Is inference to the best explanation just a special case of more general forms of confirmation procedure? 


No!  If anything, it is the other way around -- like the blind men's encounter with the elephant, other forms of confirmation procedure can be interpreted as narrowly viewed cases of inference to the best explanation.

Inference to the Best Explanation

This is a form of inductive inference that depends for its justification on the quality of explanation that the inference provides for the evidence.  Seen as a confirmation procedure, one judges that the evidence confirms the hypothesis when the hypothesis is the best available explanation of 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."

Consider 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 practical 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.  In employing IBE, one infers from the judgement that a particular hypothesis (theory) explains the evidence, to the conclusion that the hypothesis is true-enough for current purposes.  Thus, IBE is neutral with regard to the theory of truth that is brought to the discussion.

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.  A potential explanation, on the other hand, only promises to explain the evidence to some degree sufficient for our current purposes.  Potential explanations are merely assumed (possibly only for the moment) to be more likely true-enough than the competing alternatives. 

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 signify the "best" explanation.  Our evaluation of 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.  Time, and more evidence, will tell.  We are constantly adjusting our criteria of what counts as an explanation, what counts as explanatory power, and how true-enough our past inferences have been, in accordance with what we experience as we move through the world.

As Hawthorne has argued(2), if the empirical evidence is so meager that we are unable to clearly distinguish between candidate hypotheses on the basis of the evidence alone, the notion of evidential confirmation must depend on what our explanatory (non-evidential) considerations may be able to tell us.  We almost always will have some good non-evidentiary reasons to reject some logically possible but "unlovely" alternatives.  In determining what hypotheses to believe (or at least to accept for the nonce), we always do bring explanatory considerations to bear, at least implicitly.  Such considerations appeal to neither purely logical characteristics of the hypotheses, nor to evidential support. 

Combining these elements, we have two equivalent definitions of IBE -

IBE1    Given evidence E and potential explanations H1,..., Hn of E, if Hi is a more lovely explanation of E than any of the other hypotheses, infer that Hi is more likely to be true-enough than any of these others.(7)

IBE2    Given evidence E and potential explanations H1,..., Hn of E, if Hi is a more lovely explanation of E than any of the other hypotheses, E confirms that Hi is more likely to be true-enough than any of these others.

Where the "more lovely" explanation is one that delivers the greatest depth and/or breadth of understanding, and is measured in terms of criteria that are contextually dependent.

Alternative Confirmation Theories

Confirmation theory is the study of the logic by which hypotheses may be confirmed or refuted by the evidence.  A specific theory of confirmation is a proposal for such a logic.  Consider some of the more commonly referenced models of confirmation theory that appear in the literature --

·         Hume's "More of the Same" model that argues that a series of past observations that all so-far observed F have been Gs confirms the hypothesis that the next F will be a G.

·         the "Instantial Model" that argues that a collection of instances where this F is a G confirms the hypothesis that "All F is G".

·         the "Degrees of Belief as Probabilities" model (otherwise known as Bayesian Confirmation Theory) that argues that an increase in the posterior credence of an hypothesis is warranted on the basis of the likelihood of the evidence, given the hypothesis;  and

·         the "Hypothetico-Deductive" model that argues that an hypothesis is confirmed by the evidence if the evidence can be deduced from the hypothesis.

Given the number of different theories of inductive inference I have listed here, one might suppose a variety of competing principles.  A recent survey(3), however, shows that most accounts of inductive inference can be grouped into one of three families:

·         "Inductive Generalization,"

·         "Hypothetical Induction" and

·         "Probabilistic Induction."

Each family is based upon a uniquely distinct inductive principal and the different theories in the family emerge from efforts to remedy the deficiencies of the principle.

Inductive Generalization

The basic principle of this family of theories is that an instance of a hypothesis confirms the generalization.  An F that is G confirms the hypothesis that "All Fs are G".  There are two theories grouped in this family:  "enumerative confirmation" -- an observation that this F is G confirms the general hypothesis that all F are G;  and "projective confirmation" -- series of past observations  of Fs that are G confirms the hypothesis that the next F will be G. principle There are several major weaknesses inherent in the theories of this family.  The most significant is that little can be confirmed on this basis.  Few hypotheses needing confirmation are generalizations of a suitable sort.  Observation of the background microwave radiation could not be considered a confirmation of the Big Bang theory.

