experience: it is close to the way that we get an increasingly better handle on life.

“...pragmatism is the doctrine that every conception is a conception of conceivable practical effects”.

“Any hypothesis, therefore, may be admissible, in the absence of any special reasons to the contrary, provided it be capable of experimental verification and only in so far as it is capable of such verification. This is approximately the doctrine of pragmatism.”

Pragmatism serves abduction, and abduction serves the end of producing hypotheses that can be verified by experiment. There are five opinions about what experimental verification means.
*The first opinion, espoused by Auguste Comte, is that experimental verification is confined to direct perception: we are to believe “only what we actually see”. But this opinion rules out itself because it is an hypothesis that itself cannot be subject to direct perception.
*The second opinion is that experiment can support theories but not verify them because the latter implies an endless number of trials.
*The third opinion concerns “infinite multitudes”.
It is not clear what this third opinion is nor what Pierce’s response is to it. Peirce considered the “lowest grade” of “infinite multitude” to be “the multitude of all integer numbers”, i.e., the first transfinite number, N0. This third opinion has some basis in mathematics.
*The fourth opinion is attributable to mathematicians and involves the existence of infinitesimals - positive numbers that are smaller than any positive real number.
Peirce argues that the points in a line are “discrete and separate”, and that “there can be no merging of one into another”. Unfortunately, any line segment has the same cardinality as the set of real numbers. So it is unclear what Peirce is talking about here and what his point is.
*The fifth opinion is that we perceive continuity. For example, we perceive time to flow without interruption, as opposed to a sequence of instants.

Pragmatism should serve to get rid of vague ideas and make clear ideas that are difficult to understand. Thirty years ago, it was presumed that the only way ideas could be defined was by recursively defining their constituting ideas. This regression was presumed to stop with fundamental ideas such as “Pure Being, Agency, Substance”, and so on. But in fact this process is endless. The logic of relations has shown this view to be in error. Defining ideas in terms of pedestrian experiences was considered so novel as to be “utterly incomprehensible”. An example of this latter way of defining ideas is the definition of energy: we know what energy does, which we have learned by experience, but nothing about what it is. The second task of pragmatism - making clear ideas that are difficult to understand - is of higher relative importance today.

There are three attitudes about Thirdness.
*First, Thirdness cannot be verified experimentally and thus cannot be used to support theories. But this implies that there are no laws in nature.
*Second, Thirdness can be verified experimentally but not perceived. But this implies that perception does not report reality and that finally we are constrained to the present. If we ask questions, we assume that there is truth and that we cannot influence it because it is independent of us.
*Third, Thirdness can be perceived, thereby implying the three cotary propositions.
All three attitudes question the inclusiveness of perceptual judgments as “antecedents of all conditional judgments”. These objections could be answered by assuming that there is some antecedent that is not a perceptual judgment and then asking how this antecedent is generated? It could be by logic of which we are not yet aware. But it could not be by conscious activity because conscious activity is a series of steps, always with a first step.

Consciousness uses perceptual judgments in order to precipitate action that is directed to some end. It is not reasonable to base conscious activity on something other than perceptual judgment, just as it is not reasonable to perform conscious activity for some purpose other than action directed to some end.


Excerpt and condensation from LECTURE VII. PRAGMATISM AND ABDUCTION

At the end of my last lecture I had just enunciated three propositions which seem to me to give to pragmatism its peculiar character. I will call them my cotary propositions. Cos, cotis, is a whetstone. They appear to me to put the edge on the maxim of pragmatism. (CP5-180)

