1. Introduction
My goal is to contribute to a growing literature that is critical of historical inductions such as the pessimistic metainduction (PMI) argument (Poincaré Reference Poincaré1902/1952, 160; Putnam Reference Putnam1978, 25; Laudan Reference Laudan1981) and the problem of unconceived alternatives (Stanford Reference Stanford2001, Reference Stanford2006) against scientific realism, concentrating mostly on the former. The PMI can be construed in different ways (Mizrahi Reference Mizrahi2015; Wray Reference Wray2015), that is, as a counterexample to the no-miracles argument for scientific realism (e.g., Saatsi Reference Saatsi2005), as a deductive argument such as a reductio (e.g., Psillos Reference Psillos1996, Reference Psillos1999) or a modus tollens (Lyons Reference Lyons, Clarke and Lyons2002), or, as the name suggests, as an inductive argument (e.g., Poincaré Reference Poincaré1902/1952; Putnam Reference Putnam1978; Magnus and Callender Reference Magnus and Callender2004).Footnote 1 I will argue against the inductive version of the PMI—or any construal of the PMI that makes use of historical induction—by using John D. Norton’s material theory of induction (Norton Reference Norton2003, Reference Norton2018). The upshot is that one ought to be critical of historical inductions that seem to fit the general form or pattern of a good inductive argument but may in fact lack inductive warrant. Various critiques have been put against the PMI (e.g., Lewis Reference Lewis2001; Lange Reference Lange2002; Mizrahi Reference Mizrahi2013), along with some defenses (e.g., Saatsi Reference Saatsi2005). In section 2, I present the PMI and briefly discuss some criticism in order to place my own analysis in broader context. Section 3 outlines the material theory of induction and argues that it dissolves the PMI, while section 4 extends such claims to the more recent problem of unconceived alternatives. In section 5, I note that the material theory of induction does leave room for a local version of the PMI, which holds in a limited domain, such as in relation to certain medical studies (Ruhmkorff Reference Ruhmkorff2013). I end in section 6 with a short conclusion.
2. The (Inductive) Pessimistic Metainduction
The modern formulation of the PMI is usually attributed to Laudan (Reference Laudan1981), who argued that having genuinely referential theoretical and observational terms, or being approximately true, is neither necessary nor sufficient for a theory to be explanatory and predictively successful. More generally, Chakravartty characterizes the argument as follows: “[The PMI can] be described as a two-step worry. First, there is an assertion to the effect that the history of science contains an impressive graveyard of theories that were previously believed [to be true], but subsequently judged to be false. … Second, there is an induction on the basis of this assertion, whose conclusion is that current theories are likely future occupants of the same graveyard” (Reference Chakravartty2008, 152; cf. Wray Reference Wray2015, 61).
The PMI then may take the following form:
P(i) Past theory 1 was successful but not genuinely referential or approximately true.
P(ii) Past theory 2 was successful but not genuinely referential or approximately true.
…
(C) Therefore, current (and perhaps future) theories are successful but (by induction) probably not genuinely referential or approximately true.
Laudan (Reference Laudan1981) suggests that the history of science contains a graveyard of theories that were previously believed to be approximately true and genuinely referential but that subsequently were judged to be false and not referential. Estimations of the number of such superseded theories have been debated (e.g., Lewis Reference Lewis2001; Wray Reference Wray2013), and recently Mizrahi (Reference Mizrahi2016) presents evidence that challenges the “history of science as a graveyard of theories” claim. Others voice concerns regarding the period of history of science used in order to extract historical evidence (e.g., Lange Reference Lange2002; Fahrbach Reference Fahrbach2011) or the proper unit of analysis, that is, “theories” versus “theoretical entity” (e.g., Lange Reference Lange2002; Magnus and Callender Reference Magnus and Callender2004). Similarly, Park (Reference Park2011, 83) and Mizrahi (Reference Mizrahi2013, 3220–22) have argued that the PMI is fallacious because of cherry-picking data, biased statistics, and nonrandom sampling. Other charges against the PMI include that it commits the base-rate fallacy (Lewis Reference Lewis2001) and the turnover fallacy (Lange Reference Lange2002).
