Combining Texts

All the ideas for 'Defending the Axioms', 'Letters to Thomasius' and 'Reply to Fourth Objections'

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10 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 / 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]
9. Objects / D. Essence of Objects / 1. Essences of Objects
13432 The essence of a circle is the equality of its radii [Leibniz]
17. Mind and Body / E. Mind as Physical / 6. Conceptual Dualism
3643 The concept of mind excludes body, and vice versa [Descartes]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
12696 Bodies are recreated in motion, and don't exist in intervening instants [Leibniz]