Wed Nov 7, 2007
234 Moses Hall, 6–8 PM
|Working Group in the History and Philosophy of Logic, Mathematics, and Science
Kevin Kelly (Carnegie Mellon University)
Truth-conduciveness Without Reliability: A Non-theological Explanation of Ockham’s Razor
Science could not get far without a systematic bias in favor of simpler theories, often referred to as “Ockham’s razor”. Indeed, no longer is such a bias a matter of the private “bon sense” of the individual theorist—it is now very publicly implemented in the most advanced statistical and computational techniques for inferring theories and causes from empirical data. But none of the recent technical literature resolves the most obvious puzzle raised by such practice, which is, to echo the Meno paradox: if we already know that the truth is simple, we don’t need Ockham’s razor and if we don’t, then why should we suppose that Ockham’s razor is truth-conducive? In his Monadology, Leibniz embraced the first horn: knowledge that God exists implies that he would make the best (most elegant) world. In an amusing twist, Robert C. Koons has reversed the implication, arguing that if Ockham’s razor produces scientific knowledge, it must have at least some supernatural assistance. I agree in spirit with Koons’ argument, but I view it as a reductio against the thesis that truth conduciveness must imply naturalistic reliability or truth-tracking, rather than as a proof that God exists. Instead, I propose that Ockham’s razor is optimally certifiably truth-conducive even if it is unreliable or fails to track the truth. The idea (theorem) is that Ockham’s razor converges to the truth under the least certifiable bound on reversals of opinion prior to convergence, no matter how complex the truth happens to be. That raises an interesting question about whether scientific knowledge must be produced by a reliable or truth-tracking method. If so, an awkward incoherence arises within science: everything we see and do could be the same, but knowledge implies the existence of a hidden, chance correlation between simplicity and truth. Thus, attributions of scientific knowledge produced by Ockham’s razor violate Ockham’s razor!