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Full Idea
The incompletability of formal arithmetic reveals, not arithmetical truths which are not truths of logic, but that logical truth likewise defies complete deductive characterization. ...Gödel's result has no specific bearing on the logicist project.
Gist of Idea
The incompletability of formal arithmetic reveals that logic also cannot be completely characterized
Source
B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], §2 n5)
Book Ref
Hale,B/Wright,C: 'The Reason's Proper Study' [OUP 2003], p.4
A Reaction
This is the key defence against the claim that Gödel's First Theorem demolished logicism.
| 10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
| 10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [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] |
| 10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [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] |