Combining Philosophers

Ideas for Theodore Sider, Thomas Jefferson and Laura Schroeter

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3 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 / 4. Variables in Logic

13696	When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider]
	Full Idea: When a variable is not combined with a quantifier (and so is 'free'), the result is, intuitively, semantically incomplete, and incapable of truth or falsity.
	From: Theodore Sider (Logic for Philosophy [2010], 4.2)

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

13700	A 'total' function must always produce an output for a given domain [Sider]
	Full Idea: Calling a function a 'total' function 'over D' means that the function must have a well-defined output (which is a member of D) whenever it is given as inputs any n members of D.
	From: Theodore Sider (Logic for Philosophy [2010], 5.2)