These cotary propositions are as follows: .
(1) Everything in our minds is based on something generated by our senses.
Nihil est in intellectu quod non prius fuerit in sensu (Nothing is in the intellect that was not first in the senses). I take this in a sense somewhat different from that which Aristotle intended. By intellectus, I understand the meaning of any representation in any kind of cognition, virtual, symbolic, or whatever it may be. … As for the other term, in sensu, that I take in the sense of in a perceptual judgment, the starting point or first premiss of all critical and controlled thinking.
(2) The second is that perceptual judgments contain general elements, so that universal propositions are deducible from them in the manner in which the logic of relations shows that particular propositions usually, not to say invariably, allow universal propositions to be necessarily inferred from them. (This I sufficiently argued in my last lecture. I shall now take the truth of it for granted.)
(3) The third cotary proposition is that abductive inference shades into perceptual judgment without any sharp line of demarcation between them; or, in other words, our first premisses, the perceptual judgments, are to be regarded as an extreme case of abductive inferences, from which they differ in being absolutely beyond criticism. The abductive suggestion comes to us like a flash. It is an act of insight, although of extremely fallible insight. It is true that the different elements of the hypothesis were in our minds before; but it is the idea of putting together what we had never before dreamed of putting together which flashes the new suggestion before our contemplation.

On its side, the perceptive judgment is the result of a process, although of a process not sufficiently conscious to be controlled, or, to state it more truly, not controllable and therefore not fully conscious. If we were to subject this subconscious process to logical analysis, we should find that it terminated in what that analysis would represent as an abductive inference, resting on the result of a similar process which a similar logical analysis would represent to be terminated by a similar abductive inference, and so on ad infinitum. This analysis would be precisely analogous to that which the sophism of Achilles and the Tortoise applies to the chase of the Tortoise by Achilles, and it would fail to represent the real process for the same reason. Namely, just as Achilles does not have to make the series of distinct endeavors which he is represented as making, so this process of forming the perceptual judgment, because it is sub-conscious and so not amenable to logical criticism, does not have to make separate acts of inference, but performs its act in one continuous process. (CP5-181)

There are some phenomena which, I think, do aid us to see what is meant by asserting that perceptual judgments contain general elements, and which will also naturally lead up to a consideration of the third cossal proposition. (CP5-182)

I will show you a figure which I remember my father [Benjamin Peirce] drawing in one of his lectures. I do not remember what it was supposed to show; but I cannot imagine what else it could have been but my cotary proposition No. 2. If so, in maintaining that proposition I am substantially treading in his footprints, though he would doubtless have put the proposition into a shape very different from mine. Here is the figure (though I cannot draw it as skillfully as he did). It consists of a serpentine line. But when it is completely drawn, it appears to be a stone wall.

Peirce's drawing: a serpentine line vs a stone wall.
The single serpentine line can be conceived in two different ways, either as a meaningless serpentine line or as a stone wall.

The point is that there are two ways of conceiving the matter. Both, I beg you to remark, are general ways of classing the line, general classes under which the line is subsumed. But the very decided preference of our perception for one mode of classing the percept shows that this classification is contained in the perceptual judgment. So it is with that well-known unshaded outline figure of a pair of steps seen in perspective.

schroeder stair
schroeder stair

We seem at first to be looking at the steps from above (B view); but some unconscious part of the mind seems to tire of putting that construction upon it and suddenly we seem to see the steps from below (A view), and so the perceptive judgment, and the percept itself, seems to keep shifting from one general aspect to the other and back again.
In all such visual illusions of which two or three dozen are well known, the most striking thing is that a certain theory of interpretation of the figure has all the appearance of being given in perception. The first time it is shown to us, it seems as completely beyond the control of rational criticism as any percept is; but after many repetitions of the now familiar experiment, the illusion wears off, becoming first less decided, and ultimately ceasing completely. This shows that these phenomena are true connecting links between abductions and perceptions. (CP5-183)

If the percept or perceptual judgment were of a nature entirely unrelated to abduction, one would expect that the percept would be entirely free from any characters that are proper to interpretations, while it can hardly fail to have such characters if it be merely a continuous series of what, discretely and consciously performed, would be abductions. We have here then almost a crucial test of my third cotary proposition. Now, then, how is the fact? The fact is that it is not necessary to go beyond ordinary observations of common life to find a variety of widely different ways in which perception is interpretative. (CP5-184)

