Combining Texts

All the ideas for 'Defending the Axioms', 'The Golden Bowl, and Lit as Moral Philosophy' and 'Apology for Raymond Sebond'

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14 ideas

1. Philosophy / A. Wisdom / 2. Wise People
Why can't a wise man doubt everything? [Montaigne]
1. Philosophy / A. Wisdom / 3. Wisdom Deflated
No wisdom could make us comfortably walk a wide beam if it was high in the air [Montaigne]
3. Truth / A. Truth Problems / 3. Value of Truth
Virtue is the distinctive mark of truth, and its greatest product [Montaigne]
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]
7. Existence / D. Theories of Reality / 3. Reality
We lack some sense or other, and hence objects may have hidden features [Montaigne]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Sceptics say there is truth, but no means of making or testing lasting judgements [Montaigne]
15. Nature of Minds / A. Nature of Mind / 1. Mind / d. Location of mind
The soul is in the brain, as shown by head injuries [Montaigne]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
The Aristotelian idea that choices can be perceived needs literary texts to expound it [Nussbaum]