2.1. The Leading Objection to the Traditional Pessimistic Inductive Inference

The leading realist objection to the inference in the OFPI comes in several varieties, but the central idea is straightforward. In any past-to-present enumerative induction (such as the OFPI), the more evidence we have to think the past and present are relevantly dissimilar, the weaker the argument is. And we have reason to believe past scientific theories are not relevantly similar to present ones. As Magnus and Callender put it, “the realist may insist that the population of past theories was a different kettle of fish than the population of present theories” (Reference Magnus and Callender2004, 326). Different versions of this objection derive from different reasons for thinking that present theories are importantly dissimilar to past ones. Leading reasons include:

1. a) We today have more data or evidence than our predecessors did, so current theories are supported by more data than previous ones were (Lipton Reference Lipton2000, 204; Roush Reference Roush, Magnus and Busch2009, 34; Fahrbach Reference Fahrbach2011, sec. 6; Reference Fahrbach2017).

2. b) We today have more advanced instrumentation and other technologies that were unavailable to our forebears (Lipton Reference Lipton2000, 204; Devitt Reference Devitt2010, 96–98).

3. c) We today have eliminated more incorrect hypotheses than previous scientists (Ruhmkorff Reference Ruhmkorff2013, 412), and we selected better ones (Lipton Reference Lipton2000, 202). Thus, as the pool of competitors shrinks, the probability that any remaining theory is approximately true increases.

The defender of the OFPI, however, has a reasonable reply. Scientists in 1850, looking back at science in 1720, could have correctly made all of these same points a–c: the 1850 scientists had more data, had better instruments, and had eliminated more hypotheses than their predecessor scientists in 1720.

So there are apparently important differences between past and present theories, but there are also important similarities between them—thus, it is unclear whether the OFPI is doomed. Stanford recognizes this: he claims this situation generates a “stalemate” between the OFPI’s critics and its defenders (Reference Stanford2006, 11). There are many past-to-present inferences in which the present and the past are somewhat different (even in ways relevant to the truth of the conclusion). Sometimes, these inferences are still fairly strong, but other times they are weak.

How do we ascertain whether a particular enumerative induction is strong, when the past sample is not perfectly representative of the present population? As Stanford says, “enumerative induction … can lead us astray … particularly when circumstances change in some way that is relevant to the continuity of the regularity or the mechanism that grounds it” (Reference Stanford2006, 10). So to know whether a particular enumerative induction is strong, we need to know what is responsible for (i.e., what ‘grounds’) the regularity present in the historical sample. And then we need to ascertain, as best we can, whether that grounding factor is likely present in the current population. The more likely it is that this grounding connection is present in the current population, the stronger the enumerative induction is, ceteris paribus.

Thus, in order to justify the OFPI’s projection from past theories to present ones, and give us reason to think that past fundamental theories are sufficiently relevantly similar to current ones, the historically motivated antirealist should show that the reason why past fundamental theories turned out fundamentally incorrect is probably still operative in current theories. And in order to do that, the historically motivated antirealist needs an account of why past fundamental theories turned out incorrect.Footnote ²

2.2. Stanford’s Reply to the Objection

And this is precisely what Stanford’s PUA aims to accomplish. As Magnus puts it, the PUA “explains why science falls short when it falls short” (Reference Magnus2010, 804). That is, the PUA provides a reason for, or a ‘mechanism that grounds’, past scientific failures. On Stanford’s account, the reason past scientific theories are incorrect is typically because they are the result of eliminative inferences made by inquirers who failed to exhaust the space of scientifically plausible hypotheses.

And Stanford’s NI argues that this mechanism is shared with current theories: current theories are also the products of eliminative inferences made by inquirers who are often unlikely to exhaust the space of scientifically respectable hypotheses that could potentially explain the available data.

Stanford argues that this trait is shared across past and present science, since current scientists cannot be much better at exhausting the space of alternatives than scientists of the last few centuries: our psychology cannot have changed radically that quickly. Thus, since the PUA can break the stalemate with realism, but the OFPI alone cannot, historically motivated critics of realism should accept Stanford’s antirealism instead of the OFPI.

