Synthese 191 (17):4201-4229 (2014)

Authors
Markus Pantsar
University of Helsinki
Abstract
Recent years have seen an explosion of empirical data concerning arithmetical cognition. In this paper that data is taken to be philosophically important and an outline for an empirically feasible epistemological theory of arithmetic is presented. The epistemological theory is based on the empirically well-supported hypothesis that our arithmetical ability is built on a protoarithmetical ability to categorize observations in terms of quantities that we have already as infants and share with many nonhuman animals. It is argued here that arithmetical knowledge developed in such a way cannot be totally conceptual in the sense relevant to the philosophy of arithmetic, but neither can arithmetic understood to be empirical. Rather, we need to develop a contextual a priori notion of arithmetical knowledge that preserves the special mathematical characteristics without ignoring the roots of arithmetical cognition. Such a contextual a priori theory is shown not to require any ontologically problematic assumptions, in addition to fitting well within a standard framework of general epistemology
Keywords Arithmetical cognition  Philosophy of mathematics  Epistemology  Empirical study
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s11229-014-0526-y
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: 70,091
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

Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
Origins of Objectivity.Tyler Burge - 2010 - Oxford University Press.
Two Dogmas of Empiricism.Willard V. O. Quine - 1951 - Philosophical Review 60 (1):20–43.
The Origin of Concepts.Susan Carey - 2009 - Oxford University Press.

View all 42 references / Add more references

Citations of this work BETA

View all 19 citations / Add more citations

Similar books and articles

Knowledge of Arithmetic.C. S. Jenkins - 2005 - British Journal for the Philosophy of Science 56 (4):727-747.
Could Experience Disconfirm the Propositions of Arithmetic?Jessica M. Wilson - 2000 - Canadian Journal of Philosophy 30 (1):55--84.
Frege, Kant, and the Logic in Logicism.John MacFarlane - 2002 - Philosophical Review 111 (1):25-65.
On Finite Hume.Fraser Macbride - 2000 - Philosophia Mathematica 8 (2):150-159.
Hilbert's Epistemology.Philip Kitcher - 1976 - Philosophy of Science 43 (1):99-115.
The Epistemological Status of a Naturalized Epistemology.Ron Amundson - 1983 - Inquiry: An Interdisciplinary Journal of Philosophy 26 (3):333 – 344.
Quantum Mathematics.J. Michael Dunn - 1980 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
Logicism, Interpretability, and Knowledge of Arithmetic.Sean Walsh - 2014 - Review of Symbolic Logic 7 (1):84-119.
Arithmetical Interpretations of Dynamic Logic.Petr Hájek - 1983 - Journal of Symbolic Logic 48 (3):704-713.

Analytics

Added to PP index
2014-10-02

Total views
52 ( #218,083 of 2,506,367 )

Recent downloads (6 months)
3 ( #209,812 of 2,506,367 )

How can I increase my downloads?

Downloads

My notes