A website for Nathan Oseroff philosophy graduate student at King's College London. 

Sunday, 23 July 2017

Can a bad argument against a pessimistic meta-induction help to improve the pessimistic meta-induction? 

There must be something wrong with the following argument against one version of the pessimistic meta-induction.  I call this argument the historical pessimistic meta-induction (hereafter referred to as 'HPMI'), in order to contrast it with the more common scientific pessimistic meta-induction (hereafter referred to as 'SPMI'). 

In brief, the usual framing of the SPMI is over-generative: the structure of the SPMI and the plausibility of the premises in the argument applies to other disciplines other than the natural sciences, including the discipline of history.  This produces a similar HPMI that undermines the very plausibility of a core premise in the SPMI: due to a history of incompatible interpretations of the historical data, we lack any reason to accept the premise that there is a long history of incompatible mature scientific theories that were at one time successful. 

This result is, however, manifestly absurd: we do not lack any reason to accept this premise in the SPMI.  In fact, scientific realists and anti-realists alike have reason to accept this premise in the SPMI (or variations thereof).  This premise is simply not in dispute.  Therefore the structure of the SPMI must be modified in order to skirt this reductio.  I include a reconstruction of the SPMI and where it may go wrong in over-generating the HPMI, as well as how to reframe one core premise in the SPMI to bypass several objections. 

1.  The no-miracles argument

There are many different versions of pessimistic meta-inductive arguments (hereafter referred to as 'PMI') that are often first attributed to Larry Laudan (1981).  Since Laudan, philosophers have developed different versions of PMI arguments.  Some versions of PMI arguments have stronger conclusions than others, while different versions of PMI arguments target key theses accepted by scientific realists; others are more limited, and target a specific argument for scientific realism, known as the no-miracles argument (NMA).  In what follows, I'll address a version of the PMI that targets the NMA.  That is, rather than targeting a key thesis accepted by scientific realists, this PMI undermines a justification for accepting scientific realism, the NMA. 

The NMA usually runs as something approximating the following:

(R1) (Mature) scientific theories are successful at F.

(R2) The best explanation of the success at F of (mature) scientific theories is that these scientific theories are (approximately) true. 

(R3) Therefore, (mature) scientific theories are (probably approximately) true if they are successful at F.

According to the NMA, the (probable approximate) truth of scientific theories is the best explanation for success, or as Putnam put it, 'that does not make the success of science a miracle' (Putnam 1975, 73). 

1.1 What does 'successful at F' mean in this context? 

We can carve up F into two broadly different groups: (a) F is the product of our best available modes of inquiry; (b) F satisfies certain criteria without reference to modes of inquiry, such as satisfaction of theoretical virtues or predictive success. 

On the one hand, F can be thought of as a product, as the result of the way inquiry best proceeds.  F is valuable due to extrinsic properties, for example, the behaviour of the epistemic community that generated F and subsequently tested F.

Consider that, all else being equal, it would be reasonable for me to prefer sight-unseen a tool that was modeled based on the results of extensive product testing and quality control used in the construction of other token tools of this type over a tool not developed as a result of extensive product testing and quality control.  The explanation for why I prefer the first tool over the untested tool would be explained by appealing to these extrinsic properties. 

Similarly, if S is the product of our best available modes of inquiry (say, S was developed and tested by experienced scientists), it will be preferable than had S* been the product of modes of inquiry that are known to be inferior (say, S* was corroborated by haruspicy). 

On the other hand, F can include pertinent features of theories.  There are a number of intrinsic properties available, such as present empirical fit, novel predictive success, continuity of key theoretical terms, theoretical simplicity, minimum mutilation to intuitive concepts, membership within a progressive scientific research programme, and so on. 

Once carved up into these two distinct--but at times overlapping and difficult to separate--categories, we can now join them to speak generally of 'success at F', or more simply as 'success'.  In this way, 'success' carries with it a number of desirable features, and it is assumed that a number of mature scientific theories are 'successful' to varying degrees.  What is up for debate, however, is whether 'success at F' is indicative of (probable approximate) truth.  It is here that one version of the PMI is introduced. 

2.  A pessimistic meta-induction

Here is a version of the PMI argument that targets the previously mentioned version of the NMA.  In order to differentiate it from later versions, it will be referred to as a scientific pessimistic meta-induction (SPMI), in order to clarify that the PMI makes reference to the natural sciences, in contrast to other disciplines.  This SPMI takes the form of a following reductio and is partly based on the formulation popularised by Lewis (2001, 373), Psillos (1996) and Saatsi (2005):

(P1) (Mature) scientific theories are successful at F.

(P2) If there is a long history of (mature) scientific theories that are each successful at F but are incompatible with present (mature) scientific theories, then scientists cannot reasonably infer (mature) scientific theories are (probably approximately) true based on F.

(P3) Many past (mature) scientific theories were for a time successful at F and are incompatible with present (mature) scientific theories. 

