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Single Idea 10985

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

Full Idea

Those who believe mathematics goes beyond logic use that fact to argue that classical logic is right to exclude second-order logic.

Gist of Idea

We should exclude second-order logic, precisely because it captures arithmetic

Source

Stephen Read (Thinking About Logic [1995], Ch.2)

Book Ref

Read,Stephen: 'Thinking About Logic' [OUP 1995], p.54

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]