The whole series of hypnotic phenomena, of which so many fall within the realm of ordinary everyday observation --such as our waking up at the hour we wish to wake much nearer than our waking selves could guess it -involve the fact that we perceive what we are adjusted for interpreting, though it be far less perceptible than any express effort could enable us to perceive; while that, to the interpretation of which our adjustments are not fitted, we fail to perceive although it exceed in intensity what we should perceive with the utmost ease, if we cared at all for its interpretation. It is a marvel to me that the clock in my study strikes every half hour in the most audible manner, and yet I never hear it. I should not know at all whether the striking part were going, unless it is out of order and strikes the wrong hour. If it does that, I am pretty sure to hear it. Another familiar fact is that we perceive, or seem to perceive, objects differently from how they really are, accommodating them to their manifest intention. Proofreaders get high salaries because ordinary people miss seeing misprints, their eyes correcting them. We can repeat the sense of a conversation, but we are often quite mistaken as to what words were uttered. Some politicians think it a clever thing to convey an idea which they carefully abstain from stating in words. The result is that a reporter is ready to swear quite sincerely that a politician said something to him which the politician was most careful not to say.
I should tire you if I dwelt further on anything so familiar, especially to every psychological student, as the interpretativeness of the perceptive judgment. It is plainly nothing but the extremest case of Abductive Judgments. (CP5-185)

If this third cotary proposition be admitted, the second, that the perceptual judgment contains general elements, must be admitted; and as for the first, that all general elements are given in perception, that loses most of its significance. For if a general element were given otherwise than in the perceptual judgment, it could only first appear in an abductive suggestion, and that is now seen to amount substantially to the same thing. I not only opine, however, that every general element of every hypothesis, however wild or sophisticated it may be, [is] given somewhere in perception, but I will venture so far as to assert that every general form of putting concepts together is, in its elements, given in perception. In order to decide whether this be so or not, it is necessary to form a clear notion of the precise difference between abductive judgment and the perceptual judgment which is its limiting case. The only symptom by which the two can be distinguished is that we cannot form the least conception of what it would be to deny the perceptual judgment. If I judge a perceptual image to be red, I can conceive of another man's not having that same percept. I can also conceive of his having this percept but never having thought whether it was red or not. I can conceive that while colors are among his sensations, he shall never have had his attention directed to them. Or I can conceive that, instead of redness, a somewhat different conception should arise in his mind; that he should, for example, judge that this percept has a warmth of color. I can imagine that the redness of my percept is excessively faint and dim so that one can hardly make sure whether it is red or not. But that any man should have a percept similar to mine and should ask himself the question whether this percept be red, which would imply that he had already judged some percept to be red, and that he should, upon careful attention to this percept, pronounce it to be decidedly and clearly not red, when I judge it to be prominently red, that I cannot comprehend at all. An abductive suggestion, however, is something whose truth can be questioned or even denied. (CP5-186)

Long before I first classed abduction as an inference it was recognized by logicians that the operation of adopting an explanatory hypothesis -which is just what abduction is --was subject to certain conditions. Namely, the hypothesis cannot be admitted, even as a hypothesis, unless it be supposed that it would account for the facts or some of them. The form of inference, therefore, is this:

The surprising fact, C, is observed;
But if A were true, C would be a matter of course,
Hence, there is reason to suspect that A is true.

