The theory of logical atomism itself was adumbrated in a course of eight lectures that Russell delivered in London in 1918, later published under the title The Philosophy of Logical Atomism (1956).
Logical atomism is a philosophy that finds its sustenance in the new logic.
Russell used the term “atomism” in contrast to various forms of idealism, which he considered ‘holistic’ in their contention that reality constitutes a totality whose parts cannot be separated from one another without distortion. One implication of this form of holism is that no statement is wholly true or wholly false, and it was this idea that Russell rejected.
He argued that there were discrete facts that could be depicted accurately, and these were the “atoms” that formed the basic units in his philosophy.
G.E. Moore, in formulating his epistemological realism, had rejected the idealist position in favor of a common-sense, realistic view of the world in which certain statements were wholly true or wholly false, depending on whether they did or did not correspond to particular, discrete facts. Though Moore does not call his philosophy “atomistic”, it is similar in this respect to Russell’s.
The theory of logical atomism itself was adumbrated in a course of eight lectures that Russell delivered in London in 1918, later published under the title The Philosophy of Logical Atomism (1956). Among its main exponents were Wittgenstein, Ryle and Gustav Bergmann. Wittgenstein used it as the central doctrine of his Tractatus Logical-Philosophicus (1921).
The main idea of logical atomism is that there is a direct correlation between the structure of reality and the structure of the ideal language given in Principia Mathematica. The ideal language can be conceived of as a kind of map of reality. … The mapping relationship is sometimes called picture theory since in an extended sense of the term the map provides a picture of the real world. In the hands of Russell and Wittgenstein, picture theory became both a theory of meaning and a theory of truth.
Russell’s theory of descriptions rejects the oldest and simplest notion about how the elements of language acquire their meanings. Suppose one is speaking about a piece of chalk and says, “This is white”. According to this older theory, “this” and “mean respectively the piece of chalk and its color. On some accounts, the copula, “is”, refers to an ontological tie that bonds whiteness to the piece of chalk. According to Russell, however, this view collapses in the face of negative existential sentences such as “Santa Claus does not exist”. This sentence is both meaningful and true, yet there is nothing in the actual world that “Santa Claus” denotes. “Santa Claus” cannot derive its meaning from a corresponding entity, since there is no such entity. Thus, we have to explain its meaning in some other way, for which Russell proposes the theory of descriptions. On it, “Santa Claus” is not a denoting term (that is, a proper name) but an abbreviated or covert description.
But Russell and Wittgenstein thought there was something in the older theory that, though it could not be generalized to language as a whole, was right about a special segment of language that Russell calls “atomic sentences”. These are logically singular sentences of the form “Fa” whose English equivalents would be sentences in which a proper name replaces the logical constant a. “Smith is tall”, is an example of such a sentence. Atomic sentences are distinguished from molecular sentences, which are complex sentences that can take various forms. For example, two atomic sentences connected by “and” form a molecular sentence. Some general sentences such as “Some men all tall” are also molecular, since when analyzed they contain the two sentences “Something is a man”, and “Something is tall”. Since sentences containing definite descriptions are complex general sentences, they are also molecular and not singular.
Russell believes the distinction between atomic and molecular sentences is crucial. When the un-interpreted logical symbols in an atomic sentence were expressed in the words or sentences of a natural language, they had the capacity to be true or false. Thus, when “Fa” is interpreted as “Smith is tall”, it is true is Smith is tall and false otherwise. Likewise, a molecular sentence in purely logical notation, such as (∃x)(Hx.Tx) when translated, for example, as “Some men are tall”, is also true or false. It is true if at least one human male is tall and false if there is no such entity or if no existing human male is tall. It is clear that no general sentence is true unless a “value” of that sentence is true. By a value, Russell means a singular sentence. If (∃x)(Tx) is true, then at least one sentence of the logical form “Fa” must be true. Thus, a molecular sentence such as “Some men are tall” is true if and only if some atomic sentence such as “Smith is tall” is true.
Russell adhered throughout his career to the correspondence theory of truth, according to which a sentence p is true if and only if there is some fact of the world that it describes accurately.
“Smith is tall” is true if only if Smith is tall.
Though molecular sentences can be said to be true, there are no molecular facts in the world. A molecular sentence such as “If it is raining and the streets are wet” is made true because there are atomic facts, such as “It is raining” and “The streets are wet”, that are true. The corresponding theory is a theory of truth, but Russell saw that a variant of it could be used as a theory of meaning.
In the ideal language of the Principia mathematica, atomic sentences are the key to the whole system of axioms and calculi. All theorems are molecular and are thus constructed out of atomic sentences. Any molecular sentences can thus be reduced to a set of atomic sentences and will mean nothing more nor less than the combination of these sentences.
But what do atomic sentences mean? The answer lies in picture theory. According to this view, the older theory of what linguistic units mean can be explained through the distinction between atomic and molecular sentences. While the meaning of the latter are always reducible to the meaning of the former, atomic sentences have meaning because there is a one-to-one correspondence between the names and predicates occurring in them and the entities they denote. Thus, in “Smith is tall”, the name “Smith” means the object Smith and the word “tall” means the property “being tall”. In the case of “Smith”, for example, the actual person Smith is literally the meaning of the term.
Russell argued that it follows from this view that proper names have no meaning in an intensional sense, as Frege thought. If they did, they could be construed as definite descriptions, and the sentences containing them would become general sentences. But if all sentences were general, there would be no direct way of hooking them up with the world of fact, and logic could not be said to be a discipline concerned with truth. That it is so concerned means that there must be singular sentences that if true must perforce be meaningful. In turn, there can be meaningful only if their denoting constituents are meaningful.
