Combining Texts

All the ideas for 'Chapters on Scepticism', 'Defending the Axioms' and 'Counterparts and Identity'

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13 ideas

4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
18823 To say there could have been people who don't exist, but deny those possible things, rejects Barcan [Stalnaker, by Rumfitt]
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 / 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 / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
16409 Unlike Lewis, I defend an actualist version of counterpart theory [Stalnaker]
16411 If possible worlds really differ, I can't be in more than one at a time [Stalnaker]
16412 If counterparts exist strictly in one world only, this seems to be extreme invariant essentialism [Stalnaker]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / b. Scepticism of other minds
1799 If we can't know minds, we can't know if Pyrrho was a sceptic [Theodosius, by Diog. Laertius]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
16410 Extensional semantics has individuals and sets; modal semantics has intensions, functions of world to extension [Stalnaker]