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Full Idea
A notion of formal provability can be articulated in Peano arithmetic. ..This is surprisingly 'linguistic' rather than mathematical, but the key is in the Gödel coding. ..Hence we use Peano arithmetic as a theory of syntax.
Gist of Idea
A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding
Source
Leon Horsten (The Tarskian Turn [2011], 02.4)
Book Ref
Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.23
A Reaction
This is the explanation of why issues in formal semantics end up being studied in systems based on formal arithmetic. And I had thought it was just because they were geeks who dream in numbers, and can't speak language properly...
| 18006 | Chomsky's 'interpretative semantics' says syntax comes first, and is then interpreted [Chomsky, by Magidor] |
| 18007 | Syntax is independent of semantics; sentences can be well formed but meaningless [Chomsky, by Magidor] |
| 3507 | Universal grammar doesn't help us explain anything [Searle] |
| 2581 | Intuition may say that a complex sentence is ungrammatical, but linguistics can show that it is not [Block] |
| 8073 | How do we parse 'time flies like an arrow' and 'fruit flies like an apple'? [Devlin] |
| 21638 | Syntactic form concerns the focus of the sentence, as well as the truth-conditions [Hofweber] |
| 15347 | A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten] |
| 18008 | Generative semantics says structure is determined by semantics as well as syntactic rules [Magidor] |
| 18010 | 'John is easy to please' and 'John is eager to please' have different deep structure [Magidor] |