Combining Texts

All the ideas for 'fragments/reports', 'Logicism Revisited' and 'Proof that every set can be well-ordered'

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10 ideas

5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism

10061

The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]

10065

Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth

10049

Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]

10050

A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / e. Countable infinity

15897

Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic

10058

No two numbers having the same successor relies on the Axiom of Infinity [Musgrave]

6. Mathematics / C. Sources of Mathematics / 7. Formalism

10062

Formalism seems to exclude all creative, growing mathematics [Musgrave]

10063

Formalism is a bulwark of logical positivism [Musgrave]

19. Language / A. Nature of Meaning / 5. Meaning as Verification

10060

Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]

23. Ethics / A. Egoism / 1. Ethical Egoism

3031	The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius]