To bridge Gödel’s gap

Philosophical Studies 173 (8):2133-2150 (2016)
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Abstract

In “Mathematical Truth,” Paul Benacerraf raises an epistemic challenge for mathematical platonists. In this paper, I examine the assumptions that motivate Benacerraf’s original challenge, and use them to construct a new causal challenge for the epistemology of mathematics. This new challenge, which I call ‘Gödel’s Gap’, appeals to intuitive insights into mathematical knowledge. Though it is a causal challenge, it does not rely on any obviously objectionable constraints on knowledge. As a result, it is more compelling than the original challenge. It is also more general; the challenge applies equally to platonistic and non-platonistic accounts of mathematical truth. And it can be generalized beyond the case of mathematical knowledge to pose a challenge for, e.g., moral knowledge.

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Eileen S. Nutting
University of Kansas

Citations of this work

Debunking arguments.Daniel Z. Korman - 2019 - Philosophy Compass 14 (12):e12638.
Creating abstract objects.David Friedell - 2021 - Philosophy Compass 16 (10):e12783.
Neutrality and Force in Field's Epistemological Objection to Platonism.Ylwa Sjölin Wirling - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.

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References found in this work

On the Plurality of Worlds.David K. Lewis - 1986 - Malden, Mass.: Wiley-Blackwell.
On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
Realism, Mathematics & Modality.Hartry H. Field - 1989 - New York, NY, USA: Blackwell.

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