Combining Texts

All the ideas for 'Defending the Axioms', 'Letters to Samuel Masson' and 'On the Nature of Truth and Falsehood'

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10 ideas

3. Truth / C. Correspondence Truth / 1. Correspondence Truth
6343 For Russell, both propositions and facts are arrangements of objects, so obviously they correspond [Horwich on Russell]
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 / d. Actual infinite
13190 I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz]
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]
19. Language / D. Propositions / 6. Propositions Critique
7534 In 1906, Russell decided that propositions did not, after all, exist [Russell, by Monk]