1. Introduction

Over the past decade, philosophers have raised several purported scandals for Darwinian materialism, all of which share a common structure. First, it is claimed that the theory confers a very low probability on an outcome of interest, such as the origin of life or intelligence. Then, it is argued that a good scientific explanation of an outcome should show that it was highly probable. From this, it is concluded that there is something lacking in the Darwinian explanation, and therefore it ought to be supplemented or rejected outright. For example, White (Reference White2007) argues that a common assumption in origins of life research—that any good explanation of the origin of life must show that it was probable—is inconsistent with a commitment to naturalism, for life will only be probable on theories that posit some supernatural bias. Nagel (Reference Nagel2012) goes further, arguing that we ought to consider alternatives to Darwinian materialism that posit some teleological trend toward life and intelligence.

However, these challenges to Darwinism seem at odds with common explanatory standards within evolutionary biology. Rather than despair at contingency, some have argued that the acceptance of low-probability explanations is part and parcel of Darwinism itself (Gould Reference Gould1989; Beatty Reference Beatty2006). Additionally, biological theories that confer high probabilities (e.g., naive adaptationism) have often been supplanted by theories that make outcomes more contingent (e.g., neutral or mixed selection-and-drift theories).

These controversies largely turn on the question of whether high probabilities explain better in such a way that constitutes grounds for preferring those theories that confer them in inferences to the best explanation (IBE). Darwinism’s detractors assume a form of explanatory elitism, the view that “events with high probabilities are better explained than events with low probabilities—that we understand better why high probability explananda occurred” (Strevens Reference Strevens2008, 348).Footnote ¹

Explanatory egalitarians, however, deny that size matters and instead identify some other property in virtue of which probabilistic theories explain well. Here, I will focus on the egalitarian view that a theory explains well to the extent that it confers correct probabilities—probabilities that match the true objective chances of the outcomes of a chance process—not necessarily high ones. This version of egalitarianism is entailed by causal explanationism, defended by Jeffrey (Reference Jeffrey and Rescher1969) and others, according to which “a probabilistic explanation of an event is good to the degree that it provides an accurate and complete description of the probabilities involved (as well as describing, of course, the other nonprobabilistic facets of the mechanism). Whether the probabilities are low or high, lowered or raised, does not matter, provided that these features, and all others, are fully and correctly documented” (Strevens Reference Strevens2000, 371).

The strongest elaboration and defense of elitism in the context of IBE is provided by Strevens (Reference Strevens2000, Reference Strevens2008), who argues that it provides the best account of the history of explanatory practice in statistical mechanics (SM). I will argue that his test case is not a probative one since all of the explananda events in that domain have extremely high objective probabilities, and I provide an alternative egalitarian explanation of the acceptance of SM. Expanding our investigation to include probabilistic theories in biology reveals a test case—the historical acceptance of Mendel’s theory of inheritance—that does discriminate between elitism and egalitarianism. I argue that egalitarianism provides the best account of explanation in biology, and hence Darwinian evolutionary practice need not be threatened by its recent elitist critics.

2. Strevens’s Argument for Elitism

In broad strokes, elitism is the view that the size of the probability conferred by an explanation makes a difference to its explanatory quality. My target here is the view, defended by Strevens and assumed by Darwinism’s recent critics, that the size of the probabilities that a theory confers on certain explananda matters when we are selecting among theories in an IBE. This view comes in stronger and weaker forms. Absolute size elitism holds that a theory explains an outcome O well to the extent that it confers a high probability on O.Footnote ² According to relative size elitism, if one theory confers a higher probability on O than another, then it explains O better. Elitism (of both varieties) can also be held with respect to different kinds of explananda; for instance, one could be an elitist with respect to long-run frequencies, single events, or both. In subsequent sections, I discuss these various formulations of elitism in more detail and argue that some of them are much more plausible than others.Footnote ³

In general, the view under examination here is that a theory that confers low probabilities on key outcomes, or lower probabilities than a competitor, is explanatorily defective, and we ought to infer that it is false (or at least less likely to be true than that competitor).Footnote ⁴ It will be helpful to briefly distinguish this intertheoretic version of elitism from intratheoretic versions that I will not be arguing against, versions that evaluate the relative quality of explanations provided within a theory.

First, it may be the case that once we adopt a causal theory and use it to explain particular outcomes, if one of the candidate causes specified by the theory makes an effect more probable than another, it explains it better and is more likely to be its actual cause. For example, relative to our best current theory, the fact that Bob smoked two packs a day seems to better explain his lung cancer than the fact that he worked for a week in an asbestos-filled office. Second, we frequently compare compatible explanations pitched at different levels of abstraction. For example, we might ask whether a deterministic microphysical explanation showing how Bob’s smoking caused a particular cancer-causing mutation provides a better explanation than one that merely cites the fact that he smoked, even though both are true. Elitism, taken to its logical conclusion, would seem to recommend that we ought to prefer deterministic microphysical explanations when available.Footnote ⁵

Even if we grant these two elitist claims, it is still an open question whether in an intertheoretic inference to the best explanation—wherein we compare theories that make different claims about the probabilistic or causal structure of the mechanism that produced our observations—the theory that assigns higher probabilities to observed outcomes best explains them in such a way that provides grounds for inferring that it identifies the true chance mechanism. This is a claim that Strevens’s examination of SM is supposed to support and that Darwinism’s critics rely on, and so it is the one I focus on here.

Elitism and egalitarianism straightforwardly fall out of various accounts of explanation, and therefore, one could argue for or against elitism by endorsing a particular account (Strevens Reference Strevens2008, 347–55). While this is an important project, we might also hope to evaluate the merits of elitism independently and use it to arbitrate among theories of explanation. An alternative approach is to evaluate which view provides the best explanation of actual scientific practice. This stance is adopted by Strevens, who argues that “the most important source of evidence concerning our explanatory practice is the sum total of the explanations regarded as scientifically adequate in their day, together with an understanding of the background against which they seemed adequate” (37). I will follow Strevens in assuming that historical practice is a good (but fallible) indicator of explanatory quality, that particular probabilistic theories were favored (at least partly) in virtue of the probabilities they conferred on outcomes, and that theories provide good explanations of their exemplar cases, those outcomes that were instrumental in the historical acceptance of the theory.Footnote ⁶

The egalitarian position that I will defend is that a good explanation will confer the “correct” probabilities, probabilities that match the objective chances of the outcomes of the chance process that produces our observations. While there are difficult philosophical questions that arise in regard to the concept of objective probabilities, we can elide many of these questions in identifying a predictive difference between the correct and high-probability views.Footnote ⁷

In standard cases, we expect that a theory that identifies the true objective chances of event types will most accurately predict their observed frequencies.Footnote ⁸ Hence, on the egalitarian conception of IBE, we do not care about whether a theory shows outcome O to be highly probable. What we care about is whether O-type events occur with the frequency that is predicted by the objective chance probabilities specified by the explanans. In scientific practice, if a theory conferred a low probability on O but O was observed at the low frequencies that we would expect if the theory were true, egalitarianism predicts that it will have been favored in IBE.

In contrast, elitism predicts that probabilistic theories were historically accepted in virtue of the fact that they assigned high probabilities to outcomes, particularly in exemplar cases. If the record shows that theories were accepted on the basis of observations for which they conferred low probabilities (indeed lower probabilities than alternatives), this is strong historical evidence against elitism. I will argue that the history of Mendelism provides us with such evidence.

An account of explanation should do more than merely save the phenomena of historical practice.Footnote ⁹ It should also make sense of why a theory ought to have been favored. This is especially important in the debate over Darwinism since its detractors are arguing for a revision of current scientific practice. I will argue that not only did biologists accept theories that conferred low probabilities on key events, these theories were genuinely more explanatory than their competitors. Further, although biology furnishes particularly probative case studies for evaluating elitism, I will suggest that the normative facts generalize to scientific explanation more generally.

Strevens (Reference Strevens2000) argues that SM—“perhaps the best developed, most deeply probabilistic science we have”—had an explanatory advantage and was thus favored over alternative theories in virtue of the high probabilities that it assigned to individual outcomes (371). In the late nineteenth century, physicists possessed a large body of observations regarding the flow of heat—hot irons placed in cold water cool until equilibrium; when a partition separating a gas from a vacuum is removed, the gas fills the entire chamber; and so on—and a mechanical theory that explained these observations via the random motion of particles comprising the gas. However, according to Strevens, this mechanical theory was not accepted over its competitor, the caloric theory, until it met its statistical counterpart, which probabilified the initial conditions and resulting outcomes of thermodynamic molecular processes.

The probabilities that SM assigned to our previously observed outcomes were exceedingly high. According to Strevens, these high probabilities were the special contribution of the statistical part of SM (Reference Strevens2000, 373); had SM not shown known outcomes to be highly probable, it would not have added anything at all to the molecular theory.

His argument can be reconstructed as follows. For some outcome O explained by SM:

1. 1. SM showed that O was highly probable.

2. 2. Before SM, the molecular theory showed that O might possibly occur.

3. 3. SM was accepted because it improved on the explanation of O provided by the molecular theory.

4. 4. If egalitarianism is correct, then an explanation showing that an event O might possibly occur is just as good as an explanation showing that O was highly probable (Strevens Reference Strevens2000, 374)

5. 5. From 1, 2, and 4, if egalitarianism is correct, then SM did not improve on the explanation of O provided by the molecular theory.

   • Conclusion 1. Therefore, egalitarianism cannot account for the acceptance of SM.

   • Conclusion 2. Therefore, egalitarianism does not give a correct account of scientific explanation.

   • Conclusion 3. Explanatory Elitism—it was in virtue of showing that O was highly probable that SM had an explanatory advantage and was accepted.

The egalitarian about biological science could respond by denying the move from conclusion 1 to conclusion 2, offering a disunified account according to which what makes something a good explanation is different in physics than in biology.Footnote ¹⁰ However, this is unstable ground for the egalitarian, given significant parallels between the explanatory structure of SM and population genetics (Walsh, Lewens, and Ariew Reference Walsh, Lewens and Ariew2002).

How, then, should an egalitarian about biological explanation respond? The first thing to note is that SM is not a probative test case for arbitrating between elitism and egalitarianism. The elitist proposes that SM improved on the explanation of O provided by the molecular theory in virtue of conferring a high probability. Here, the size of the probability is intrinsically explanatorily valuable.Footnote ¹¹ However, my egalitarian proposal, that what we are trying to do in IBE is to find the theory that will ultimately assign the true objective probabilities to our observations, can explain the explanatory advantage of SM equally well. That is because in the domain of SM, the objective probabilities of observed outcomes falling under its purview are all high probabilities, so high that the chance of the opposite occurring is “so unlikely one would not expect it to occur even once in the lifetime of the universe” (Strevens Reference Strevens2000, 372). The egalitarian will agree that high probabilities explain better in this domain but only because they happened to coincide with the correct probabilities.Footnote ¹²

Egalitarians also ought to deny premise 4. On any plausible egalitarian theory, an explanation would be lacking if it entailed merely that O could possibly happen while remaining silent about what the extent of this “possibility” is. The egalitarian-friendly suggestion here is that the special achievement of theories like SM and population genetics was in imposing a probability model with a clearly defined state space and a sampling or causal process operating over it that then generated precise and true probabilities on outcomes.

The elitist may respond that while probabilifying outcomes is indeed explanatorily important, it was only the high-probability outcomes that were important for the favoring of those theories; the low-probability events were merely along for the ride. Hence, the existence of cases in which an accepted theory assigned a low probability to particular outcomes is not a mark against elitism. This is closer to the picture provided by Strevens (Reference Strevens2008). On his account, the optimal explanation of O will balance accuracy—the size of the probability of O given the explanans—with generality and causal cohesion.

Take Strevens’s example of a wheel of fortune with 90 red wedges and 10 black. We could give a deterministic explanation of its landing on red, citing idiosyncratic details about this particular wheel and spin. A probabilistic explanation, citing the causal properties of wheels of fortune in general and the fact that this one has 90% red wedges, would still be highly accurate but more general and cohesive. In part, this generality is purchased by subsuming the red events under a more general class (outcomes of a wheel of fortune), where this class includes low-probability events (black outcomes) that are not well explained.

Including low-probability events adds to the generality of the explanation, but only the high-probability events add to its accuracy and are well explained by it. Hence, elitism gets the right result if the highly probable outcomes are the ones that contributed the most to favoring the theory over alternatives. If, however, low-probability outcomes were to play an important role in the acceptance of the theory, then this would count in favor of the egalitarian interpretation that I have suggested.

3. The Evidence for Mendel’s Theory, Part 1

The historical acceptance of Mendelism is a more useful test case since it does furnish us with low-probability exemplar cases. In this section and the next, I give a brief overview of the three types of outcomes that were instrumental in the acceptance of Mendel’s theory of inheritance, including those that favored it over its chief competitor, Galton’s biometric theory. I argue that none of the key exemplar cases were assigned high probabilities, and indeed, Mendel’s theory often assigned lower probabilities than did Galton’s.

After the rediscovery of Mendel’s work in the late nineteenth century, Bateson—one of Mendel’s earliest and most ardent defenders—effused that from the general law that his “long lost papers provided we have reached a point from which classes of phenomena hitherto proverbial for their seeming irregularity can be recognized as parts of a consistent whole.” As a result, “a new world of intricate order previous undreamt of is disclosed. We are thus endowed with an instrument of peculiar range and precision” (Bateson Reference Bateson1913, v, 17). Notably, in their explication and defense of the theory, the early Mendelians do not argue that the theory showed that outcomes of inheritance were highly probable.

Instead, the theory’s explanatory advantage was due to its subsumption of disparate, heterogeneous events under a single explanans that assigned precise (and often low) probabilities to explananda under its purview. As we will see, careful observations of the outcomes of inheritance gave biologists good reasons to believe that these probabilities described the true objective chances. Mendel himself argues that this was the chief advantage of his theory, compared to previous accounts of inheritance that failed to “determine the number of different forms under which the offspring of hybrids appear, or to arrange these forms with certainty according to their separate generations, or definitely to ascertain their statistical relations” (Reference Mendel and Bateson1866/1913, 336).

Mendel’s work was groundbreaking not only in his development of a novel probabilistic model of inheritance but in the extensive data he provided in its support. In his experiments with pea plants, Mendel recorded trait frequencies extremely close to those that would be maximally likely given his laws. For example, for the F₂ results of crosses of pure lines for yellow (GG) and green (gg) seeds—which his model predicts will result with probabilities of $.75/.25$ —Mendel reported an observed frequency of 6,022:2,001. This remarkably close fit for such a large sample size was highly influential in persuading scientists of the truth of his theory.

An interesting episode in this history illustrates a first serious problem for elitism. The close fits throughout Mendel’s data struck R. A. Fisher as suspicious, leading him to wonder whether the numbers had somehow been cooked (Franklin Reference Franklin, Franklin, Edwards, Fairbanks and Hartl2008). The crux of his allegation was that such observed frequencies are highly improbable and thus cannot be adequately explained by the hypothesis that the data were produced by a Mendelian process and reported accurately.Footnote ¹³ Putting aside the question of impropriety on Mendel’s part, notice that the case illustrates a more general fact: the absolute probability of any conjunction of outcomes of a chance process will decrease as the number of trials increases, so that in almost any case in which we have many observations, no observed frequency will have a high probability (Sober Reference Sober2008, 34).Footnote ¹⁴ Indeed, in a prominent defense of Mendel, Sturtevant argues that explanatory elitism about frequencies leads to absurdity: “It is possible to question the logic of the argument that a fit is too close to expectation. … If now I report that I tossed 1000 coins ten times, and got 500:500 every time, our statistician will surely conclude that I am lying, though this is the most probable result thus exactly specified. The argument comes perilously close to saying that no such experiment can be carried out, since every single exactly specified result has a vanishingly small probability of occurring” (Reference Sturtevant1965, 13).

