The principle of parsimony

Many scientists or philosophers of science operate with two criteria: methodological naturalism and the principle of parsimony. They have other criteria as well. Right now I just wish to concentrate on simplicity, especially in terms of how that relates to methodological naturalism. 

Before proceeding, we need to say more about simplicity as a criterion in scientific theorizing. 

The view that simplicity is a virtue in scientific theories and that, other things being equal, simpler theories should be preferred to more complex ones has been widely advocated in the history of science and philosophy, and it remains widely held by modern scientists and philosophers of science. It often goes by the name of “Ockham’s Razor.” The claim is that simplicity ought to be one of the key criteria for evaluating and choosing between rival theories, alongside criteria such as consistency with the data and coherence with accepted background theories. Simplicity, in this sense, is often understood ontologically, in terms of how simple a theory represents nature as being—for example, a theory might be said to be simpler than another if it posits the existence of fewer entities, causes, or processes in nature in order to account for the empirical data. However, simplicity can also been understood in terms of various features of how theories go about explaining nature—for example, a theory might be said to be simpler than another if it contains fewer adjustable parameters, if it invokes fewer extraneous assumptions, or if it provides a more unified explanation of the data.There are many ways in which simplicity might be regarded as a desirable feature of scientific theories. Simpler theories are frequently said to be more “beautiful” or more “elegant” than their rivals; they might also be easier to understand and to work with. However, according to many scientists and philosophers, simplicity is not something that is merely to be hoped for in theories; nor is it something that we should only strive for after we have already selected a theory that we believe to be on the right track (for example, by trying to find a simpler formulation of an accepted theory). Rather, the claim is that simplicity should actually be one of the key criteria that we use to evaluate which of a set of rival theories is, in fact, the best theory, given the available evidence: other things being equal, the simplest theory consistent with the data is the best one.Many scientists and philosophers endorse a methodological principle known as “Ockham’s Razor”. This principle has been formulated in a variety of different ways. In the early 21st century, it is typically just equated with the general maxim that simpler theories are “better” than more complex ones, other things being equal. Historically, however, it has been more common to formulate Ockham’s Razor as a more specific type of simplicity principle, often referred to as “the principle of parsimony”...However, a standard of formulation of the principle of parsimony—one that seems to be reasonably close to the sort of principle that Ockham himself probably would have endorsed—is as the maxim “entities are not to be multiplied beyond necessity”. So stated, the principle is ontological, since it is concerned with parsimony with respect to the entities that theories posit the existence of in attempting to account for the empirical data. “Entity”, in this context, is typically understood broadly, referring not just to objects (for example, atoms and particles), but also to other kinds of natural phenomena that a theory may include in its ontology, such as causes, processes, properties, and so forth.It is important to recognize that the principle, “entities are not to be multiplied beyond necessity” can be read in at least two different ways. One way of reading it is as what we can call an anti-superfluity principle (Barnes, 2000). This principle calls for the elimination of ontological posits from theories that are explanatorily redundant.Mill also pointed to a plausible justification for the anti-superfluity principle: explanatorily redundant posits—those that have no effect on the ability of the theory to explain the data—are also posits that do not obtain evidential support from the data. This is because it is plausible that theoretical entities are evidentially supported by empirical data only to the extent that they can help us to account for why the data take the form that they do. If a theoretical entity fails to contribute to this end, then the data fails to confirm the existence of this entity. If we have no other independent reason to postulate the existence of this entity, then we have no justification for including this entity in our theoretical ontology.When the principle of parsimony is read as an anti-superfluity principle, it seems relatively uncontroversial. However, it is important to recognize that the vast majority of instances where the principle of parsimony is applied (or has been seen as applying) in science cannot be given an interpretation merely in terms of the anti-superfluity principle. This is because the phrase “entities are not to be multiplied beyond necessity” is normally read as what we can call an anti-quantity principle: theories that posit fewer things are (other things being equal) to be preferred to theories that posit more things, whether or not the relevant posits play any genuine explanatory role in the theories concerned (Barnes, 2000). This is a much stronger claim than the claim that we should razor off explanatorily redundant entities. The evidential justification for the anti-superfluity principle just described cannot be used to motivate the anti-quantity principle, since the reasoning behind this justification allows that we can posit as many things as we like, so long as all of the individual posits do some explanatory work within the theory. It merely tells us to get rid of theoretical ontology that, from the perspective of a given theory, is explanatorily redundant. It does not tell us that theories that posit fewer things when accounting for the data are better than theories that posit more things—that is, that sparser ontologies are better than richer ones.Another important point about the anti-superfluity principle is that it does not give us a reason to assert the non-existence of the superfluous posit. Absence of evidence, is not (by itself) evidence for absence.Consider the following list of commonly cited ways in which theories may be held to be simpler than others:

