Concept grounding and knowledge of set theory

Philosophia 38 (1):179-193 (2010)

Jeffrey W. Roland
Louisiana State University
C. S. Jenkins has recently proposed an account of arithmetical knowledge designed to be realist, empiricist, and apriorist: realist in that what’s the case in arithmetic doesn’t rely on us being any particular way; empiricist in that arithmetic knowledge crucially depends on the senses; and apriorist in that it accommodates the time-honored judgment that there is something special about arithmetical knowledge, something we have historically labeled with ‘a priori’. I’m here concerned with the prospects for extending Jenkins’s account beyond arithmetic—in particular, to set theory. After setting out the central elements of Jenkins’s account and entertaining challenges to extending it to set theory, I conclude that a satisfactory such extension is unlikely.
Keywords Epistemology  Mathematics  Arithmetic  Set theory  Concepts
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DOI 10.1007/s11406-009-9186-4
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References found in this work BETA

Epistemic Luck.Duncan Pritchard - 2005 - Oxford University Press UK.
Parts of Classes.David LEWIS - 1991 - Blackwell.
Discrimination and Perceptual Knowledge.Alvin I. Goldman - 1976 - Journal of Philosophy 73 (November):771-791.
The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford University Press.

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