The Monist 103 (4):427-441 (2020)

Authors
Juliet Floyd
Boston University
Abstract
I defend Putnam’s modal structuralist view of mathematics but reject his claims that Wittgenstein’s remarks on Dedekind, Cantor, and set theory are verificationist. Putnam’s “realistic realism” showcases the plasticity of our “fitting” words to the world. The applications of this—in philosophy of language, mind, logic, and philosophy of computation—are robust. I defend Wittgenstein’s nonextensionalist understanding of the real numbers, showing how it fits Putnam’s view. Nonextensionalism and extensionalism about the real numbers are mathematically, philosophically, and logically robust, but the two perspectives are often confused with one another. I separate them, using Turing’s work as an example.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
DOI 10.1093/monist/onaa015
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 61,025
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Philosophical investigations.Ludwig Wittgenstein & G. E. M. Anscombe - 1953 - Revue Philosophique de la France Et de l'Etranger 161:124-124.
Models and Reality.Hilary Putnam - 1980 - Journal of Symbolic Logic 45 (3):464-482.
It Ain’T Necessarily So.Hilary Putnam - 1962 - Journal of Philosophy 59 (22):658-671.
Mathematics Without Foundations.Hilary Putnam - 1967 - Journal of Philosophy 64 (1):5-22.

View all 17 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Putnam’s Argument That the Claim That We Are Brains-in-a-Vat is Self-Refuting.Richard McDonough - 2018 - Meta: Research in Hermeneutics, Phenomenology, and Practical Philosophy 10 (1):149-159.
Wittgenstein and the Real Numbers.Daesuk Han - 2010 - History and Philosophy of Logic 31 (3):219-245.
Primitive Recursive Real Numbers.Qingliang Chen, Kaile Su & Xizhong Zheng - 2007 - Mathematical Logic Quarterly 53 (4‐5):365-380.
Some Objections to Putnam’s “Consistency Objection”.John A. Humphrey - 1993 - Journal of Philosophical Research 18:127-141.
Some Objections to Putnam’s “Consistency Objection”.John A. Humphrey - 1993 - Journal of Philosophical Research 18:127-141.
Wittgenstein’s Early Philosophy of Mathematics.Steven F. Savitt - 1979 - Philosophy Research Archives 5:539-553.
Wittgenstein and Realism.Hilary Putnam - 2008 - International Journal of Philosophical Studies 16 (1):3 – 16.
A Note on Putnam and the Transitivity of the Real.Charles E. Cardwell - 1972 - Philosophical Studies 23 (6):414 - 417.
Wittgensteins Diagonal-Argument: Eine Variation auf Cantor und Turing.Juliet Floyd - forthcoming - In Joachim Bromand & Bastian Reichert (eds.), Wittgenstein und die Philosophie der Mathematik. Münster: Mentis Verlag. pp. 167-197.
Putnam Beyond Putnam: Understanding, Pragmatism, Humanism.Ulvi Doguoglu - 2008 - Poznan Studies in the Philosophy of the Sciences and the Humanities 95 (1):103-124.

Analytics

Added to PP index
2020-09-16

Total views
11 ( #814,397 of 2,439,609 )

Recent downloads (6 months)
2 ( #282,563 of 2,439,609 )

How can I increase my downloads?

Downloads

My notes