Thus, A cannot be abductively inferred, or if you prefer the expression, cannot be abductively conjectured until its entire content is already present in the premiss, "If A were true, C would be a matter of course." premiss, "If A were true, C would be a matter of course." (CP5-189)

If you carefully consider the question of pragmatism you will see that it is nothing else than the question of the logic of abduction. That is, pragmatism proposes a certain maxim which, if sound, must render needless any further rule as to the admissibility of hypotheses to rank as hypotheses, that is to say, as explanations of phenomena held as hopeful suggestions; and, furthermore, this is all that the maxim of pragmatism really pretends to do, at least so far as it is confined to logic, and is not understood as a proposition in psychology. For the maxim of pragmatism is that a conception can have no logical effect or import differing from that of a second conception except so far as, taken in connection with other conceptions and intentions, it might conceivably modify our practical conduct differently from that second conception.
Now it is indisputable that no rule of abduction would be admitted by any philosopher which should prohibit on any formalistic grounds any inquiry as to how we ought in consistency to shape our practical conduct. Therefore, a maxim which looks only to possibly practical considerations will not need any supplement in order to exclude any hypotheses as inadmissible. What hypotheses it admits all philosophers would agree ought to be admitted. On the other hand, if it be true that nothing but such considerations has any logical effect or import whatever, it is plain that the maxim of pragmatism cannot cut off any kind of hypothesis which ought to be admitted. Thus, the maxim of pragmatism, if true, fully covers the entire logic of abduction. It remains to inquire whether this maxim may not have some further logical effect. If so, it must in some way affect inductive or deductive inference. But that pragmatism cannot interfere with induction is evident; because induction simply teaches us what we have to expect as a result of experimentation, and it is plain that any such expectation may conceivably concern practical conduct. In a certain sense it must affect deduction. Anything which gives a rule to abduction and so puts a limit upon admissible hypotheses will cut down the premisses of deduction, and thereby will render a reductio ad absurdum and other equivalent forms of deduction possible which would not otherwise have been possible. But here three remarks may be made.
First, to affect the premisses of deduction is not to affect the logic of deduction. For in the process of deduction itself, no conception is introduced to which pragmatism could be supposed to object, except the acts of abstraction. Concerning that I have only time to say that pragmatism ought not to object to it.
Secondly, no effect of pragmatism which is consequent upon its effect on abduction can go to show that pragmatism is anything more than a doctrine concerning the logic of abduction.
Thirdly, if pragmatism is the doctrine that every conception is a conception of conceivable practical effects, it makes conception reach far beyond the practical. It allows any flight of imagination, provided this imagination ultimately alights upon a possible practical effect; and thus many hypotheses may seem at first glance to be excluded by the pragmatical maxim that are not really so excluded. (CP5-196)

Admitting, then, that the question of Pragmatism is the question of Abduction, let us consider it under that form. What is good abduction? What should an explanatory hypothesis be to be worthy to rank as a hypothesis? Of course, it must explain the facts. But what other conditions ought it to fulfill to be good? The question of the goodness of anything is whether that thing fulfills its end. What, then, is the end of an explanatory hypothesis? Its end is, through subjection to the test of experiment, to lead to the avoidance of all surprise and to the establishment of a habit of positive expectation that shall not be disappointed. Any hypothesis, therefore, may be admissible, in the absence of any special reasons to the contrary, provided it be capable of experimental verification, and only insofar as it is capable of such verification. This is approximately the doctrine of pragmatism. But just here a broad question opens out before us. What are we to understand by experimental verification? The answer to that involves the whole logic of induction. (CP5-197)

