A corollary to Occam's Razor

The law of parsimony, otherwise known as Occam's Razor, tells us that “among competing hypotheses, the one with the fewest assumptions should be selected”. In other words, if we have various possible options that explain equally well an event, the simplest is the most probable.

This idea has been around for centuries, used by philosophers and scientists to guide their explorations of the universe. It is not a scientific law, but a principle. You could even say it's a belief, one that could be wrong. But the fact is that its validity has been observed continuously for a very long period of time.

For example, a few centuries back, Europe was struggling with that idea that the Earth might orbit the Sun, instead of the other way around – the Copernican model. Another competing system was presented by Tycho Brahe, the Tychonian model, in which Earth stood still while the Sun orbited the Earth, and the various planets orbited the Sun.

It's been said those systems account equally well for the perceived movements of the planets, and let's assume so: they have equal explanatory power. Then why we believe Capernicus is right and Tycho is wrong? Both postulated circular orbits and were equally simple in principle. But in fact, Tycho had the upper hand because the Copernican model still had to explain why we don't feel the Earth move, and why we don't observe the parallax of stars. Has Occam's Razor failed us?

Not at all. That's because there are two ways to evaluate simplicity: it can be structural or ontological. The structural one is easy. If Tycho's model required more orbits and epicycles (in other words, if it had to bend over backwards to explain observations), then it would be more complicated. The ontological one is more interesting though. Ontology deals with the fundamental nature of beings. To be ontologically simple is to basically say 'there's few kinds of things'. To be ontologically complex is to say 'the are multiple kinds of fundamentally different things'.

Tycho's model required us to believe there are three distinct categories of bodies: an immovable Earth, a light emmiting Sun that binds the other planets, and the other planets. Copernicus required us to believe in two kinds of bodies: a heavy light emmiting Sun, and planets. The complexity of Corpernicus model is structurally the same, but it is ontologically simpler.

This is valid for numerous other theories where advanced mathematics (structural complexity) is necessary to understand an underlying simple model (ontological simplicity). Not only the ontological corollary follows from Occam's Razor, but it is necessary for it to apply.

Occam's Razor: among competing hypotheses with equivalent explanatory power, the one with the fewest assumptions should be selected.
Corollary: hypothesis ontologically simple are preferred to hypothesis ontologically complex.

In a meta-analysis, to postulate a new way to analyse speech amounts itself to new ontological complexity. But let me try to clarify this potential contention. The power to explain the universe doesn't make a theory true, but only more likely. Secondary problems derived from the theory don't make it false, but only less likely. Finally, complexity doesn't make a hypothesis false, be it structural or ontological complexity. Both make it less likely. Occam's ontological corollary makes Occam's Razor more complex, but with more explanatory power. Of course, this leaves us with the question, is structural or ontological complexity preferable in a hypothesis?