Mill attempts to extend the basic principle by adding the notion of cause.  The "Causal Inference" model of induction 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.  This results in Mills' four "methods" -- the Method of Agreement; of Difference; of Residues; and of Variations.  The companion confirmation theory thus argues that an hypothesis is confirmed if the evidence can be seen within a suitable cause-effect relation.

Yet there remain a number of other serious difficulties.  Hempel's Raven paradox, for example, applies the principle of logical equivalence to the hypothesis "All Ravens are Black" to reach the apparently paradoxical conclusion that a white shoe confirms the hypothesis.  Goodman's semantic paradox, as another example, challenges the assumption that our usual predicates (like "black") are logically distinguishable from such "bent" predicates as "blite" (black if observed, white otherwise).  Goodman argues that since there is no principled basis for preferring "black" over "blite", an observation of a black raven equally confirms the hypothesis that "all ravens are blite".  Hence there is an infinity of alternative hypotheses that any evidence confirms.

If inductive generalization is understood as a variant of IBE, on the other hand, then we can consider that the observation that F is G confirms the hypothesis that "All F are G" just in case the hypothesis that "All F are G" is the best available explanation for the observation.  This approach neatly sidesteps both Hempel's and Goodman's challenges.  And the fact that so few hypotheses needing confirmation are generalizations is explained by the hypothesis that Inductive Generalization is just one small field of application of IBE.

Hypothetical Induction

The basic principle of this family of theories is that the ability of an hypothesis to deductively entail the evidence confirms the hypothesis.  This is the Hypothetico-Deductive model of confirmation  --  if (H and I and A) deductively entail O, then O confirms (H and I and A) -- where H is the hypothesis, I is the initial conditions, and A is some collection of auxiliary premises needed to connect the hypothesis to observational statements.  The principle weakness of this theory of confirmation is that it assigns confirmation too indiscriminately.   If O then what is confirmed is not necessarily H, but the concatenation of (H and I and A).  If not-O then what is refuted is the same concatenation.  This means that falsification of an hypothesis is not only ambiguous, but a practical impossibility.  Duhem-Quine thesis of holism points out, our cohering collection of beliefs can always be "tuned" to permit the consistency of the hypothesis in question and any evidence at all.  This is the argument that theory is always underdetermined by the evidence -- there is always alternative hypotheses that are empirically equivalent with the evidence (eg. the classic curve-fitting problem).  This means that the evidence cannot be considered to confirm one hypothesis over its competitors. 

Add to this the problem pointed out by Clark Glymour(4) -- one can add any arbitrary clause to the logical concatenation of (H and I and A), and then interpret the evidence O as confirming (H and I and A and X), making the evidence confirm any arbitrary clause.

However, if one wraps the Hypothetico-Deductive model of confirmation within IBE, these difficulties dissolve.  IBE puts explanatory constraints on the contents of the concatenation (H and I and A).  The concatenation must explain the evidence O in a fashion that meets the contextually relevant criteria of a "good" explanation.  This eliminates arbitrary clauses.  And it constrains the flexibility of one's coherent set of beliefs so that the extent to which (H and I and A) can be "tuned" into consistency with obstinately recalcitrant evidence is strictly limited.  Falsification is possible if (H and I and A) does not explain O.

Probabilistic Induction

The application of the Probability Calculus to probabilistic induction and confirmation results in  the well known Bayesian Confirmation Theory.  One key virtue of Bayesianism is that if we want to combine competing models of inductive inference, and we do that within the framework of the Bayesian probability calculus, we have the assurance that the combination will be at least be consistent.  On the other hand, Bayesianism, as a stand alone theory of confirmation, has a number of well known difficulties.  Chief among them is the problem of how to interpret the concept of probability -- a problem that infects any philosophy that employs the concept.  But others include the debateable assumption that there is a real-valued ascertainable magnitude for P(h/e); the problem of how to handle uncertainty versus ignorance; and the problem of unknown priors.  There are a number of convergence theorems that show that regardless of the initial choice of prior probabilities, after sufficient iteration of Bayesian conditionalization on the evidence, divergent priors will eventually converge on a common set of posterior probabilities.  But this sort of procedure will not work on unique situations -- like that of the microwave background and the Big bang theory.

