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Is there any reason to suppose that the conclusion of an inference to the best explanation is likely to be true?

 

What is “Inference to the Best Explanation”?

“Inference to the best Explanation” is the label of a particular method of drawing inductive inferences from the evidence.  Gilbert Harman gave the method its label (henceforth “IBE”) in his 1965 article of that title⁽¹⁾ — while acknowledging that the method was not his creation and has been around for a while.  In Harman’s description of IBE, he says:

“The inference to the best explanation” corresponds approximately to what others have called “abduction,” “the method of hypothesis,” “hypothetic inference,” “the method of elimination,” “eliminative induction,” and “theoretical inference.”  . . .  I prefer my own terminology because I believe that it avoids most of the misleading suggestions of the alternative terminologies.

In making this inference one infers, from the fact that a certain hypothesis would explain the evidence, to the truth of that hypothesis. In general, there will be several hypotheses which might explain the evidence, so one must be able to reject all such alternative hypotheses before one is warranted in making the inference. Thus one infers, from the premise that a given hypothesis would provide a “better” explanation for the evidence than would any other hypothesis, to the conclusion that the given hypothesis is true.”

Although Harman equated IBE with “abduction”, his description of it did not exactly match with Charles Sanders Peirce’s trifurcation of reasoning into Deductive, Inductive and Abduction⁽²⁾.  Peirce argued that to “abduce” an explanation A from an observed circumstance B is to “guess” that A may be true because then B would be a matter of course.⁽³⁾  Thus, to abduce A from B involves judging that A is sufficient (or nearly sufficient), but not necessary, for B.⁽⁴⁾  Rene Descartes, in his Discourse on Method, Book VI, gives an even earlier description of something very close to IBE.⁽⁵⁾ 

In employing IBE, one infers from the judgement that a particular hypothesis (theory) explains the evidence, to the truth of that hypothesis.  It is an element of inductive logic, rather than deductive logic, and hence the conclusions reached are not necessarily true, but only presumed likely to be true.  In particular, it is a form of inductive inference that depends for its justification on the quality of explanation that the inference provides for the evidence.  Unlike deductive reasoning, inductive reasoning is not examined in a vacuum.  IBE must therefore be understood in an “all things considered” context.  All available background knowledge must be brought to bear on the justification of the inference, and the understanding of explanation. 

To understand the interplay between inference and explanation, a few words are warranted on the implications of “inference”, “explanation”, and “best”.  IBE does not separate the process of hypothesis generation from hypothesis confirmation.  The other models of inductive inference do separate these.  Consider some of the more common models of inference —

• • • Hume’s “More of the Same” model that warrants the inference that the future will be like the past, whatever the past is;
    • the “Instantial Model” that warrants the inference that “All F is G” from a collection of instances that this F is G; 
    • the “Degrees of Belief as Probabilities” model (otherwise known as Bayesian Confirmation Theory) that warrants an increase in the posterior credence granted to an hypothesis on the basis of the likelihood of the evidence, given the hypothesis; 
    • the “Hypothetical-Deductive” model that warrants the inference of the hypothesis if the evidence can be deduced from the hypothesis; 
    • the “Causal Inference” model that warrants a causal inference if it can be seen as meeting the demands of Hume’s or Mill’s strictures on the nature of a cause; or
    • the “Theoretical Unity” model that warrants an inference if it unites (coheres) well with the background information we have. 

All of these, considered individually, have their critics.  For example, the deductive-nomological model of explanation, with its associated hypothetical-deductive model of theory confirmation, says nothing about how the hypothesis is to be derived.  Hence, one of the major criticisms of this pair of models (and some of the others) is their lack of constraint on the hypotheses that may be entertained.  IBE, by comparison, tightly binds inference and explanation into a mutually supporting unity.  According to IBE, our generation of hypotheses (potential explanations) is governed (guided and constrained) by explanatory considerations. 

The “explanation” involved must be understood as a “potential” explanation rather than an “actual” explanation.  The difference is that an actual explanation actually does explain the evidence in hand, and is thus by definition true.  Whereas a potential explanation only promises to explain the evidence to some degree if it is true.  Potential explanations are not necessarily true, merely assumed (possibly only for the moment) to be more likely to be true than the competing alternatives.  IBE is relatively neutral on the details of just what constitutes an explanation.  There are several models of explanation with which IBE is compatible —

• • • the “Reason” model that claims that explains some evidence E by offering reasons for expecting E to be the case;
    • the “Familiarity” model that explains the surprising fact that E in terms of familiar facts and processes;
    • the “Deductive Nomological” model that explains the evidence E by deducing it from some Laws of Nature (and some other “background” or “auxiliary” premises);
    • the “Unification” model that explains some evidence E by showing how E is an example of some larger more unified pattern;
    • the “Necessity” model that explains some evidence E by showing how it is necessary that E;
    • the “Causal” model that explains some evidence E by showing some context relevant details of it causal history; and
    • the “Contrastive” model that explains some evidence E by showing how it is E rather than Q.

(It should be noted that this list pretends to be neither exhaustive nor mutually exclusive.)  

The tracks in the snow are evidence for the inference that a rabbit passed by.  But the argument from underdetermination demonstrates that there are always multiple possible explanations for the evidence.  The argument from underdetermination goes: Given that (i) each theory (hypothesis / inference) has empirically equivalent rivals, and that (ii) in determining whether some theory is “true” or not we have only its empirical consequences to go on, we are never in a position to justify the belief that some theory is true.  To say that an outcome is underdetermined is to say that some information about initial conditions and rules of principles does not guarantee a unique solution.  If an inference is inductive, then by definition it is underdetermined by the evidence and the rules of deduction.  However, as various critics have noted, IBE denies premise (ii) by arguing that other factors besides empirical fit – most notably, explanatory power – can help determine the truth-likeliness of a theory.  The method of IBE reasons that, given all of our background information, the inference that the evidence is explained by a passing rabbit rather than something else, is the “loveliest” conclusion to draw.

Which brings us to the meaning of “best” — also commonly called the “loveliest”.  The “best” involved must be understood in a comparative context.  The explanation involved need not be the “absolute best” possible explanation — whatever that concept might mean.  The inference is drawn to the best of the currently available potential explanations.  The preferred explanation is always one of a collection of competing potential explanations (the collection P and not-P in the limit).  So an inference to the “best/loveliest” explanation is only an inference that H₁ is explanatorily better than H₂.  Thus IBE contains two epistemic filters — one to constrain the pool of potential “live” candidate explanations, and one to select the best among them.  The “best” is not necessarily the “likeliest”.  IBE argues that the “loveliness” of an explanation is a good guide to the likeliness of the hypothesis to be true, but there is room for a disconnect here.  “Loveliness” is a measure of the depth and breadth of understanding delivered by the hypothesis.  And it is readily acknowledged that we do not have a thorough understanding of what this means.

It is, however, well understood that explanatory loveliness is contextually relative and informed by empirical considerations.  We develop standards of explanatory merit on the basis of broad empirical considerations within a context of application.  The standards in quantum physics would be markedly different from the standards in psychology, or in day to day social interactions.  Explanatory merits are justly considered relevant to an assessment of plausibility precisely because our standards evolve with the rest of our empirical knowledge.  A formal theory of explanation, such as Hempel’s Deductive-Nomological model⁽⁶⁾, can thus only do part of the work.  In each field of inquiry, a development of explanatory standards of loveliness is closely linked to other field specific empirical and conceptual considerations.  Philosophical debates often focus on the link between credibility and explanatory warrant, while ignoring the empirical basis of our development and evaluation of standards of explanatory “loveliness”.

Combining all these elements, we have

IBE*   Given evidence E and potential explanations H₁,…, H_n of E, if H_i is a more lovely explanation of E than any of the other hypotheses, infer that H_i is closer to the truth than any of these others.⁽⁷⁾

Why might one suppose that such inferences are true?

In his Meaning and the Moral Sciences⁽⁸⁾, Hilary Putnam famously argues that an account that denies that our best scientific theories are at least approximately true would make their success a miracle.  If the account above of what IBE is, and how it works, is even roughly accurate, then most of those successful scientific theories have been the result of successful application of IBE.  Baring a generalized Humeian scepticism about the past being any guide to the future, this past track record for IBE is sufficient evidence to warrant an inference (using, perhaps, the Instantial Model of inference) to its reliability in arriving at hypotheses that will enjoy some substantial measure of empirical success.

