15 ideas
17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
10121 | Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal] |
10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
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] |
10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
10626 | Objects just are what singular terms refer to [Hale/Wright] |
10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |