Combining Texts

All the ideas for 'Defending the Axioms', 'Morality and Human Sexuality' and 'The New Organon'

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12 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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
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
Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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
Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Only individual bodies exist [Bacon]
9. Objects / C. Structure of Objects / 2. Hylomorphism / c. Form as causal
There are only individual bodies containing law-based powers, and the Forms are these laws [Bacon]
14. Science / B. Scientific Theories / 2. Aim of Science
Science must clear away the idols of the mind if they are ever going to find the truth [Bacon]
25. Social Practice / F. Life Issues / 5. Sexual Morality
Why do sexual relationships need permanence, if other relationships don't? [Punzo]
Does engaging in sexual intercourse really need no more thought than playing tennis? [Punzo]