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.
let me start by setting your expectations low: I really know very little indeed about medieval philosophy, and what I do know isn’t about this area. I may easily just be missing the point about how simplicity principles were used in that context. And I am not an expert on the topic of simplicity in contemporary philosophy. Still, in part because I found this idea quite interesting, I hope you will humor my curiosity about the following point.
I am slightly worried about bridging the gap between a principle that we ought to *act* in simpler ways and an epistemic principle about the desirability of having beliefs with simple *contents*. Say we buy into an idea like: all else equal, the best way of doing some action is to do it while expending the least possible effort. (Or even the stronger claim about what the action is.) So now take an epistemic task, like coming up with a theory that accounts for a bunch of data; the principle says that the best way to do this is to form an account while expending the least effort. (Or, to account for the theory is, whatever else it is, to expend the least effort possible while satisfying the other parts of the definition.) But what is the justification for thinking that to do this will result in a set of beliefs with simpler content?
Worse than simply pointing out a gap, there seem to be prima facie examples where the theory that is easy to understand, believe, or use is not the one that is simplest or most elegant account. Consider a set of ”data” that is represented as a bunch of points on a plane (say we have some good reason to believe that the y-value depends on the x-value). Say we want to ”account” for it in part by fitting a curve to the points. It may take much less effort to just draw a piecewise function with straight lines in between the points (or a loose freehand smooth curve) than to come up with a mathematically elegant smooth curve that hits (maybe approximately hits) all of them.
Consider another case, one way in which objects attract one another. We explain this phenomenon with a physical theory, general relativity, which may be elegant and simple in some sense. But it is not simple in the sense that we expend little effort in grasping it, believing it (at least in a sense where believing something requires understanding it even roughly, not just outright deferral), or using it to account for the observed data. Our epistemic *actions* that involve the theory are not particularly simple, even if the *content* of the theory is simple.
Contrast this with a ridiculous theory of gravitation, on which object attraction is to be explained by the existence of invisible fairies that coordinate their actions to push around objects in a certain way. (Perhaps they even intend for the appearances to display a kind of regularity.) This seems like an easy theory to grasp and it does causally account for the data. There are various things you might say about why it is a bad theory to endorse, but I would predict that one thing at least some contemporary philosophers would say is that the theory posits many additional entities, and so our actual physical theories are in some relevant sense simpler.
Or (one more), think of the paranoid delusions of someone who is mentally ill and sees strange conspiracies everywhere: the person may have an answer to every objection, and may appear to be consistent in constructing a baroque global account of the world. But we (some of us) want to say that they are making very strange inferences from the observed data we agree with them about: they are making an inference to a bizarre explanation instead of to the best one. Constructing and believing such a theory may be difficult for *us*, but comes easily and naturally to *them*. But it seems wrongly parochial to insist that they should not have their beliefs because *we* find it easier to not use such a theory to account for the evidence. My hunch is that fans of simplicity principles are often hoping for something a bit more objective than amount of effort in this sense, for the principle is to justify our ability to criticize the crazy inferences as crazy and the resulting beliefs as likely false (not, say, inconvenient for our own use).
Although these are sorts of cases where people seem prone to wheel out a simplicity principle, in each of them it seems plausible enough that all else is not equal, or that those people were wrong to think that the theory that is intuitively better is so for a simplicity based reason. But is there a reason to be confident that there will be no such counterexample, at the end of the day?
Many thanks for your response! Your examples raise many worries, and rightly so. One worry seems to be that it’s unclear what counts as simple in the first place. But the worry that is perhaps most problematic with regard to my suggestion concerns the relation between (epistemic) action and content (of the theory proposed in such an action). You ask: “But what is the justification for thinking that to do this will result in a set of beliefs with simpler content?” – Several replies are possible it seems, but let me try to explain my initial idea.
While I don’t think that simple actions *necessarily* result in sets of beliefs with simpler *content*, I think that simple epistemic actions may well be taken to result in simpler *sets of beliefs*, i.e. sets with fewer beliefs. You might for instance think of Fodor’s “Principle P” to minimise accidents (given as an argument for the Language of Thought, see pages 287-288: https://www.ida.liu.se/~nilda08/CST-papers/Fodor.pdf ) So the basic idea is that making fewer assumptions (simplicity of action) might minimise accidents (epistemic merit). Of course, this is not an infallible idea, but it does seem to tie in with other principles, such as avoiding infinite regress etc.
As I said, I think that Ockham’s version of the principle is particularly hard to justify. The suggestion to link it to agency might not seem attractive, but going from the context of (divine) action it seemd not entirely unwarranted.
But I keep wondering whether there might already be some discussion amongst ancient philosophers.
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