May 16, 2011
taking the strap to Ockham’s razor
The obvious question to ask about Ockham’s razor is: why? On what basis are we justified to think that, as a matter of general practice, the simplest hypothesis is the most likely one to be true? Setting aside the surprisingly difficult task of operationally defining “simpler” in the context of scientific hypotheses (it can be done, but only in certain domains, and it ain’t straightforward), there doesn’t seem to be any particular logical or metaphysical reason to believe that the universe is a simple as it could be.
Indeed, we know it’s not.
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This presents a number of overlapping arguments–which perhaps demonstrates the importance of not decrying Ockham’s razor too strenuously. It is clearly true that the most simple and beautiful explanation in a given context can turn out to be dreadfully wrong. It is also true that a clear sense of moral imperative can lead to horrific actions. In both cases the issue is what is manageable? What will open one to no chance of meaningful actions, and what will suggest a path? The universe is, in my view, not shaped specifically to suit our need to understand it, but when action is required–economy and a sense of beauty still seem the best guides.
On another note–in America it is an untimely moment to make argumentative points by casting doubt on Ockham’s razor. Here the most fantastic sense of “possibilities” leads to millions voting against efforts to limit suffering.
Occam’s Razor is better quoted as “one should not multiply entities beyond necessity”. The important addition here is “necessity”. For instance, the Keplerian versus Copernican orbit example ignores the fact that predictions made on the Kepler model are much more accurate than their Copernican compatriots. General Relativity then puts them both to shame at the cost of significantly more complexity! Theories do not all explain with the same power, therefore you have the weigh simplicity against error. Occam’s Razor does not concern economy as much as probability.
(This is precisely the intuition of model comparison measures like the one Pigliucci mentions — the “in certain domains” link. They attempt to balance error in prediction against freedom of explanation of the model.)
The question of why follow Occamian principles remains, however. Some say it’s a consequence of probabilistic logic. I think I’m still with the camp that just likes it because it seems to work. In either case, it’s clear that adding more detail to an explanation can only make that explanation less likely, so it’s easy to say, at least very simple circumstances, that Occamian principles are unavoidable.
That all said, there is a growing interest in studying the principle of sparsity. I don’t know many of the developments here, but the suggestion seems to be that in “real” situations, using a tiny amount of very carefully chosen effort is more robust and economic than being thorough.
I think this is more a tool for parsing human psychology than for parsing the nature of the universe. Occam’s razor helps you throw out convoluted post hoc arguments created to try to make contradictory evidence fit your original hypothesis.