During a recent workshop in Bucharest I asked the participants to connect two dots on a piece of paper.* Guess what! They all chose the simplest way of doing it and drew a perfectly straight line. This is perhaps not surprising. What I would like to suggest, however, is that this example might hint at a neglected way of understanding what is often called “Ockham’s razor”, the “principle of simplicity” or the “principle of parsimony”.
Along with the principle of non-contradiction and the principle of divine omnipotence, the principle of parsimony counts as one of the crucial principles in Ockham’s thought. Without much ado, he applies it to underpin his semantics, epistemology and ontology. But how, if at all, is the principle justified?
As Elliott Sober points out in a widely circulated article, the justification of Ockham’s razor and its variants is a matter of continuous debate. Already in medieval discussions we encounter the simplicity principle long before Ockham and in a number of contexts. Echoing the Aristotelian idea that nature does nothing in vain, much of the debates before and after Ockham are about the question whether the principle is founded on natural teleology. But Ockham, of all people, does not seem to offer any justification.
As I see it, the crucial context for this question is the debate about divine action and power. Comparing, for example, the positions of Thomas Aquinas and William of Ockham, we can clearly see two contrary versions of the simplicity principle. Aquinas endorses a teleological version, when he states that “Deus et natura nihil frustra faciunt” and that “natura non facit per duo, quod per unum potest facere.” Now, as is well known, Ockham often uses the simplicity principle in a merely explanatory sense when he writes, for instance: “frustra fit per plura quod fieri potest per pauciora”. Indeed, Ockham directly contradicts the claim of natural simplicity when he states that “frequenter facit Deus mediantibus pluribus quod posset facere mediantibus paucioribus, nec ideo male facit, quia eo ipso quod iste vult, bene et iuste facit.” (In I Sent., d. 17, q. 3)
So Ockham tells us that God often violates the principle of simplicity and takes diversions, even if there might be simpler ways. Now Ockham also clearly sees that, in claiming this, he might contradict the usual justification of simplicity. This is why he adds that God, in taking diversions, does not act without justification or badly. Rather it is the other way round: the fact that God wills to act thus and so makes it the case that it is good and apt.
What’s going on here? Although the distinction between rationalism and voluntarism is often misleading, it might help to use it for illustration. Aquinas is a rationalist, which means that for God reason is prior to will, not the other way round. God acts out of reasons that are at least partly determined by the way natural things and processes are set up. Doing “nothing in vain” means not to counter this order. Ockham takes the opposite position: something is rational or right because God wills it, not vice versa.
Now this result seems to render Ockham as an outright opponent of what is called Ockham’s razor. For if God sets the standards and God might often will complex diversions, there seems to be not only no justification for the simplicity principle, rather Ockham’s idea seems to undermine any epistemic value it might have.
So is there any non-teleological justification of the simplicity principle that Ockham could invoke? I think there might be an option once we consider the formulations of the principle. In the literature, discussions of the simplicity principle often concentrated on the nouns “natura”, “deus”, “entia”, “causae rerum” etc. But “frustra” is used as an adverb; it qualifies “facere”, “agere”, or “ponere” – making, acting, making assumptions. The point I want urge, then, is that the razor is about action. If you do something, there is a simple way of doing it. This would make it a principle of means-ends rationality as opposed to the divine or natural simplicity that Aquinas relies on.
While the natural-teleological version of the simplicity principle seems very much at home amongst fairly laden principles such as the principle of sufficient reason or the principle of the uniformity of nature, Ockham’s razor seems to be resonating with a different set of principles, such as the idea that explanations have to end somewhere and that infinite regresses should be avoided. These principles weigh with us not solely because we might reach an epistemic goal. Sometimes we don’t, and then we have to practise epistemic humility or agnosticism. It often makes sense for us limited beings to act with as little effort as possible, but it’s not always conclusive.
Connecting these ideas to the discussion about divine action might be insightful. Ockham contends that God can do things in complex ways without acting improperly. The upshot might be that humans cannot do this in the same way, since the human will does not set the norms of how things should be. Thus, for us, it is important to come to an end, not in the natural-teleological sense but in the profane sense of finishing or stopping.
You might say this is too profane to justify the principle. But maybe the point is conceptual. Maybe the simplest way of performing an action is what defines a certain type of action in the first place. As soon as you pick a more complex way, you do it improperly, unless you are God. So if you’re asked to combine two dots, you might think the goal is to combine them in a perfect way, whatever that might mean. But you might also assume that the point is to get it done with the least effort. And if you take a diversion, you do it improperly. One might even argue that a diversion constitutes a different action altogether. Combining three dots is different from combining two.
In any case, I hope to have pointed to a promising way of justifying Ockham’s razor (in the medieval discussion) without invoking a supposed simplicity in nature. As I will begin to run a project on the simplicity principle in medieval and early modern philosophy soon, I would be very grateful for any kind of feedback.
*Thanks to the participants of this workshop I now can connect a few more historical and conceptual dots. Special thanks to Peter Anstey, Laura Georgescu, Madalina Giurgea, Dana Jalobeanu and Doina-Cristina Rusu as well as to many of my colleagues in Groningen.