2.1 Care in the construction of the SPMI

The SPMI is designed to be fairly weak for a number of reasons.  For example, the conclusion drawn from the SPMI is not that we can reasonably infer that (mature) scientific theories are false; rather, the conclusion is directed at the scientific realist that appeals to success at F as a reason to believe the theory is (probably approximately) true. 

Given the available historical evidence, so the anti-realist claims, the realist must show how the apparent historical evidence fails to support P3--for example, that any enumerated list of past scientific theories were not mature or successful at F. The realist's response to the SPMI then follows the usual path of critical analysis of whether these examples satisfy whatever conditions of maturity and success they adopt as licencing the inference from maturity and success to (probable approximate) truth. 

In addition, (so the anti-realist may claim) the realist must provide a better account of history of science to make the inductive inference that past success is more likely to predict continued future success than not.  For example, one could attempt to construct, as Nicholas Maxwell (2017) does in support of his aim-oriented empiricism, an optimistic meta-induction (OMI) that preferable future scientific theories will share similarities with current and past preferred scientific theories, such as unity of disciplines or an increase in explanatory depth and breadth.  Similarly, Ludwig Farbach (2011a) proposes his own OMI that our current (mature) scientific theories are more successful and more mature than past scientific theories (which were only moderately successful and moderately mature). 

Furthermore, P3 is designed to sidestep a few potential argumentative pits.  A stronger version of the SPMI available to the anti-realist can run as follows: if the realist is to make the inference from past success to (probable approximate) truth, they must take seriously what we learn from the past.  We must also make the inference from repeated cases of momentary past success in some field to eventual failure.  Thus, at least in these fields with a history of failure, the realist should take seriously the concern that the existence of repeated failure despite success shows there aren't suitable grounds to infer (probable approximate) truth. 

This stronger variation of P3 that permits inferring from momentary success to eventual failure could require reasonable belief or knowledge that past scientific theories accepted based on success are (probably) false.  However, this includes a premise too difficult for many to accept, namely we have reasonable belief or knowledge that there is a long history of failure in the natural sciences.  The anti-realist need not go so far in order for the SPMI to do its work.  In its current form, however, P3 affirms merely that there exists past (mature) scientific theories that were (for a time) successful and that they are incompatible with present (mature) scientific theories that are successful. 

Part of the reason P3 is further restricted to '(mature) scientific theories' that are śuccessful at F' rather than merely 'currently accepted scientific theories' is twofold: first, the anti-realist acknowledges the realist's objection that we ought to restrict our focus to the relevant set of scientific theories in history of science, that is, theories that have proved their mettle: scientific theories that are genuinely mature and genuinely successful at F (whatever 'mature' and 'success' may mean to the realist).  After all, many current scientific theories are likely not successful or mature, thus the realist does not make an NMA about these theories. 

Furthermore, our focus is on an inference from success to probable approximate truth rather than truth, since such an inference will often be mistaken: even in our everyday lives, we may engage in activities that are successful for a time, but eventually lead to error.  By analogy, I would not want to conclude that since I successfully rode my bike to work each morning, and I have a demonstrated track record as a capable bicyclist, I will therefore continue to successfully ride my bike to work every morning: since such an abductive inference cannot account for popped tyres, inclement weather or inattentive drivers.  Therefore, we want an abductive inference from success to (probable approximate) truth in the natural sciences that would be in line with everyday forms of abductive inference from past success to (probable approximate) truth. 

2.2 Why accept P3 in the SPMI? 

What would make P3 true--or at least plausible--given the available historical evidence?  The anti-realist's focus on the disconnect between momentary and fleeting success and (probable approximate) truth is that the inference drawn outside the most mundane cases of engagement in everyday circumstances is--at least to the anti-realist--epistemically optimistic to the point of licensing a large number of incompatible beliefs. 

Even with restrictions to mature scientific theories and to probable approximate truth, however, the realist must deal with an uncomfortable fact: 'at least some past theories that pass all realist tests of maturity and success are still considered false' (Psillos 1996, S307) (or at least incompatible with our accepted scientific theories).  This does not mean the realist must concede immediately when faced by the SPMI.  After all, if one were to go back far enough into the past, even our best commonsensical ways of inquiry have changed (targeting modes of inquiry as indicative of success): we no longer resolve disputes by trial by combat or trial by ordeal, for example.  Similarly, there may have existed a number of false commonsensical beliefs that were once 'successful' (made without reference to modes of inquiry).  The realist and anti-realist alike would not want to make the inference that commonsensical beliefs are similarly undermined by a variation of a PMI.  This is not to say that the SPMI is dismissed on those grounds; rather, once historical evidence for P3 accumulates, there is a certain tipping point at which it is no longer reasonable to hold R2 in the NMA. 

Implicit in the motivation to adopt the SPMI is that the NMA does not or should not cover beliefs that extend beyond the empiricist's safe home--we should be either equally concerned or concerned to an even greater extent over the relationship between (mature) theories and successes at F and truth in other fields that go beyond the available empirical evidence and have such a disreputable history. 

