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The Philosophy of Logical Atomism
by Bertrand Russell
Overview
This material consists of the text of eight lectures given in London in 1918. The subject matter is mainly the relationship between language and reality, culminating with a metaphysical view "on what there is". The ideas about language derive from the advances in mathematical logic on which Principia Mathematica is founded, and assume that these advances provide an insight into the structure of ideal languages in terms of which a correct analysis of the meaning of ordinary language must be based. The relationship between language and reality is based on but not the same as ideas of Wittgenstein later published in his Tractatus Logico-Philosophicus.
Though metaphysics is nominally reserved for the last lecture, we are launched straight into it, and Russell post-Meinongian parsimony is prominent. Atomic facts exist (this Russell thinks uncontroversial). Propositions, whose truth values are connected with the existence of related atomic facts, do not exist.
Lecture II - Particulars, Predicates and Relations
Atomic propositions express, and facts are, the holding of relations between particulars, which are simple. Complexes are facts. This is not a way of saying "it is a fact that there are complexes", it should be taken more literally. The complex is identified with an atomic proposition which expresses that relationship, between the parts which form the complex, which consists in their being fitted together in the way that they are.
Lecture III - Atomic and Molecular Propositions
There are negative facts but not molecular facts, the truth value of the molecular propositions is determined by the relevant atomic facts.
Lecture IV - Propositions and Facts with more than one verb; Beliefs, etc.
Apparently Russell did once believe that propositions existed, but has by now come to believe that they do not. It is therefore not possible for him to explain intentional occurrences of propositions in the same way as occurrences of other kinds of thing. He doesn't really have an explanation to offer, he is only certain about some kinds of explanation not working. This is probably the point at which he was impacted by Wittgenstein's criticism of "Our Knowledge of the External World", in which Wittgenstein has evidently trashed Russell's account without supplying a viable alternative.
Lecture V - General Propositions and Existence
Russell holds that general and existential facts exist (by contrast with Wittgenstein in the Tractatus).
Lecture VI - Descriptions and Incomplete Symbols
Russell's theory of descriptions and of other kinds of incomplete symbol are an important part of his method of applying Occam's razor. It is a general device for explaining away apparent references to entities which Russell wishes to do without. The main problem with this is that Russell does not have a firm grip on when he needs these things to be in the scope of quantifiers, we have to look to Quine for a good analysis of this issue (see his "Set Theory and its Logic"), after which Russell's spartan ontology is no longer tenable. Quine's critique does not however impact Russell's theory of descriptions, which falls to pragmatic objections rather than ones of principle.
Lecture VII - The Theory of Types and Symbolism; Classes
Lecture VIII - Excursus into Metaphysics: What There Is
Lecture I - Facts and Propositions
Though metaphysics is nominally reserved for the last lecture, we are launched straight into it, and Russell post-Meinongian parsimony is prominent. Atomic facts exist (this Russell thinks uncontroversial). Propositions, whose truth values are connected with the existence of related atomic facts, do not exist.

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