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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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.
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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.
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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.
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Lecture V - General Propositions and Existence
Russell holds that general and existential facts exist (by contrast with
Wittgenstein in the Tractatus).
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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.
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Lecture VII - The Theory of Types and Symbolism; Classes
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Lecture VIII - Excursus into Metaphysics: What There Is
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