The continued reliability of commonsensical beliefs in everyday circumstances and no clear genealogical history of repeated failures shows that if the realist were to make an NMA or any other form of abductive inference from success to (probable approximate) truth, (so the anti-realist argues) it is best constrained to commonsensical beliefs, for they simply have the historical track record of apparent success (or lack a historical track record of apparent failures).  It is only when this abductive inference is extended beyond everyday circumstances that we are left with a questionable track record: a scientific theory may be, at least for a relatively short period of time, immensely successful at F, but the bar is set far higher than for commonsensical beliefs. 

The natural sciences are, presumably, one of our best modes of empirical inquiry outside of everyday or commonsensical belief-formation.  In fact, the methods and evidence available in the natural sciences may be far better in its methods and track record than in the historical sciences.  This explains why most versions of the PMI are almost exclusively constructed as a variation of a SPMI, rather than other domains.  However, there are other versions of the PMI.  The PMI isn't limited to the natural sciences, but may also extend to the historical sciences. 

In short, the natural sciences presumably satisfy P3; however, other forms of inquiry, such as the historical sciences, may also satisfy their respective version of P3 as well. 

[Note: the present use of language is meant only to reflect the structure of the SPMI directed at the natural sciences.  It is merely a quirk in the development of the English language that the past and the discipline are referred to as 'history';it is a reflection of current academic institutions that we do not often refer to 'historical theories' and choose to categorise history as belonging to the humanities rather than the sciences.  The term 'historical sciences' is meant in much the same way as the 'social sciences' are understood: as rigorous disciplines with reputable and accepted standards, as a form of Wissenschaft, with present (mature) theories deserving of general praise, careful consideration or credence that is not granted to different forms of inquiry that approach these problems that are thought to be deserving of condemnation or dismissal (e.g. pseudo-history).] 

3.  A no-miracles argument in the historical sciences

Assume for the moment that the historical sciences are on similar epistemic footing than the natural sciences.  That is to say, whatever counts as 'success' in the historical sciences about (mature) historical theories is either equal to what counts as 'success' in the natural sciences about (mature) scientific theories. 

The plausibility of such an assumption may be due to any number of reasons: the methods available to historians may be less reliable than methods available to scientists, the available historical evidence may be so limited as to lead to frequent cases of underdetermination that cannot be resolved by further evidence, and so on.  My focus is on, however, the following thesis: Many past (mature) historical theories were once successful at F, and are incompatible with our present (mature) historical theories successful at F.The use of the term 'historical theories' serves not merely to provide an analogue to the term 'scientific theories'; it is as follows: oftentimes historians are concerned with explanations for phenomena that go beyond the available evidence; they make novel predictions or retrodictions; these theories are constructed to fit the available evidence, are well-integrated into a theoretical system and satisfy a number of theoretical virtues; theories both provide some narrative to historical episodes, as well as help develop agreement between historians that some historical episode took place.  That is to say, historians do not simply read off what is written in books, but engage with the available texts on numerous levels and using numerous different forms of testing, including disputing the origins and veracity of a text using methods such as linguistic analysis or analysis of typefaces, the function and purpose of a historical site based on geology, astronomy or radio-carbon dating, and so on.  History is not an 'open book', but must be interpreted (and reinterpreted).If there were an equal or greater history of incompatible mature historical theories, any NMA in the historical sciences will therefore either be just as strong or weaker than in the natural sciences. 

4.  A pessimistic meta-induction in the historical sciences

Here are two premises that share structural similarities with P2 and P3:

(Q2) If there is a long history of (mature) historical theories that are each successful at F but contract present (mature) historical theories, then historians cannot reasonably infer (mature) historical theories are (probably approximately) true based on F.

(Q3) Many past (mature) historical theories were for a time successful at F and contradict present (mature) historical theories. 

What is of interest here is that Q3 is, if we accept what historiographers have to say, most likely true.  While there may be a consensus among historians on a number of historical claims, that consensus has developed over a long period of time, requiring immense historical scholarship.  I will not get into the evidence for Q3 here, but I will assume that this is the case due to limited space. 

In sum, if there is a 'safe home' for commonsensical beliefs, and beliefs that fall outside this 'safe home' require an NMA or some other similar abductive inference from success to (probable approximate) truth, there must be an analogous NMA for the historical sciences in order to accept historical theories.  If, however, there is an NMA in one discipline that licences making an inference from success to (probable approximate) truth, there will a PMI following close behind. 

To give credence to Q3, I can only appeal to some commonsensical beliefs:

(a) historians today are often believed to be usually better at doing historical scholarship than past historians; (b) the explanations from present historians are often usually better explanations than past historians; (c) modern historians have access to better evidence than past historians; (d) there exists disagreement between modern historical scholarship and past historical scholarship; (e) present historians are capable at finding errors in the work of previous historians (but previous historians are, naturally, incapable of finding errors in the work of present historians); (f) we should prefer modern historical scholarship and distrust past historical scholarship if past historical scholarship is incompatible with present scholarship; (g) there are improvements and refinements in historical scholarship over time, etc. 