My own criticism of the inductive PMI comes from a different avenue. I will assume that the antirealist possesses randomly sampled historical evidence from the correct period of history and with the proper unit of analysis, which is not biased or cherry-picked. Still, on the material theory of induction the PMI will not be a cogent argument. In other words, I aim to identify what I take to be a more fundamental (although not categorically different) problem with the PMI.
3. PMI Meets the Material Theory
3.1. The Material Theory of Induction in a Nutshell
Consider the following formally identical inductive inferences (Norton Reference Norton2003, 649):
(P1) Some samples of the element bismuth melt at 271°C.
(C1) Therefore, all samples of the element bismuth melt at 271°C.
(P2) Some samples of wax melt at 91°C.
(C2) Therefore, all samples of wax melt at 91°C.
What makes the first argument an inductively strong and cogent argument, while the second is a weak and noncogent inductive argument? Norton (Reference Norton2003, Reference Norton2018) has argued that formal theories of induction, which provide universal schemas that are meant to identify the inductions that are licit and those that are not, stand against an insurmountable difficulty when facing such a question.Footnote 2 Instead, he offers a material account of induction: “In a material theory, the admissibility of an induction is ultimately traced back to a matter of fact, not to a universal schema. We are licensed to infer from the melting point of some samples of an element to the melting point of all samples by a fact about elements: their samples are generally uniform in their physical properties. … All inductions ultimately derive their licenses from facts pertinent to the matter of the induction” (Norton Reference Norton2003, 650). Norton calls the local facts that power inductive inferences “material postulates.” Material postulates themselves are supported by other instances of induction that are licensed by different material postulates.
3.2. Material Analysis of PMI
Many of the criticisms of the inductive PMI discussed above amount to the claim that the universal schema used by the likes of Laudan (Reference Laudan1981)—namely, (P3) Some A’s are B’s. (C3) Therefore, all A’s are B’s—does not apply in the context of the PMI. This is so because various criteria needed to implement said scheme (e.g., random sampling, correct historical period, proper unit of analysis) have not been met. What I wish to do here is conduct a material analysis of the PMI. Considering the above presentation of the PMI in its Inductive Generalization PMI form, we may ask, what powers the inductive inference, that is, what material postulate licenses the pessimistic conclusion?
In context of the two inductive arguments considered in section 3.1, we note that there is no material postulate that licenses the inductive inference in the case of wax (P2 to C2), but there is one in the case of bismuth (P1 to C1): generally, chemical elements are uniform in their physical properties. By analogy, the presumption of the metainduction is that each historical case study looked at is an instance of the same thing, a discovery of induction in science. If we are to perform the metainduction, then there needs to be something in the background facts that unifies all such inductions, just like the fact chemical elements are generally uniform in their physical properties warrants the inductive inference regarding the melting point of bismuth. Let us consider several options.
First, perhaps the material fact is that most scientists use a common rule or method in constructing or discovering successful theories, something along the lines of Mill’s (Reference Mill1872/1916, bk. 3, chap. 7) methods of experimental inquiry. If so, the properties of the rule would be used to authorize the induction. Is there such a rule or maybe some common scientific method? A glance at the history of science suggests that this is unlikely. Newton’s deduction from the phenomena is very different from Darwin’s inference to the best explanation, which in turn differs radically from Einstein’s thought experiments with light beams, trains, and elevators.Footnote 3 In fact, there seems to be a consensus among historians and philosophers of science that something like the “scientific method” is really more of an umbrella term for very different methods used by scientists to construct and discover theories. After all, novel problems necessitate novels solutions, and the commonality that does arise in different cases, say, attempts to minimize error or to be objective, is not the kind of commonality that we seek in powering the PMI and drawing the pessimistic conclusion. For instance, Kwa (Reference Kwa2011, 11) argues that there is no single, fundamental method used in science: “there is not just one form of Western scientific rationality; there are at least six.” The framework of six “styles of knowing,” includes the deductive, experimental, hypothetical-analogical, taxonomic, statistical, and evolutionary styles. It is based on Crombie’s (Reference Crombie1994) three-volume work. Similarly, Ian Hacking (also taking the lead from Crombie’s work) has argued that there are distinct “styles of reasoning” used in science, such as the postulational style, the style of experimental exploration, the style of hypothetical construction of models by analogy, the taxonomic style, the statistical style, the historical derivation of genetic development, and the laboratory style (Hacking Reference Hacking1992). This further corroborates the idea that scientific methods used for theory construction and discovery, as well as for scientific explanation, are very diverse.
