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Full Idea
Are there perhaps modes of inference peculiar to mathematics which …do not belong to logic? Here one may point to inference by mathematical induction from n to n+1.
Gist of Idea
Does some mathematical reasoning (such as mathematical induction) not belong to logic?
Source
Gottlob Frege (Logic in Mathematics [1914], p.203)
Book Ref
Frege,Gottlob: 'Posthumous Writings', ed/tr. Hermes/Long/White etc [Blackwell 1979], p.203
A Reaction
He replies that it looks as if induction can be reduced to general laws, and those can be reduced to logic.
| 19597 | Logic (the theory of relations) should be applied to mathematics [Novalis] |
| 16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
| 16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
| 14462 | In modern times, logic has become mathematical, and mathematics has become logical [Russell] |
| 10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| 10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
| 13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |