Building Better Beliefs - Science as a Mode of Critical Thought

"Nature ... is not always noted for its parsimony." - Donald A. Dewsbury

In this post, I want to follow up on my previous comments regarding simplicity and the dubious role it plays in the unificationist agenda for science. At no point in that discussion did I refer to Occam's razor (or the Law of Parsimony, as it is sometimes called), and this was a peculiar oversight on my part given its central place in the unificationist playbook. In fact, while few unificationists would ever explicitly identify themselves as such (the label being more of a shorthand used by philosophers of science), the majority will almost certainly invoke Occam's razor at some point in their career, so much so that it has become a standard fixture in the dramatic depiction of science-types (or their adversaries) in popular drama, due in large part to the success of the film adaptation of Carl Sagan's Contact. Noteworthy mentions since then include The X-Files (Season 8, Episode 4, "Patience"), Scrubs (Season 7, Episode 1, "My Own Worst Enemy"), House M.D. (Season 1, Episode 3, "Occam's Razor"), and The Big Bang Theory (Season 1, Episode 9, "The Cooper-Hofstadter Polarization").

Okay, so what is this rule? This is a deceptively simple question, as I intend to demonstrate, but in a nutshell, it is the application of the principle of economy ("never do for more what you can do for less") to explanatory matters: "Plurality [in explanation] should never be posited unnecessarily." The rule takes its name from the 12th Century philosopher William of Ockham, though he was hardly the first to suggest it; it can be traced back to influential Hellenistic philosophers like Aristotle and Ptolemy, and variants of the rule were in wide circulation during Ockham's time, as well.

Since then, several well-known figures in science have given expression to the rule, or at least to rules that resemble it. This includes Isaac Newton's "we are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances," Ernst Mach's "scientists must use the simplest means of arriving at their results and exclude everything not perceived by the senses," and of course the Einsteinian pseudepigrapha that "everything should be made as simple as possible, but not simpler." It also includes various expressions of the tenet that "extraordinary claims require extraordinary evidence," made popular (once again) by Carl Sagan (Cosmos, Episode 12, "Encyclopedia Galactica").

At face value, the proliferation of paraphrases of the rule in both academic and popular media might be taken as an indicator of the rule's power and centrality in scientific practice. Careful consideration of their wording, however, betrays a considerable degree of conceptual disparity between them, worthy of further consideration:

While some versions of the rule focus on the number of "moving parts" included in the causal account, others focus instead on the plausibility or credibility of these parts regardless of number (Newton's "admission of causes that are true"; Mach's "exclusion of everything not perceived by the senses"). Some articulations of the rule dodge such considerations simply by insisting on the "simplest" explanation.
Among the versions of the rule that focus on the plausibility or credibility of the cause, these vary between expressions that treat "credibility" as if sharply divided between known and unknown (e.g., Newton's "admission of causes that are true") and those that are relatively more liberal in their allowance for a range of confidences in the truth of various claims. The fictional and ever-entertaining Dr. House ascribes to the latter: "Why is one simpler than two? It's lower, it's lonelier, but is it simpler? Each one of these conditions is about a thousand to one shot. That means that any two of them happening at the same time is a million to one shot. [Dr.] Chase says the cardiac infection is a ten million to one shot, which makes my idea ten times better than yours." In other words, any explanation involving a joint probability of two relatively uncommon conditions is still vastly superior to one involving a single probability of an incredibly rare condition, or in the words of Dr. Cox, "if you hear hoof beats, you just go ahead and think 'horseys'" (unless, of course, you happen to live in zebra country):

The tenet that "extraordinary claims require extraordinary evidence" is also an extension of this perspective, because our sense of a claim's plausibility is subject to change as new information comes in, though not by much unless the information is strongly in the opposite direction of prior belief.
While some versions of the rule assert that adherence is more likely to yield correct explanations, or even that contrary explanations cannot be true, others simply assert that such adherence is "better" without saying why, and yet others dispense entirely with the effort to justify adherence.
Only a few versions suggest that the process of simplification can be taken too far. For example, Okham's "do not posit unnecessarily" suggests that some degree of plurality in explanation is desirable. Similarly, the pseudo-Einsteinian "but not simpler" suggests that oversimplification is just as grave a mistake as is needless complexity.
A careful reading of Newton's version of the rule reveals that it is not concerned with efficiency at all but instead with the plausibility and sufficiency of the causal account on offer; if the posited causes are unlikely to produce the effect in question, or if their truth is in doubt, then the account fails no matter how many or few are suggested.

Deeper into the quagmire of Occam's ambiguous rule

In scientific practice, alleged adherence to the rule likewise masks multiple, qualitatively distinct practices. To illustrate what I mean, I introduce to you one of the tools that logicians use to evaluate the validity of certain kinds of arguments. The tool of which I speak is known as 'predicate logic,' and it belongs to a larger logician's toolkit, 'symbolic logic,' which is similar to symbolic algebra in that both describe relationships between variables of unspecified value by combining letters (representing the variable under investigation) and operators (representing their relationships), according to specific rules constraining their possible combinations.

Predicate logic is made up of elements that take the form 'Px', where x stands for the subject of a proposition and P stands for the predicate of the proposition (i.e., the part of the sentence describing the subject; essentially Px means "x is P"). When it comes to formulating expressions in predicate logic that adequately capture the conceptual structure of explanations, we need to combine statements about some earlier, causal condition - something like Cx - with statements about some later, outcome condition or effect - something like Ex. Specifically, we can combine such statements in one of three possible conditional statements. (Conditional statements relate two statements in an "if, then" manner). However, choosing the right combination to accurately convey our causal concept takes some careful consideration. These are the three candidates:

Cx → Ex: "if situation x exhibits condition C, then it will exhibit condition E."
Ex → Cx: "if situation x exhibits condition E, then it will exhibit condition C" (or in other words, "only if situation x exhibits condition C will it exhibit condition E").
Cx ↔ Ex: "if and only if situation x exhibits condition C will it exhibit condition E" (or vice versa).

The first statement establishes a characteristic outcome-state for situation x, E, given that it previously exhibited condition C. In this formulation, Cx is identified as a 'sufficient condition' for Ex to be true, and this is very different from an alternative and rather vacuous statement

Cx → (Ex ˅ ~Ex): "if situation x exhibits condition C, then it will either exhibit condition E, or it won't."

The second statement, on the other hand, gives condition C exclusive access to condition E: if we see that condition E characterizes situation x, then situation x must formerly have been characterized by condition C. In this formulation, Cx is identified as a necessary condition for Ex to be true (if Cx is not true, then neither is Ex). Finally, the third statement, known as a biconditional statement, establishes a doubly exclusive relationship between C and E, such that Cx is both a necessary and sufficient condition for Ex.

The first inferential activity masquerading as Occam's razor involves favoring Cx as both a necessary and sufficient condition for Ex, in other words favoring the biconditional formulation above. If we attach an index to C in order to distinguish between alternative, mutually exclusive causal accounts, C_ix, where 'i' is a placeholder for a specific C, then the statement "C₁x ↔ Ex" precludes alternative conditional statements linking C₂x to Ex. In other words, if it is true that situation x will exhibit condition E if and only if it had previously exhibited condition C₁, then it is false that situation x had previously exhibited some alternative condition C₂.

All of the above formulations, however, apply only to a single subject, the situation symbolized x. If a researcher wishes to expand the scope of their explanation using predicate logic to cover a set rather than a single subject, one of two additional statements is added:

(x)( ... ): "for every x, ...," where the ellipsis within the second set of parentheses is a placeholder for a logical statement (for example any of the three formulated above).
(Ǝx)( ... ): "for some x, ..."

