Inference to the Only Explanation: The Case of the Cretaceous/Paleogene Extinction Controversies

Abstract

In the sciences of the deep past, it is taken for granted that the hypothesis that offers the best explanation is the best confirmed. I examine in detail the debate over the K/Pg mass extinctions that began in 1980 with the publication of the paper by Alvarez et al. that proposed the impact extinction hypothesis. I summarize this debate and show how the impact hypothesis eventually achieved consensus as the best explanation. I then consider the relevance of that case study to an evaluation of the employment of inference to the best explanation (IBE) in the earth sciences. I first reject a number of the standard objections to IBE and then strongly endorse John Norton’s claim that no form of ampliative inference can receive a priori justification. Nevertheless, drawing on the case study and other instances, we may identify four “abductive virtues” that characterize many of the most successful instances of IBE, making them attractive and even compelling.

1. Introduction

Abductive reasoning or inference to the best explanation (IBE) has recently received a rigorous statement and defense [1]. That such forms of reasoning are commonly employed by scientists as one of many means for the assessment of theories is beyond question. Of the numerous prominent instances, perhaps the most famous application is by Charles Darwin in On the Origin of Species. Most of the facts cited by Darwin were already known to naturalists. So, Darwin’s case did not rest on new discoveries but, in Ernst Mayr’s words, offered, “…a novel integration of previously known facts. ([2], p. 856).” The “novel integration” was achieved by a theory that was highly consilient; that is, it united many seemingly disparate facts under a common explanatory scheme—descent with modification.

Numerous other historical and contemporary employments of confirmation by explanatory efficacy could be mentioned. For instance, astrophysicists postulated the existence of “dark matter” to account for various phenomena, such as the observed rotational velocities of galaxies, which differ dramatically from what would be expected if galaxies consisted only of familiar baryonic matter ([3], p. 172). Though dark matter had not been detected or identified (hence “dark”), by 1980, astronomers generally accepted some sort of cosmic dark matter model as the only plausible account of a large body of observations ([3], p. 172). Some dissidents proposed an alternative theory, Modified Newtonian Dynamics, which they also supported with IBE.

When a methodological practice has, for centuries, figured prominently, indeed essentially, in the performance of the most successful natural sciences, there can be no reasonable doubt that it is a rational procedure. But in what precisely does its rationality consist? Michel Janssen has suggested that IBE and, in particular, a subset of such inferences he calls “common origin inference” (COI) generally are not employed to confirm the truth of theories, but only their promise. A theory, like Darwin’s, that offers a simple explanation that unites diverse facts under a single explanatory framework is a theory that scientists should take seriously as offering a promising research program, but should not accept it as true (or truthlike) until more direct evidence is forthcoming. In the meantime, the inferences serve to incentivize further research into the theory’s credentials.

Here I shall contend that, in various fields of science, notably including many of the earth sciences, explanatory hypotheses that offer a compelling account of diverse data are commonly taken to be well-confirmed. Indeed, for such hypotheses, there may be no other means of confirmation than to establish that if the hypothesis is true, the data follow as a matter of course.

2. The Rationality of Science

The question, then, is how IBE figures into scientific rationality. What role has it played historically and in recent assessments of theories? My understanding of scientific rationality has been strongly shaped by two books, The Discourses of Science by Marcello Pera and Beyond Objectivism and Relativism by Richard Bernstein.

Pera argues that in their quotidian activities, scientists are largely engaged with the practical aims of confuting opponents and convincing colleagues ([4], pp. 46–51). Scientists practice rhetoric, not in the current sense in which “rhetoric’ is commonly identified with subterfuge, but in the classical sense of Aristotle’s Rhetoric, which is the art of employing the arguments that will be most convincing for the intended audience. Scientific discourse contains a great diversity of types of rational argument, including IBE as one type among many. Pera defends a “dialectical” sense of scientific rationality:

A theory T is rationally acceptable if and only if it is supported by valid arguments, or if the arguments supporting T are stronger than those supporting [competing theory] T’.

([4], p. 144)

Pera claims that this dialectical analysis of scientific rationality is more tolerant than a concept that ties rationality to a narrow set of methodological strictures, and it allows for a free-ranging debate that may invoke many distinct kinds of rational considerations. Further, it is more adequate than social constructivist accounts that appeal exclusively to extraneous social and political factors. In short, Pera holds that scientific communities converge over time on the theories that are supported by stronger arguments. Darwin (or his proxies) and Galileo confuted their opponents and convinced their colleagues.

In the Postscript (written in 1969) to the second edition of The Structure of Scientific Revolutions, and in various post-Structure writings (e.g., Kuhn 1977 [5]), Thomas Kuhn emphasizes that theory choice is rational but not in the sense that there are any systematic or algorithmic decision procedures. Rather, there are salient desiderata of good theories (accuracy, simplicity, etc.) that serve as values guiding rational debate. Scientific communities will move towards consensus behind the theory that, in the collective judgment of the community, best manifests the relevant theoretical virtues.

Richard Bernstein interprets Kuhn as saying that the reasoning employed in scientific theory choice parallels the concept of phronesis, practical wisdom, developed by Aristotle in the Nicomachean Ethics ([6], p. 54). For Aristotle, the practically wise man is one who knows the good and has the practical experience and acumen to deliberate effectively about how to realize the good in concrete situations. Thus, a wise judge will know how to achieve justice, not just in the abstract, but given the thorny details of a particular case. Likewise, the good scientist will know in general (even if largely tacitly) what a good theory should look like—the kind of standards it should meet—and will be skilled in the process of deliberation and debate over the assessment of the credentials of particular theories.

The picture of scientific rationality that emerges from Pera and Bernstein is this:

…theory choice is rational because it is brought about through a process of reasoned dialogue and debate between qualified discussants who draw upon broadly shared standards and values and a vast amount of deeply grounded background beliefs about theories, facts, methods, etc. At no point will any sort of incommensurability be encountered, nor will there be any need to resort to rhetoric [in the pejorative sense], threats, cajolery, or disguised appeals to social interests…

([7], p. 169)

If such a view of scientific rationality in its broadest and barest outlines is acceptable, then we need to see what role appeals to the best explanation have played in the rational process of science. How have such appeals entered into the details of scientific debate? What kinds of conclusions were they adduced to support? How widely were such appeals accepted? How did inferences to the best explanation guide scientists in their deliberations about theory choice? Did such appeals lead to consensus, or were they ineffective in settling contentious issues? Were appeals to the best explanation superseded by other, stronger considerations?

3. The K/Pg Extinction Controversy

To address these sorts of questions, a particular case study is needed. Here, I focus on the rousing (and sometimes rancorous) controversies over the cause (or causes) of the Cretaceous/Paleogene (K/Pg) extinctions—at the time called Cretaceous/Tertiary (K/T) extinctions—that saw the last of many species and higher taxa, most notably the non-avian dinosaurs. These debates are particularly illuminating because appeals to the best explanation figured prominently in the arguments adduced by all sides of the controversy. I will focus on the approximately twenty-year period following the 1980 publication in the journal Science of “Extraterrestrial Cause of the Cretaceous-Tertiary Mass extinction,” by L.W. Alvarez, W. Alvarez, F. Asaro, and H.V. Michel ([8]).

For much of the history of paleontology, the question of dinosaur extinction was either a non-issue or a matter for speculation, with theories postulating testable hypotheses beginning only in the mid-1960s ([9]). However, as judged by the surge in publications, interest in the topic of the end-Cretaceous extinctions spiked after the 1980 publication of the article by Alvarez et al. ([9]). There followed a controversy that was remarkable for its intensity and shameful for its viciousness1.

What was it about the Alvarez paper that piqued such interest and/or ire? Perhaps the heat of the debate was partially due to resentments going back decades, perhaps to Ernest Rutherford’s famous sneer circa 1920 that all sciences other than physics were mere “stamp collecting” ([10], p. 11). He meant that where other sciences merely collect and categorize, only physics offers deep theories that are stringently testable by hard data. In short, physicists are the only real scientists. Luis Alvarez, one of the authors of the 1980 Science article, was a famous physicist and winner of the Nobel Prize. Earth scientists, who are as jealous of their own turf as any specialists, perhaps regarded Alvarez as a bumptious and condescending intruder, intent on telling them their business.

Worse, the invocation of extraterrestrial causes appeared to hark back to the sorts of catastrophist scenarios that had supposedly been banished from the earth sciences. By and large, and with some notable exceptions ([9]), in the 150 years since the 1830 publication of Charles Lyell’s Principles of Geology, earth scientists had adhered to the Lyellian methodological principle that all geological hypotheses should invoke only known earthly causes—such as uplift and erosion. Lyell and his predecessor, James Hutton, had sought to proscribe appeal to ad hoc catastrophes to explain major faunal upheavals and other apparent large-scale changes in earth history. Only thus could geology claim to be a genuine science, explaining in terms of verae causae rather than fanciful scenarios.

Turning to the controversy itself, it had long been recognized that a major extinction event occurred at the end of the Cretaceous that affected both marine and terrestrial ecosystems:

In the oceans, ecologically diverse groups such as the ammonites, calcareous nannoplankton, planktonic foraminifera, inoceramid and rudistid bivalves, and marine reptiles either died out or were reduced to a fraction of their former diversity. On land, dinosaurs and pterosaurs are the most widely recognized victims of the terminal Cretaceous extinctions, with other clades of vertebrates such as marsupial mammals showing major declines in diversity.

([11], p. 195)

To explain these extinctions, three sorts of hypotheses were offered during the 1980–2000 period. With Hegelian neatness, they may be classified as thesis, antithesis, and synthesis:

• Thesis: The K/Pg extinctions were solely or primarily caused by the impact of a large bolide (comet or asteroid), causing cataclysmic environmental damage of such magnitude that the extinctions were simultaneous worldwide and literally sudden, occurring over hours, days, or, at most, months.
• Antithesis: A bolide impact, if it occurred at all, had little or nothing to do with the K/Pg extinctions. While the extinctions were geologically sudden, they took place over thousands of years, and there is no evidence that they were literally sudden. The causes were terrestrial in nature, involving extraordinary volcanism, sea level changes, oceanic oxygen levels, etc.
• Synthesis: A bolide impact did occur near the end of the Cretaceous, and had a major effect on species diversity, but it delivered the coup de grace to faunas and floras that were already in significant decline. It was the last of the major environmental stressors of the latest Cretaceous that had already put many organisms on the road to extinction.

It would be impossible here to follow every twist and turn of a multi-year and extremely productive debate. Fortunately, because of public interest in dinosaurs and their extinction, participants produced excellent semi-popular books to bring these arguments to a broader readership. Jerome Lawrence Powell defends the impact theory in Night Comes to the Cretaceous: Dinosaur Extinction and the Transformation of Modern Geology (1998), and so does Walter Alvarez, one of the authors of the 1980 paper, in T. rex and the Crater of Doom (1997). Charles Officer and Jake Page defend the terrestrial theory in The Great Dinosaur Extinction Controversy (1996). J. David Archibald offers a synthetic theory in Dinosaur Extinctions and the End of an Era (1996), as does Anthony Hallam in Catastrophes and Lesser Calamities: The Causes of Mass Extinction (2004). These books do an excellent job of summarizing the debates and the relevant science.

Dinosaurs were one of the most successful groups of animals in the history of the Earth. For 150 million years, from the Triassic to the end of the Cretaceous, they were the dominant land animals. Mammals evolved at about the same time as dinosaurs but remained small and probably nocturnal. In the oceans, ammonites and marine reptiles were prolific. The Earth underwent many changes from the Triassic through the Cretaceous. The supercontinent Pangaea split up into northern and southern continents, Laurasia and Gondwana. Epicontinental seas rose and fell. By the end of the Cretaceous, the continents’ current configuration had largely taken shape. Dinosaurs persisted and thrived through these changes, reaching maximum species diversity in the Campanian, the penultimate stage of the Cretaceous, or the early Maastrichtian, the final stage. What factor or factors could bring to extinction such flourishing faunas, both marine and terrestrial?

4. The Impact Hypothesis

Walter Alvarez, one of the authors of the 1980 Science paper, quipped, “Sometimes you have a really bad day, and something falls from the sky.” The impact hypothesis, as presented in the books cited above, is that a bolide, probably an asteroid, of 10 km diameter, hit the Earth near the Yucatan Peninsula at the end of the Cretaceous, about 66 million years ago2. The object was traveling at cosmic speeds, approximately 30 km/sec. The impact caused an explosion equivalent to 100 million megatons of conventional explosive, far greater than the simultaneous detonation of all nuclear weapons. The impact blasted a crater 150–200 km wide ([12], pp. 7–8).

I have summarized the impact’s effects:

…the immediate effect of such an impact would be cataclysmic in the extreme. Vast amounts of superheated rock would be blasted from the earth’s crust at the point of impact. Launched into ballistic trajectory, these incandescent ejecta would fall all over the earth, even on the side opposite the blast. Raging fires would start in forests worldwide, and in many places the air itself would be heated to broiling temperatures. Should the object land in the ocean…tsunamis much larger than those created by earthquakes would devastate the surrounding land areas. The long-term effects would be even more severe. After the fires had burned out, the smoke and soot would remain in the atmosphere, blocking sunlight and bringing temperatures below freezing worldwide, even in the tropics. Photosynthesis would stop, and the herbivores, starving and freezing in the dark, would quickly die, as would the carnivores that feed on them.

([13], p. 127)

Clearly, such an impact would be an extinction-level event:

The initial evidence for impact was geochemical, the detection of an iridium anomaly in the precise boundary layer marking the end of the Cretaceous and the beginning of the Paleogene. Iridium and other platinum-group metals are siderophile (“iron-loving”) elements that tend strongly to bond with iron. Since nearly all of these elements present in the primordial earth are thought to have bonded with iron and to have descended with most of earth’s iron into the core, only trace amounts, about 300 parts per trillion, are found in the crust. However, at the Italian Gubbio site, the thin clay layer marking the juncture of the Cretaceous and the Paleogene, iridium was found to be enriched to a value thirty times higher. At another such boundary site in Denmark, the concentration was 160 times higher than background ([14], pp. 13, 14). Other boundary sites worldwide, both in terrestrial and marine rocks, show such enhanced content of iridium.

([15], p. 196)

Extraterrestrial objects such as asteroids, comets, and meteoroids, being relics of the primitive solar system, lack massive iron cores and have their original compositions, including much higher iridium content than the Earth’s crust. The Alvarez team therefore hypothesized that the impact of a large bolide at the end of the Cretaceous could account for the enriched presence of iridium in the precise geological layer marking the boundary between the Cretaceous and the Paleogene. The enormous force of impact would have vaporized the bolide, and the subsequent explosion would have distributed its material worldwide.

Other evidence was soon forthcoming. Quartz, one of the most common minerals in the Earth’s crust, exhibits a “shocked” structure with crosshatched bands called “lamellae” when subjected to high pressure. Shocked quartz can be caused by explosive volcanism, but some forms, those with multiple intersecting lamellae, are diagnostic of the extreme pressures associated with meteor impact or nuclear explosions. Starting in 1984, granules of this extremely deformed quartz were found in the K/Pg boundary layers in various sites around the world ([16], pp. 27–31). Two other mineral phases of quartz, coesite and stishovite, can also be formed under the extreme pressures associated with impacts, and these have been associated with K/Pg sites ([14], pp. 45, 46).

Famously, the “smoking gun” of the end-Cretaceous extinctions was the impact crater found at Chicxulub in the Yucatan, which dated precisely to the K/Pg boundary. In the early 1990s, a large circular crustal feature, long known to petroleum explorers, was reinterpreted as a buried impact crater ([16], pp. 90–93). The location, size, date, and geology of the feature made it an excellent candidate for the site of the impact that caused the K/Pg extinctions ([14], pp. 104–115). Impact theorists therefore believed that they had discovered a cause sufficient for the end-Cretaceous extinctions, and one supported by many converging lines of evidence (only a small part of which can be mentioned here).

5. The Volcanist Hypothesis

The contrasting hypothesis, that the extinctions were caused by earthly processes, devoted much energy to the attempt to debunk the impact hypothesis. The most vigorous debunker was Charles Officer, late research geologist at Dartmouth, who summarized his case in The Great Dinosaur Extinction Controversy, coauthored with Jake Page. Most basically, he argues, there is no evidence that the dinosaurs died out simultaneously and literally suddenly. On the contrary, in the Hell Creek, Montana formation, one of the most productive fossil fields of late-Cretaceous dinosaur fossils, dinosaur bones become scarcer well below the iridium-enriched layer identified by the Alvarez team ([17], pp. 66–67).

Concerning iridium-enriched and shocked quartz, Officer argues that large volcanic eruptions often eject iridium-enriched particles into the stratosphere, thereby distributing them globally (p. 112). Further, citing a study by Helen Michel, one of the authors of the original 1980 Science article, he claimed that the iridium-enriched material collected not suddenly but gradually over 400,000 years or more (pp. 117–121). He regards the shocked quartz evidence as ambiguous at best. He argues that the particular form of deformed quartz associated with impacts is found only in North America and not worldwide, indicating, at most, a local impact (p. 125). Elsewhere, the shocked quartz is of a kind typically produced by volcanic eruptions.

As for the Chicxulub structure, he says that it is not an impact crater but contains shocked quartz of the type of the sort typically formed by volcanic or tectonic forces (p. 155). He argues that the rocks from Chicxulub are of many different compositions and are deposited in a series of layers, indicating a series of volcanic eruptions. A massive impact would produce a single, chemically homogeneous melt sheet (pp. 154–155). Further, the impact would have destroyed the upper Cretaceous rock, yet limestone-bearing Cretaceous microfossils remain interstratified with volcanic material (p. 154). Officer concludes that the petroleum geologists who discovered the Chicxulub structure were correct in identifying it as volcanic.

According to Officer, the Earth itself was the killer (p. 157). For 500,000 years across the K/Pg boundary, episodes of massive flood volcanism occurred in what is now the Indian subcontinent. The Deccan Traps, vast steplike basaltic structures in Central India, indicate the extent of that extraordinary volcanism. Such massive volcanism would have polluted the atmosphere with noxious and deleterious substances, generating a number of dire effects. Coinciding with these volcanic episodes was the subsidence of the shallow epicontinental sea that covered the center of what is now North America during the Cretaceous and a severe regression of sea levels worldwide. The loss of shallow water habitats would have doomed many creatures. Similarly, the loss of the lush environments around the inland sea would have a much harsher and more arid environment. Officer holds that the combination of these circumstances would have been sufficient for the gradual extinction of the dinosaurs and other late-Cretaceous life (pp. 158–177).

Needless to say, the pro-impact theorists were not without replies to Officer’s critiques. Charles Frankl summarizes some of their replies with respect to the Chicxulub structure:

The arguments put forth by the volcanists were not convincing. The so-called interstratification of “volcanic and sedimentary” layers was probably nothing more than the mixing of the pods of impact melt with the slumped sediment at the edge of the crater Neither did the chemical variability of the igneous rocks speak against an impact origin. On the contrary, impact specialists had long shown that in large astroblemes, melt lenses were chemically diverse, because of the diversity of rocks that are fused and mixed together. As for the shocked minerals, their deformation in crisscrossing planes was symptomatic of impact and not of volcanism, an interpretation which no longer suffered any contest among qualified specialists.

([16], p. 98)

The strongest argument of the anti-impactors was the fossil evidence of a gradual rather than sudden decline. If dinosaurs and other fauna, such as the ammonites, began to disappear well beneath the K/Pg transition layer, then the hypothesis of sudden extinction at precisely the K/Pg boundary is seemingly refuted. However, the appearance of gradual extinction can be due to a sampling error, as shown in a highly influential paper published by Phil Signor and Jere Lipps ([18]).

First, they noted that apparent diversity in the fossil record correlates strongly with the abundance of sedimentary rock deposited (and therefore available for paleontological exploration) at any given time. Less sedimentary rock means that a smaller and less representative sample of contemporaneous fauna will be represented. More rock means a bigger and more representative sample. Hence, even if actual diversity remained constant, diversity will appear greater at times when deposition is higher, thus providing greater opportunity for fossilization to be a more representative sampling.

The second effect, the eponymous “Signor–Lipps Effect,” can make species that actually became extinct at the same time appear in the fossil record to have done so at different times. Again, it is a sampling effect. In any given environment, fossilization is a stochastic process. Rarer species in that environment will therefore be less well represented in the fossil record than more abundant ones. Further, it is less likely that the final fossil appearance of a rare species will occur in the fossil record simultaneously with its actual disappearance than that the last appearance of an abundant species will coincide. Rarer species will be harder to find anywhere in the fossil record, much less right at the point of extinction ([14], p. 137).

Suppose, then, that Edmontosaurus and T. rex both went extinct on the same day, the final day of the Cretaceous. Since Edmontosaurus was far more numerous than T. rex, and since fossilization is a random process, you would expect that the final appearance of the former in the fossil record would fall closer to extinction day than the latter. This would make it appear that T. rex went extinct before Edmontosaurus, even if both went out on the same day. Hence, the appearance of differential extinction dates may well be an artifact of the sampling process that is fossilization.

Signor and Lipps therefore showed that interpretation of apparent extinction dates for species cannot be read literally. Final appearances of species at various locations in the fossil record might be compatible with simultaneous extinction. Therefore, anti-impactors cannot simply adduce disappearance from the fossil record without considering the rates of deposition of sedimentary rock and the relative rarity or abundance of the species being compared.

6. The Synthetic Hypothesis

By the late 1990s, and despite the polarized and acrimonious nature of the debates, a considerable amount of agreement had emerged. The 1997 compendium The Complete Dinosaur featured an exchange between Dale A. Russell, a proponent of catastrophic extinction, and Peter Dodson, a gradualist ([19], pp. 662–672). They agree that dinosaur diversity appears to have reached a peak several million years before the end of the Cretaceous and then declined (p. 664). However, they also agree that a major impact coincided with the end of the Cretaceous (p. 665).