Different opinions which we actually find men holding today:
*In the first place, we find men who maintain that no hypothesis ought to be admitted, even as a hypothesis, any further than its truth or its falsity is capable of being directly perceived. This is what was in the mind of Auguste Comte, who is generally assumed to have first formulated this maxim. Of course, this maxim of abduction supposes that we "are to believe only what we actually see"; and that it is unscientific to make predictions --unscientific, therefore, to expect anything. One ought to restrict one's opinions to what one actually perceives. I need hardly say that that position cannot be consistently maintained. It refutes itself, for it is itself an opinion relating to more than is actually in the field of momentary perception. (CP5-198)
*In the second place, there are those who hold that a theory which has sustained a number of experimental tests may be expected to sustain a number of other similar tests, and to have a general approximate truth, the justification of this being that this kind of inference must prove correct in the long run, as I explained in a previous lecture. But these logicians refuse to admit that we can ever have a right to conclude definitely that a hypothesis is exactly true, that is that it should be able to sustain experimental tests in endless series; for, they urge, no hypothesis can be subjected to an endless series of tests. They are willing we should say that a theory is true, because, all our ideas being more or less vague and approximate, what we mean by saying that a theory is true can only be that it is very near true. But they will not allow us to say that anything put forth as an anticipation of experience should assert exactitude, because exactitude in experience would imply experiences in endless series, which is impossible. (CP5-199)
* In the third place, the great body of scientific men hold that it is too much to say that induction must be restricted to that for which there can be positive experimental evidence. They urge that the rationale of induction as it is understood by logicians of the second group, themselves, entitles us to hold a theory, provided it be such that if it involve any falsity, experiment must some day detect that falsity. We, therefore, have a right, they will say, to infer that something never will happen, provided it be of such a nature that it could not occur without being detected. (CP5-200)
*We are thus led to a fourth opinion very common among mathematicians, who generally hold that any one irrational real quantity (say of length, for example) whether algebraical or transcendental in its general expression, is just as possible and admissible as any rational quantity, but who generally reason that if the distance between two points is less than any assignable quantity, that is, less than any finite quantity, then it is nothing at all. If that be the case, it is possible for us to conceive, with mathematical precision, a state of things in favor of whose actual reality there would seem to be no possible sound argument, however weak. For example, we can conceive that the diagonal of a square is incommensurable with its side. That is to say, if you first name any length commensurable with the side, the diagonal will differ from that by a finite quantity (and a commensurable quantity), yet however accurately we may measure the diagonal of an apparent square, there will always be a limit to our accuracy and the measure will always be commensurable. So we never could have any reason to think it otherwise. Moreover, if there be, as they seem to hold, no other points on a line than such as are at distances assignable to an indefinite approximation, it will follow that if a line has an extremity, that extreme point may be conceived to be taken away so as to leave the line without any extremity, while leaving all the other points just as they were. In that case, all the points stand discrete and separate; and the line might be torn apart at any number of places without disturbing the relations of the points to one another. Each point has, on that view, its own independent existence, and there can be no merging of one into another. There is no continuity of points in the sense in which continuity implies generality. (CP5-204)
*In the fifth place it may be held that we can be justified in inferring true generality, true continuity. But I do not see in what way we ever can be justified in doing so unless we admit the cotary propositions, and in particular that such continuity is given in perception; that is, that whatever the underlying psychical process may be, we seem to perceive a genuine flow of time, such that instants melt into one another without separate individuality. (CP5-205)

There are two functions which we may properly require that Pragmatism should perform; or if not pragmatism, whatever the true doctrine of the Logic of Abduction may be, ought to do these two services.
Namely, it ought, in the first place, to give us an expeditious riddance of all ideas essentially unclear. In the second place, it ought to lend support, and help to render distinct, ideas essentially clear, but more or less difficult of apprehension; and in particular, it ought to take a satisfactory attitude toward the element of thirdness. (CP5-206)

Of these two offices of Pragmatism, there is at the present day not so crying a need of the first as there was a quarter of a century ago when I enunciated the maxim. The state of logical thought is very much improved. Thirty years ago .1 when, in consequence of my study of the logic of relations, I told philosophers that all conceptions ought to be defined, with the sole exception of the familiar concrete conceptions of everyday life, my opinion was considered in every school to be utterly incomprehensible. The doctrine then was, as it remains in nineteen out of every score of logical treatises that are appearing in these days, that there is no way of defining a term except by enumerating all its universal predicates, each of which is more abstracted and general than the term defined. So unless this process can go on endlessly, which was a doctrine little followed, the explication of a concept must stop at such ideas as Pure Being, Agency, Substance and the like, which were held to be ideas so perfectly simple that no explanation whatever could be given of them. This grotesque doctrine was shattered by the logic of relations, which showed that the simplest conceptions, such as Quality, Relation, Self-consciousness could be defined and that such definitions would be of the greatest service in dealing with them. By this time, although few really study the logic of relations, one seldom meets with a philosopher who continues to think the most general relations are particularly simple in any except a technical sense; and of course, the only alternative is to regard as the simplest the practically applied notions of familiar life. We should hardly find today a man of Kirchhoff's rank in science saying that we know exactly what energy does but what energy is we do not know in the least. For the answer would be that energy being a term in a dynamical equation, if we know how to apply that equation, we thereby know what energy is, although we may suspect that there is some more fundamental law underlying the laws of motion. (CP5-207)

