Abstract
Many scholars claim that a parsimony principle has ontological implications. The most common such claim is that a parsimony principle entails that the “world” is simple. This ontological claim appears to often be coupled with the assumption that a parsimony principle would be corroborated if the “world” were simple. I clarify these claims, describe some minimal features of simplicity, and then show that both these claims are either false or they depend upon an implausible notion of simplicity. In their stead, I propose a minimal ontological claim: a parsimony principle entails a minimal realism about the existence of objects and laws, in order to allow that the descriptions of the relevant phenomena contain patterns.
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Notes
Some substantive alternatives include defining simplicity as degree of falsifiability (Popper 1959) or informativeness (Sober 1975). These accounts need not be inconsistent with the claims that I make here regarding the ontological simplicity and corroboration claims, but the notion of simplicity that I use is meant to be intuitive and not revisionary. Also common in the literature are semantic shifts. For example, Simon uses the term “simplicity” ambiguously, so that the “complexity” and “simplicity” of measurements is the quantity of measurements that we have; and the “complexity” and “simplicity” of a theory is the size of our best current theory. He then defines parsimony as the ratio between these two (2001: 35).
Adolf Grunbaum excoriated this view, and in so doing seemed to agree with Swinburne’s adoption of the ontological simplicity claim: “WHY should we suppose at all, let alone avow a priori, that the overall simpler of two rival theories is more likely to be true?” He characterizes this view as “this dogma of the ontological simplicity of the world” (2008: 188; emphasis in original). Swinburne’s account of parsimony is confused, as in the space of a few pages he offers several versions of a parsimony principle which are not equivalent (and at least one of which is inconsistent with the parsimony principle which I propose here); however, the one version of a parsimony principle that Swinburne’s arguments depend upon is comparative, and all of the proxy measures for simplicity that Swinburne offers are unbounded (see 1997: 24ff), and so his ontological simplicity claim is inconsistent with his own parsimony principle, as is shown in the arguments that follow below.
Part of my point here is a basic but often overlooked fact. Science may explain (in some sense) all of nature without predicting all facts from laws alone. We can see that this is so from several kinds of cases. First, there may be brute historical facts that never fall under the purview of the sciences. For example, in a steady state universe of infinite duration, each historical event might be wholly explained by scientific reason and the observation of prior events. However, there would be no way to predict some particular events without referring to prior events—that is, science alone could not predict the relevant events, but only scientific theory coupled with historical facts. Or, if there is some randomness to the universe, or if the historical facts of the universe were very complex, then as a practical matter we will need to refer to (typically recent) historical facts as contingent natural events that cannot be determined by theory alone. We respect this principle without reflection in normal scientific practice; we do not think it a failure of ecology, for example, that it cannot predict how many leaves are in some particular forest, or a failure of astronomy that it cannot predict how many planets unobserved stars must have, and so on. Second, if there is any randomness in the universe then that randomness by definition is not predictable. And, third, if it were possible to create collections of descriptions of randomly made and unrelated observations (which seems self-evidently possible), then such observations are not the stuff of scientific theory. In each of these cases the phenomena which are not entailed by theory alone are not unnatural, otherworldly, unreal, or outside our universe. And thus, those who believe there is some kind of implication from parsimony to simple phenomena would be unjustified in assuming anything stronger than what I have called the general ontological simplicity claim.
Causus rerum naturalium non plures admitti debere, quan quae et verae fint et earum phaenomenis explicandis sufficient. Dicunt utique philosophi: Natura nihil agit frustra, et frustra fit per plura quod fieri potest pauciora. Natura enim simplex est et rerum causis superfluis non luxuriat. (Regula 1, 1726 edition)
A standard overview is Li and Vitanyi (2008).
Kolmogorov complexity does have two limitations: it is undecidable for any arbitrary description how Kolmogorov complex that description is (this means there is no algorithm that can effectively determine the Kolmogorov complexity of any arbitrary description); and Kolmogorov complexity as defined is highly idealized and assumes noise-free observations. Too much can be made of these limitations. Much of math is undecideable (that is, for many mathematical problems there is no algorithm that can solve any arbitrary instance of that kind of problem), but we are not about to drop those techniques as tools. We simply use them in the decidable cases, and turn to best estimations in the other cases. Similarly, it does not follow from this undecidability that we cannot, given two particular descriptions, determine which is less Kolmogorov complex than the other. Also, noise-free observations are an idealization that must always come into scientific theories at some point. No theory escapes this idealization.
In order not to be misled by an illustration like this, it is important to note that although we should presume that if the theory is a mature and successful theory for the phenomenon, then it will be about as complex as the phenomenon, it is not the case that if the theory is about as complex as the phenomenon, then the theory is adequate for the phenomenon.
Russell saw this view of objects as a consequence of neutral monism. It is beyond the scope of this paper to assess, but still interesting to raise the question of, whether neutral monism entails an ontology like this. If it does, then neutral monism would be inconsistent with the parsimony principle, and those of us who adhere to the parsimony principle would have a reason to reject neutral monism.
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DeLancey, C. Does a Parsimony Principle Entail a Simple World?. Int Ontology Metaphysics 12, 87–100 (2011). https://doi.org/10.1007/s12133-011-0078-2
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DOI: https://doi.org/10.1007/s12133-011-0078-2