For present purposes, I grant that Stanford’s view is superior to the OFPI in isolation, because the PUA provides the needed supplement to ground the projective inference that the OFPI lacks. But that does not show that Stanford’s position is the best version of historically motivated antirealism. There could be alternative explanations of ‘why science falls short when it falls short’ that still break the stalemate and ground the induction from past scientific activities to present ones just as well as the PUA does—and perhaps better. The following section describes and defends one such alternative explanation: the Problem of Misleading Evidence (PME).

3.1. What Is the Problem of Misleading Evidence?

In a nineteenth-century discussion of Linneaus’s taxonomy, systematist George Johnson anticipates the PME, although with restricted scope: “Were we to analyze the genera [of zoophytes and lithophytes in the 12th edition of Linneaus’s Systema Naturae] we should find, in almost every one of them, species that properly belong to a different class of animals, or whose characters are at variance with those assigned to the genus: but many of these misplacements were the almost necessary consequences of the then state of knowledge relative to the beings in question” (Reference Johnson1838, 58; my emphasis). Johnson says Linneaus’s taxonomy is mistaken, yet given the evidence available to the scientific community at the time Linneaus proposed his taxonomy, Linneaus offered the best supported taxonomy possible. The PME generalizes this basic idea beyond systematics to fundamental science more generally:

What does ‘misleading’ mean here? Here are two examples. If someone has been very effectively framed for a crime he or she did not commit, then the exhibits the prosecution enters into evidence, such as the defendant’s fingerprints at the crime scene, count as misleading evidence. Similarly, a coin-tossing trial of 20 flips, which resulted in 20 heads in a row, would count as misleading evidence, if the coin is actually fair. In these cases, E is misleading evidence for H: evidence E (incrementally) confirms hypothesis H, but H is not (even approximately) true.Footnote ⁴ The PME provides an another explanation of why science falls short, when it falls short, distinct from the PUA: it is not a cognitive limitation on scientists’ part—a failure of imagination—but rather a problem with the scientists’ evidential environment, which (if scientists follow the evidence where it leads) systematically leads them away from the truth.

Here are examples of the PME in action. In the Almagest (I.5), Ptolemy considers the possibility that the earth is moving from place to place, including the possibility that it is orbiting the sun once a year. Why does Ptolemy reject this hypothesis? The ancient Greeks knew that the earth is very far from the sun. If the earth were revolving around the sun, then we should observe stellar parallax. But no stellar parallax was detected. So either the earth is not going around the sun or twice the distance from the earth to the sun is as nothing with respect to the size of the cosmos. Ancient astronomers reasonably concluded that the former is more likely than the latter. The evidence available to ancient astronomers, namely, the absence of stellar parallax, was misleading: it confirmed a geostatic model of the universe over a geokinetic model, even though the geostatic model is incorrect.

Here is a second historical example in which the PME explains why past scientists failed to accept the (by current lights) correct theory. One famous episode in the spontaneous generation debates was the controversy between Lazzaro Spallanzani, on the one hand, and John Needham and Comte de Buffon, on the other, between 1765 and 1780. In experiments first published in 1748, Needham sealed containers of gravy, boiled them, and then examined the resulting liquid under his microscope. He and Buffon saw what they thought were small living creatures (Strick Reference Strick2000, 6). Since the gravy had been boiled, presumably any microorganisms that had previously been in the gravy were killed, and since the container was sealed, presumably no new microorganisms could enter the gravy. So this appeared to be a case of spontaneous generation of life from nonliving materials. Spallanzani attempted to replicate the experiment but observed no microorganisms in his boiled gravy, so he rejected this purported demonstration of spontaneous generation, claiming that the microorganisms Needham observed must have gotten in despite Needham’s attempt to seal the container.