I take it that both realists and anti-realists alike believe (a)-(g) as well as numerous other related beliefs. 

(In what follows, a 'historical NMA' or 'HNMA' is contrasted to a 'scientific NMA' or 'SNMA', in order to distinguish an NMA that applies to the natural sciences and an NMA that applies to the historical sciences.) 

If we are to accept P2 and P3, we should accept Q2 and Q3 on either equal grounds accepted for P2 and P3.  For any HNMA over whether to accept, based on the success of mature historical theories, it will be just as strong as any SNMA (R2). 

If we accept an SPMI, (presumably) we must also accept a similar version of the PMI in the historical sciences, referred to as a historical pessimistic meta-induction (HPMI):

(Q1) (Mature) historical theories are successful at F.

(Q2) If there is a long history of (mature) historical theories that are each successful at F but contract present (mature) historical theories, then historians cannot reasonably infer (mature) historical theories are (probably approximately) true based on F.

(Q3) Many past (mature) historical theories were for a time successful at F and contradict present (mature) historical theories. 

5.  The HPMI undermines P3

If an anti-realist accepts P1-P4 as undermining the SNMA, they must similarly accept Q1-Q4 on similar grounds: both areas lie outside the empiricist's safe home for an NMA, for both P3 and Q3 are true. 

Here is the (apparent) problem for the SPMI: P3 must be accepted based on historical evidence.  Historical evidence is only reasonably accepted based on a HNMA; but the reasons for accepting an SPMI entail accepting an HPMI.  Accepting an HPMI entails rejecting an HNMA, but in order to accept P3 we must accept a HNMA. 

Since the only evidence for P3 is (presumably) historical, and relies on a HNMA, no one should be convinced by the SPMI, for by accepting the SPMI, there can be no acceptable historical evidence for the key premise in the SPMI, P3.  In sum, the PMI in its current form is over-generative, and the reasons to accept a SPMI entail accepting a HPMI.  If this general argument that the SPMI is self-undermining should hold, this version of the SPMI is not a good argument, for it undermines a core premise in the SPMI, P3, by entailing that we should accept a HPMI. 

6.  A few plausible responses to the PMI in the historical sciences

In what follows (6.1a-6.7b), I set out a few obvious objections and replies.  In brief, there is something fundamentally wrong with this version of the HPMI as undermining a core premise P3.  The conclusion is not just absurd, but laughably so.  However, by examining where the HPMI may be mistaken, it does help clarify how philosophers of science can be clearer in setting out P3 in the SPMI. 

6.1a There is a salient epistemic distinction between theory and evidence

One approach at explaining why the HPMI and SPMI are disanalogous would be to point out that on the one hand the SPMI deals with scientific theories, but in the historical sciences, we are dealing with historical evidence or data, rather than historical theories.  This reflects, naturally, how our intuitive conceptual categories and ways of speaking about the distinctions between data/interpretation or evidence/theory would be undermined in order for the HPMI and SPMI to hold the salient similarities. 

We can construct how this objection would work as follows: scientific theories are the very subject of the SNMA and SPMI, but historical theories, however, are not necessary for there to be success in interpreting the historical record, and are not the subject of the HNMA.  If not subject to the HNMA, it follows historical data is not subject to the HPMI. 

Historical theories, under this interpretation, would involve broad theories of the general arc of history (or lack thereof); sociological trends (or lack thereof); norms or principles for how to interpret historical evidence or data; general posits about how people in the past behaved, based on our present behavour; and so on.  While these historical theories may be subject to the HPMI, the HPMI as it is constructed would not target the historical evidence for accepting P3 in the SPMI. 

Once we reframe the HPMI as about historical data or evidence, rather than historical theories, we undermine accepting Q3 on historical grounds: historiographers may have numerous examples of past historians accepting historical theories that conflict with our current historical theories, but there may be few examples of past historians accepting past historical evidence incompatible with currently accepted historical evidence. 

6.1b There is no salient epistemic distinction between history and the natural sciences

However, the distinction between historical 'evidence' and historical 'theory' isn't as obvious upon further examination.  Historians infer from extant historical documents that a number of past scientists accepted particular scientific theories, that these theories were interpreted in some ways and not others, that these scientific theories were perceived by these individuals as genuinely 'mature' or were in fact 'mature' by our present standards, and that these individuals accepted that these theories were successful at F rather than successfully attaining external or internal features that are not accepted today (and should not have been accepted then) or were indeed successful at F for a time. 

In some cases (presumably) this involves a great deal of inference and conjecture, albeit inferences and conjectures that are (at least to our eyes) reasonably held.  But the issue is not whether these inferences are reasonably held per se, but rather whether these inferences are reasonably held by the anti-realist's lights.  So long as there is an HNMA invoked, the HPMI rolls in. 