Synthetic theories build upon such points of consensus. Tony Hallam, late professor of geology at Birmingham University, surveys fourteen major extinction episodes from the late Precambrian to the late Eocene ([20], pp. 195–202). He notes that of these, only the K/Pg extinction is associated with bolide impact (p. 196). He continues:

Even here [the K/Pg extinction] impact was not the whole story of the mass extinction at this time but merely the culminating coup de grace, albeit a spectacularly catastrophic and important event. The earth has undoubtedly endured in the Phanerozoic time a succession of impacts from outer space, as the cratering record shows, but they seem to have disturbed the biota on a global scale remarkably little…biotic catastrophes and calamities have their origins for the most part in entirely Earth-bound causes, which tie up with events in the mantle.

(p. 198)

With respect to the impact hypothesis, he concludes that even a moderate change in the environment lasting over a prolonged period may have a greater effect on mass extinctions than a single extreme event (pp. 201–202). Along with bolide impact, extreme volcanism, global cooling, and the regression of sea levels are associated with the end of the Cretaceous (p. 197). Like the volcanists, synthetic theorists contend that the fossil evidence does not support a scenario of instantaneous extinction. The evidence is too scanty and is concentrated in North America, so evidence of an instantaneous worldwide extinction is absent ([21], pp. 13–18). Synthetic theorists therefore emphasize that major extinction events are complexly caused and gradualistic, with perhaps a final knockout blow from an impact.

In a very recent study of mass extinctions, Michael Benton claims that the impact theory has now won out. He cites the original geochemical evidence and other facts that indicate impact as the only plausible explanation:

…the reality of the asteroid impact is accepted because of the worldwide iridium spike which as we have seen is taken to mark the boundary between the Cretaceous and Paleogene periods. There is no known process other than the impact of a huge asteroid that could have generated this worldwide iridium-bearing layer, which is found in both marine and terrestrial rocks. It confirms that a dust cloud encircled the Earth, and the dust (plus iridium) fell with rain, forming an Earth-wrapping blanket a few millimeters thick. In some places geologists have also identified coesite and stishovite, and shocked quartz in the impact layers.

([15], p. 196)

So, we now know three things:

(1)

A mass extinction occurred at the end of the Cretaceous and the beginning of the Paleogene. The dinosaurs and many other flora and fauna went extinct at that time.

(2)

Accumulating and converging lines of independent evidence indicate that a massive bolide strike occurred precisely at the K/Pg boundary.

(3)

Such an occurrence would have been sufficient to cause the K/Pg mass extinctions.

The impact theory is therefore now the consensus account of the end-Cretaceous extinctions. However, as always in science, even the best evidence is often not conclusive for everyone, and consensus depends upon the collective judgment of the scientists. There are a few remaining dissidents who reject the consensus (see the fascinating portrait of Gerta Keller by Bianca Bosker in the September 2018 issue of The Atlantic [22]).

7. Observations on These Debates

1. Theories about deep time, like those about deep space, seldom admit of direct experimental or observational confirmation. Perforce, theories are judged the most plausible if they explain the precise and detailed facts better than any rival. Hence, that the mode of argument broadly characterized as IBE was employed was never debated but simply assumed in the K/Pg extinction controversies. Further, that the theory that accounted best for all the complex, detailed, and diverse data would be the best confirmed was also not questioned. The debate was almost exclusively over the nature of the evidence, and these debates were minutely detailed and precise. In the debates over the K/Pg extinctions, the rival theories staked their claims on which one best accounted for the paleontological, lithological, geochemical, mineralogical, stratigraphic, and astronomical details. To the satisfaction of the solid majority of earth scientists, these facts have been extensively verified, and all alternative explanations duly considered and ruled out by the accumulated evidence.

A philosopher wishing to explicate the rationality of these debates should not focus on the abstract forms of argument—which was a non-issue—but on the nature of the detailed debates over evidence and the character of the collective and individual judgments of scientists—and the dissidents. What factors convinced the majority, and why are there still some holdouts?

2. Three of the familiar objections to IBE can be rejected. First, it is objected that all IBE can do is to select from the ranks of extant theories, but this may be nothing other than picking the best of a bad lot. Yet sometimes the details of the evidence strongly delimit the “lot”, leaving only a small number of possible candidate explanations. In the earth and planetary sciences, if we omit theistic explanations (as we should; [23]), the specifics of the data will often only admit of a very few types of explanations, and the role of IBE is to choose among the only possible alternatives. For instance, for much of the nineteenth century, there was a lively debate over whether lunar craters were caused volcanically or by impact; no other hypotheses were the least feasible. Humans may create a “bad lot” of hypotheses, but nature does not.

Second, we are told that we do not know what explanation is, so we cannot adduce it in support of theories. Once again, though, the particulars of the data and the theories might make very clear just how an explanation works in a given case. When massive faunal deaths are caused by the shock, burning, and catastrophic climate change of an asteroid impact, such an explanation is not vitiated by the lack of consensus among philosophers over a general definition of “explanation.” If philosophers never contrive a one-size-fits-all theory of explanation, this will not in the least mean that there are no explanations or that we cannot know how they explain or cannot adduce them in support of theories.

Third, Bayesian theorists tell us that IBE is either superfluous or irrational. It is superfluous if its conclusions concur with the results of Bayesian calculations and irrational if they differ from them. The book by Igor Douven mentioned earlier (2022) argues that IBE sometimes does lead to conclusions not sanctioned by Bayesian analysis, but that these are rational nonetheless. Here, I will merely observe that useless to the Bayesian does not mean useless to the working scientist. As Bayesians admit, the actual reasoning of scientists need not and usually does not explicitly consist of Bayesian calculations. As Pera noted, scientists employ many kinds of arguments and a great diversity of types of reasoning. Some of these may be expressed explicitly in probability calculations, but very often they will not be. Whether they can all even be modeled in terms of the probability calculus is questionable.