Strevens himself acknowledges this problem for his view, although he underestimates its importance: “[One] situation in which a microconstant model may explain a low-probability frequency is a case in which the frequency matches the strike ratio but the explanandum puts very narrow bounds on the fact about the frequency that is to be explained. Suppose, for example, that you want to explain why the frequency of red in 500 spins on the wheel of fortune was between 49% and 51%. … I conclude, very provisionally, that low complex probabilities may occasionally explain” (Reference Strevens2008, 415). On the elitist picture, the observed frequency that is most probable and would thus seem to most strongly favor a theory is the one that has a maximal likelihood, where the observed frequencies of outcomes match the predicted probabilities as closely as possible.Footnote ¹⁵ As the sample size increases, the probability of the maximum likelihood frequency decreases. Given that larger sample sizes should constitute stronger evidence, an increase in confirmational power corresponds to a decrease in the absolute probability of the explanandum given the explanans.

The upshot is that if we insist that a good explanation of an outcome must show it to be highly (or even somewhat) probable, then Mendel’s theory did not explain any of the trait frequencies that he observed, even those that corresponded almost perfectly to what his theory predicted. But, the egalitarian position can make sense of how these low-probability outcomes were explained and why they contributed to the acceptance of Mendel’s theory. Contra Strevens’s premise 4, the precise probabilification of patterns of inheritance was a tremendous explanatory improvement, and contra Strevens’s conclusion 3—that it was in virtue of showing that O was highly probable that the theory had an explanatory advantage—Mendel’s advantage was in virtue of its assigning the true probabilities, which was confirmed when they matched observed frequencies.

4. The Evidence for Mendel’s Theory, Part 2

In the previous section, I argued that elitism has difficulty accounting for how Mendel’s theory can explain any of the observed frequencies that so strongly supported it. The picture becomes even more complicated when we compare Mendel’s theory to its chief competitor, the biometric theory, first proposed by Galton and elaborated by biologists such as Pearson and Weldon.Footnote ¹⁶ Because long-run, aggregate frequency data did not always discriminate between these two theories, predictions they made about subclasses of the data were crucial. An examination of these cases will show that Mendel’s theory was accepted on the basis of outcomes to which it often assigned a lower probability than its competitor.

The Mendelians differed from the biometricians in both their general approach and the causal theory they provided. First, Galton was largely concerned with how offspring characters were correlated with parental characters in general and, as such, used statistics that aggregated over different traits and different lineages.Footnote ¹⁷ In contrast, Mendel’s approach was to isolate particular characters and analyze offspring of particular crosses in order to discern the causal mechanisms of inheritance. The Mendelians then argued that these mechanisms were responsible for the global statistical patterns described by Galton, whose “formula should in all probability be looked upon rather as an occasional consequence of the actual laws of heredity than in any proper sense one of those laws,” resulting in the “concealment of that order which it was ostensibly undertaken to reveal” (Bateson Reference Bateson1913, 6–7). Johannsen, who coined the term “gene,” made this a particular point of emphasis, arguing that “the famous Galtonian law of regression and its corollaries elaborated by Pearson … may be social statistics in optima forma, but they have nothing at all to do with genetics or general biology” (Reference Johannsen1911, 138).

Although many biometricians eschewed talk of the unobservable elements that were causally responsible for their statistical laws (Norton Reference Norton1975), a brief examination of Galton’s causal theory of inheritance will help to bring out the disagreements between the two theories.Footnote ¹⁸ I will assume that the basics of Mendel’s laws are well known, so a quick sketch will suffice (I will risk anachronism for ease of exposition and will use modern terminology here).

Mendel’s Law of Segregation states that each sexually reproducing parent has two tokenx alleles at each locus, which segregate randomly during meiosis (such that each allele has a .5 probability of being found in a particular gamete). The offspring receives one allele from each parent. The phenotype is determined by the genotype, and it is often the case that one allele is dominant, such that heterozygotes display the dominant phenotype. So, to explain why Ray, the child of two brown-eyed parents, has blue eyes, the Mendelian cites the Law of Segregation, that the brown eye allele (B) is dominant to the blue eye allele (b) and that his parents are heterozygous ($\mathrm{Bb}\times \mathrm{Bb}$). The explanans entails that offspring of this pairing will have blue eyes (bb) with probability .25 and that the expected frequency of blue eyes among offspring will be 1/4.

In contrast, Galton stated his Law of Ancestral Heredity as follows: “The two parents contribute between them on the average one-half, or (0.5) of the total heritage of the offspring; the four grandparents, one-quarter, or (0.5)²; the eight great-grandparents, one-eighth, or (0.5)³, and so on. Thus, the sum of the ancestral contributions is expressed by the series { $\left(0.5\right)+{\left(0.5\right)}^2+{\left(0.5\right)}^3$ , &c.}, which, being equal to 1, accounts for the whole heritage” (Reference Galton1897, 402). This statistical law predicts the offspring phenotype as a function of the phenotypes of all of its ancestors.Footnote ¹⁹ To explain Ray’s blue eyes, the biometrician cites the eye color of each of his ancestors, where the probability that he will have blue eyes is given by the weighted contribution of each of his ancestors, which is calculated by the proportion of blue-eyed ancestors in each generation, weighted by that generation’s distance from the offspring.

