The Hedgehog, the Fox, and the Magister's Pox

by Stephen Jay Gould

  But, Whewell then adds, such colligation remains unexpansive (whatever the ice does literally!) in that, by simply repeating a set of identical circumstances over and over, and reaching a generality by induction from invariant results, we only learn a general something about a limited set of objects. We also need to recognize an inductive method that expands outward beyond repeated observation of the same set of occurrences. Hence, Whewell recognizes a second, more powerful, mode of observational inference that he terms “consilience of inductions.” Here we face a very different circumstance, frequently encountered in the natural sciences, and bearing the fascinatingly conjoined (and superficially opposite but actually reinforcing) properties of extreme frustration and great potential fruitfulness.

  Instead of twenty observations on the same cracking of rocks by ice—a bit boring, but at least leading to a clear prediction and explanation—we now face twenty entirely distinct and apparently disparate observations about a set of objects. But this bundle of facts looks like a total mess. Each may be true and interesting, but each has no apparent bearing upon any other; no thread unites these observations into any commonality. We may have a favored hypothesis about one of these events, but what can we do with the others, for none of these additional events speaks to this hypothesis in any evident way at all?

  But then we achieve the great insight for which Whewell invented the beautifully appropriate term consilience. We recognize that each and every one of these apparently disparate facts can, after all, be made to cohere—but (and now we state the distinctive feature of consilience), they can so join in one, and absolutely only one, possible way: that is, as consequences of the sole coordinating theory or explanation that could, in principle, bring them thus together into a single, simple, and elegant structure of explanation. Otherwise the facts only stand as disparate and unrelated items of information, with no coordinating or explanatory power beyond their independent existence.

  Now, does this kind of situation prove that the single conceivable coordinating explanation must be a correct theory for explaining the joint existence of this large and otherwise entirely incoherent set of facts? Well, such coordination of unrelated bits, as Whewell realizes, does not constitute a formal deductive proof for the proposed explanation. We cannot even say that the coordination corresponds to our usual notion of induction by simple enumeration (the repetitive observation that Whewell had called colligation). But we certainly get a powerful feeling that if one, and only one, kind of explanation can bring all these exceedingly diverse, yet undoubtedly documented, facts together—and no other cause could possibly account for the conjunction in principle—well, what can we do but conclude that this explanation ought to be treated as probably true, or at least as placing us upon a highly useful path to better understanding? What else can one say? At least we should advance potential truth as our hypothesis and try to challenge the explanation by predicting other (presently unrecorded) facts that this coordinating explanation ought to generate.

  But what should such a “jumping together” of disparate facts into a common structure of explanation be called? The English language contained no term for this distinctive and important concept, so Whewell took the usual Latin way out and named the process “consilience of inductions”—from salire, to jump, and con, together: in other words, the “jumping together” of items that appear to be so separate. (I must confess that I always liked Whewell’s word because it uses the same root as a famous Latin proverb, cited by Linnaeus, Leibniz, and Darwin as a keystone for their beliefs about natural processes, a conviction that led me to spend much of my career in opposition through studies of punctuated equilibrium and other modes of potentially rapid change in biology: Natura non facit saltum (nature does not proceed by jumps). In any case, Whewell defined both the meaning and superior power of his newly minted consilience of induction in the following two paragraphs (page 230):The evidence in favor of our induction is of a much higher and more forcible character when it enables us to explain and determine cases of a kind different from those which were contemplated in the formation of our hypothesis. The instances in which this has occurred, indeed, impress us with a conviction that the truth of our hypothesis is certain. No accident could give rise to such an extraordinary coincidence. No false supposition could, after being adjusted to one class of phenomena, so exactly represent a different class, when the agreement was unforeseen and uncontem-plated. That rules springing from remote and unconnected quarters should thus leap to the same point, can only arise from that being the point where truth resides.

  Accordingly the cases in which inductions from classes of facts altogether different have thus jumped together, belong only to the best established theories which the history of science contains. And as I shall have occasion to refer to this peculiar feature in their evidence, I will take the liberty of describing it by a particular phrase; and will term it the Consilience of Inductions.

  Whewell gave two primary examples of successful consilience in the triumphs of his nation’s greatest scientific hero: Newton’s undulatory theory of light and, especially, his inverse square law and the principle of universal gravitation. Whewell explains how Newton’s single principle encompasses all three of Kepler’s previously uncoordinated laws (pages 230–31):It [consilience of inductions] is exemplified principally in some of the greatest discoveries. Thus it was found by Newton that the doctrine of the attraction of the sun varying according to the inverse square of the distance, which explained Kepler’s third law of proportionality of the cubes of the distances to the squares of the periodic times of the planets, explained also his first and second laws of the elliptical motion of each planet; although no connection of these laws had been visible before.