From the modern point of view, Spallanzani was correct. But what explains this difference in experimental outcomes? Spallanzani claimed (and later scholars repeated) that Needham and Buffon’s microscopes were inferior to his own. This fits nicely with the realist claim mentioned in section 2.1 above: past scientists made their mistakes in part because of their inferior instruments, and later scientists are more likely to find the (approximate) truth because of their advanced instrumentation. For example, if Ptolemy had twentieth-century technology, he could have detected stellar parallax. Interestingly, this is not what happened in the Needham-Spallanzani controversy. Sloan (Reference Sloan1992) has shown that Needham and Buffon had a better microscope than Spallanzani. Specifically, Needham’s microscope could detect bacteria in Brownian motion, whereas Spallanzani’s could not. So Needham and Buffon could see certain objects that showed signs of being alive, which Spallanzani could not. And another contemporaneous scientist, von Gleichen-Russworm, attempted to replicate Spallanzani’s results with a better microscope than Spallanzani’s, but he could not and thus sided with Needham and Buffon (433). So from the current point of view, having more evidence, as a result of having better instruments, actually led Needham and Buffon (and von Gleichen-Russworm) away from what later became the successor theory. That is, the data generated by the superior microscopes were misleading.

Parallel to the OFPI and the NI, we can formulate a Misleading Evidence Induction:

3.2. The Case for the PME

The most straightforward consideration in favor of the PME is that, for many historical episodes, it makes the right ‘predictions’: the reason a particular past theory was accepted is that the evidence available at that earlier time was misleading. For example, Ptolemaic astronomers believed the sun revolved around the earth because the evidence available to them made it look that way. Much of the evidence that would support the geokinetic hypothesis, for example, actual stellar parallax (not detected until 1838) and the phases of Venus (not detected until 1610), was unavailable to Ptolemy and his successors for centuries. Needham and Buffon believed their observations supported spontaneous generation, because their microscope was powerful enough to detect bacteria in Brownian motion, and particles in Brownian motion appear to be alive. Note that in both cases, the successor hypotheses were conceived at the earlier time, so the PUA cannot explain them.

The PME can explain many other examples. Scientists who accepted the caloric theory of heat in the early nineteenth century had substantial evidence against the kinetic theory of heat. This theory was certainly conceived, since it was preferred by the earlier mechanical philosophers, and had been articulated as roughly the current version of the kinetic theory of gases by Daniel Bernoulli in 1738. Brush outlines six reasons physicists from the middle to late eighteenth century did not accept it; perhaps the strongest was “the fact that heat … can be transmitted across empty space (as from the sun to the earth) without any accompanying motion of molecules” (Reference Brush1976, 20–21). Another historical episode that appears to fit the PME pattern is Alfred Wegener’s theory of continental drift, proposed in 1912 but whose central claims were not accepted until half a century later. The historical evidential situation is complicated, but among historians of geology “there has been a general agreement that it was rational to reject Wegener’s theory of drift when it first appeared in … 1912–1915” (Šešelja and Weber Reference Šešelja and Weber2012, 148). In other words, the total evidence available to earth scientists in the early twentieth century did not favor Wegener’s hypothesis.

Consider three further examples that historical antirealists would presumably like to appeal to in making their case against realism, which the PME explains in a natural and straightforward way. Physicists in 1800 accepted the Galilean transformations over the Lorentz transformations, because those physicists had no evidence that the relative velocity of a moving body to its observer would alter the length of that moving body in the observer’s frame. And there was no evidence that the length of moving bodies depends on the speed of light. Similarly, there was no evidence in 1800 that, at sufficiently small scales, the equations of classical mechanics would break down and quantum mechanics would provide more accurate predictions. Finally, before Onnes discovered mercury’s superconducting state in 1911, scientists inferred that a body’s heat capacity is proportional to its temperature and its electrical resistivity is proportional to temperature cubed. Onnes observed that below 4.2K, both quantities fall quickly to nearly zero. There was no evidence, before that discovery, that mercury would behave radically differently below a certain temperature. In each of these three cases, historical scientists lacked a sufficiently representative sample: for example, they only had observations of objects moving much slower than the speed of light, or of systems too large for quantum effects to be detectable, or of temperatures too high for superconductivity to be observed. In short, the historical record contains (rational) scientists often basing their inferences on (what from our current vantage point is) unrepresentative or misleading evidence.

