Combining Texts

All the ideas for 'Clitophon', 'fragments/reports' and 'Philosophy of Mathematics'

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6 ideas

2. Reason / D. Definition / 8. Impredicative Definition

10882

Predicative definitions only refer to entities outside the defined collection [Horsten]

5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms

10884

A theory is 'categorical' if it has just one model up to isomorphism [Horsten]

6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics

10885

Computer proofs don't provide explanations [Horsten]

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

13007

Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

10881

The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]

22. Metaethics / B. Value / 2. Values / f. Altruism

1590	The just man does not harm his enemies, but benefits everyone [Plato]