If so, the anti-realist must develop a better version of the SPMI in order to skirt this potential problem that historical theories are subject to a HPMI than simply appealing to pre-theoretical concepts or linguistic use: both scientists and historians use theories that go beyond the available evidence in order to interpret the evidence; 'evidence' is not theory-neutral, but are themselves smaller, more localised theories about occurrences in particular spatio-temporal regions, and are differentiated from commonsensical beliefs in that (1) we no longer have epistemic access to in the ways we have access to many commonsensical beliefs and (2) there exists a long history of (mature) historical theories that contradict our current (mature) historical theories. 

6.1.1a A further reply

Analogous to Kitcher (1993, 149), we can differentiate between 'working posits (the putative referents of terms that occur in problem-solving schemata)' that generate the success at F and 'presuppositional posits (those entities that apparently have to exist if the instances of the schemata are to be true', which are suspect.  Similarly, we can limit ourselves to theories in the historical sciences that are about historical series of episodes that occurred in specific world-states, such as 'According to our current understanding, there were a number of past scientific theories that were mature, successful at F, but contradict our current (mature) scientific theories successful at F'.  These historical theories are (presumably) not in dispute by historians of science, since they do away with talk about what past scientists believed. 

While scientists and historians both operate and interpret the data within theoretical frameworks, these are not unlike Kitcher's presuppositional posits; our interest in the HPMI is limited to working posits, namely core relevant historical episodes that support P3. 

6.1.1b A further response

However, as evidenced by historiographers of science have reëvaluated how historians arrived at and checked their historical theories, as well as their standards and assumptions, claims that are restricted to working posits are not closed (see: 6.3b). 

Furthermore, if the anti-realist should accept this approach, the anti-realist may give too much away to the realist in order to salvage the PMI: this is implicitly following the structure of one of Kitcher's arguments for why we should be entity realists about unobservables. 

Still, there is something to the issue raised with taking 'historical theories' to encompass every member of the theoretical whole that historians adopt--the anti-realist is not interested in what past scientists believed, for example, but only whether past scientific theories contradicted present scientific theories, whether they were genuinely mature, and whether they were genuinely successful (for a time) at F. By that same token, there is a similar issue with taking 'scientific theories' to include all assumptions made by scientists, even presuppositional posits.  We want to focus on the relevant parts of the scientific theories that are 'mature' and 'successful' in both the HPMI and HNMA, as well as the SPMI and SNMA. 

This brings up a similar issue with the scope of Q1-Q4 in the HPMI...

6.2a ... Q3 should be limited to the relevant domain: historical evidence in history of science

This objection is one of a lack of specificity: our focus is too broad to be informative, since it includes everything within an entire academic discipline.  However, it is more or less an accident of academic administration that 'history' is applied as an umbrella term to a number of unrelated problems: those working on translating ancient Babylonian cuneiform tablets often have a different history of success or failure, methodology and standards when compared to those working on history of early twentieth century theoretical physics in the Austro-Hungarian empire.  It would be unreasonable to compare past success (or eventual failure at F) in the former as if it supported or undermined the latter--in fact, it would be just as unreasonable to blame the son for the sins of the father or my neighbour for my failure to turn off my lights.  Just as we restrict the relevant class to mature scientific theories that are successful, we must similarly restrict the relevant class to mature theories in history of science, not merely mature theories in history.  Thus we should amend Q3 to Q3':

(Q3') Many past (mature) theories in history of science were for a time successful at F and contradict present (mature) theories in history of science. 

This amendment looks far more reasonable than Q3. 

However...

6.2b ... we should similarly limit P3 to the relevant domain

The relevance condition may lead to restricting P3 even more (say, to P3'):

(P3') Many past (mature) scientific theories in some area P were for a time successful at F and contradict present (mature) scientific theory in some areaP.

We should not conclude, for example, that (by supposition) because there existed numerous (mature) scientific theories in biology that were successful at F that were incompatible with one another that present (mature) scientific theories in the climate sciences successful at F are therefore doubtful.  Spontaneous generation was rejected, therefore... present (mature) theories in climate change are not (probably approximately) true?  Biology may simply be (by supposition) on shakier ground than the climate sciences. 

Naturally, a version of the SPMI that accepted P3' rather than P3 would be far more plausible to realists in virtue of it permitting a failed PMI so long as there has not been a long history of incompatible scientific theories within some limited domain; however, what this modified SPMI gives with one hand to the realist it takes away from the anti-realist: by the sake token, it does not target a number of SNMA that are drawn in subfields in which there have not been a history of incompatible theories. 

But by that sake token, Q3' should be amended even further to be in line with P3':

(Q3'') Many past (mature) theories in some area of history of scienceP were for a time successful at F and contradict present (mature) theories in some area of history of science P.

6.3a Accepting historical evidence does not rely on a HNMA; the historical evidence is instead prima facie (probably approximately) true

A good deal of historical evidence, such as diaries, newspapers and court proceedings, are presumably forms of testimonial evidence, and testimonial evidence isn't accepted based on either a scientific or historical NMA.  On whatever grounds testimonial evidence is accepted, it would be on grounds that an anti-realist would accept.  Historical evidence would be accepted on those same grounds.  Thus accepting historical evidence does not rely on accepting a HNMA, and since it does not rely on a HNMA, the anti-realist need not accept Q3, Q3' or Q3'' as undercutting a HNMA, therefore this does not undermine the reasonableness of accepting P3'.  However...

