Combining Texts

All the ideas for 'Defending the Axioms', 'Spinoza's Ethics' and 'Self, Body and Coincidence'

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10 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought

21855

Only in the 1780s did it become acceptable to read Spinoza [Lord]

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]

8. Modes of Existence / C. Powers and Dispositions / 5. Powers and Properties

14534

Shoemaker moved from properties as powers to properties bestowing powers [Shoemaker, by Mumford/Anjum]

15. Nature of Minds / C. Capacities of Minds / 10. Conatus/Striving

21866

Hobbes and Spinoza use 'conatus' to denote all endeavour for advantage in nature [Lord]