Combining Texts

All the ideas for 'Later Letters to Dedekind', 'Logicism Revisited' and 'Reliabilism'

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12 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17831 Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
10065 Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
10061 The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10050 A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
10049 Logical truths may contain non-logical notions, as in 'all men are men' [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
10063 Formalism is a bulwark of logical positivism [Musgrave]
10062 Formalism seems to exclude all creative, growing mathematics [Musgrave]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
19727 Reliabilist knowledge is evidence based belief, with high conditional probability [Comesaņa]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
19725 In a sceptical scenario belief formation is unreliable, so no beliefs at all are justified? [Comesaņa]
19726 How do we decide which exact process is the one that needs to be reliable? [Comesaņa]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
10060 Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]