If the anti-realist is able to assert that history of science is done in a way that historians of science do not rely on an HNMA but rather grounds for accepting testimonial evidence (or some other suitable grounds), the HPMI still undermines P3', thus undercutting the SPMI: historiography of science (it is assumed, in this post) further reveals a long history of incompatible theories about whether scientific theories were in conflict with present theories, about whether past scientific theories were genuinely mature and about whether past scientific theories were successful at F.

Put aside any problems with historiography of science for the moment and consider that the present conflict in history of science over the PMI is borne out in Laudan's examples reveals that there exists the current dispute in the realist/anti-realist debate over whether or not the number of historical examples provided by Laudan genuinely support Laudan's PMI.  However, at the time the examples provided in Laudan's PMI were first introduced, this dispute did not exist. 

Hence, at one time in the relatively recent past philosophers of science were in agreement that Laudan's examples were genuine cases of mature scientific theories successful at F that were incompatible with our present mature theories that were successful at F. But there is now disagreement by philosophers of science.  The realist need only point at this very dispute in philosophy of science to establish the plausibility of Q3'' for each of Laudan's examples. 

The realist may respond as follows: should we not infer on these same grounds that any new examples provided to supplement Laudan's own could similarly be overturned by future historical scholarship?  The realist may turn the tables on the anti-realist and make the HPMI that even though there exists present agreement in history of science over whether a past scientific theory was genuinely mature, successful at F and incompatible with our present theories, we simply lack the grounds to bridge the gap between this success and the (probable approximate) truth of our historical theory.  This objection may seem absurd to the anti-realist, but if such an objection should hold, it would shine light equally on both the HPMI and the SPMI. 

6.4a Many historical theories are on surer epistemic footing than scientific theories

Assume historical theories are, all else being equal, on stronger epistemic footing than in the natural sciences, especially the closer the theories are to the present, the more historical texts and other forms of evidence are available to support them, and how they fit within other historical theories. 

Therefore many historical theories (perhaps the most interesting and popular theories) are on surer epistemic footing than scientific theories.  R2* would be true, and the scope of R2* is limited to a set of historical theories that include the pertinent historical theories about whether certain scientific theories were accepted by past scientists, were believed to be mature and had genuine successes. 

6.4b Historical theories are not on surer epistemic footing

Put aside the strangeness of an anti-realist affirming that a questionable field is likely to produce (probably approximately) truth so long as the (mature) theory is successful in making novel predictions, fit the available evidence and satisfies other theoretical virtues.  There is a deeper problem with this sort of response that would elevate the 'historical sciences' over the 'natural sciences'. 

If the use of the term 'scientific' in the SPMI is understood as a descriptor for some domain of inquiry, then use of the term 'scientific' encompasses a number of historical theories.  For example, there are many 'scientific' disciplines that involve retrodictions about the past, such as the age of the Earth, stars or universe; when and where certain species likely evolved or went extinct, or how to reconstruct the behaviour or physiology of extinct animals. 

There are plenty of examples of (mature) historical theories about the behaviour or physiology of extinct animals that are now incompatible with present theories, (mature) past cosmological theories incompatible with present theories, (mature) theories about the age of the Earth, etc. 

Philosophers of science must employ a theoretical framework in order to determine which counts as relevant in P3: some demarcation criteria, even if implicitly adopted, are required to sort between different historical communities--the theories produced by natural philosophers, astrologers and alchemists, depending who you consult, are 'in' or 'out' as viable examples that support P3; the theories produced by the Presocratics are 'out', etc.  There must be some boundaries set on the relevant domain of (mature) scientific theories in the SPMI and HPMI, otherwise both PMI would overlap with one another.  The term 'scientific' would be little more than an ascription of value. 

Furthermore, if 'scientific' is meant as an ascription of value, the historical sciences may be understood as a special instance of the sciences, which just are, at least in the SNMA, some important and desirable way of engaging in empirical inquiry differentiated from more everyday forms of empirical inquiry in some respects, viz.  the 'scientific theories' in the SNMA attempt to solve problems so difficult that they require inter-generational attempts at resolving them, and involve so many people working in consort as a group that they require certain social structures and incentives in place to organise work on solving these problems. 

These salient similarities unify the work of historians of science and scientists together as working within massive social groups that are inter-generational, and have a long history of apparent successes at explicating some unexplained phenomena, followed by eventual failure.  The SPMI and HPMI are, in fact, noting but artificially separated versions of thegeneral version of the PMI that makes no reference to the natural sciences, but applies equally to all modes of empirical inquiry that extend beyond the 'safe house' of commonsensical belief that have such a long history of success:

(Q1) (Mature) theories in some area P are successful at F.

