Actual and Potential Infinity

Noûs 53 (1):160-191 (2017)
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Abstract

The notion of potential infinity dominated in mathematical thinking about infinity from Aristotle until Cantor. The coherence and philosophical importance of the notion are defended. Particular attention is paid to the question of whether potential infinity is compatible with classical logic or requires a weaker logic, perhaps intuitionistic.

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Author Profiles

Øystein Linnebo
University of Oslo
Stewart Shapiro
Ohio State University

Citations of this work

Platonism in the Philosophy of Mathematics.Øystein Linnebo - forthcoming - Stanford Encyclopedia of Philosophy.
Generality Explained.Øystein Linnebo - 2022 - Journal of Philosophy 119 (7):349-379.
In defense of Countabilism.David Builes & Jessica M. Wilson - 2022 - Philosophical Studies 179 (7):2199-2236.
Mathematical and Moral Disagreement.Silvia Jonas - 2020 - Philosophical Quarterly 70 (279):302-327.

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Truth and Other Enigmas.Michael Dummett - 1978 - Philosophical Quarterly 31 (122):47-67.
The potential hierarchy of sets.Øystein Linnebo - 2013 - Review of Symbolic Logic 6 (2):205-228.

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