I shall take it for granted that as far as thought goes, I have sufficiently shown that thirdness is an element not reducible to secondness and firstness. But even if so much be granted, three attitudes may be taken:
(1) That thirdness, though an element of the mental phenomenon, ought not to be admitted into a theory of the real, because it is not experimentally verifiable;
(2) That thirdness is experimentally verifiable, that is, is inferable by induction, [abduction?] although it cannot be directly perceived;
(3) That it is directly perceived, from which the other cotary propositions can hardly be separated. (CP5-209)

The man who takes the first position ought to admit no general law as really operative. Above all, therefore, he ought not to admit the law of laws, the law of the uniformity of nature. He ought to abstain from all prediction, however qualified by a confession of fallibility. But that position can practically not be maintained. (CP5-210)

The man who takes the second position will hold thirdness to be an addition which the operation of abduction introduces over and above what its premisses in any way contain, and further that this element, though not perceived in experiment, is justified by experiment. Then his conception of reality must be such as completely to sunder the real from perception; and the puzzle for him will be why perception should be allowed such authority in regard to what is real. (CP5-211)

The man who takes the third position and accepts the cotary propositions will hold, with firmest of grasps, to the recognition that logical criticism is limited to what we can control. In the future we may be able to control more but we must consider what we can now control. Some elements we can control in some limited measure. But the content of the perceptual judgment cannot be sensibly controlled now, nor is there any rational hope that it ever can be. Concerning that quite uncontrolled part of the mind, logical maxims have as little to do as with the growth of hair and nails. We may be dimly able to see that, in part, it depends on the accidents of the moment, in part on what is personal or racial, in part is common to all nicely adjusted organisms whose equilibrium has narrow ranges of stability, in part on whatever is composed of vast collections of independently variable elements, in part on whatever reacts, and in part on whatever has any mode of being. But the sum of it all is that our logically controlled thoughts compose a small part of the mind, the mere blossom of a vast complexus, which we may call the instinctive mind, in which this man will not say that he has faith, because that implies the conceivability of distrust, but upon which he builds as the very fact to which it is the whole business of his logic to be true.
That he will have no difficulty with Thirdness is clear enough, because he will hold that the conformity of action to general intentions is as much given in perception as is the element of action itself, which cannot really be mentally torn away from such general purposiveness. There can be no doubt that he will allow hypotheses fully all the range they ought to be allowed. The only question will be whether he succeeds in excluding from hypotheses everything unclear and nonsensical. It will be asked whether he will not have a shocking leaning toward anthropomorphic conceptions. I fear I must confess that he will be inclined to see an anthropomorphic, or even a zoömorphic, if not a physiomorphic element in all our conceptions. But against unclear and nonsensical hypotheses, [of] whatever ægis [he will be protected]. Pragmatism will be more essentially significant for him than for any other logician, for the reason that it is in action that logical energy returns to the uncontrolled and uncriticizable parts of the mind. His maxim will be this:
The elements of every concept enter into logical thought at the gate of perception and make their exit at the gate of purposive action; and whatever cannot show its passports at both those two gates is to be arrested as unauthorized by reason.
The digestion of such thoughts is slow, ladies and gentlemen; but when you come in the future to reflect upon all that I have said, I am confident you will find the seven hours, you have spent in listening to these ideas, have not been altogether wasted. (CP5-212)