Each of these formalities, known as the 'universal quantifier' and 'existential quantifier,' respectively, is used to extend the coverage of the statement within the second set of parentheses to a whole set of subjects, either the more inclusive "every x" when using the universal quantifier, or the more exclusive "some x" when using the existential quantifier.

Applying the universal quantifier to the third, biconditional, formulation above is the second practice masquerading as Occam's razor: "(x)(C₁x ↔ Ex)", in other words "It is true of every situation that, if and only if it exhibits condition C₁, it will exhibit condition E." In doing so, the researcher relieves him or herself of the need to consider novel causes for each newly described instance of Ex, since C₁x is both necessary and sufficient in every situation. In effect, this formulation globalizes the relationship between E and C₁, making a general principle or law of it and transforming subsequent explanations of C₁x into a highly redundant operation.

The next two practices subsumed under the heading of Occam's razor involve (1) the expansion of condition E to include multiple, qualitatively distinct effects, and (2) the suppression of condition C to include as few separate causal terms as possible:

(x)(C₁x ↔ (E₁x ∙ E₂x)): "it is true of every situation that, if and only if it exhibits condition C₁, it will exhibit both condition E₁ and E₂ (and E₃ and ...)."
~~(x)(C₁x ∙ C₂x) ↔ Ex): "it is true of every situation that, if and only if it exhibits conditions C₁ and C₂, it will exhibit condition E.~~

The first of these practices exhibits the same sort of economy as does killing two birds with one stone; it reduces the need to engage in novel explanatory efforts for every new phenomenon encountered. The second of these practices, on the other hand, is a formalization of the "minimal moving parts" imperative discussed above.

Abstraction, the fifth and final Ockhamian practice, involves expressing C and E in such a way that some degree of variation around an ideal is tolerated: "situation x exhibits something like condition C" or "situation x exhibits a condition similar to E." Inclusive expressions like these allow researchers to capture a significantly wider range of individual cases under their explanatory account than can a more rigid expression that demands an exact resemblance between them. Abstraction, in other words, allows researchers to pigeonhole nonidentical cases into lawful conformity, further reducing the need to produce novel explanations for every new case.

Some examples of Occam's ambiguous razor in the historical sciences

While Occam's razor is frequently treated as if axiomatically true and invoked to legitimate one or two of these practices at a time, it is rare to encounter a researcher ambitious enough to attempt all five at once. One exceptional example comes from archaeology (my home discipline): British archaeologist Colin Renfrew's explanation of the language geography of our modern world.

In several regions across the globe, clusters of languages bearing close affinities to one another enjoy wide geographic distribution. For example, the Indo-European languages (e.g., Hindi, Farsi, the Baltic, Slavic, Germanic, Celtic, Hellenic, and Romance languages) dominate the European linguistic landscape, as well as significant areas of Iran, Pakistan, Afghanistan, and India. Historical linguists have long argued that the shared traits characterizing many of these language clusters exist as a dwindling legacy of a shared linguistic ancestry, for example "Proto-Indo-European" (or PIE for short) in the case of the Indo-European languages. However, historical linguists also argue that the gradual disappearance of shared traits between related languages will eventually progress to such a degree that their family resemblance entirely fades away, after a threshold of perhaps no more than 8,000 years. Conversely, the family resemblance existing between the Indo-European languages is still discernible, suggesting that populations speaking different Indo-European languages have not been separated from one another for more than a few thousand years. Even so, Europe and Southcentral Asia have been occupied continuously for tens of thousands of years, implying that the Indo-European languages now spoken in these regions could not have descended from the languages originally spoken there by the populations living their tens of thousands of years prior. Instead, Renfrew argues, the establishment of the Indo-European-speaking communities currently occupying these regions must have involved replacement of older populations by an influx of PIE speakers within the last few thousand years. In Renfrew's account, this PIE population, practicing an agricultural economy and driven by the explosive population growth that such an economy supports, expanded out of its original homeland (perhaps in Anatolia, perhaps ~8000 years ago) to overwhelm the much more sparsely distributed hunter-gatherer populations previously inhabiting Europe and Southcentral Asia.