On Galton’s causal theory, hereditary material consists of particulate elements in the germ plasm, half of which are contributed by each parent; however, there is an indefinite number of such elements that give rise to a particular trait instead of just two on the Mendelian picture (Bulmer Reference Bulmer1998, Reference Bulmer1999; Leuridan Reference Leuridan, Russo and Williamson2007). Through a chance process, some of these elements are expressed in the phenotype (patent elements) while others remain unexpressed (latent elements). On this picture, Ray’s parents each possess a large collection of elements, including both blue- and brown-eyed factors, inherited from their parents. A random collection of these elements is transmitted from each parent to Ray, and an element is randomly selected from this pool to determine his eye color.

In effect, Galton imported statistical properties of the global correlation of offspring and ancestor phenotypes into the causal mechanism of inheritance; the phenotypic correlation with distant ancestors is reflected by their literal contribution to the large set of elements that determine offspring character. As a result, the two theories predicted extremely similar aggregate population-level trait frequencies. However, despite the “numerous examples where the arithmetical results predictable by either system are nearly or quite the same,” Bateson nevertheless argued that “further breeding would of course reveal that even in these cases the applicability of the Galtonian method was only superficial” (Reference Bateson1913, 56). That is, a more detailed examination of the data would show that Mendel’s theory assigned the true objective chances to particular outcomes of inheritance. To understand the two types of evidence that were crucial in arbitrating between the two theories, note that Galton’s causal theory of inheritance differs from Mendel’s in two key ways.

First, Mendelian dominance is typically fixed for each trait (e.g., brown eyes are always dominant to blue).Footnote ²⁰ Yet, Galton assumes that within a generation, each element “coding” for a trait has an equal chance, p, of being sampled for expression in the phenotype and that p is the same for all traits. Hence, holding ancestry fixed, every trait will exhibit the same probability of inheritance and expression. Galton’s theory thus predicts far more homogeneity in inheritance across traits and lineages than does Mendel’s.

From our vantage point, it might seem obvious that some traits (the dominant ones) have a higher probability of being expressed than others, in contravention of Galton’s theory. However, Bulmer (Reference Bulmer1998, 581) notes that Galton’s predicted ancestral correlation (.5)ⁱp is equivalent to the Mendelian correlation if p is replaced by the narrow heritability, h ², which measures the degree of variation in a population that is attributable to genetic variation. For quantitative traits (where the phenotype is a function of many independent alleles) or for population-level frequencies averaging over many traits, the Mendelian h ² will average out to give an estimate roughly equal to Galton’s p.

However, these averages conceal significant heterogeneity in patterns of inheritance across traits. Indeed, Bateson and other early Mendelians argued that one of the key facts of inheritance to be explained was its discontinuous and varied nature. Any practical breeder knows that “while he can rapidly fix some characters, some never come true at all, and others will not come true with any certainty after long selection; the expectation after simple selection is, in fact, quite different for different characters” (Bateson and Saunders Reference Bateson and Saunders1902, 158). For example, selection for heterozygotes never produces a pure strain, regardless of how many heterozygous ancestors a strain has.

Here is an (imperfect) analogy with Strevens’s roulette wheel example. Suppose that we have a population of roulette wheels that have landed on red roughly 90% of the time. The analogue of the biometric theory, H₁, posits that every wheel has an objective chance of .9 of landing on red. The alternative Mendelian theory, H₂, posits that the population is made up of two types of wheels, with objective chances of .85 and .95. Theories H₁ and H₂ predict the same mean observed frequency of red in the global population, but they will make different predictions about other statistical features; for example, H₂ will predict greater variance in the frequencies we will observe. Theories H₁ and H₂ will also make different predictions within subclasses of the data, with H₁ predicting that the expected frequency in every subclass is .9.

A second key predictive difference stems from the fact that, on Galton’s theory, the probability that a trait will be patent in an offspring given that it was patent in an ancestor i generations back is (.5)ⁱp. Because every ancestor makes a diminishing but nonzero probabilistic contribution to the offspring phenotype, the offspring phenotype is probabilistically dependent on its entire ancestry, and there is no fact about the parents that screens off prior generations (Bateson and Saunders Reference Bateson and Saunders1902, 133; Leuridan Reference Leuridan, Russo and Williamson2007). In contrast, Mendelian genotype evolution is a Markov process, in which the genotype of the parents screens off facts about the genotypes of past generations.

As a result, in addition to predicting too much homogeneity in inheritance across different traits, Galton’s theory predicts too much homogeneity across lineages of the same trait. One phenomenon that puzzled breeders was the reemergence of “rogues.” For example, after many generations of selection for the beardless trait in wheat, strains would occasionally give rise to bearded offspring. Bateson and Saunders argue that the hypothesis “that such a ‘rogue’ is a recessive form may give a complete explanation of this phenomenon in many cases,” for if beardlessness is dominant, “the chances are that it will always produce a certain proportion of bearded plants” (Reference Bateson and Saunders1902, 133).Footnote ²¹

Galton predicts that the reemergence of rogues is possible for any strain that resulted from mixed ancestry; if there is a bearded ancestor anywhere down the line, there is a nonzero probability of a bearded offspring. In contrast, Mendel’s theory predicts that pure strains (in which the probability of rogues is 0) are also possible if the founding cross was between two homozygous dominants. The important point for the debate at hand is that Mendel’s theory was taken to better explain these phenomena not because it assigned higher probabilities to their occurrence. Rather, the problem with Galton’s theory is that it assigned probabilities that were too homogeneous; by statistically averaging over lineages, it assigned probabilities to events in specific lineages that were alternately too low and too high.