• Quantitative ontological parsimony
(or economy): postulating a smaller number of independent entities, processes, causes, or events.

• Qualitative ontological parsimony
(or economy): postulating a smaller number of independent kinds or classes of entities, processes, causes, or events.

• Common cause explanation
: accounting for phenomena in terms of common rather than separate causal processes.

• Symmetry
: postulating that equalities hold between interacting systems and that the laws describing the phenomena look the same from different perspectives.

• Uniformity
(or homogeneity): postulating a smaller number of changes in a given phenomenon and holding that the relations between phenomena are invariant.

• Unification
: explaining a wider and more diverse range of phenomena that might otherwise be thought to require separate explanations in a single theory (theoretical reduction is generally held to be a species of unification).

• Lower level processes
: when the kinds of processes that can be posited to explain a phenomena come in a hierarchy, positing processes that come lower rather than higher in this hierarchy.

• Familiarity (or conservativeness)
: explaining new phenomena with minimal new theoretical machinery, reusing existing patterns of explanation.

• Paucity of auxiliary assumptions
: invoking fewer extraneous assumptions about the world.

• Paucity of adjustable parameters
: containing fewer independent parameters that the theory leaves to be determined by the data.

http://www.iep.utm.edu/simplici/

One caveat: I think it's arbitrary to define simplicity as favoring bottom-up processes over top-down processes. If anything, a top-down process would be more economical. 

Suppose a cosmologist challenges a creationist to address evidence for the antiquity of the universe. Suppose a Darwinian challenges a creationist to address fossil evidence for the evolutionary narrative. Suppose a creationist responds by invoking mature creation or omphalism? That clearly violates methodological naturalism. 

Of course, since methodological naturalism is methodological rather than metaphysical, since it doesn't prejudge (much less prove) how nature actually operates, why should we care whether we violate methodological naturalism? Isn't science supposed to describe how nature actually works?

But for now I'd like to focus on another point. Although methodological naturalism conflicts with mature creation, it also conflicts with Occam's Razor. For mature creation satisfies several virtues of the simplicity criterion. It posits a single agent (God), a single process (divine fiat), a common casual explanation (fiat creation). It posits fewer causes, processes, and events. It posits fewer changes. It provides a unified explanation. It's consistent with the data. Divine agency is not explanatorily redundant. To the contrary, this furnishes an elegant, economical account with enormous explanatory power. Far more so than mainstream cosmology and paleontology. 

So we have conflicting criteria. Which takes precedence: Occam's Razor or methodological naturalism? 

Likewise, suppose a Darwinian challenges a creationist to account for the genetic and morphological similarities between certain organisms? Suppose he points to a continuum of intermediate forms? Suppose the creationist responds by invoking the principle of plenitude. God chose to make a world with maximal variety. That, in turn, entails continuity and gradation. 

Now that clearly violates methodological naturalism. Yet appealing to a divine intention to make a world in which most-all compossible combinations are exemplified satisfies several virtues of the simplicity criterion. Far more so than the evolutionary alternative, with its wasteful, inefficient version of natural history.