Combining Texts

All the ideas for 'Mathematics without Numbers', 'works' and 'Aspects of the Theory of Syntax'

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6 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5

7791	The simplest of the logics based on possible worlds is Lewis's S5 [Lewis,CI, by Girle]

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]

10. Modality / A. Necessity / 2. Nature of Necessity

11002

Equating necessity with informal provability is the S4 conception of necessity [Lewis,CI, by Read]

19. Language / C. Assigning Meanings / 1. Syntax

18006

Chomsky's 'interpretative semantics' says syntax comes first, and is then interpreted [Chomsky, by Magidor]