  More important, Whewell adds, Newtonian gravitation provided a single, and mathematically precise, explanation for two kinds of motion that couldn’t seem more different in form or principle: the linear trajectory of an object (apple or otherwise) falling to the earth’s surface, and the basically circular motion of the moon around the earth. Whewell summarizes his examples with a lovely phrase from Herschel (page 232):The theory of universal gravitation, and of the undulatory theory of light, are, indeed, full of examples of this Consilience of Inductions. With regard to the latter, it has been asserted by Herschel, that the history of the undulatory theory was a succession of felicities. And it is precisely the unexpected coincidences of results drawn from distant parts of the subject which are properly thus described.

  Ironically—for, as we shall see, Whewell could not abide the later evolutionary theory of his former protégé Darwin—the establishment of evolution as the unifying principle behind the relationships and history of life provides the most instructive case for consilience in all of science. Indeed, I would argue (see Gould, 1986, and, especially, Gould, 2002, for more details than you will ever want to know) that the Origin of Species may achieve its most accurate sound bite of description as the most brilliant example ever constructed for the power and efficacy of consilience as a method of proof in natural history. Darwin could not “see” evolution by direct observation in the large (for any substantial change requires more time than humans have inhabited the earth), and he well understood that numerous cases of small change in observable time (breeds of pigeons or dogs, improvement of crop plants) do not prove that large transformations occurred by a similar natural cause. So Darwin used consilience as his primary method. With his unparalleled knowledge of natural history, and his remarkable skills in synthetic argument (he may not have been a great deductive reasoner, but I can think of no greater master of synthesis in the history of science), Darwin constructed the Origin of Species as a brief for evolution by consilience. In short, he argues: I present you, in this book, with thousands of well-attested facts drawn from every sub-discipline of the biological sciences—from the transitory and vestigial teeth of embryonic whales, to transitional forms in the fossil record, to the invariant order of life in geological strata throughout the w
orld, to documented cases of small-scale change in agriculture and domestication, to the use of the same bones for such different functions as a horse’s run, a bat’s flight, a whale’s swim, and my writing of this manuscript, to the observation that faunas of isolated oceanic islands always resemble forms of nearby mainlands, but only include creatures that can survive transport across the waters, et cetera, ad infinitum, through thousands of equally firm and disparate facts. Only one conclusion about the causes and changes of life—the genealogical linkage of all forms by evolution—can possibly coordinate all these maximally various items under a common explanation. And that common explanation must, at least provisionally, be granted the favor of probable truth.

  Moreover, Darwin explicitly attacks creationism most severely for its failure to forge consilience. Over and over again, Darwin tells us how evolution makes coordinated sense of a set of observations, whereas creationism can only regard each separate item as distinct and wondrous. In one passage—a rare expression of annoyance from such a genial man—Darwin explicitly compares creationism to the useless, and nonconsilient, idea once held by some premodern paleontologists that fossils, even though they look just like animals, must have a separate and unknown origin in the mineral kingdom. To provide the full context, Darwin demonstrates how evolution provides a simple and coordinated explanation for the various forms of striping found in the coats of all horse species—from the permanent and prominent coloration of zebras, to the occasional striping of aberrant horses, to weak bands of color that often appear in hybrids between unstriped species, to bands of color that sometimes form in juveniles but disappear in adult life—whereas creationist accounts, with their central premise of a disconnected origin for each species, offer nothing but empty verbiage about divine preferences for order or propensities to craft common signals as aids for human understanding. Darwin compares this lingering mysticism in creationist arguments with a standard caricature supported by describing the foolish delusions of early paleontologists (Darwin, Origin of Species, 1859, page 167):To admit this [creationist] view is, as it seems to me, to reject a real for an unreal, or at least for an unknown, cause. It makes the works of God a mere mockery and deception; I would almost as soon believe with the old and ignorant cosmogonists, that fossil shells had never lived, but had been created in stone so as to mock the shells now living on the sea-shore.

  Nothing so far discussed about Whewell’s concept of consilience bears upon any potential conflict between Ed Wilson and me on the relationship of science to the humanities. Nor can we yet grasp why Wilson revived Whewell’s word as the title for his book and epitomized description of his program. The resolution lies in the primary implication that Whewell then drew from his concept of consilience, and also regarded as the most important consequence of the idea beyond the basic formulation itself.

  In the next pages of his 1840 text, Whewell turns to the question of distinguishing true from false theories—and suggests a property of consilience as a chief criterion. Because consilient theories synthesize apparent mishmashes of large numbers of complex and independent items under the explanatory rubric of a single causal theory (and because consilience seems to point toward true explanations), an additional virtue of consilience should reside in this advantageous property of simplification itself. Therefore, a primary indication of good and true theories should lie in their capacity to simplify by subsumption and to harmonize by covering disparate items with a single coordinating explanation:We have to notice a distinction which is found to prevail in the progress of true and false theories. In the former class all the additional suppositions tend to simplicity and harmony; the new suppositions resolve themselves into the old ones, or at least require only some easy modification of the hypothesis first assumed: the system becomes more coherent as it is further extended. The elements which we require for explaining a new class of facts are already contained in our system. Different members of the theory run together, and we have thus a constant convergence to unity. In false theories, the contrary is the case. The new suppositions are something altogether additional;—not suggested by the original scheme; perhaps difficult to reconcile with it. Every such addition adds to the complexity of the hypothetical system, which at last becomes unmanageable, and is compelled to surrender its place to some simpler explanation.