What Bayesians offer, then, is not a description of the scientific process but a rational reconstruction. By offering a model of ideal rationality, philosophers of science have an analytical tool, perhaps their best tool, for displaying essential aspects of scientific rationality, but they cannot dictate scientific practice. A good scientist might go his or her whole career without making any explicitly Bayesian calculation while making numerous appeals to the best explanation as confirming hypotheses. A Bayesian might reconstruct such reasoning in Bayesian terms, but that does not mean that appeals to the best explanation were not useful or even essential to specific contexts of confirmation. If evolutionary theory had to wait until it could be explicated in explicitly Bayesian terms, there never would have been On the Origin of Species.

IBE is often dismissed as “only a slogan”, but the injunction to update your priors in the light of new evidence is itself a slogan, a caricature, or, at best, a sketch of how scientists really argue things out “in the trenches.” As noted, the goal of achieving the best explanation was simply accepted as a matter of course by all sides of the debate. The real confrontation was highly detailed debates over what counted as evidence, and what goes on there is best understood on its own terms rather than in the light of any philosophical theory of scientific rationality. Of course, scientists want the theory that explains best. Of course, they want to proportion their beliefs to the evidence. This is like saying that the way to get rich on the stock market is to buy low and sell high. The details of scientific rationality have to be learned from scientists, not philosophers3.

3. I strongly agree with John Norton that no form of ampliative (non-deductive) inference can receive a priori justification. Justifications for the application of such reasoning must be local and empirical rather than, as with deductive logic, justified as substitution instances of universal schemas:

…we have sought formal theories of induction based on universal inference schemas [Norton includes all ampliative inference, including IBE, under “inductive.”]. These are templates that can be applied universally. We generate a valid inductive inference by merely by filling the slots of the schema with terms drawn from the case at hand. The key elements are that the schemas are universal—they can be applied anywhere—and that they supply the ultimate warrant for any inductive inference.

([24], p. 25)

However, (a) we have never found such a formal theory of ampliative inference, (b) there is no reason to think we ever will, and (c) we do not need such a formal theory to justify ampliative inferences4.

Ampliative inference, including IBE, is justified by the local factual particularities of individual instances of inference. Their justification lies not in their universal character nor their adherence to a schema or model, but in the factual particulars of each individual case. A particular instance of IBE is justified by the particularities of explananda and explanans in that specific case, a process we have already seen exemplified in the articulation, defense, and final acceptance of the impact model of the K/Pg extinctions.

Nevertheless, though no model, schema, or universal format of IBE is applicable, generalization is always helpful. So, drawing upon the case study and other examples, we may identify four “abductive virtues” of successful inferences to the best explanation, virtues that can make these hypotheses first promising and finally compelling. These will not apply universally to all successful instances of IBE, but I think they characterize a significant subset of the most successful ones—certainly in the earth sciences, which is my emphasis here.

First, as adumbrated above, a successful inference will not be a selection from a “bad lot” but will be a member of a set of candidate hypotheses delimited by the specific character of the explananda. The data might impose such limits in numerous ways, more than can be listed here, though the examples here illustrate the point. So, the first sort of abductive virtue a hypothesis can possess is to be a member of a tractable set of candidate hypotheses, as delimited by the data to be explained.

For instance, the size of the effects to be explained may require causes of extraordinary scale, and hence rarity. Consider mass extinctions, those that eliminate a high percentage of species across a diversity of environments worldwide. Mass extinctions are exceedingly difficult to achieve, and have occurred only rarely in the geological record, so their causes must be of exceptional power and lethality. Plausible sources of such power and lethality are relatively few and can be designated as terrestrial or extraterrestrial. Among terrestrial causes, the most likely candidate would be extreme volcanism and the deleterious ecological effects that would follow. Among extraterrestrial causes, a massive bolide impact would be the most plausible. Hence, it is unsurprising that the debate over the K/Pg mass extinctions resolved to the consideration of these two types of hypotheses, or a synthesis of them.

Another way that the particularity of the data might delimit candidate explanations is that a well-confirmed theory imposes strict limits on the types of allowable explanations in a given kind of case. For instance, if a massive star is in orbit around a center of gravity with an invisible companion, what could that companion be? Very well-established physics recognizes only three possible highly collapsed states of stellar matter: white dwarfs, neutron stars, and black holes. Using a Keplerian calculation, the observed orbital data reveal the mass of the unseen companion, and since mass is fate for stellar remnants, astrophysicists might conclude that the indicated mass is beyond the Chandrasekhar Limit, so the unseen companion must be a black hole.

As a final example, a particular hypothesis might indicate previously unsuspected connections between seemingly disparate facts, unexpected connections that permit them to have a unitary explanation. This is a favorite device of detective fiction (see note 5), but it also frequently applies in science. In the mid-nineteenth century, biological science was aware of a number of mysterious and seemingly unrelated facts: The skeletal homologies between organisms of very different sort; the similarity of embryonic development in diverse organisms; the presence of vestigial organs, like the small non-functional hind limbs of boas and other constrictors; the geographic distribution of organisms, with island faunas resembling, but seemingly modified from, the faunas of the nearest mainland; and the taxonomic classifications of organisms that took the form of a hierarchy of nested groups, with species encompassed by genera, and these by families, families by orders, and so on. The genius of Darwin was to see that, when taken together, these highly diverse facts all pointed to a common explanation in terms of a branching pattern of descent with modification. Thus, many mysteries succumbed to a singular explanation.

