Combining Texts

All the ideas for 'Defending the Axioms', 'Truth and Probability' and 'Structuralism Reconsidered'

expand these ideas     |    start again     |     specify just one area for these texts

11 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 / 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 / 3. Nature of Numbers / d. Natural numbers
8923 Numbers are identified by their main properties and relations, involving the successor function [MacBride]
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 / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
8926 For mathematical objects to be positions, positions themselves must exist first [MacBride]
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 / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
13766 'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey]
14. Science / C. Induction / 6. Bayes's Theorem
19143 Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson]