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Full Idea
Logic has become more mathematical, and mathematics has become more logical. The consequence is that it has now become wholly impossible to draw a line between the two; in fact, the two are one.
Gist of Idea
In modern times, logic has become mathematical, and mathematics has become logical
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVIII)
Book Ref
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.194
A Reaction
This appears to be true even if you reject logicism about mathematics. Logicism is sometimes rejected because it always ends up with a sneaky ontological commitment, but maybe mathematics shares exactly the same commitment.
| 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] |