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Single Idea 13241

[filed under theme 5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics ]

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.

The 8 ideas with the same theme [logic that is used in the practice of mathematics]:

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]