More generally, scientific theories are not the sort of things that portray the type of uniformity needed to license inductive inferences on Norton’s material theory. Albeit in a different context, a similar point is nicely made by Mizrahi (Reference Mizrahi2013, 3218):
A uniform—as opposed to diverse—sample might be a sample of, say, copper rods. From a sample of just a few copper rods that are tested for electrical conductivity, it is reasonable to conclude that all copper rods conduct electricity because, if you have seen one or two copper rods, you have seen them all (given their uniform atomic structure). Scientific theories, however, are not as uniform as copper rods. The point, then, is that any sample of theories is not going to be uniform in a way that is required for a “seen one, seen them all” inductive generalization.
Similarly, and second, perchance there are some facts about investigating scientist themselves, how they work, or the problem situations that they work in that can unify the historical evidence in a way that provides us with the inductive warrant we seek. Maybe such facts will include something about the psychology of scientists: their fastidiousness and fear of error, their facility at jumping to conclusions, or possibly their curiosity, logic, creativity, skepticism, and so on. However, the history of science furnishes us with scientists who are heterogeneous enough in their psychological traits, and work in such varied contexts, so as not to allow for a unification of the various historical cases in a way pertinent to licensing the pessimistic inference of the PMI.
Third, we may want to construe the PMI in its inductive generalization form as a kind of abductive argument with the following type of material postulate:Footnote 4
P(i) The success of past theory 1 (constructed using method m) is not best explained by its truth.
P(ii) The success of past theory 2 (constructed using method m) is not best explained by its truth.
…
(MP-PMI) Scientific theories constructed using method m are generally uniform with respect to what best explains their predictive success.
(C) The success of our best current (and perhaps future) theories (constructed using method m) are not best explained by their truth.
Stating the PMI as above has the merit of directly engaging with the “no miracles argument” for scientific realism, namely: “That terms in mature scientific theories typically refer [to things in the world], … that theories accepted in a mature science are typically approximately true, that the same term can refer to the same thing even when it occurs in different theories—these statements are viewed by the scientific realist not as necessary truths but as part of the only scientific explanation of the success of science, and hence as part of any adequate scientific description of science and its relations to its objects” (Putnam Reference Putnam1975, 73). But worries abound. First, the realist may very well deny P(i), P(ii), and so on, and argue that the success of past theories is best explained by their truth but that, as it turns out, the best explanation did not hold in this case or else that there is some sense in which past theories, insofar as they were successful, were approximately true or on the road to truth. Second, construing the argument as an abduction opens up a Pandora’s box of problems associated with the notion of explanation: What is explanation? Are there accounts of explanation for which success is best explained by truth and ones for which it is not? If so, which account of explanation is relevant in this context? And so on.
Third, how would we establish MP-PMI? One option is to appeal to the PMI itself, but this would be either circular or else push us to look for another material postulate. Another option is to grant the MP-PMI as a reasonable assumption, but surely the realist would reject such an assumption as question begging. Alternatively, we could look in detail at said “method m.” For example, phenomenological models are good candidates for the type of things that can provide empirical success but are not generally approximately true—their empirical success is explained by the fact that they are created to fit the data. However, this means that the cogency of the above argument depends on the idea that all theories appealed to were constructed with the same method m. But we already judged that there is no one method that is relevant to constructing scientific theories. Thus, at best, the above argument can power a kind of local PMI: successful theories constructed by method m are not approximately true. We consider one such case in more detail in section 5.
In short, on the material theory of induction, inductive arguments are powered by material postulates (i.e., by facts), but in the context of the PMI it seems unlikely that any such non-question-begging postulates, which would not render the PMI obsolete, can be found. This is so even if, say, the historical data were not cherry-picked, and the right unit of analysis and correct period of history were used. In other words, I am equally skeptical of projects that attempt to block the pessimistic conclusion by, for example, taking a random sample of past scientific theories (e.g., Mizrahi Reference Mizrahi2013, 3222). In the following section I attempt to extend such claims to the problem of unconceived alternatives.