(Q2) If there is a long history of (mature) theories in some area P that are each successful at F but contract present (mature) theories in P, then scientists cannot reasonably infer (mature) theories are (probably approximately) true based on F in P.

(Q3) Many past (mature) theories in some area P were for a time successful at F and contradict present (mature) theories in P.

(Q4) We cannot reasonably infer (mature) theories are (probably approximately) true in some area P based on success at F in P.

Thus the SNMA is not directed solely at current work in the natural sciences, but a whole class of epistemically valued ways of engaging in empirical inquiry that fall short of the anti-realist's standards; similarly, the SPMI does not solely undermine beliefs based on mature, successful theories in the natural sciences, but a whole class of other fields that require immense effort and resources to solve, including the historical sciences. 

6.5a The SPMI is not a historical argument...

One desperate approach to resolving this puzzle would be to claim this version of the SPMI is not making a historical claim per se, for such a claim would require a great deal of historical evidence for it, the historical evidence is subject to the HPMI, and we are left dealing with an argument that is obviously mistaken.  And yet it is difficult to tease out the differences between the HPMI and SPMI in such a way so as to save the SPMI from triviality.  But the SPMI is not obviously trivial, but immensely informative, contrasted to the HPMI. 

The existence of disagreement over whether the historical evidence support P3' is a sideline to the main event; instead, the SPMI is really about the existence of a plethora of past (mature) scientific theories that satisfied success at F for some time, but contradict our current (mature) scientific theories successful at F. This would bypass any potential issues about history, but it would require understanding P3' not as a historical claim, but rather as a version of a underdetermination argument framed in historical garb. 

6.5b ... but the SPMI is a historical argument

The problem is that Larry Laudan, the person most recognised as creating the PMI, as well as the philosophers of science and historians of science that engage in this very dispute over whether the historical evidence supports or undermines P3' did not understand the SPMI. 

Furthermore, if what is needed is simply the existence of contradictory scientific theories that satisfy success at F in order for the SPMI to succeed, it follows that simply the existence of contradictory historical theories that satisfy success at F are needed for the HPMI to succeed as well--and these contradictory historical theories did once exist, thus undermining, by the anti-realist's lights, any historical reason to accept P3' even though it is obvious independent of the HPMI that P3' is acceptable. 

Perhaps we can construct an OMI for the historical sciences?  In brief, our current (mature) historical theories are more successful, better supported and more stable than past historical theories, and have been developed in a relatively short period of time, perhaps only in the past hundred years or so.  This reflects a shift in historical scholarship and historiography that makes success at F fundamentally different today than in the past.  On these grounds, we can make a historical OMI, and on the basis of the historical OMI, infer P3', thus permitting accepting a SPMI.  Thus, present historical scholarship lets us infer that there did in fact exist a number of scientific theories that were genuinely mature and were genuinely successful at F, and are in fact incompatible with our present (mature) scientific theories successful at F.

Thus P3' is no more controversial than determining that a philosopher once held an opinion in her early writings, and held them on grounds that we find in the present day to be eminently plausible, and in accordance with the best available evidence, but then learning that this philosopher changed her opinion as time went on, and adopted an opinion in her later work that was incompatible with her past opinion, and nevertheless supported by eminently plausible arguments, and in accordance with the best available evidence.  Historical scholarship has simply reached this level of analysis that, if we are capable of determining through careful reading of texts that two opinions are incompatible, well-reasoned and plausible, historians are just as capable of making this determination over past scientific theories and comparing them to present theories. 

6.6b Present natural science is better than past natural sciences

One response to the historical OMI is that for any argument drawn in favour of a historical OMI, a structurally similar argument with perhaps even greater empirical evidence for a dissimilarity between past and present success at F can be drawn in the natural sciences, thereby concluding 'our current best theories enjoy far higher degrees of success than any of the refuted theories in the past, which enjoyed only fairly low degrees of success' (Farbach 2011b, 1285). 

As Farbach claims, we may assume the examples provided by Laudan may show a long history of incompatible scientific theories that were modestly successful at F, but our current theories have a very high degree of success at F. What is good for the goose is good for the gander, thus by accepting a historical OMI in response to a HPMI, the anti-realist may open the door for the realist to accept a scientific OMI in response to the SPMI on even stronger grounds. 

6.7a There exists historical evidence for P3'

The anti-realist may reject all the previously covered points and note that something has gone terribly wrong somewhere down the line: this has been nothing but word games and sophistry, and no matter what, there is empirical evidence for the existence of past (mature) scientific theories that are incompatible with (mature) scientific theories. 

All these objections have trussed up something so obviously plausible by using the word 'historical' to mask the true nature of the SPMI: the anti-realist places in front of the realist a scientific theory that, for a time, satisfied any necessary and sufficient conditions for maturity and success, and then shows how it is incompatible with currently accepted scientific theories, places another theory... and another... and so on. 

We must restate the HPMI as follows:

(Q1') (Mature) theories in history of science are successful at F.