But, what does it mean for an inference to be “true”.  There are three models of “truth” that can be brought to bear on this question —

(a)    Truth is ultimately an epistemic notion (also known as anti-realism or non-realism — truth is determined by the evidence; includes Conventionalism and Instrumentalism);

(b)   Truth is ultimately a metaphysical notion (also known as realism or evidence transcendence — no matter how much evidence we have in support of our inference, it remains logically possible that the hypothesis is false);

(c)    Truth is ultimately a pragmatic notion (also known as pragmatism — truth is determined by the utility of the consequences).

Typically, realists approve of IBE, while non-realists do not.  But IBE, as a method of inductive reasoning, is entirely neutral on the matter of which notion of truth applies.  The unfortunate association of IBE with realism has developed as a consequence of the frequent and much criticized employment of IBE in efforts to “infer” that realism is true — that scientific realism is the best explanation of the empirical success of scientific theories.  But this association need not taint IBE as a method of inductive inference.  I suggest that there is no empirically discernible difference between the three models of truth as they apply to the understanding of IBE.

Consider, for example, a somewhat pragmatist notion of “true-enough” — where an hypothesis is “true-enough” if and only if it is empirically successful (results in predictions and deductive entailments that correctly describe our empirical experiences, within the accuracy of our empirical requirements).  Obviously, this notion is context relative.  That the length of this table is 5 feet (or 1.5 meters) is true-enough if I am ordering a table cloth.  But not nearly true-enough if I am cutting a piece of glass to top the table.  Newton’s theory of Gravity is true-enough if we are plotting a trip to the Moon.  It is not true-enough if we are trying to predict the precession of the orbit of Mercury.  That the tracks in the snow were the result of a passing rabbit is true-enough if little rides on the inference.  It may not be true-enough if we have to bet our life on the inference.

Bas van Fraassen⁽⁹⁾  has argued that IBE is incoherent because there is no a priori guarantee that the true hypothesis is among the potential explanans we consider.  This is what he refers to as the “Best of a Bad Lot” argument.  But the flaw in his reasoning is that he ignores the evolutionary co-development of our hypotheses and our standards of explanation.  We must not consider a single instance of IBE in isolation.  Rather we must consider the iterative exploitation of IBE in gradually refining our theories in response to our growing demands for greater accuracy and precision, in the face of a constant flow of new evidence.  Even if, this time around, we end up inferring to the best of a bad lot, the future will provide new evidence on whether this inference, as bad as it supposedly was, was true-enough for our purposes at the time, and our purposes as they evolve over time.  This new evidence will be incorporated into the next iteration of IBE, and will therefore result in a better theory — a theory that will (hopefully) be true-enough for our purpose at that time.  If it is not, we simply try again.  Van Fraassen argues that all that IBE can warrant is that our inference is “empirically adequate”.  But if we measure “empirical adequacy” in terms of the number of successful predictions, the variety of tests passed, the relative (vs competing hypotheses) precision of the predictions, the novelty (surprisingness) of new predictions, the volume of predictions, the variety of predictions, relative simplicity, etc., I see no practical difference between his “empirically adequate” and my “true-enough”.  Philosophers may debate the logical consequences of the various notions subsumed beneath true-enough.  But for discerning the difference between enjoying lunch and becoming lunch, all that really matters in the long run, true-enough is sufficient.

Nancy Cartwright, in her How the Laws of Physics Lie⁽¹⁰⁾ argues that the truth does not explain much and should not be expected to.  She argues that “… the falsehood of fundamental laws is a consequence of their great explanatory power”(p.4).  In particular, she disputes the fundamental premise of IBE that explanatory loveliness is an indicator of likeliness.  “There is no reason to think that the principles that best organize will be true, nor that the principles that are true will organize much”(p. 53).  Cartwright argues that there is a trade-off of truth and explanatory power.  The best scientific explanations are not very likely to be true (because based on false scientific laws), whereas the most credible laws are the least explanatory (because they are false in almost all actual situations).  On this account, the explanatory power of an hypothesis is completely separated from its probable truth.  But as with van Fraassen’s criticism, Cartwright does not pay sufficient attention to the iterative evolutionary consequences of repeated applications of IBE, and the context and historically relevant standards of true-enough.

