Combining Texts

All the ideas for 'Defending the Axioms', 'A Serious Proposal to the Ladies I' and 'Letters to Mersenne'

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11 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism
My Meditations are the complete foundation of my physics [Descartes]
3. Truth / A. Truth Problems / 2. Defining Truth
Truth is such a transcendentally clear notion that it cannot be further defined [Descartes]
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]
24. Political Theory / A. Basis of a State / 3. Natural Values / a. Natural freedom
If men are born free, are women born slaves? [Astell]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
I can't prove the soul is indestructible, only that it is separate from the mortal body [Descartes]