Combining Texts

All the ideas for '', 'Realism in Mathematics' and 'The Logical Syntax of Language'

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10 ideas

4. Formal Logic / F. Set Theory ST / 7. Natural Sets
8755 Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
13342 Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap]
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
13251 Each person is free to build their own logic, just by specifying a syntax [Carnap]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
11210 Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10718 A natural number is a property of sets [Maddy, by Oliver]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
8756 Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17733 We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
19. Language / F. Communication / 3. Denial
11214 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]