The egalitarian position is that Mendel’s theory was explanatorily better in virtue of its assigning the true probabilities to outcomes. This holds with respect to frequency distributions across populations; although both theories predict roughly the same means, Mendel better predicts higher moments, such as the variance of the probability distribution of observed frequencies, and better predicts frequencies within subclasses of the data. According to Bateson, it also holds with respect to single-case outcomes; Mendel’s theory better explains the emergence of a rogue trait or Ray’s blue eyes by conferring the correct probability on those events, even though this probability will frequently be lower than the one conferred by Galton’s theory.Footnote ²²

The same point obtains with respect to the third kind of evidence marshaled in favor of Mendel’s theory. Recall that for Galton, offspring traits are probabilistically dependent on their entire ancestry, whereas Mendelian parental genotypes screen off past ancestry from offspring traits. Two problems arose for distinguishing between the two theories here. First, unlike genotype evolution, Mendelian phenotype evolution is not a Markov process (due to dominance, epistasis, etc.), and the phenotype is all that could be directly observed. Second, the probabilistic dependencies between generations that Galton’s theory predicts will be largely accurate when averaging over different possible ancestral histories.

To solve these problems, early Mendelians cleverly exploited the fact that on Galton’s theory, the probability that an individual will display a phenotype is strongly dependent on the number of ancestors with that phenotype. Bateson demonstrates that this dependence does not always hold, by drawing on data from horse breeders: “In the breeding of thoroughbred race-horses the heredity of chestnut colour is that of an ordinary recessive. … No difference is manifested between colour-inheritance of chestnuts which have had many chestnut ancestors in recent generations, and those that have no chestnut progenitor in the nearer degrees” (Reference Bateson1913, 49). Hence, Galton’s theory will often confer the incorrect conditional probabilities on events, such as a particular horse’s having a chestnut coat conditional on its ancestry. In the event that the horse had many chestnut ancestors, it will confer a probability that is too high. Once more, the egalitarian has a natural interpretation of such cases.

I have argued that Mendel’s theory was explanatorily revolutionary, not just because it probabilified the outcomes of inheritance (for Galton’s theory did this as well) and not because it assigned high probabilities to key outcomes (for it often conferred lower probabilities than Galton’s). Instead, in line with the egalitarian position, Mendel’s theory provided good explanations because it conferred probabilities—albeit ones that were low, heterogeneous, and discontinuous—that biologists had good reason to believe described the true objective chances. This case study is more probative in evaluating the merits of elitism and egalitarianism, for unlike the phenomena described by SM, biology is a messy affair in which many outcomes of interest have a low objective chance of occurring. The best explanations in that domain will not be ones that show that observed phenomena were highly probable but rather why they were predictably and projectably irregular. Given that egalitarianism can also account for the explanatory success of SM—the high probabilities it conferred were also the true probabilities—egalitarianism provides a more general and unified account of scientific explanation.

5. Elitist Response: Relative Elitism about Frequencies

In the previous sections, I surveyed three types of exemplar cases that Mendel’s theory explained better than alternative theories of inheritance—frequency data from large sets of observations, heterogeneous patterns of inheritance across different traits and ancestries, and patterns of (in)dependence among inheritance events—to which Mendel’s theory assigned low probabilities, in the former case, and probabilities both higher and lower than Galton’s, in the latter two. What kind of alternative explanation can the elitist give for these episodes? In this section, I consider two elitist accounts for how Mendel’s theory explained the long-run frequency data. In the next, I explore whether the elitist can account for its explanation of single-case outcomes.

Since the data that Mendel derived from his experiments with pea plants constituted the strongest reasons for his theory’s acceptance, elitism would take a major hit if it entailed that Mendel’s theory did not explain it. More normatively, it is unreasonable to require that a good explanation of an observed frequency show that it was highly probable since the degree of evidential support provided by a set of observations will usually be inversely proportional to its likelihood given the explanans.

The elitist could opt for a disunified account here, according to which high probabilities are not required for explanations of conjunctions of observations but are required for explanations of single conjuncts. Granted, this is not an option that prominent elitists have tended to take; Hempel argues that “there is only a difference in degree between a sample consisting of just one case and a sample consisting of many cases” (Reference Hempel1962, 132), and Strevens argues that SM “explains the non-probabilistic fact that heat never flows from cold to hot in exactly the same way that it explains the particular event of, say, a hot iron cooling in cold water” (Reference Strevens2000, 375).

Second, elitists could instead adopt a weaker form of elitism, where only the relative size of the probability matters. According to relative size elitism, if one theory confers a higher probability on O than another, then it explains O better. This move has some independent motivation, since on most theories of confirmation, favoring, and IBE, theory choice is a contrastive enterprise.

