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

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

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.

Andrew Blitzer: What Extended Mind Thesis?

At the Australian National University:

Date and time: 

Tue, 02/08/2011 - 16:00 - 18:00

 

Location: 

Coombs Seminar Room B

Abstract: Alonzo Church (1958) argued that “no discussion of an ontological question ... can be regarded as intelligible unless it obeys a definite criterion of ontological commitment.” In this paper, I apply Church’s standard to discussions of the Extended Mind Thesis (EMT).  Such discussions, I argue, are presently defective (if not unintelligible) because extended mind theorists vacillate systematically and indiscriminately between ontological and non-ontological articulations of their thesis. I present strong textual evidence to this effect, and head off some natural objections. The conclusion of this paper suggests a way forward.  I urge extended mind theorists to abandon the ontological articulation of EMT.  If their basic aim is what they say it is—namely to promote cognitive scientific progress—then the ontological dimension of their enterprise is dead weight.  Or so I contend.