Tuples all the Way Down?

Thought: A Journal of Philosophy 7 (3):161-169 (2018)
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We can introduce singular terms for ordered pairs by means of an abstraction principle. Doing so proves useful for a number of projects in the philosophy of mathematics. However there is a question whether we can appeal to the abstraction principle in good faith, since a version of the Caesar Problem can be generated, posing the worry that abstraction fails to introduce expressions which refer determinately to the requisite sort of object. In this note I will pose the difficulty, and then propose a solution. Since my solution appeals to a plausible constraint on the introduction of new expressions to a language, it is of interest independently of the particular case of terms for pairs. Since these provide the occasion for discussion we should nonetheless review the use of abstraction for pairs before the argumentative business of the paper commences.

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Simon Hewitt
University of Leeds

References found in this work

No Work for a Theory of Grounding.Jessica M. Wilson - 2014 - Inquiry: An Interdisciplinary Journal of Philosophy 57 (5-6):535-579.
Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.
Parts of Classes.Michael Potter - 1993 - Philosophical Quarterly 43 (172):362-366.

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