As Alison Wylie has argued, a central component of Renfrew's support for his account is an appeal to its parsimony, and he has certainly succeeded on this point, quite well. First, he has suggested that his account might take on global relevance if applied to the explanation of the geographic distribution of the world's other major language families (Occam's razor as universal quantification), dismissing alternative accounts in the process (Occam's razor as advocacy of necessary and sufficient causal relationships). Second, he has formulated his account in such a way that it explains not only the language geography of Europe and parts of Asia but also the emergence of agricultural economies in Europe, and tentatively the geographic distribution of genetic variabilty there, as well (Occam's razor as the explanation of many effects by a single cause). Third, by attributing these economic, linguistic, and genetic changes to a single process of population expansion and replacement, Renfrew has disfavored more eclectic causal accounts, for example involving a mixed process that includes the sharing of ideas and languages between neighboring groups in addition to population expansion and replacement (Occam's razor as suppression of causal terms; this book on contact-induced language change is an engaging read on contact-induced language change and may well be my favorite book ever). Fourth and finally, Renfrew's account explicitly concedes that the ongoing process of population expansion may have varied in detail as it unfolded (e.g., regarding the rate of population expansion, the degree to which expanding agriculturalists outnumbered hunter-gatherers, and so on; Occam's razor as abstraction).

Yet, despite the simplifying ambition of Renfrew's account, few archaeologists have actually been impressed by it. Wylie summarizes the numerous critiques that have accrued since the model was first advanced, these variously focusing on the empirical implausibility and the lack of "causal efficacy" (in other words, sufficiency) of Renfrew's account. In short, many archaeologists contend that his model runs slipshod over archaeological data and are quick to point out that these data necessitate an eclectic account. The virtue of simplification in this case is far from obvious.

Other examples of Occam's razor in scientific practice come from the contentious debate over the cause(s) of the Late Quaternary megafaunal extinctions. Between approximately 50,000 and 10,000 years ago, a number of large-bodied animal species in Eurasia, Australia, and the Americas went extinct, including mammoths and mastodons, woolly rhinos, giant marsupials, giant ground sloths, and a number of other large-bodied ungulates and predators. For decades, paleontologists and archaeologists have debated what might have led to this series of extinctions, with climate change and human impacts (including over-predation, habitat alteration, and the introduction of deadly, inter-specifically contagious diseases or "hyper-diseases") being the two main contenders. For some participants in the debate, causal accounts that suggest a combination of these various elements, or that the demise of some species owes to one factor while the demise of other species owes to the other, are regarded as "a relatively weak approach epistemologically; ... an admission of defeat rather than a breakthrough in understanding" (MacPhee and Marx 1997:209; Occam's razor as disfavoring multi-term causes). It is worth mentioning that MacPhee and Marx instead endorsed the hyper-disease hypothesis, which has been widely dismissed for its implausibility and insufficiency. Instead, at least some researchers are confident in their multi-cause stance.

Perhaps one of the most controversial accounts of the North American extinctions was Richard Firestone and coauthors' recent suggestion that one or more extraterrestrial (ET) bodies impacted the Laurentide ice sheet covering southeastern Canada during the last ice age, approximately 12,900 years ago, triggering the breaking up of the ice sheet, the climatic cooling episode known as the Younger Dryas (YD), megafaunal extinctions in the Americas (but not elsewhere), extensive biomass burning across North America, significant population depression and economic reorganization of the Paleoindians inhabiting North America, and the formation of a variety of distinctive geological deposits. In the primary article advancing this account, the authors offer the synchroneity of these phenomena as evidence congruent with the ET impact event.

