Combining Texts

All the ideas for 'Defending the Axioms', 'A Combinatorial Theory of Possibility' and 'works'

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11 ideas

3. Truth / B. Truthmakers / 6. Making Negative Truths
Negative existentials have 'totality facts' as truthmakers [Armstrong, by Lewis]
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]
10. Modality / B. Possibility / 1. Possibility
All possibilities are recombinations of properties in the actual world [Armstrong, by Lewis]
14. Science / B. Scientific Theories / 1. Scientific Theory
You have only begun to do real science when you can express it in numbers [Kelvin]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy
Energy has progressed from a mere formula, to a principle pervading all nature [Kelvin]