4. Extension to the Problem of Unconceived Alternatives
Recently, Stanford (Reference Stanford2001, Reference Stanford2006) has developed what may be characterized as a new version of the PMI:
I propose the following New Induction over the History of Science: that we have, throughout the history of scientific inquiry and in virtually every field, repeatedly occupied an epistemic position in which we could conceive of only one or a few theories that were well-confirmed by the available evidence, while subsequent history of inquiry has routinely (if not invariably) revealed further, radically distinct alternatives as well-confirmed by the previously available evidence as those we were inclined to accept on the strength of that evidence. … Thus, the history of scientific inquiry offers a straightforward inductive rationale for thinking that there typically are alternatives to our best theories equally well-confirmed by the evidence, even when we are unable to conceive of them at the time.
(Stanford Reference Stanford2001, S9)The problem of unconceived alternatives as an argument against scientific realism has been criticized on various grounds (e.g., Chakravartty Reference Chakravartty2008; Mizrahi Reference Mizrahi2015), but my goal here is simply to note that the discussion of section 3 can be extended to this new version of the PMI, which can be construed as follows:
P(i) In the past time of theory 1, theory 1 was successful, but there were unconceived alternative theories that were as well supported by available evidence but with radically different hypotheses or ontology.
P(ii) In the past time of theory 2, theory 2 was successful, but there were unconceived alternative theories that were as well supported by available evidence but with radically different hypotheses or ontology.
…
(C) Therefore, in present times, current theories are successful but most likely (by induction) there are unconceived alternative theories that are as well supported by available evidence but with radically different hypotheses or ontology.
What we need for the material analysis is something like the following material postulate: generally, successful theories are underdetermined by data because of possible unconceived alternative theories. In a similar fashion to the MP-PMI, we could look to some common rule used by scientists to conceive theories, or some common psychological traits among scientists, that may ground the idea that successful theories are such that serious, empirically adequate (unconceived) alternatives always exist. But for the same reasons discussed above, it seems unlikely that any such common rule or traits will be found. That said, perhaps cognitive facts about human scientists might support the inductive inference to the conclusion that we always miss some alternative theories, which in turn are consistent with the available evidence. What is attractive about this line of thought is that it does seem plausible that because of our cognitive limitations there are always “unconceived alternatives.”Footnote 5 However, mere cognitive limitations do not support the further conclusion that there are unconceived alternative theories that are consistent with available evidence, at least not without appealing to another historical induction.
Alternatively, one may think that Stanford’s new induction circumvents the material objection: modal reflections alone convince us that there are always unconceived alternative theories that can explain and predict empirical phenomena just as well or better than conceived theories. But how can we come to such a conclusion based on modal reflections alone? Is it not conceivable, if not possible, that there would be a point in history with no unconceived alternatives? And is it not conceivable, if not possible, that we are at such a point in time in history? Moreover, it is unclear what to make of theory-independent modal claims (unless one has logical modality in mind, which is not the case here). Certainly, we can talk about different physically possible worlds given a particular physical theory. For instance, various solutions to the Einstein field equations are taken to denote different possible universes according to relativity theory. But it is not clear what is meant by different possible or alternative conceivable theories given no metatheory as a constraint, so to speak.Footnote 6 Certainly, the structure of the space of unconceived alternative theories will matter when considering whether the inductive step (in the problem of unconceived alternative) is warranted, but it is not clear how we can know what this structure is. In any case, if we know, based solely on modal reflections, that unconceived alternative theories, which are consistent with the evidence, always exist, then the historical induction is doing no work for us at all.
5. Room for a Local, Material Pessimistic Induction?
Although the material analysis given here may prompt us to be skeptical of historical inductions (insofar as one is moved by the material theory of induction), it can help us understand why local pessimistic inductions may be tenable. Specifically, I want to look at a recent discussion by Ruhmkorff (Reference Ruhmkorff2013), who contends that meta-analyses in medicine (e.g., Ioannidis Reference Ioannidis2005a, Reference Ioannidis2005b), which show that a disconcertingly high percentage of prominent medical research findings are refuted by subsequent research, can be developed into a local pessimistic induction. Ioannidis (Reference Ioannidis2005a, Reference Ioannidis2005b) is concerned with studies, denoted “M-studies,” which satisfy the following criteria: “being highly cited, using contemporary research and statistical methods, and being among the first studies to investigate a question at issue” (Ruhmkorff Reference Ruhmkorff2013, 420). Ruhmkorff (Reference Ruhmkorff2013, 421) then uses the various conclusions of Ioannidis (Reference Ioannidis2005a, Reference Ioannidis2005b) to generate a local PMI in the field of medicine (PMI-M):
E1. 41% of the associative or causal claims made by M-studies in the sample were inconsistent with the results of subsequent published studies either (1) because the later studies provided evidence against the existence of the association or effect; or (2) because the later studies provided evidence that the magnitude of the association or effect was significantly different.