Once again, however, few have found Firestone and coauthors' argument compelling, in large part because ET impact events in general have not been convincingly linked to any of the various lines of evidence cited by them and in part because few if any of their critics are impressed by the unifying power of this account alone. Instead, archaeologists, geologists, and paleoclimatologists have seen the article as a transparent play at grabbing attention and prestige for its authors. In an intellectual climate already strained by limited research funding, researchers dedicated to understanding Late Quaternary extinctions are instead vexed by Firestone and coauthors' sensationalism for its threat at diverting funding away from the pursuit of explanations based on more credible premises.

Occam's baby and Occam's bathwater

Simplification is not the epistemological virtue that unificationists claim it to be, as I argued in my previous post. It should by now be apparent that Occam's razor should do little to change our minds on this point, and many researchers have little patience for it (e.g., the quote with which I began this essay). To begin with, any impression of solidarity that the frequent invocation of the rule may give is spurious, given the multiple disparate intellectual practices that are lumped together under this single, equivocal heading. "The" law of parsimony, as it turns out, is an epistemological Mr. Potato Head, able to be remade into whichever visage best serves the researcher's argument.

As spurious as the rule may be as a mask, however, there is nothing obviously defective with any of the various practices that it lumps together. Rather, each one deserves careful scrutiny on its own. In so doing, we have no reason to expect that all will remain standing, but nor do we have reason to think that all will fall. What we want to ask of each one is, "will this practice point me toward more realistic and accurate understandings of nature/the universe? Why or why not?"

Biconditionality

Binding a particular cause to a particular effect together in a necessary and sufficient relationship certainly simplifies the labor of a researcher: the statement (x)(Cx ↔ Ex) means that, if he or she has encountered Ex, then he or she already knows what caused that state of x; Ex stands as a proxy for Cx, and explanatory accounts that are structured in this way are tremendously helpful in applied sciences, for example clinical diagnosis. When knowing the cause is critical to successful policy-making, medical treatment, or similar, possession of explanatory accounts like this are time-saving (and stress-, life-, and grief-saving) devices.

Be that as it may, such accounts are incredibly hard to come by. I don't mean that it is particularly difficult to formulate such accounts. In the internet age, where hypochondria meets WebMD, it is all too easy to find hypochondriacs thinking "all patients will develop a fever if and only if they have the bubonic plague." The ease of formulating such statements, however, is hardly virtuous, because establishing the empirical plausibility of necessary and sufficient relationships between cause and effect is a profoundly elusive enterprise.

The easy part, as it turns out, is establishing empirical support for statements with the following structure: (x)(Cx → Ex) ("every situation that exhibits condition C will exhibit condition E"). Causal accounts exhibiting this sort of structure are easy to demonstrate experimentally, a dime a dozen, really. The hard part is getting the arrow to point in both directions, because on the contrary, it is much easier to make paired observations like

(x)(C₁x → Ex) ∙ (x)(C₂x → Ex): "every situation that exhibits condition C₁ will exhibit condition E, but every situation that exhibits condition C₂ will also exhibit condition E."

In other words, we are all too aware that many phenomena of interest may be explained by either of two (or more) equally plausible, mutually exclusive causes. In archaeology, we refer to such unhappy circumstances as cases of 'equifinality' (a term borrowed from general systems theory), while geologists prefer the term 'polygeneity'. Equifinality is what makes drawing straightforward equivalences like "fever = bubonic plague" so misinformed and medically disastrous, instead warranting the much more complicated (and expensive) enterprise of differential diagnosis.

The solution is a lot of research, not Ockhamian flag-waving and offhanded dismissal of alternative explanations, even if it means sacrificing explanatory (and financial) efficiency. In differential diagnosis, this requires the prior establishment of symptom complexes or syndromes, combinations of signs and symptoms that are indicative of particular medical conditions:

(x)(C₁x ↔ (E₁x ∙ E₂x)) ∙ (x)(C₂x ↔ (E₁x ∙ ~E₂x)): "Every situation will exhibit conditions E₁ and E₂ if and only if it exhibits condition C₁, while every situation will exhibit condition E₁ but not E₂if and only if it exhibits condition C₂.

