Reason and Creativity

It seems that so often, reason (and its handmaid logic) and creativity are paired off as opposites. They control different spheres. Reason is the realm of the scientist; creativity of the artist. However, many times scientists and philosophers of science state that creativity is an integral part of the field. As a mathematician, I can attest that a merely logical mathematician won't get terribly far; creativity is absolutely necessary to be a good at math, particularly higher mathematics. Am I saying that mathematics is fundamentally irrational, or at least not a rational subject? By all means no. This confusion is part of the whole misunderstanding of creativity and reason being opposites. The most rational person has both; creativity is not against reason, but shows the most promising routes for it. Sometimes, one has to take a leap with reason, whether because there are multiple open routes ahead or none. Logic is the guide along the known path, creativity the woodsman looking for a new trail or to see which trail is best. Reason is the overall process of making it through the woods. Creativity therefore can be considered a part of a full concept of reason at times, depending on how it is used.

Gödel's incompleteness theorem (my senior paper topic) may say something about this. According to J.R. Lucas (at http://users.ox.ac.uk/~jrlucas/Godel/implgoed.html), the theorem shows that in general, the concept of truth outruns the concept of provability. This, however, is not to mark the end of reason; merely the end of strictly formalized, single-method reason. For example, 1st order logic (logic that allows one to look at every simple object as a group, but not at all propositions or functions of the simple objects at once; see http://en.wikipedia.org/wiki/First_order_logic for a better, more detailed explanation) is complete; one can prove every true statement expressible in the system starting with the standard axioms. However, it is not decidable (one cannot apply a test to see if a statement is true or false).

The implications of being complete but non-decidable are this: one can show that any true statement is true (just start with the axioms and start cranking out theorems until you get to the right one). However, there is no methodical way of telling that a given statement is false; one can tell that certain statements are false, but there is no single method (however complex) which works for all false statements. However, this is a problem for formalizability, not reason. A person could conceivably come up with an unlimited number of ways of showing propositions to be false; this is where creativity comes in. All of these ways are rational, there just is no single method of judgement. Thus, neither modernism with its criterion of methodology nor postmodernism with its avoidance of reason have it entirely correct.

As Lucas puts it,

Reason is creative and original. It goes beyond antecedently established canons of right reasoning. And it can do so in a personal way, so that one man's original insight may differ from another's without either being wrong. Just as different men, using different codings, may pick out different Gödelian formulae, each of them true, so in other disciplines too, different thinkers may develop the subject in their own individual ways without any of them being necessarily wrong. We have been too long in thrall to a monolithic view of reason, supposing that it must yield just one right answer valid for all men in all places and at all times. And then we have felt that reason's uniform light obliterated all personal idiosyncrasy and individuality, and that real fulfilment was to be found in feeling and sensibility rather than rationality and common sense, and that the life of reason was a poor thing, cold and lacking all romance. But it is a false antithesis resting on a false view of reason. Reason not only can be original, but original in very variegated ways, well capable of accommodating the variety of individual genius.

Which I agree with in that the same truth may be expressed in multiple ways, or that truth can be complex and multi-faceted, though not (of course) in that there could be multiple truths or that truth is subjective.

On a side note, I've been playing some strategy games of late (most notably Go, along with Shogi (Japanese chess, which allows one to put captured pieces back into play on ones own side) and Xiang Qi (Chinese chess, which tends to be quicker and more aggresive than Western chess)). They're forcing me to think ahead and be patient rather than trigger-happy (which is a good thing that I sorely need). I found a rather interesting chess variant here: http://www.chessvariants.org/shogivariants.dir/taikyoku_english.html with a "playable" version here: http://taikyokushogi.hp.infoseek.co.jp/taikyoku.html. I have no idea how one would even start playing that....