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Title: Grounding concepts : an empirical basis for arithmetical knowledge
Author: Jenkins, C.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2004
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Abstract:
This dissertation is a philosophical discussion of arithmetical knowledge. I investigate the possibility of a new kind of epistemology for arithmetic, one which will respect three intuitions. (a) that arithmetic is a priori, (b) that arithmetical realism is correct, i.e. that arithmetical truth is independent of us, and (c) that scientific or naturalistic concerns enforce empiricism, the view that all knowledge of the independent world is obtained through the senses. I propose that we could develop an epistemology respecting these three intuitions if we were prepared to accept three claims: (1) that arithmetical truths are known through an examination of our arithmetical concepts, (2) that (at least our basic) arithmetical concepts map the arithmetical structure of the independent world. (3) that this mapping relationship obtains a virtue of the normal functioning of our sensory apparatus. Roughly speaking, the first of these claims protects a priorism, the second realism and the third empiricism. In the first chapter I try to determine in exactly what sense the realist should say that arithmetic is independent of us. Other preliminaries necessary at this stage include a defence of epistemic externalism and empiricism, two crucial parameters of the work. It then proceed by developing an account of what knowledge is in general, within which to locate my discussion of arithmetical knowledge. In the second chapter I indicate how one might develop an epistemology for arithmetic respecting intuitions (a)-(c). I suggest that our arithmetical concepts are empirically ‘grounded’, i.e. that they accurately represent the arithmetical structure of the world because they are sensitive to the structure of our sensory input. This, I argue, means that when we acquire knowledge of arithmetic through an examination of those concepts, we are relying in an essential way upon the sensory input which grounds them. This input does not, however, amount to sensory evidence for arithmetical propositions. So arithmetic remains a body of conceptual truths knowable a priori. The latter sections of chapter 2 are taken up with clarification and development of this proposal. Then in chapter 3, I consider and respond to a range of objections. In my Final Remarks, I consider the impact of the ideas developed here upon other philosophical debates, and their potential to stimulate further research.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.605088  DOI: Not available
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