The research efforts involved in establishing these relationships fall under the heading of symptomatology, whereas the application of such knowledge falls under the general heading of diagnosis, including its differential variety. Note that the observation of a single symptom, in this case annotated E₁, cannot be explained unambiguously, even if both conditions C₁ and C₂ are sufficient to cause it. Instead, a successful diagnosis may require further evaluations of a patient (though this should be balanced with other considerations). As has been argued elsewhere, the invocation of Occam's razor to rule out explanations that do not make the same predictions is illicit, even if a part of their respective predictions is identical.

Archaeologists engage in a similar sort of reasoning: when confronted with situations of equifinality, when we really want to know which human activity led to the formation of an archaeological deposit, or if it was human activity at all, we need to draw on a body of knowledge that ties particular patterns of cultural debris to particular behavioral or natural processes. We call this body of knowledge 'middle range theory' or 'formation theory,' which is built from 'actualistic research' (including experimental archaeology, ethnoarchaeology, and computer simulation). Often, the archaeological reconstruction of past human activities and natural processes requires us to draw on multiple lines of archaeological evidence when single lines prove to be equivocal.

Universal quantification

While biconditionality is hard to come by in scientific research but still worth pursuing, formulating explanatory accounts that assume universal quantification is an essential requirement. Consider the alternative case of existential quantification:

(Ǝx)(Cx ↔ Ex): "There are some situations which will exhibit condition E if and only if they exhibit condition C."

This formulation is capricious and unreliable; it leaves us wondering which situations are covered by the explanation and which ones are not. In fact, on this point a logician would be quick to point out that the existential quantifier does not even rule out the possibility of universal quantification, but nor does it necessitate it; a universally quantified rule implies that the rule is also existentially quantified ("if all x are P, then some x are P, necessarily"), but an existentially quantified rule does not necessarily imply its universal quantification ("if we know that at least some x are P, then we cannot say for sure whether all x are P or not."). Statements involving existential quantification are useful tools for description, but when applied to the task of explanation, such statements leave us in the dark as to why certain situations should exhibit well-specified cause-effect relationships while others may or may not. Worse still, we might imagine a disingenuous researcher variously invoking and dismissing the applicability of an existentially quantified explanation to particular situations, conditional on self-serving motives rather than any honest concern for improving our understanding of nature.

Even worse would be the case of an unquantified rule:

Cx ↔ Ex: "The individual situation x will exhibit condition E if and only if it exhibits condition C."

The rationale in making such statements is entirely obscure: why is Cx necessary and sufficient for Ex in this one situation but potentially not in others? Such statements are entirely unsatisfying, and fortunately few researchers actually make such locally specific statements.

If we rule out these two alternatives for their indecisiveness and vulnerability to deceitful manipulation, we are left with universal quantification, with explanatory accounts that are meant to apply to every situation. It also makes the identification of empirically inaccurate explanations easy: if the rule "breaks down" in light of empirical data, for example if its applicability seems to be conditional on some other condition that is not included in its specification, then it is insufficient and needs to be reformulated accordingly.

Abstraction

In evaluating the epistemological merit of abstraction, we should be aware of the fact that this practice exists in essential tension with universal quantification and biconditionality. When the latter two practices are combined, in other words when our formulation of an explanatory account takes the form (x)(Cx ↔ Ex), we transform Ex into a decisive, diagnostic outcome of Cx, dodging the pitfall of making noncommittal statements like:

(x)(Cx ↔ (Ex ˅ ~Ex)): "If and only if any given situation exhibits condition C, it will either exhibit condition E or it won't"; or
(Ǝx)(Cx ↔ Ex) ∙ (Ǝx)(Cx ↔ ~Ex): "There are some situations that exhibit condition E if and only if they exhibit condition C, and there are some other situations that don't exhibit condition E if and only if they exhibit condition C."