E2. Therefore, we can expect approximately 41% of the associative and causal claims made by M-studies to be inconsistent with subsequent published studies.
On Norton’s theory we need to appeal to a material postulate to license the pessimistic inductive inference in the transition from E1 to E2. Since we are now working in a limited domain without many heterogeneous examples as in the whole history of science, it may be possible to find some significant commonality between the methods used in different M-studies that can act as licensing facts. What are the background facts that power the PMI-M? Here are some options extracted from Ioannidis’s diagnosis of his meta-analysis and quoted in Ruhmkorff (Reference Ruhmkorff2013, 419):
Contributing factors include: bias in research (Ioannidis Reference Ioannidis2005b); non-randomized trials (Ioannidis Reference Ioannidis2005a); smaller rather than larger sample sizes in refuted studies (Ioannidis Reference Ioannidis2005a, 224); and publication and time-lag biases (whereby studies with highly significant and potentially aberrational positive results are overrepresented among published articles in major journals and are published more quickly than other articles) (Ioannidis Reference Ioannidis2005a, 224). Particularly intriguing is the idea that large-scale features of the structure of medical and biological inquiry contribute to the high contradiction rate. Having a number of distinct working groups looking at the same problem increases the chances that at least one of them will find something statistically significant, especially if they are looking at a wide array of possible relationships (Ioannidis Reference Ioannidis2005b, 697–98). The computational power and richness of data sets available to researchers increases the chance that some of them will be successful in achieving statistical significance, even when no real relationship exists (Ioannidis Reference Ioannidis2005b, 701).Footnote 7
These various factors, insofar as they are common to most M-studies, are the type of background facts that warrant the pessimistic induction from a material point of view. One may worry of course that the pessimism associated with local PMI generalizes since, presumably, facts about biases and the like are facts about researchers in general, not just researchers in medical science in particular. But, although all scientific studies have to deal with challenges such as bias, it may be the case that a particular local subfield, because of its specific nature and whatever social norms are in place for collecting and disseminating evidence, is especially challenged in a way that can justify the pessimistic induction. The above suggests that this is indeed the case for M-studies.
To end, Ruhmkorff (Reference Ruhmkorff2013) argues against global PMI on independent grounds (namely, he argues that the PMI is self-undermining and that it commits a statistical error previously unmentioned in the literature), but he also argues for the plausibility of a local PMI (i.e., PMI-M). He contends that there are clear advantages of the (local) PMI-M over the (global) PMI. What I wish to note here is that an additional advantage of the PMI-M, or local pessimistic induction generally speaking, is that while the global PMI dissolves upon a material analysis, a material account of the PMI-M does seem viable.
6. Conclusion
I have argued that historical inductions such as the (global) PMI and the problem of unconceived alternatives dissolve if we work with the material theory of induction. The reason is that we lack the material postulates needed to license the pessimistic inference: the great heterogeneity of case studies from the history of science of conceiving, constructing, and discovering (explanatory and predictively successful) theories along with the abundant variety of context that scientists find themselves in and traits that they exhibit make it unlikely that any commonality will be found strong enough to authorize the induction. One may of course object: so much the worse for the material theory of induction. This is a fair point, but there is a more general upshot to consider. In various situations one may be able to appeal to the notion of “induction” without much being at stake, but in the context of historical inductions like the PMI and the problem of unconceived alternatives, “induction” is doing a lot of (philosophically) heavy lifting, and so the situation rightfully calls for scrutiny. Such scrutiny has led to the various discussed criticisms that are presented in the context of more traditional, nonmaterial theories of induction. Accordingly, it seems appropriate to show that—even if we assume randomly sampled historical evidence from the correct period of history and with the proper unit of analysis that is not biased or cherry-picked, with no statistical error, and so on—historical inductions do not fare well on the material side of things. I leave objections to the effect that one ought to construe the PMI as a deductive argument, or through a different framework for induction, for example, via hypothetical or probabilistic induction, for future work.
