Combining Texts

All the ideas for 'Presidential Address of Am. Math. Soc', 'The Concept of Logical Consequence' and 'Mathematics without Numbers'

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8 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
10247 We have no adequate logic at the moment, so mathematicians must create one [Veblen]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
18812 Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
13344 X follows from sentences K iff every model of K also models X [Tarski]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
13343 A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
8698 Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
9557 Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
10263 Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
19. Language / E. Analyticity / 1. Analytic Propositions
13345 Sentences are 'analytical' if every sequence of objects models them [Tarski]