However, when we deliberate insert an imprecise expression of E into the formulation (x)(Cx ↔ Ex), we sacrifice a degree of the decisiveness we originally gained by combining universal quantification and biconditionality. In theory, we might even accomodate for such a large degree of imprecision in the formulation of E that the noncommittal statement (x)(Cx ↔ (Ex ˅ ~Ex)) is the better fit, if we are being honest.

However, our willingness to engage in abstraction need not be seen as entailing a slippery-slope descent into explanatory impotence. In practice, this is rarely the case, because our allowance for imprecision is usually tempered by statistical constraint: "every situation that exhibits condition C will exhibit something like condition E, even if not condition E exactly, and not a condition very different from it." Imagine an experiment in which a group of lab mice are exposed to a performance-altering substance (the 'treatment group') while a second group remains unexposed (the 'control group'). When a mouse from one of these two groups is then placed in a maze, no individual from the treatment group completes the maze more quickly than any mouse from the control group. However, the time to completion does vary between individuals within each group. The results of the experiment are then formalized in terms of the following two causal accounts:

(m)(~Sm ↔ Om): "Any mouse will complete the maze in approximately one minute if and only if they have been exposed to the performance-altering substance."
(m)(Sm ↔ Tm): "Any mouse will complete the maze in approximately two minutes if and only if they have been exposed to the performance-altering substance."

While this example is hypothetical, real experiments often exhibit similar distinctions between groups, with limited or no overlap in the outcome. Such cases illustrate the fact that constrained imprecision in the expression of E does not necessarily weaken the explanatory power of an explanatory account; we still understand the world a little better when we understand that mice that are exposed to the substance in question suffer a disadvantage of time in navigating a maze relative to those who are unexposed. At the same time, we are being honest with the influence of a given causal condition on an outcome condition when we acknowledge the imprecision that characterizes its influence on time to completion. The realism that such statements permit, not their parsimony, is what should convince us to accept abstraction as a good practice in formulating explanatory accounts.

Diverse effects

Unlike universal quantification, biconditionality, and abstraction, the practice of subsuming explanations of multiple, qualitatively distinct phenomena under a single account has no merit. Renfrew sought to do so by linking the spread of agriculture and linguistic and genomic geographies to a single process of population expansion and replacement. Similarly, Firestone and coauthors sought to do so by linking American megafaunal extinctions, economic reorganization, climate change, and the formation of a handful of poorly understood geologic deposits to a single extraterrestrial impact. But why should we be impressed by such syntheses? On the contrary, we observe coincidences all the time in the course of our daily lives, and this ought to be reason enough not to be taken in by such grand syntheses. Instead, the burden is on the researcher to provide a convincing argument for why qualitatively distinct phenomena ought to be linked to a common cause.

Suppression of causal terms

There is also little reason to think that the number of premises involved in a causal account should be few in number. The question is not "how many working parts are invoked?" but rather "how plausible is the particular combination of working parts that has been invoked? (what is their joint probability?)."

My own work in archaeological demography focuses on identifying factors that influenced patterns of stability and change in the population growth rates of high-latitude hunter-gatherer populations of the past. The population growth rate is a net balance of the 'four flows' of demography - fertility, mortality, in-migration, and out-migration - and therefore any explanation for patterns of stability or change in a population's growth rate record must refer to a change in one or more of these flows. It would be convenient for me if I could pursue my explanatory efforts under the assumption that any observed change in my study population's growth rate was caused by a change in a single flow, but such singular changes are rare. Whatever factors have led to change in one flow have the stubborn habit of driving change in one or more of the others, as well. Changes in per capita subsistence productivity, for example, can influence fertility (with nutritional income bearing on reproductive health and/or decision-making), mortality (through deficiency diseases, compromised immune systems, and/or violence fueled by subsistence shortfalls), and/or migration ("stick around if food is bountiful; consider moving on to more productive lands if it is not"). Ironically, explanations for growth rate change that focus on changes in individual flows are frequently less plausible than those that focus on changes in multiple flows.

