Some recent existential appeals to mathematical experience

Vol 10, No 2 (2006) • Principia: an international journal of epistemology

Autor: Michael J. Shaffer

Abstract:

Some recent work by philosophers of mathematics has been aimed at showing that our knowledge of the existence of at least some mathematical objects and/or sets can be epistemically grounded by appealing to perceptual experience. The sensory capacity that they refer to in doing so is the ability to perceive numbers, mathematical properties and/or sets. The chief defense of this view as it applies to the perception of sets is found in Penelope Maddy’s Realism in Mathematics, but a number of other philosophers have made similar, if more simple, appeals of this sort. For example, Jaegwon Kim (1981, 1982), John Bigelow (1988, 1990), and John Bigelow and Robert Pargetter (1990) have all defended such views. The main critical issue that will be raised here concerns the coherence of the notions of set perception and mathematical perception, and whether appeals to such perceptual faculties can really provide any justification for or explanation of belief in the existence of sets, mathematical properties and/or numbers.

 

ISSN: 1414-4217

DOI: https://doi.org/10.5007/%25x

Texto Completo: https://periodicos.ufsc.br/index.php/principia/article/view/14509/13287

Principia: an international journal of epistemology

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"Principia: an international journal of epistemology" was founded in 1997 and regularly publishes articles, discussions and review. The journal aims to publish original scholarly work especially in epistemology area , with an emphasis on material of general interest to academic philosophers. Originally published only in print version (ISSN: 1414-4247), in 2005 the journal began to be published also in online version (ISSN: 1808-1711). Since 1999 are published three issues per year: in April, August and December. Qualis CAPES: A2