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Ideas for 'Parmenides', 'Writing the Book of the World' and 'The Theory of Logical Types'

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2 ideas

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

15019	Define logical constants by role in proofs, or as fixed in meaning, or as topic-neutral [Sider]
	Full Idea: Some say that logical constants are those expressions that are defined by their proof-theoretic roles, others that they are the expressions whose semantic values are permutation-invariant, and still others that they are the topic-neutral expressions.
	From: Theodore Sider (Writing the Book of the World [2011], 10.3)
	A reaction: [He cites MacFarlane 2005 as giving a survey of this]

5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic

21566	'Propositional functions' are ambiguous until the variable is given a value [Russell]
	Full Idea: By a 'propositional function' I mean something which contains a variable x, and expresses a proposition as soon as a value is assigned to x. That is to say, it differs from a proposition solely by the fact that it is ambiguous.
	From: Bertrand Russell (The Theory of Logical Types [1910], p.216)
	A reaction: This is Frege's notion of a 'concept', as an assertion of a predicate which still lacks a subject.