The other difficulty arises because the mathematics of Bayesianism provides no constraints on the hypotheses entertained.  So the concatenation of arbitrary clauses to a "reasonable" hypothesis generates the same kind of confirmation of nonsense as was described by Glymour in the case of the hypothetico-deductive procedure described above.

On the other hand, if the Bayesian confirmation calculus is viewed as a mathematization of a probabilistic form of IBE, then these problems can be minimized -- if not completely dissolved.  Because IBE does not separate the process of hypothesis generation from hypothesis confirmation, the problem of arbitrary clause addition can be dismissed.   As Peter Lipton has argued(5), Bayesianiam can be seen as the mathematical calculation of posterior probabilities, given the prior probabilities, while IBE can be seen as the determination of the prior probabilities on the basis of explanatory considerations.


From the foregoing discussion, it is obvious that IBE cannot be viewed as a special case of any of the other forms of confirmation procedure.  All of the other forms of confirmation procedure are more detailed and specific than is IBE, not more general.  The application within IBE of explanatory considerations to the process of hypothesis confirmation can be seen as correcting some of the difficulties faced by the other forms of confirmation procedure, when those are considered on their own.  IBE and Bayesianism are particularly closely intertwined as a single confirmation theory.  The other forms of confirmation theory are best understood (admittedly employing IBE) as narrow applications of IBE to particular areas of confirmation.  But despite this integrative view of IBE and other confirmation procedures, one must always keep in mind that any account of IBE must recognize that it is not intended to be the sole candidate for an ampliative and context-sensitive defeasible rule of inference(5).


Notes & References

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

(2)  Hawthorne, John;  "Confirmation Theory" in Handbook of the Philosophy of Science, Volume 7 (Philosophy of Statistics), Prasanta S. Bandyopadhyay & Malcolm R. Forster (Eds), Dov M. Gabbay & Paul Thagard & John Woods (Series Eds.)  , North Holland Publishing, Reed Elsevier Group, Amsterdam, Netherlands, 2010. ISBN 978-0-444-51862-0.

(3)  Norton, John D. "A Little Survey of Induction" in Scientific Evidence: Philosophical Theories and Applications. P. Achinstein (ed.), Johns Hopkins University Press, 2005. pp. 9-34.

(4)  Glymour, Clark;  Theory and Evidence, Princeton University Press, Princeton, New Jersey, 1980. ISBN 978-0-691-07240-1.

(5)  Psillos, Stathis;  "The Fine Structure of Inference to the Best Explanation" in Philosophy and Phenomenological Research, Vol 74, No 2 (Mar 2007).


Ben-Menahem, Yemina;  "The Inference to the Best Explanation" in Erkenntnis, Vol 33, no 3 (Nov. 1990), pp. 319-344. URL=<>.

Douven, Igor;  "Testing Inference to the Best Explanation" in Synthese, Vol 130, No 3 (Mar, 2002), pp 355-377. URL=<>.  Huber, Franz;  "Confirmation and Induction" in The Internet Encyclopedia of Philosophy, URL=<>.

Huemer, Michael;  "Confirmation Theory: A Metaphysical Approach" in The Epistemologiucal Research Guide, URL=<>.

Joyce, James M. & Hajek, Alan;  "Confirmation" in The Routledge Companion to the Philosophy of Science, S. Psillos and M. Curd, eds., Routledge, New York, New York, 2008. ISBN 978-0-415-35403-5.

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

Maher, Patrick;  "Confirmation Theory" in Encyclopedia of Philosophy 2nd edition, Donald M. Borchert (ed.), Macmillan Reference, New York, New York, 2006. ISBN 978-0-028-65780-6.

McGrew, Timothy;  "Confirmation, Heuristics, and Explanatory Reasoning" in the British Journal for the Philosophy of Science, vol 54 (2003), pgs 553-567.

Norton, John D.;  "Challenges to Bayesian Confirmation Theory" in Handbook of the Philosophy of Science, Volume 7 (Philosophy of Statistics), Prasanta S. Bandyopadhyay & Malcolm R. Forster (Eds), Dov M. Gabbay & Paul Thagard & John Woods (Series Eds.)  , North Holland Publishing, Reed Elsevier Group, Amsterdam, Netherlands, 2010. ISBN 978-0-444-51862-0.

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

Wikipedia contributors, "Deductive-Nomological Model" in Wikipedia, The Free Encyclopedia, URL=<>.

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