Tuples all the way down?

Abstract

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 short paper I will pose the difficulty, and then propose a solution.

Links

PhilArchive

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

Similar books and articles

Abstraction Relations Need Not Be Reflexive.Jonathan Payne - 2013 - Thought: A Journal of Philosophy 2 (2):137-147.
Reconsidering ordered pairs.Dana Scott & Dominic McCarty - 2008 - Bulletin of Symbolic Logic 14 (3):379-397.
On pairs of free modules over a Dedekind domain.Saverio Cittadini & Carlo Toffalori - 2006 - Archive for Mathematical Logic 45 (1):75-95.
Composition as Abstraction.Jeffrey Sanford Russell - 2017 - Journal of Philosophy 114 (9):453-470.
Introduction.Øystein Linnebo - 2009 - Synthese 170 (3):321-329.
Plural quantification.Ø Linnebo - 2008 - Stanford Encyclopedia of Philosophy.
Logic and Plurals.Salvatore Florio & Øystein Linnebo - 2018 - In Kirk Ludwig & Marija Jankovic (eds.), The Routledge Handbook of Collective Intentionality. Routledge. pp. 451-463.
The Mereological Foundation of Megethology.Massimiliano Carrara & Enrico Martino - 2016 - Journal of Philosophical Logic 45 (2):227-235.
The Logic of Finite Order.Simon Hewitt - 2012 - Notre Dame Journal of Formal Logic 53 (3):297-318.
Abstractionism: Essays in Philosophy of Mathematics.Philip A. Ebert & Marcus Rossberg - 2016 - Oxford, England: Oxford University Press UK.

Analytics

Added to PP
2018-01-17

Downloads
356 (#57,306)

6 months
139 (#26,369)

Historical graph of downloads
How can I increase my downloads?

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.
Parts of Classes.Michael Potter - 1993 - Philosophical Quarterly 43 (172):362-366.
Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.
Frege meets dedekind: A neologicist treatment of real analysis.Stewart Shapiro - 2000 - Notre Dame Journal of Formal Logic 41 (4):335--364.

View all 8 references / Add more references