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Full Idea
The model theory of classical predicate logic is mathematics if anything is.
Gist of Idea
The model theory of classical predicate logic is mathematics
Source
JC Beall / G Restall (Logical Pluralism [2006], 4.2.1)
Book Ref
Beall,J/Restall,G: 'Logical Pluralism' [OUP 2006], p.40
A Reaction
This is an interesting contrast to the claim of logicism, that mathematics reduces to logic. This idea explains why students of logic are surprised to find themselves involved in mathematics.
19597 | Logic (the theory of relations) should be applied to mathematics [Novalis] |
16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [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] |