Notice, however, that only a particular version of relative elitism will work here. As I showed in the previous section, the Mendelian and biometric theories conferred roughly the same probabilities on many outcomes, particularly population-level outcomes that aggregate over many different lineages and traits. They only made different predictions about observed frequencies when biologists looked at subsets of the data, such as particular lineages resulting from pure crosses.

Hence, in order to make sense of the claim that Mendel’s theory was better than Galton’s because it assigned higher probabilities to observed trait frequencies, the elitist will have to take more features of the data into account. Hempel’s discussion of Mendel’s theory is instructive here. The theory explains why “in a random sample taken from a population of pea plants each of whose parent plants represents a cross of a pure white-flowered and a pure red-flowered strain, approximately 75 per cent of the plants will have red flowers and the rest white ones” (Hempel Reference Hempel1962, 141). Hempel notes that the probabilistic generalization cited in the explanans may also contain information about higher-order properties of these observed frequencies. For example, Mendel’s (often violated) Law of Independent Assortment states that the probability of a gamete receiving an allele of one trait is independent of any other trait. This law does not predict the expected frequency of a trait but merely how it will be correlated with the frequency of other traits (here, not at all).

The elitist view that emerges is one on which a theory can well explain a low-probability observed frequency if it confers a higher probability on it, including its higher moments, than does a competitor. Relative elitism renders the correct verdict about Mendel’s theory and states an independently plausible view connection between high probabilities and theory confirmation: if we pay attention to our total evidence and it is sufficiently large and probative, then the theory that makes the evidence most probable best explains it and is most strongly favored by it.Footnote ²³ Nevertheless, I do not think that elitism scores a significant victory here.

In a justified IBE, we expect that the best theory will typically assign a high probability to the total evidence; otherwise, it is hard to see why we should expect the results of an IBE to be true. If that is right, then elitism with respect to our total evidence runs into the same problem as Strevens’s original SM test case: it does not distinguish between the high-probability and the correct-probability views. Is it in virtue of assigning the total evidence a high probability, or in virtue of assigning the correct probability (which will often happen to also be a high one), that our best theory explains the data? The latter egalitarian option accounts for Mendel’s explanation of the frequency data just as well.

6. Elitist Response: The Problem of the Single Case

Even if we grant that relative elitism can account for Mendel’s long-run frequency data, the explanatory status of single events under its purview is still in question. Since Galton’s and Mendel’s theories predicted similar aggregate trait frequencies, it was necessary to look at observed frequencies and patterns of dependence among subsets of the data. Mendel’s theory was favored by these subset outcomes, even though it assigned lower probabilities to many of them. Because Strevens posits a tight link between explanatory quality and theory acceptance, he needs to give an account of these exemplar cases that is consistent with elitism. I will consider four, according to which low-probability events are explained directly, explained indirectly, or not explained (and hence not exemplars) at all.

When we are deciding between probabilistic hypotheses, low-probability events will often be extremely important. Suppose that a set of events, $e_1-e_{\text{n}}$, comprise the frequency data that are used to evaluate a theory, T. Is it the case that those e_i that are shown to be highly probable are those that best favor T? I will grant that relative to a background containing no observations, a high-probability event may “contribute” more to favoring T. However, relative to a set of initial conditions including the outcomes of previous trials, low-probability events carry more weight. For example, suppose you want to test H₁ (the probability of red = .9) against H₂ (the probability of red = .95). You have already spun the wheel nine times with it landing red every time. Relative to this background, an improbable black outcome would confirm H₁ more than another red, although by the absolute elitist’s lights, H₁ would not explain it well. Hence, the link between reasons for a theory’s acceptance and what it explains is severed.

As in the case of long-run frequency explananda, here the elitist might insist that it is only the relative size of the probability that matters. If a good explanation of a single event need only make it more probable than its competitors, H₁ does explain the black outcomes in the scenario above. This move will not work as well for the scenario presented in section 4. In that case, H₁ posits that every wheel has an objective chance of .9 of landing on red, and H₂ (correctly) posits that the population is made up of wheels with objective chances of .85 and .95. For half of the black outcomes, H₁ assigns too low a probability (so H₂ does better by elitist lights), but for the other half, it assigns a probability too high. Hence, if H₂ does a better job of explaining particular black spins, despite assigning low probabilities (either absolutely or relatively) to them half of the time, then the relativizing move will not neatly solve the problem of the single case.Footnote ²⁴

Next, the elitist may dig in her heels and maintain, as Strevens (Reference Strevens2008) does, that while probabilistic theories do explain high-probability single-case events under their purview, they simply do not explain the low-probability single events. For example, Mendel’s theory does not explain why Ray has blue eyes (probability = .25), but it does explain why his sister has brown eyes (probability = .75). The elitist will then hold that the high-probability events were important for the theory’s acceptance, although the low-probability ones came along for the ride.

I find this view unsatisfying for several reasons. First, it would either leave a wide array of biological phenomena simply unexplained or entail very different explanatory standards for otherwise similar outcomes. For example, either Ray’s blue eyes have no explanation, or we are required to explain them via some complicated developmental story, whereas his sister’s brown eyes are adequately explained simply by citing the probabilistic facts of Mendelism. This is odd since the two outcomes resulted from the same causal process. If providing an understanding of the causal mechanism that produces an event ever suffices to adequately explain it, and the same mechanism can produce both high- and low-probability events, then parity suggests that both kinds of events are well explained (Jeffrey Reference Jeffrey and Rescher1969).

