Combining Texts

Ideas for 'Substance and Individuation in Leibniz', 'Logic for Philosophy' and 'Gentzen's Analysis of First-Order Proofs'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

3 ideas

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13825 Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz]
     Full Idea: With Gentzen's natural deduction, we may say that the introductions represent, as it were, the 'definitions' of the logical constants. The introductions are not literally understood as 'definitions'.
     From: Dag Prawitz (Gentzen's Analysis of First-Order Proofs [1974], 2.2.2)
     A reaction: [Hacking, in 'What is Logic? §9' says Gentzen had the idea that his rules actually define the constants; not sure if Prawitz and Hacking are disagreeing]
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)