Combining Texts

All the ideas for 'Logicism Revisited', 'Set Theory and related topics (2nd ed)' and 'Ethics without Principles'

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10 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes

8920	Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz]

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 / 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]

22. Metaethics / B. Value / 1. Nature of Value / a. Nature of value

18681

The base for values has grounds, catalysts and intensifiers [Dancy,J, by Orsi]