This example also illustrates another reason that most realistic (= plausible) explanations involve multiple terms. In thinking about the factors that influence population growth, the four flows are proximate determinants: any factor other than fertility, mortality, in-, or out-migration that has an influence on population growth must act through one or more of these four flows. Environmental change, predation, infectious disease, subsistence productivity, education, contraception, violence, genetic disorders, and other factors that might bear on population growth are thus most accurately conceived as distal determinants, and any explanatory effort focusing on such indirect influences must therefore include as many causal terms as it takes to adequately describe the chain of influences linking the indirect determinant of interest to population growth. This, I think, is exactly the sort of necessary plurality that Ockham had in mind when he warned against unnecessary plurality.

Newton's razor

In the end, there is no reason to pay such deference to Occam's razor as unificationists do. When it is invoked, the effect (at least for those who buy it) is to prevent a more thorough scrutiny of the plausibility and sufficiency of an explanatory account; instead, the target is a low cause-to-effect ratio, with lower ratios facilitating more redundancy in explanation. In the process, all manner of intellectual activities are offered as examples of good Ockhamian behavior, conjuring the impression of epistemological solidarity among those who invoke it, despite the demonstrable qualitative differences standing between these practices.

Newton's razor, on the other hand, has considerable appeal to it: "we are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances." Whereas Occam's razor is primarily a numbers game, Newton's makes no particular demand for economy but instead requires sufficient and plausible causes.

On the matter of sufficiency, it is important to distinguish between formal sufficiency and causal efficacy. From a strictly grammatical standpoint, it is easy to construct causal accounts that follow the form

(x)(Cx → Ex)

for example "pre-menopausal women who continue to live in close proximity to each other for extended periods of time will exhibit increasingly synchronized menstrual cycles over time." On the other hand, not all such constructions are equaling compelling. Many researches call this often-repeated account into question for its lack of causal mechanisms.

Establishing plausibility is a separate issue. We might conceive of causal accounts that make a lot of sense hypothetically but whose causal terms are unlikely to be true (= implausible). For example, it does not take any great act of imagination to envision a scenario in which the terrestrial impact or air burst from a large extraterrestrial object leads to a cataclysmic extinction event. This is the favored account for the extinction of the dinosaurs approximately 65 million years ago, and if popular entertainment is any measure of the credibility of mechanism in a causal account, the back-to-back release of Deep Impact and Armageddon in 1998 is a further indication of this scenario's general credibility. (On the other hand, the idea of menstrual synchrony is frequently enough repeated that popularity should not be treated as the final arbiter of sufficiency). Instead, what makes Firestone and colleagues' explanation of American megafaunal extinctions and economic and climatic change so unconvincing is that, despite centuries of geological, paleontological, and archaeological research in North America, none of the tell-tale symptoms of an ET impact at aprroximately 12,900 years ago have made themselves known. Instead, Firestone and colleagues make their case based on a round-up of nonspecific lines of geological, paleontological, and archaeological evidence. The medical analogue would be a clinician who diagnosis an unconscious patient with Hantavirus Pulmonary Syndrome based on the observation of a mild cough, split ends, and a swollen thumb. Such malpractice borders on gross negligence, and one would hope that censure, if not revocation of the clinician's medical license, would follow. Or, if you favor a less socially charged example, a healthy lawn may require watering, and lawns in rainy areas may do well on that count, but if I have a healthy lawn in a drought-stricken area, it's not because of the rain.

In short, what Newton's razor demands of any explanation, and what we should demand of it as well, is not that it is efficient but instead that it makes sense, not only in an abstract way (sufficiency) but also when it is applied to a particular case (plausibility). If Newton's razor saves us any effort, it is only as a side-effect: in shaving off the incredible from consideration, we don't have to waste the time, or limited research funding, investigating it.