Further, Mendel’s theory gives us good reason to expect that blue-eyed offspring will regularly occur 1/4 of the time, and it is difficult to see how it licenses such inferences without explaining them (but see Emery Reference Emery2015, 113–14). Finally, this view does not seem to make sense of Mendelism’s acceptance. Galton’s theory assigned higher probabilities than Mendel’s to many single cases and the same probabilities to many long-run frequencies, so it is not clear that when we tally up the explanatory successes that Mendel’s theory will come out ahead. As we have seen, Galton’s high probabilities were considered explanatory liabilities, not strengths.

A third tack that the elitist can take is to hold that probabilistic theories do explain low-probability single events indirectly, via the good explanations they provide for other outcomes; the low-probability cases inherit their explanations from the high-probability single cases or overall frequency outcomes. On this view, Mendel’s theory does explain Ray’s blue eyes because it explains his sister’s brown eyes, the overall relative frequencies of brown and blue eyes, or both.

I also find this explanation unsatisfying. If Mendel’s laws explain (provide understanding of, license one to expect, give us reason to believe the Mendelian story about, etc.) Ray’s blue eyes, then they explain both the occurrence and nonoccurrence of brown eyes. It is very hard to see why high probabilities are important at all at this point. Indeed, a prominent motivation for elitism is Salmon’s (Reference Salmon1990) argument that a good explanation of event e must show why e occurred rather than ~e, and thus only the higher probability event is well explained.

Second, if Mendel’s laws explain blue eyes, they do not seem to do so by showing that brown eyes were probable. Presumably, low-probability events would inherit their explanatory status by contributing to the generality of the Mendelian explanation (Strevens Reference Strevens2008, 429). This has the odd consequence that adding a generality to the explanans that subsumes an alternative non-e event, e*, improves our explanation of e, but at the same time, this regularity would not explain e*, or at least not explain it well, if it had occurred. Moreover, low-probability events contribute to the theory’s generality and ability to match the overall frequency facts in virtue of being low-probability events of the same causal process. If this is how low-probability events earn their keep, then why not think that the low probabilities explain all by themselves?

Finally, the elitist can hold that probabilistic theories do not explain single events at all (see also Emery Reference Emery2015, sec. 5). Faced with the seeming irregularity of the biological world, we may have held onto elitism but changed our views about the proper explananda of scientific explanations. What probabilistic theories in biology and elsewhere explain are the relations among outcomes (frequency distributions and their higher order properties), and these are shown to have a high probability.

This view of biological explanation is developed by Helgeson (Reference Helgeson2013) with respect to Darwin’s theory in the Origin of Species. While “Darwin’s common ancestry hypothesis has nothing to say about where any particular organism should be found on the globe, or what morphological characteristics an organism should display,” it does explain higher-order facts, such as why species in adjacent but climactically varying environments are more closely related than those in similar but distant environments (59). The lesson is that a theory that does not predict or explain single-case outcomes may “stick its neck out when it comes to certain abstract, ‘high level’ features of the same set of observations” (37).

In a similar vein, defenders of the statistical conception of evolutionary theory argue that factors such as natural selection and drift are aggregate-level statistical summations over the genuine causes of evolution: the births, deaths, and reproductions of individuals. Evolutionary theory is just not in the business of explaining individual outcomes; “as natural selection theory does not deal in the causes of these individual-level phenomena, it cannot yield causal explanations of them. If the statistical conception is correct, then natural selection theory can no more explain why a particular individual has the traits it has than the kinetic theory of gases can explain why a particular molecule has the velocity it has” (Walsh et al. Reference Walsh, Lewens and Ariew2002, 469–70).

While I think that this view has nonintuitive consequences—Mendel’s laws do not provide any explanation of why Ray has blue eyes or his sisters have brown ones—I will emphasize two other problems instead. First, as I argued in section 5, the egalitarian has a perfectly good account for why, in an IBE, we ought to favor the theory that confers the highest probability on the total body of evidence; the best theory will assign it the correct, and coincidentally a high, probability. Further, because egalitarianism can also account for how the single events that comprise it are explained, egalitarianism provides a more general and unified theory of scientific explanation.

Finally, according to this version of elitism, the probabilities conferred on isolated phenomena do not license theory choice in an IBE; instead, we will have to wait and see which theory does best with respect to the total evidence. This might be correct, but elitism so formulated will not do the work that it is often enlisted to do. Returning to the issue with which this article started, consider how elitism has been wielded by Darwinism’s recent critics. They argue that because the theory shows that key individual outcomes (such as the origin of life) are improbable, it is explanatorily deficient and should be rejected. However, on the only remaining version of elitism that can make sense of probabilistic explanation in biology, this is no reason to reject Darwinism.

In an IBE, we ought to select the theory that, as far as we can tell, best describes the true objective chances. Unlike in SM, the outcomes of biological processes—even the important ones—are often improbable, heterogeneous, and projectably irregular. Yet they are law-like. Egalitarianism is the account that sheds the clearest light on how probabilistic theories help us impose explanatory order on seeming chaos, or how “classes of phenomena hitherto proverbial for their seeming irregularity can be recognized as parts of a consistent whole” (Bateson Reference Bateson1913, v).