### Abstract

Original language | English |
---|---|

Journal | Synthese |

Volume | 191 |

Issue number | 17 |

Pages (from-to) | 4201-4229 |

Number of pages | 29 |

ISSN | 0039-7857 |

DOIs | |

Publication status | Published - 2014 |

MoE publication type | A1 Journal article-refereed |

### Fields of Science

- 611 Philosophy

### Cite this

*Synthese*,

*191*(17), 4201-4229. https://doi.org/10.1007/s11229-014-0526-y

}

*Synthese*, vol. 191, no. 17, pp. 4201-4229. https://doi.org/10.1007/s11229-014-0526-y

**An Empirically feasible approach to the epistemology of arithmetic.** / Pantsar, Markus.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - An Empirically feasible approach to the epistemology of arithmetic

AU - Pantsar, Markus

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - 611 Philosophy

U2 - 10.1007/s11229-014-0526-y

DO - 10.1007/s11229-014-0526-y

M3 - Article

VL - 191

SP - 4201

EP - 4229

JO - Synthese

JF - Synthese

SN - 0039-7857

IS - 17

ER -