  Whewell never exactly extends the argument to Wilson’s intricate marriage of reductionism and consilience, but I don’t deny that his words about the progress of unification in scientific theory point in that general direction. Whewell certainly identifies, as a major feature of consilience, the discovery that one class of facts achieves a better explanation under “another class of a different nature.” And, given reductionistic traditions that have always dominated modern science, no one could accuse Wilson (or anyone else, for I suspect that Whewell himself would have agreed, though he doesn’t say so directly) of misrepresenting the intent of this claim by assuming that, in general, the better “class of a different nature” will lie within a science located nearer to the periphery of Ariadne’s labyrinth (in Wilson’s interpretation)—that is, a more reduced science based upon properties of smaller constituent parts. For Whewell (page 238) describes “that great characteristic of true theory; namely, that the hypotheses which were assumed to account for one class of facts are found to explain another class of a different nature.”

  Again, Whewell may never tie his concept of consilience directly to a classic chain of reductionism, but the closing words of his chapter 5 surely argue that the continued application of consilience among theories will generate an overall simplification in the structure of scientific explanation—and that such a process leads toward unity by successive generalization. Thus, Whewell certainly links consilience with unification, as an actual consequence if not a logical necessity, in the overall chronology of a trend in science that he would surely have designated as progress (pages 238–239):Two circumstances . . . tend to prove, in a manner which we may term irresistible, the truth of the theories which they characterize: —the Consilience of Inductions from different and separate classes of facts;—and the progressive Simplification of the Theory as it is extended to new cases. [Note Whewell’s own emphases by his capitalizations and italics, here retained.] . . . The Consiliences of our Inductions give rise to a constant Convergence of our Theory towards Simplicity and Unity . . . successive steps by which we gradually ascend in our speculative views to a higher and higher point of generality.

  In the next chapter, on the logic of induction, Whewell then introduces a metaphorical image, based on consilience, but even more strongly linked to conventional chains of subsumption inevitably suggested by hierarchies of reductionism from maximally complex sciences of large and messy systems like human societies, right down to minimal and highly mathematical theories about a limited number of basic particles that construct all material reality. Whewell now introduces an explicitly genealogical metaphor linked to trees and tributaries flowing into a main river. He even, in one passage (page 244), speaks of “a Genealogical Tree of scientific nobility.” Whewell writes in his basic statement (page 241):By this means the streams of knowledge from various classes of facts will constantly run together into a smaller and smaller number of channels; like the confluent rivulets of a great river, coming together from many sources, uniting their ramifications so as to form larger branches, these again uniting in a single trunk. The genealogical tree of each great portion of science, thus formed, will contain all the leading truths of the sciences arranged in their due coordination and subordination.

  I do not think that Wilson adequately separates Whewell’s special meaning of consilience from the general, and far older, scientific procedure (or philosophy) of reductionism, but I surely won’t quibble on this point, if only because Whewell himself conflates the two concepts so frequently in stressing the simplifying and coordinating powers of both processes, albeit in their rather different ways (consilience by affirming a particular theory through its sol
e ability to coordinate otherwise unconnectable facts, and reductionism through its power to resolve complex phenomena by analysis to constituent parts whose simpler, more regular, or more quantifiable properties provide better sources for explanation).

  Still, as we shall see in the next section, Wilson really discusses reductionism when he advocates consilience as his basis for uniting the sciences and humanities—and reductionism cannot validate the argument, whereas Whewell’s own meaning of consilience, which Wilson uses correctly to analyze explanatory styles in science, cannot be extended into the humanities for reasons that Whewell himself emphasized (in other important writings) with a commitment as firm as his belief in the validity of consilience within science. But, for now, I must move on to a critique of reductionism and pull a MacArthur for consilience, to which, I promise, I shall return—for the logic works better in this disjointed sequence, as the inadequacy of consilience as an ultimate defense must follow the outflanking of reductionism as an initial strategy.

  THE ULTIMATE INADEQUACY OF REDUCTIONISM WITHIN THE SCIENCES

  Whatever my personal views about full or ultimate success, only a fool or an enemy of science could possibly deny the extraordinary power and achievements of reductionism since the beginning of the Scientific Revolution. Most of the technological accomplishment, and most of the theoretical success, of science emanates from this basic “instinct” for taking complex materials and concepts, breaking them down into smaller constituent parts, and then analyzing the parts, preferably in experimental and quantitative ways, to determine their regularities and, ultimately, the “laws of nature” underlying their repeated and predictable properties.