(Q2') If there is a long history of (mature) theories in some area P of history of science P that are each successful at F but contract present (mature) theories in P, then historians cannot reasonably infer (mature) theories in history of science are (probably approximately) true based on F in P.

(Q3'') Many past (mature) theories in in some area P of history of science were for a time successful at F and contradict present (mature) theories in P of history of science. 

(Q4') Historians cannot reasonably infer (mature) theories are (probably approximately) true in some area P of history of sciencebased on success at F in P.

Restating the HPMI may permit the existence of historical evidence for P3' by arguing the scope of P does not include some list of theories (say, Laudan's list). 

6.7b We cannot restate Q1-Q4 without making similar changes in P1-P4. 

One obvious rejoinder to 6.7a would be to note that P likely includes Laudan's list, in virtue of the controversy surrounding the list over the past few decades.  Put this objection aside. 

If we accept historical evidence for P3', then we must reject a core premise in the HPMI based on one of the previously mentioned (or other unarticulated) reasons, hence the HPMI is a bad argument.  But by R2, the HPMI is a stronger argument against the HNMA than the SPMI against the SNMA.  It is only when Q1-Q4 are changed to Q1'-Q4' that we can infer P3'.  What would such a change in the SPMI look like? 

(P1) (Mature) scientific theories are successful at F.

(P2') If there is a long history of (mature) scientific theories in some area P of natural science that are each successful at F but contract present (mature) scientific theories in P, then scientists cannot reasonably infer (mature) scientific theories are (probably approximately) true based on F in P.

(P3') Many past (mature) theories in science in some area P were for a time successful at F and contradict present (mature) theories in science in P.

(P4') Scientists cannot reasonably infer (mature) scientific theories are (probably approximately) true in some area P based on success at F in P.

These adjustments to P1-P4 suitably weaken the SPMI to the point that it remains effective and skirts the later version of the HPMI, but only if there is a long history of incompatible scientific theories in some limited domain P. This, coincidentally, may be an argument so weak that some scientific realists are willing to accept it as almost trivial.  The question becomes whether a specific scientific theory rests within or without domain P, whether other theories also fall within P, and whether all of them were both successful at F and mature theories. 

7.  Reframing P3' to reflect a veil of ignorance about our place in history

I am of the opinion that this whole mess has to do with the framing of the SPMI as a historical argument, hence why so many philosophers of science began post-Laudan to delve into history of science to determine if history of science supported or undermined P3. 

Further augmentation to P3' to eliminate any historical claims would look like the following: instead of making historical claims about whether certain theories were moderately or highly successful or mature, we should take a page out of John Rawls' veil of ignorance:

First, imagine that we are faced with a veil of ignorance, not knowing what time we would be born into, and are practicing scientists that have a number of (mature) scientific theories that are successful at F.

Second, the anti-realist now makes a modal or counterfactual claim about how present scientists and their current standards of success at F would similarly accept other (mature) theories that are known to be incompatible with our presently accepted (mature) theories.  This modal or counterfactual claim is made, rather than the anti-realist making historical claims about whether past scientists genuinely accepted these theories, whether these past theories were genuinely mature (and to what degree), or whether these theories were genuinely (moderately or significantly) successful at F.

That is to say, were we a random scientist living at any time in the past, present or future, it is reasonable to believe that we would have considered these other theories to be mature and successful at F?  If so, the matter is (provisionally) settled over whether the theory is to be considered mature and successful at F, for it is relative to our current standards and assessments. 
When speaking about the past, we have this counterfactual question that produces a PMI: Had we lived before this certain date that the theory was rejected based on defeating reasons, it is reasonable to believe we would have similarly inferred that these other theories were (probably approximately) true based on their maturity and success at F?  If so, the realist is willing to make this inference, claiming as they would after accepting a NMA that the best possible explanation for the (mature) theory's success at F is that the theory is (probably approximately) true. 

Under a veil of ignorance, are we willing to make that bet?  The anti-realist, like Rawls, isn't willing: the scientist doesn't know their place in history of science (analogous to our ignorance of our place in society), and consequently it isn't epistemically prudent to make the inference.  After all, these theories are attempts at explaining certain phenomena that require numerous repeated attempts; and the members of the community have explored many once-thought viable approaches in possibility space, only later to reverse course and adopt another approach. 

It is still reasonable to conclude, as many scientific realists and anti-realists do, that our present (mature) theories in some discipline P that are successful at F are better than past theories, and are preferable to these past theories, and perhaps even have a greater degree of verisimilitude than past theories in P, but the general PMI still stands. 

In sum, it is far better to play it safe, given the available space of possibilities (so the anti-realist claims).  The realist, on the other hand, may be willing to take the bet, and the veil is lifted, to reveal a theory that cannot be maintained, for we know that in these cases, the chosen theory would be no longer successful at F at some future time.  After several iterations of this procedure, the realist may find themselves despondent, and far more amenable to the anti-realist's claims over the disjunct between success at F and (probable approximate) truth, rather than the far more modest claim of the relationship between the superiority of present mature scientific theories and preferability when compared to past mature scientific theories.