The Four-Color Theorem Solved, Again: Extending the Extended Mind to Philosophy of Mathematics

Res Cogitans 2 (1):215-228 (2011)
Abstract
In 1977 when Appel, Haken and Koch used a computer to mathematically solve the century old four-color-problem philosopher Thomas Tymoczko thought that the epistemic justification in mathematics had been changed. Essentially, Tymoczko, and others, argue we can now have mathematical epistemic justification through a posteriori means. This has obvious implication in philosophy of mathematics and epistemology because this would be the first case where mathematics isn’t justified through a priori means of investigation. However, I ultimately disagree with Tymoczko. I argue that computer-aided-proofs still warrant an a priori means of justification. In order to show this, I refer to advances in philosophy of mind, mainly, the extended mind thesis. I will argue that our mind has evolved to enter into symbiotic relationships with non-organic entities in order to offload certain internal capacities. I believe that this is what constitutes humans amazing gift of rationality and intelligence. Thus, when we use a computer-aided-proof to solve unsurveyable proofs, we are really extending our minds into these cognitive tools and extending our method of proof checking to be more efficient and quicker. Thus, the a priori is saved because the computer is just a part of the causal cognitive loop that constitutes our mind.
Keywords Philosophy of Mind  philosophy of cognitive science  Philosophy of Mathematics  Epistemology  Extended Mind  Four Color Theorem
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index Translate to english
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 11,793
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.

Citations of this work BETA
Similar books and articles
Terence Sullivan (2007). The Mind Ain't Just in the Head-Defending and Extending the Extended Mind. The Proceedings of the Twenty-First World Congress of Philosophy 6:145-149.
Eric T. Olson (2011). The Extended Self. Minds and Machines 21 (4):481-495.
Analytics

Monthly downloads

Added to index

2011-08-15

Total downloads

17 ( #101,193 of 1,099,722 )

Recent downloads (6 months)

1 ( #301,057 of 1,099,722 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.