Withdraw
Loading…
Mathematics, cognition, and you!
Bohall, Jordan Michael
Loading…
Permalink
https://hdl.handle.net/2142/97532
Description
- Title
- Mathematics, cognition, and you!
- Author(s)
- Bohall, Jordan Michael
- Issue Date
- 2017-01-25
- Doctoral Committee Chair(s)
- Carr, Jennifer
- Committee Member(s)
- Sanders, Kirk
- Waskan, Jon
- Hummel, John
- Department of Study
- Philosophy
- Discipline
- Philosophy
- Degree Granting Institution
- University of Illinois at Urbana-Champaign
- Degree Name
- Ph.D.
- Degree Level
- Dissertation
- Keyword(s)
- Philosophy
- Mathematics
- Abstract
- In what follows I argue for an epistemic bridge principle that allows us to move from real mathematics to ideal mathematics (and back again) 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 (though not limited to) 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 (i) a new naturalistic metaphysics for under- standing “where mathematics comes from”, (ii) recent psychological findings in the the nature of mathematical reasoning, (iii) the concatenation of two historical forms of reasoning (real and ideal), (iv) the possibility of an epistemic bridge between real and ideal methods, and (v) the implication of this new bridge principle for the long-standing concern that Go ̈del’s Incompleteness Theorems shake the foundation of modern mathematics.
- Graduation Semester
- 2017-05
- Type of Resource
- text
- Permalink
- http://hdl.handle.net/2142/97532
- Copyright and License Information
- Copyright 2017 Jordan Bohall
Owning Collections
Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at IllinoisManage Files
Loading…
Edit Collection Membership
Loading…
Edit Metadata
Loading…
Edit Properties
Loading…
Embargoes
Loading…