Tuesday, August 2, 2011

Casey M. Rufener: "The Four-Color Theorem Solved, Again"

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

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.

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