display all the ideas for this combination of philosophers
3 ideas
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] |
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) |
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) |