Hence, proper names are meaningful, but the only candidates left for them to mean are the objects they denote. Accordingly, the basic sentences if the ideal language are logically singular sentences whose subject terms denote actually existing objects.
Logical atomism is thus a metaphysical view that claims that mathematical logic mirrors the structure of reality. The theory of descriptions is a key component in the theory. Translating an English sentence into the perspicuous notation of (a process Russell called “analysis”) reveals its basic structure and its real meaning. For example, if a sentence contains a description, it will never be a singular sentence, and thus it will never be an identity sentence or a trivial truism in the way that each identity sentence is. Moreover, no sentence containing a description will mirror those basic features of the world that Russell labels atomic facts. Those facts are reflected only in the atomic sentences of the ideal language, which are all singular sentences containing proper names. Logical atomism is thus a metaphysical construction concerning the relationship among language, meaning, and the world of fact.
After its original, powerful thrust, logical atomism began to lose adherents and has virtually disappeared today. At least two factors were responsible for its eclipse, the first of which was the rise of logical positivism, another philosophy influenced by the development of mathematical logic. According to this doctrine, metaphysics was nonsense, and since logical atomism is a form of metaphysics, it was rejected by thinkers who accepted the newer view.
A different approach was developed by P.F. Strawson in a celebrated paper, “On Referring” (1950). Strawson argued that Russell and other logical atomists committed at least three errors: They confused denoting with referring; failed to distinguish meaning from referring; and conflated the grammatical forms of linguistic units (such as names, phrases, and sentences) with their referential, ascriptive, and statement-making uses. It is people who use language in its various forms to refer to or mention particular individuals or places or things, and it is a mistake to think that words or sentences per se have these properties. Meaning and statement making, for example, must be distinguished.
Meaning is a property of linguistic expressions. Thus, “The present king of France is wise” Has the same meaning in all contents of its use. But while its meaning is a function of the meaning of its lexical constituents, it can be used on different occasions by speakers to refer to or mention different individuals. When the individuals referred to exist (say, when a seventeenth-century Englishman used those words to refer to Louis XIV), the speaker is then making a statement that is either true or false. But the words themselves, taken out of any context, are neither true nor false. Further, if they were to be used when no such person existed, certain statement-making presuppositions would have been violated, and accordingly no statement would have been made; in such a case the locution would be neither true nor false. Strawson’s attack on Russell and on the presuppositions of logical atomism were generally accepted as correct and became one of the factors leading to the demise of the earlier view.
In On Denoting and later papers Russell constantly speaks of the activity of the philosopher as being one of analysis. By analysis he means a technique of substituting a logically clear form of words for another form of words which was in some way logically misleading. His theory of descriptions was for long a paradigm of such logical analysis.
But in Russell’s mind, logical analysis was far more than a device for the clarification of sentences. He came to believe that once logic had been cast into a perspicuous form it would reveal the structure of the world.
Logic contained individual variables and propositional function: corresponding to these the world contained particulars and universals. In logic, complex propositions were built up out of simple propositions as truth-functions of the simpler propositions. Similarly, in the world there were independent atomic facts corresponding to the simple propositions. Atomic facts consisted either in the possession by a particular of a characteristic, or else in a relation between two or more particulars. This theory of Russell’s was called ‘logical atomism’.
The theory of descriptions was the great analytic tool of logical atomism. Russell began to apply it not only to round squares and to Platonic entities, but also to many things which common sense would regard as perfectly real, such as Julius Caesar, tables, and chairs. The reason for this was that Russell came to believe that every proposition which we can understand must be composed wholly of items with which we are acquainted. “
“Acquaintance” was Russell’s word for immediate presentation: we were acquainted, for instance, with our own sense-data, which correspond in his system to Hume’s impressions or the deliverances of Cartesian consciousness. But Russell still retained something of his earlier Platonism: he believed that we had direct acquaintance with the universals which were represented by the predicates of the reformed logical language. But the range of things which we could know by acquaintance was limited: we could not be acquainted with Queen Victoria or our own past sense-data. Those things which were not known by acquaintance were known only by description; hence the importance of the theory of descriptions.
In the sentence ‘Caesar crossed the Rubicon’, uttered in England now, we have a proposition in which there are apparently no individual constituents with which we are acquainted. In order to explain how we can understand the sentence Russell analyses the names ‘Caesar’ and ‘Rubicon’ as definite descriptions. The descriptions, spelt out in full, no doubt include reference to those names, but not to the objects they named. The sentence is exhibited as being about general characteristics and relations, and the names with which we become acquainted as we pronounce them.
For Russell, then, ordinary proper names were in fact disguised descriptions. A fully analyzed sentence would contain only logically proper names (words referring to particulars with which we are acquainted) and universals (words referring to characters and relations). It was never altogether clear what counted as logically proper names. Sometimes Russell seemed to countenance only demonstratives such as ‘this’ and ‘that’. An atomic proposition, therefore, would be something like ‘(this) red’ or “this) beside (that)’.
An engineer, a physicist, and a mathematician are on a train in Scotland.
The engineer looks out the window and sees a black sheep. He comments, "Look, they have black sheep in Scotland".
Then physicist looks and comments, "From this observation, we can only say there is at least one black sheep in Scotland."
The mathematician then looks and comments, "Actually, from this we can only say there is at least one sheep in Scotland that's black on one side."