Does mathematics need new axioms

Bulletin of Symbolic Logic 6 (4):401-446 (1999)
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Part of the ambiguity lies in the various points of view from which this question might be considered. The crudest di erence lies between the point of view of the working mathematician and that of the logician concerned with the foundations of mathematics. Now some of my fellow mathematical logicians might protest this distinction, since they consider themselves to be just more of those \working mathematicians". Certainly, modern logic has established itself as a very respectable branch of mathematics, and there are quite a few highly technical journals in logic, such as The Journal of Sym-



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Penelope J. Maddy
University of California, Irvine

Citations of this work

Objectivity and reliability.Justin Clarke-Doane - 2017 - Canadian Journal of Philosophy 47 (6):841-855.
On the question of absolute undecidability.Peter Koellner - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Philosophia Mathematica. Association for Symbolic Logic. pp. 153-188.
Arithmetic is Determinate.Zachary Goodsell - 2021 - Journal of Philosophical Logic 51 (1):127-150.

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References found in this work

Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
The strength of some Martin-Löf type theories.Edward Griffor & Michael Rathjen - 1994 - Archive for Mathematical Logic 33 (5):347-385.
Naturalism and the A Priori.Penelope Maddy - 2000 - In Paul Boghossian & Christopher Peacocke (eds.), New Essays on the A Priori. Oxford University Press. pp. 92--116.
In the Light of Logic.G. Aldo Antonelli - 2001 - Bulletin of Symbolic Logic 7 (2):270-277.

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