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Empiricism and Mathematical Knowledge

Citation

Leeper, Gideon J. (2019) Empiricism and Mathematical Knowledge. Other, California Institute of Technology. doi:10.7907/7B38-2T90. http://resolver.caltech.edu/CaltechTHESIS:11042016-141839141

Abstract

Empiricism asserts that sensory perceptions and experiences are the basis of all knowledge, i.e. essentially everything we know has either been directly perceived or deduced from perceived knowledge. This would seem to conflict with the wealth of mathematical knowledge that we have accrued as a civilization. Mathematics consists primarily of facts concerning ideal objects, such as topological spaces, groups, and categories, which we have never encountered in physical reality, and cannot reasonably expect to. Then from an empiricist perspective, it seems impossible for us to know so much about these objects, when there is no sensory experience on which we can base our knowledge. I first assert that mathematical knowledge is not knowledge in the sense used by empiricists, and thus its existence does not conflict with their views. However, I argue that first-hand mathematical knowledge, specifically one's belief in the validity of a proof, in some sense has an empirical component.

Item Type:Thesis (Other)
Subject Keywords:Hixon Prize for Writing , Empiricism, Mathematics
Degree Grantor:California Institute of Technology
Division:Humanities and Social Sciences
Major Option:Humanities
Awards:Alexander P. and Adelaide F. Hixon Prize for Writing, 2016
Thesis Availability:Restricted to Caltech community only
Research Advisor(s):
  • Unknown, Unknown
Group:Hixon Writing Center, Alexander P. and Adelaide F. Hixon Prize for Writing in Freshman Humanities, Alexander P. and Adelaide F. Hixon Prize for Writing
Thesis Committee:
  • None, None
Defense Date:2016
Record Number:CaltechTHESIS:11042016-141839141
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:11042016-141839141
DOI:10.7907/7B38-2T90
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9973
Collection:CaltechTHESIS
Deposited By: Leslie Rico
Deposited On:04 Nov 2016 22:21
Last Modified:26 Apr 2019 20:02

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