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Single Idea 17789

[filed under theme 5. Theory of Logic / K. Features of Logics / 6. Compactness ]

Full Idea

No logic which can axiomatise arithmetic can be compact or complete.

Gist of Idea

No logic which can axiomatise arithmetic can be compact or complete

Source

John Mayberry (What Required for Foundation for Maths? [1994], p.412-1)

Book Ref

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.412

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A Reaction

I take this to be because there are new truths in the transfinite level (as well as the problem of incompleteness).