Combining Texts

All the ideas for 'Defending the Axioms', 'Wittgenstein's 'Tractatus Logico-Philosophicus'' and 'Life of Pythagoras'

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9 ideas

4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic

23505

Aristotelian logic cannot express 'Everyone loves someone' [White,RM]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

17610

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

17620

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

17605

Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]

17625

If two mathematical themes coincide, that suggest a single deep truth [Maddy]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis

17615

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

17618

Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

17614

The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]

28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question

1515	Pythagoreans believe it is absurd to seek for goodness anywhere except with the gods [Iamblichus]