Tuesday, December 20, 2005

Ockham's Razor in the Age of Statistics

In philosophy, ontology . . . is the most fundamental branch of metaphysics. It studies being or existence as well as the basic categories thereof—trying to find out what entities and what types of entities exist. Ontology has strong implications for the conceptions of reality. (From Wikipedia's article about "Ontology.")

[O]ntological parsimony. . . is summed up in the famous slogan known as “Ockham's Razor,” often expressed as “Don't multiply entities beyond necessity.” Although the sentiment is certainly Ockham's, that particular formulation is nowhere to be found in Ockham's texts. Moreover, as usually stated, it is a sentiment that virtually all philosophers, medieval or otherwise, would accept; no one wants a needlessly bloated ontology. The question, of course, is which entities are needed and which are not. (From an article about "William of Ockam" at Stanford Encyclopedia of Philosophy.)
The question of which entities are needed and which are not is today an empirical one. If phenomenon "A" can be explained by the observed operation of factors X and Y, then factor Z should be not be introduced to the explanation unless doing so leads to an unambiguously better explanation of A. Determining whether or not the explanation is unambiguously better requires a robust test of the predictive powers of the two competing theories: the one with X and Y as predictors; the other with X, Y, and Z as predictors.

Ockham's Razor, then, is a prudent, pre-statistical rule for choosing the preferred explanation of a phenomenon.