Combining Texts

All the ideas for 'Defending the Axioms', 'Lecture on Applicability of Mathematics' and 'Reference and Necessity'

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19 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
16405 To understand a name (unlike a description) picking the thing out is sufficient? [Stalnaker]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
8732 It is spooky the way mathematics anticipates physics [Weinberg]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
9. Objects / C. Structure of Objects / 7. Substratum
16407 Possible worlds allow separating all the properties, without hitting a bare particular [Stalnaker]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
16397 If it might be true, it might be true in particular ways, and possible worlds describe such ways [Stalnaker]
16399 Possible worlds are ontologically neutral, but a commitment to possibilities remains [Stalnaker]
16398 Possible worlds allow discussion of modality without controversial modal auxiliaries [Stalnaker]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
16396 Kripke's possible worlds are methodological, not metaphysical [Stalnaker]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
16408 Rigid designation seems to presuppose that differing worlds contain the same individuals [Stalnaker]
19. Language / A. Nature of Meaning / 1. Meaning
16406 If you don't know what you say you can't mean it; what people say usually fits what they mean [Stalnaker]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
16404 In the use of a name, many individuals are causally involved, but they aren't all the referent [Stalnaker]
19. Language / C. Assigning Meanings / 2. Semantics
16403 'Descriptive' semantics gives a system for a language; 'foundational' semantics give underlying facts [Stalnaker]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
16401 To understand an utterance, you must understand what the world would be like if it is true [Stalnaker]