Dissertation, University of Illinois at Urbana-Champaign (2017)

Authors
Michael Jordan
Texas A&M University, Corpus Christi
Abstract
In what follows I argue for an epistemic bridge principle that allows us to move from real mathematics to ideal mathematics without losing anything that is characteristic of either methodological class. Mathematics is a collection of actions performed in the pursuit of mathematical understanding. The actions are the processes of proving claims that come in such forms as lemmas, theorems, or conjectures. These proofs can be accomplished through a variety of means including logical deduction, geometric intuition, diagramming, or computer assistance. What is common to each of these is the characteristic of being convincing to a sound mathematical mind. Even though what in particular makes each of these methods of proof convincing differs, that they are convincing is enough to usher forth mathematical understanding. The chapters of this dissertation explore a new naturalistic metaphysics for under- standing “where mathematics comes from”, recent psychological findings in the the nature of mathematical reasoning, the concatenation of two historical forms of reasoning, the possibility of an epistemic bridge between real and ideal methods, and the implication of this new bridge principle for the long-standing concern that Go ̈del’s Incompleteness Theorems shake the foundation of modern mathematics.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 59,107
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Whether philosophers need contemporary mathematics?V. A. Erovenko - 2013 - Liberal Arts in Russia 2 (6):523--530.
Towards a Philosophy of Applied Mathematics.Christopher Pincock - 2009 - In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan.
Magic world of mathematics has found 'common face'.V. P. Kazaryan - 2013 - Liberal Arts in Russia 2 (3):252--261.
Mathematical Instrumentalism, Gödel’s Theorem, and Inductive Evidence.Alexander Paseau - 2011 - Studies in History and Philosophy of Science Part A 42 (1):140-149.

Analytics

Added to PP index
2017-08-12

Total views
12 ( #765,866 of 2,428,027 )

Recent downloads (6 months)
1 ( #511,645 of 2,428,027 )

How can I increase my downloads?

Downloads

My notes