Constitutive vs. Regulative Concepts

This interview is trivial. This guy never seems to say anything substantive about math or philosophy, but there was one thing he said that I knew was just plain wrong:

Netz: That's the question really: Do things exist?! There are many people who say that we should adopt what's known as Occam's razor—namely, don't assume things that are not necessary. Very often this is taken as an argument in philosophy. If you can produce something without a particular assumption, then don't assume the existence of this particular assumption. If you can do without it, better assume it doesn't exist.

I actually don't see the validity of Occam's razor. I think that things can exist even if they don't serve any purpose. My tendency is to be pluralistic. Yeah, I think infinity is a coherent concept. I think I tend to like it. So yes, I tend to believe that infinities exist—all of them, all the way up.

This represents a fundamental misunderstanding of Ockham's Razor and a great opportunity for me to digress on a philosophical distinction - the distinction between constitutive and regulative concepts.

First, let's have Ockham's Razor stated clearly, instead of the paraphrases that often replace the original, twist its meaning, and confuse coherent thought about what the principle is supposed to mean. "Do not multiply entities beyond necessity." The idea here is that when we are giving an explanation of some phenomenon, the simplest explanation is to be preferred. If we can explain the falling of a stone to the earth as the product of one force, the force of gravity, this explanation is to be preferred over one that posits the existence of, say, hundreds of supernatural forces acting upon the stone in ways the visible manifestation of which appears as a falling stone. This is not to say that the second explanation might not be true, since it is possible to conceive a system of complex supernatural forces combining in just such a way that, every time they cause some effect, it resembles exactly what we would expect from a theory that relies on common-sense notions of physics.

This is the most misunderstood point of Ockham's Razor. The concept does not say that the simplest explanation is true or metaphysically the best, but simply that we ought to seek simplicity and not "multiply entities beyond necessity." Some people take this to mean that we ought not to multiply entities at all, and ought to adhere to monism, but this is false - if monism cannot give a coherent account of the universe, then positing more than one existence is not going beyond necessity but actually reflecting the necessity of a more complex explanation. But I've missed the point with which I started this paragraph - Ockham's Razor does not, as Dr. Netz seems to imply, preclude the existence of seemingly superfluous entities but merely advises us not to seek for more entities than are necessary. This makes Ockham's Razor regulative, whereas he mistakes it for a constitutive concept.

What's the difference? Well, a constitutive Ockham's Razor would say "The simplest explanation is true" whereas Ockham's Razor as it is says "Seek simplicity in explanations." Ockham's Razor is a regulative guide that keeps up thinking in certain ways without claiming to know that this way is better. It is just more useful to seek simplicity. Constitutive concepts say "This is how things are" whereas regulative concepts say "Use this principle as a guide in your research."