Combining Texts

All the ideas for 'fragments/reports', 'works' and 'The Identity of Indiscernibles'

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11 ideas

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

17892

For clear questions posed by reason, reason can also find clear answers [Gödel]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

10196

The Axiom of Choice needs a criterion of choice [Black]

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic

9188	Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett]

5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth

10620

Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel]

5. Theory of Logic / K. Features of Logics / 5. Incompleteness

17883

Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

17885

Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner]

10614

The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel]

9. Objects / A. Existence of Objects / 5. Individuation / b. Individuation by properties

10194

Two things can only be distinguished by a distinct property or a distinct relation [Black]

9. Objects / F. Identity among Objects / 5. Self-Identity

10193

The 'property' of self-identity is uselessly tautological [Black]

9. Objects / F. Identity among Objects / 7. Indiscernible Objects

10195

If the universe just held two indiscernibles spheres, that refutes the Identity of Indiscernibles [Black]

28. God / C. Attitudes to God / 3. Deism

1558	Clearly the gods ignore human affairs, or they would have given us justice [Thrasymachus]