We do not possess a priori criteria of what an adequate explanation is.  Nor do we possess a priori criteria as to what measures of explanatory power indicate the “best” explanation.  Our evaluation of an hypothesis’ explanatory success must therefore depend on our knowledge of, and repeated interaction with, the world.  For any given inference to the best explanation, we may not be able to judge whether it will be empirically fruitful or not.  But the past successes of repeated applications of IBE is strongly suggestive (Instantial model of inference) that the IBE process results in empirically successful inferences more often than not.  Time, and more evidence, will tell.  We are constantly adjusting our criteria of what counts as an explanation, what counts as explanatory power, what counts as “loveliness”, and how true-enough our past inferences have been, in accordance with what we experience as we move through the world.  Separating the explanatory and the truth-tropic elements of IBE constitutes a regression to a non-empirical account of methods of inductive inference.

Notes & References

(1)  Harman, Gilbert;  “The Inference to the Best Explanation” in The Philosophical review, Vol 74 (1965), pgs 88-95.

(2)  Burch, Robert, “Charles Sanders Peirce” in The Stanford Encyclopedia of Philosophy (Fall 2010 Edition), Edward N. Zalta (ed.), URL=<http://plato.stanford.edu/archives/fall2010/entries/peirce/>.

(3)  Peirce, C. S. (1903), Harvard lectures on pragmatism, Collected Papers v. 5, paragraphs 188–189.

(4)  Wikipedia contributors, “Abductive Reasoning” in Wikipedia, The Free Encyclopedia, URL=http://en.wikipedia.org/w/index.php?title=Abductive_reasoning&oldid=463196621

(5)  Descartes, Renes;  Discourse on Method, Book VI, URL=http://www.bartleby.com/34/1/6.html

“[F]or it appears to me that the reasonings are so mutually connected in these Treatises, that, as the last are dem  onstrated by the first which are their causes, the first are in their turn demonstrated by the last which are their effects. Nor must it be imagined that I here commit the fallacy which the logicians call a circle; for since experience renders the majority of these effects most certain, the causes from which I deduce them do not serve so much to establish their reality as to explain their existence; but on the contrary, the reality of the causes is established by the reality of the effects.”

(6)  Wikipedia contributors, “Deductive-nomological model” in Wikipedia, The Free Encyclopedia, URL=http://en.wikipedia.org/w/index.php?title=Deductive-nomological_model&oldid=450654926

(7)  Douven, Igor;  “Testing Inference to the Best Explanation” in Synthese, Vol 130, No 3 (Mar, 2002), pp 355-377. URL=http://www.jstor.org/stable/20117222 

Kuipers, Theo A. F.;  From Instrumentalism to Constructive Realism: On Some Relations Between Confirmation, Empirical Progress, and Truth Approximation, Synthese Library Vol 287, Kluwer Academic Publishers, Dordrecht, Netherlands, 2010. ISBN 978-90-481-5369-5.

(8)  Putnam, Hilary;  Meaning and the moral Sciences (Routledge Revivals), Routledge, New York, New York, 1978/2010. ISBN 978-0-415-58124-0.

(9)  van Fraassen, Bas C.;  Laws and Symmetry, Oxford university Press, New York, New York, 1989. ISBN 0-198-24860-1.

(10)  Cartwright, Nancy;  How the Laws of Physics Lie, Oxford University Press, New York, New York, 1983. ISBN 0-198-24704-4.

Ben-Menahem, Yemina;  “The Inference to the Best Explanation” in Erkenntnis, Vol 33, no 3 (Nov. 1990), pp. 319-344. URL=http://www.jstor.org/stable/20012310

Lipton, Peter;  Inference to the Best Explanation, 2^nd Edition, Routledge, New York, New York, 2004, ISBN 0-415-24203-7.

Ruben, David-Hillel;  Explaining Explanation, Routledge, New York, New York, 1990. ISBN 0-415-08765-1.

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