So, once we are in possession of a tractable set of candidate hypotheses, how do we choose among them? Another abductive virtue is that the hypothesis explains a considerable variety of data, effects of not just one sort but of many distinct kinds. A hypothesis that does so satisfies the “consilience of inductions” that has long been held to be a theoretical virtue. A highly consilient hypothesis offers, at least, a considerable degree of promise.

One of the paradigmatic cases of confirmation by IBE is the acceptance, during the 1960s, of the reality of continental drift and the theory of plate tectonics. One of the most interesting aspects of the history of continental drift is that it illustrates the progression of a hypothesis supported by IBE from promise to confirmation. Alfred Wegener proposed the hypothesis of continental drift, or mobilism, in articles published in 1912 and in a subsequent book, Origin of Continents and Oceans, first published in 1915. According to Henry Frankel, Wegener claimed that mobilism accounted for a number of geological and paleontological facts that were otherwise unexplained:

According to Wegener, continental drift solved the…coastline congruency problem, the geological matchups between the continents surrounding the Atlantic Ocean, the origin of Atlantic and Pacific-type coastlines, the origin of the most recent mountain ranges, the origin of island arcs, the disjunctive distribution of many life forms [i.e., the distributions of the fossil ranges of extinct organisms on continents now separated by oceans], The origin of the Permo-Carboniferous ice cap, and the two basic elevations of the earth’s surface [continental plateaus and ocean basins].

([25], p. 125)

The received fixist [no drift] theories could account for some but not all of these.

However, though Wegener thus claimed that his mobilist hypothesis was the best explanation of the facts, he did not argue for its complete acceptance, but only that it be regarded as a working hypothesis ([25], pp. 125, 126). He acknowledged that he could not offer a cogent explanation of the forces and mechanisms that could move continents ([25], p. 126). For a time, then, the debate between mobilists and fixists was stalemated, and most earth scientists remained fixists ([25], p. 129).

To move from promise to acceptance, a hypothesis should exhibit the virtue of explaining in terms of verae causae, causal forces that are robustly confirmable and demonstrably adequate to generate the effects. This is what clinched continental drift.

Worldwide, there is a network of oceanic ridges. It was proposed in the early 1960s that new seafloor is created when molten material rises from the mantle, powered by convection currents within the mantle, and spreads horizontally from the axes of the ridges. As it does so, it pushes the older seafloor away from those axes. Should a continental land mass be on top of a forming ridge, it will be split in two, and a new ocean basin will form where the continents have cleaved, and the former conjoined land masses will continue to drift apart. With the idea that the world’s seafloor thus constitutes various mobile plates, driven by convection currents within the mantle, and with the power to carry continents with them, the mechanism of drift was supplied.

Paleomagnetic evidence confirmed this hypothesis. The polarity of the Earth’s magnetic field has shifted many times over geological time. When igneous rock forms, its magnetic properties take on the polarity of the Earth’s field at that time. As this seafloor spreading process occurs, the igneous rocks forming the seafloor will take on the polarity of the Earth’s magnetic field. The hypothesized conveyor belt motion in opposite directions away from the ridges should mean that the seafloor, the same distance from the ridges on either side, should be the same age, and should therefore display the same magnetic polarity. This symmetry of alternating seafloor strips of normal and reversed polarity was found. Further, Canadian geologist J. Tuzo Wilson proposed that a new kind of fault, transform faults, would exist if seafloor spreading had occurred ([25], p. 130), and their existence was confirmed. Frankel reports the result:

With the confirmation of both these corollaries [symmetrical seafloor strips of normal and reversed polarity and transform faults], most of the active researchers who had not been in favor of continental drift immediately accepted mobilism because of the explanatory advantages offered by sea-floor spreading when coupled with its two corollaries.

([25], p. 131)

Thus, a promising hypothesis becomes the accepted explanation as evidence for that explanation mounts to a tipping point.

Finally, a maximally strong explanation will, uniquely among the candidate hypotheses, account for the granularity of the data in its very precise and detailed features. As previously noted, the debate over the evidence for mass extinction hypotheses concerned a very detailed analysis of the data. In the K/Pg debates, the focus was on a relentless examination of many exact particulars and what could or could not cause them. It was not just the presence of shocked quartz that identified an impact, but the presence of shocked quartz with multiple intersecting lamellae that was diagnostic. It was not the presence of one or two K/Pg boundary sites with enhanced iridium ratios, but an abundance of such sites worldwide in both marine and terrestrial rocks. The very detailed analyses of the fossil record concerned the timing of dinosaur extinctions, with volcanists and synthetic theorists arguing that they were gradual and impactors invoking the Signor–Lipps Effect to claim that the extinctions were consistent with suddenness.

When, therefore, out of a tractable number of candidate hypotheses, one is found to explain the effects not just broadly but in detail, and the hypothesis also explains a great variety of data and explains in terms of causes that are both confirmable and sufficient for the effects, consensus among earth scientists will converge around that hypothesis, as the case study has shown.

4. The upshot is that IBE is best thought of not as a universal argument form, where the form, per se, confers legitimacy to conclusions, but as a set of argument paradigms—real or imaginary instances whereby the data strongly delimit the possible explanations, and the accepted explanation uniquely accounts for the granularity of the data. Such paradigms abound in detective fiction, and a fortiori, in science5.

In other words, the phrase “IBE” refers to the general format of a family of argument exemplars, those, fictitious or real, we can point to as displaying a particularly tight relationship between data and hypothesized explanation. In these exemplars, we see that the data permit only a small and well-defined set of possible explanations, while the best explanation accounts, in detail, for the data in all of its specificity and diversity. These exemplars provide explanations that are not only intuitively satisfying but have a strong record of success in the history of science.