3.3. Objection: The PUA Explains the Historical Record Just as Well as the PME

Now, a defender of the PUA has a plausible objection: the PUA can explain these last three historical episodes too. No one in 1800 had conceived of special relativity or quantum mechanics. No one in 1900 had conceived that the electrical resistance of certain materials would drop rapidly to nearly zero below a certain critical temperature. So these examples do not favor the PME over the PUA.

The PME proponent has two replies. In my view, these replies show why the PUA is insufficient to account for the patterns of acceptance and rejection we see in historical scientists and why the PME is necessary. First, some of the earlier above historical examples involve conceived alternatives. Specifically, Ptolemy had conceived of the heliocentric theory of the cosmos, caloric theorists had conceived of the kinetic theory of heat, Needham and Buffon had conceived of the hypothesis that spontaneous generation does not happen, and Wegener’s opponents had conceived of the claim that the earth’s current land masses were once contiguous and subsequently moved apart.

The PUA defender might retort that each of these are not detailed enough to count as genuinely conceiving the successor: for example, the mechanical philosophers’ slogan ‘Heat is the motion of constituent parts’ is not sufficiently specific to count as genuinely conceiving the kinetic theory as it was accepted in the nineteenth century (Stanford Reference Stanford2006, 53). However, Daniel Bernoulli had in fact proposed more or less the modern kinetic theory of gases in 1738, a full century before it was eventually accepted by the scientific community (Brush Reference Brush1976, 20). And other examples of successor theories were conceived in more or less full detail and nonetheless rejected at an earlier time. For example, shortly after Dalton claimed that water is HO, Avogadro proposed that it was H₂O. However, “Avogardo’s ideas were rejected by Dalton and most other chemists as ad hoc, speculative, and implausible, and not generally accepted until half a century later” (Chang Reference Chang2012, xviii). In cases such as these, in which the eventual successor theory was conceived and rejected at an earlier time, the PUA cannot explain why the superseded theory was accepted at that earlier time, but the PME can. So one reason to accept the PME is that it can account for a wider variety of historical cases that historically motivated antirealists want to use as part of their brief against realism. An antirealist who restricts herself to the PUA cannot use these ‘greatest hits’ from the antirealist catalog.

The PME defender has a second reply. I grant that the PUA can give an explanation of why scientists in 1800 did not accept special relativity, quantum mechanics, and the existence of superconducting materials: nobody had proposed the Lorentz transformations, the Schrödinger equation plus the projection postulate, or the existence of critical superconducting temperatures back then. However, I believe the PME provides a better explanation for each of these three than the PUA does. Why? Imagine a physicist in 1800 who proposed replacing the Galilean transformations with the Lorentz transformations. Or one who says that, below certain scales, classical equations of motion fail to hold and should be replaced with the Schrödinger equation. In other words, imagine that the PUA is removed from these historical cases: imagine the successor theory is conceived.

If the real reason scientists in 1800 accepted classical mechanics and not quantum mechanics was that scientists in 1800 had failed to conceive of quantum mechanics (as the PUA proponent predicts), then in this alternative imagined history, the scientists in 1800 should accept quantum mechanics. But it is extremely unlikely that the scientific community of 1800 would accept quantum mechanics (or special relativity or superconductivity), because these new theories introduce extra complications that are unsupported by any evidence available in 1800. Such theories would involve unmotivated reductions in theoretical parsimony. And presumably, if the PUA were the (primary) mechanism driving past scientists’ failure to accept later successor theories, then ‘removing’ the PUA would lead scientists to accept the successor theory. But in at least these three counterfactual scenarios, this seems very unlikely. So for several famous historical cases, the PUA does not appear to be the correct explanation for the scientists’ acceptance.