CPM Report No.: CPM-02-99
By: Bruce Edmonds
Date: 3rd June 2002
In this paper I will argue that, in general, where the evidence supports two theories equally, the simpler theory is not more likely to be true and is not likely to be nearer the truth. In other words simplicity does not tell us anything about model bias. Our preference for simpler theories (apart from their obvious pragmatic advantages) can be explained by the facts that humans are known to elaborate unsuccessful theories rather than attempt a thorough revision and that a fixed set of data can only justify adjusting a certain number of parameters to a limited degree of precision. No extra tendency towards simplicity in the natural world is necessary to explain our preference for simpler theories. Thus Occam's razor eliminates itself (when interpreted in this form).
I will start by arguing that a tendency towards elaboration and the pragmatic advantages are sufficient to explain our preference for simper theories. Then I will briefly look at a couple of a priori arguments justifying a bias towards simplicity. I follow this by reviewing some evidence as to whether simpler theories are likely to be true taken from the field of Machine Learning, followed by a section discussing some special cases where we have some reason to expect there to be a bias towards simplicity. I will briefly consider some of the concepts that have been called "simplicity" in the literature before I conclude with a plea for the abandonment of the use of simplicity as justification.