It therefore remains useful, perhaps necessary, to identify an argument format known as “inference to the best explanation.” In my analysis, IBE is the generalized format of families of paradigmatically good arguments. We just have to remember that “IBE” points not to a schematic essence, but to a set of family resemblances between argument paradigms, where such resemblances indicate instances of particularly close relations between data and explanatory hypothesis. In these close relationships, the data constrain the types of possible explanations, and the explanations compellingly account for the data in its detail and diversity.

Finally, to speak of “possible” explanations is somewhat vague. On one construal of “possible,” anything is possible. Putative explanations appealing to gods, ghosts, djinns, spells, hexes, or whatever are “possible.” I have been taking for granted that “possible” is delimited not only by the data but both by (a) the sorts of regulative assumptions that must guide natural science (to make it natural) and (b) by currently accepted scientific knowledge.

Natural science, by definition, must reject appeals to putative supernatural causes and restrict attention to possible natural ones. This is the “methodological naturalism” excoriated by theistic philosophers such as Alvin Plantinga but amply justified by the abundant historical success of naturalistic explanations in replacing entrenched supernatural ones. The real threat science poses to religion is to leave God unemployed, without significant work to do ([26,27]). Further, there is at any given time a body of well-confirmed and broadly accepted scientific knowledge, and I have taken “possible” to require coherence or at least compatibility with that background.

5. Should arguments of the general IBE format, even the intuitively strong ones, be taken as confirming a hypothesis, or merely showing its promise? If the K/Pg extinction controversies are any guide, what we will typically see is a movement from promise to confirmation. When the Alvarez team first proposed the impact hypothesis, it was, despite the strident objections, a very promising hypothesis. It offered hard, measurable geochemical evidence and clearly was not one of the old speculative scenarios. Those attracted to the impact hypothesis began to look for further evidence, and soon they found it. As the data points piled up, they provided more successes for the impact explanation and more difficulties for the competing terrestrial and synthetic hypotheses.

On the other hand, much, if not most, of the excitement over the Alvarez hypothesis was due to the strident opposition of those who regarded it as comprehensively wrong. For the purposes of stimulating research, is it therefore more important that a hypothesis be controversial than promising? However, a hypothesis has to be promising to be controversial. No scientist, unless taking on a task of supererogation (like arguing with creationists), will bother refuting an obviously crackpot hypothesis. It is only worth the time and effort to criticize a hypothesis that appears to promise an important advance but, the critic holds, fails to do so.

Did the discovery of the Chicxulub crater clinch the case for the impact hypothesis, and not the previous IBE-style arguments? Prior to the discovery of the “smoking gun,” should the impact hypothesis be regarded as merely promising and not as confirmed? Do IBE-style arguments therefore have to be supplemented by more direct evidence, evidence that does the real work of confirmation? Before the discovery of Chicxulub, the impact hypothesis already had broad and burgeoning support among paleontologists, and the reason was that it explained so many detailed and diverse pieces of evidence. Further, the Chicxulub structure was not at first universally identified as an impact remnant. The original discoverers regarded it as volcanically caused, and impact hypothesis opponents such as Officer continued to argue for its volcanic origin. Impact theorists successfully argued that the detailed features of the Chicxulub structure could only be explained by a massive bolide impact. So, IBE-style arguments entered every stage of the confirmation of the impact hypothesis.

So, drawing on the lessons of the K/Pg controversy, it appears that a hypothesis promising a good explanation, like the Alvarez hypothesis, can move through stages of confirmation as the accumulating evidence makes a promising explanation into a good one, a good one into a better one, and a better one into the best one.

8. Conclusions

Considered in general or abstract terms, IBE cannot be justified as a legitimate mode of inference. Indeed, following John Norton, I have argued that no form of ampliative inference can be justified in abstract and general terms but only in the context of specific applications. Considered generally and abstractly, the standard critiques of IBE hold. It is merely a slogan. It might, at best, only permit us to choose the best of a bad lot of hypotheses. There is no univocal meaning of “explanation,” so no general appeal to the “best” explanation can have any force. It is like saying that the best system of government is the one that guarantees maximum freedom when “freedom” has no clear definition.

The strength of an application of IBE is not determined by its instantiation of a universal schema but by the particular fit between explanation and data, as explicated above in terms of the abductive virtues. IBE is strong when the specific character of the data stringently delimits the kinds of explanations that may be considered, and the best explanation will be the one that accounts for the data, not just generally, but in detail. Diversity of data is also important. The more diverse kinds of data there are, the more stringently candidate explanations will be limited. Darwin’s “long argument” was that only a branching pattern of descent with modification can plausibly explain the facts of paleontology, anatomy, embryology, biogeography, and taxonomy. Of course, not every instance of IBE meets such strict standards, but those that do provide strong confirmation.

Did the Alvarez impact hypothesis, by offering a common explanation of geochemical anomalies in different K/Pg boundary sites, thereby support the truth of the hypothesis or merely incentivize a possibly fruitful line of inquiry? In the polarized debate that followed, pro-impactors took the evidence as conclusive, and opponents rejected it as worthless. Of course, when tempers flare, scientists, like everyone else, are subject to overstatement. Maybe now, in hindsight, we can say that the Alvarez hypothesis did stimulate a huge amount of interest that gave an enormous boost to extinction studies. However, the boost was not so much that it was regarded as promising as that it was rejected as spurious. Yet, as evidence accumulated, the tectonics of scientific consensus shifted. Particularly persuasive was the discovery of phenomena, such as the specific kind of shocked quartz that is diagnostic of impact, and of other effects plausibly attributable only to impact.

The upshot is that when scientific communities conclude on what they regard as the best explanation, it is more by the elimination of competing hypotheses than any sort of “unification” per se. The limiting case of the best explanation is the only explanation.