Combining Texts

All the ideas for 'works', 'Defending the Axioms' and 'Essential vs Accidental Properties'

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14 ideas

1. Philosophy / A. Wisdom / 2. Wise People
Tell cleverness from answers, but wisdom from questions [Mahfouz]
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]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
The extremes of essentialism are that all properties are essential, or only very trivial ones [Rami]
9. Objects / D. Essence of Objects / 3. Individual Essences
An 'individual essence' is possessed uniquely by a particular object [Rami]
9. Objects / D. Essence of Objects / 5. Essence as Kind
'Sortal essentialism' says being a particular kind is what is essential [Rami]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
Unlosable properties are not the same as essential properties [Rami]
10. Modality / A. Necessity / 3. Types of Necessity
Physical possibility is part of metaphysical possibility which is part of logical possibility [Rami]
10. Modality / B. Possibility / 2. Epistemic possibility
If it is possible 'for all I know' then it is 'epistemically possible' [Rami]