Combining Texts

All the ideas for 'works (all lost)', 'Remarks on axiomatised set theory' and 'Lectures on the Philosophy of (World) History'

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7 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason

21753

If we look at the world rationally, the world assumes a rational aspect [Hegel]

2. Reason / A. Nature of Reason / 1. On Reason

21974

The world seems rational to those who look at it rationally [Hegel]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17879

Axiomatising set theory makes it all relative [Skolem]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17878

If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics

17880

Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

17881

Mathematician want performable operations, not propositions about objects [Skolem]

13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism

2667	A false object might give the same presentation as a true one [Arcesilaus, by Cicero]