And so, at last, we arrive, by circuitous ways, at the account of inference toward which all of this has been tending. By now, its outlines should be moderately clear.

Beginnings. Let us return for a moment (only a moment!) to the seventeenth century. We left Bacon an inductivist but with a hint that this would not quite do. In Book II of the New Organon, he lays out a

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case-study in order to illustrate his new method. What is the nature of heat? He eventually concludes that it reduces to motion. But in the case of ordinary bodies, the motion of what? Bacon postulates minute particles whose constrained motion is responsible for the impression of heat when we feel a hot iron. But surely no inductive process of generalization could arrive at such a conclusion? Bacon’s alchemical background leads him to emphasize the importance of “latent process” that “escapes the sense”; it is on this that the observed properties of things ultimately depend. An understanding of the “latent configurations” of “things infinitely small” is needed.111 He never explicitly recognizes that the induction- by-generalization he has proposed in the opening aphorisms of the New Organon will not suffice to reach such configurations. He does, however, sketch a method of testing hypotheses, /82/ laying the groundwork for a very different conception of science, one where hypothesis takes an honored place, and the old ideal of demonstration is finally laid aside. Bacon himself did not, however envision this denouement. For him, science still connoted certainty, though he must have suspected that the configurations of “things infinitesimally small” would not readily yield such a result.

The story of how this suspicion grew as the century progressed is a fascinating one, too complex to follow here.112 Descartes saw that hypothesis was the only way in which the motions and sizes of the imperceptibly small corpuscles on which the observable properties of things depend could be reached, but hoped that certainty might still be attained either by eliminating all alternative explanations save one, or by finding one that fits the phenomena of nature so well “that it would be an injustice to God” to believe that it could be false.113 Boyle more realistically set about formulating the criteria to be used in evaluating or comparing causal hypotheses, where the causes are postulated, not directly observed. After an acute analysis of the difficulties facing explanations that call upon imperceptible corpuscles, Locke concluded that physics of the traditional demonstrative sort is “forever out of reach,” but that the skillful use of analogy may still allow the /83/ natural philosopher to attain the “twilight of probability.”

Newton was misled by the quasi-demonstrative form he had been able to impose upon his mechanics into supposing that hypothesis could be dispensed with in science proper. Though he himself made extensive and ingenious use of unobservable entities of all sorts in the Queries appended to the Optics, he believed he could construct a mechanics and a geometrical optics without their aid. (He was relying here on the plasticity of his key concept, force: are forces unobservable causal agencies, or are they merely dispositions to move in a certain way?114) Because of his enormous influence on those who came after him, his restriction of science proper to two modes of inference only, deduction and induction, was to have negative repercussions for decades to come, until the atoms and

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ether-vibrations of the early nineteenth century once and for all showed causal inference to underlying structure to be indispensable to the work of the physical scientist.

This is much too rapid an excursion, but it may give some hint, at least, of how long it took the practitioners of the new natural science to realize how powerful a tool their causal hypotheses could become, how far beyond the small world of the human senses they could reach, and how secure a knowledge they could ultimately yield, /84/ despite their apparent logical fragility. This was just as surely a discovery as was that of the planet, Neptune, and like the latter, it was made in the first instance by the scientists themselves, not by philosophers reflecting on the quality of knowledge that scientists ought to aim at.

Whewell. The most perceptive nineteenth-century commentator on these issues was probably William Whewell, whose Philosophy of the Inductive Science, Founded upon their History (1840) made plain that only a detailed study of the actual history and practice of science could allow one to say how science is made.115 Though he recognized, and indeed emphasized (against Mill) a third mode of inference in science besides deduction and empirical generalization, he applied the old label, “induction,” to it which may have obscured the importance of the point he was making. Induction for him is, first and foremost, an untidy inventing of hypotheses meant to “colligate,” or bind together, the known facts and to reveal new ones. The first step is the crucial one of finding the appropriate “conceptions” that will enable the facts to fall together in an intelligible order. This is the distinctive contribution of mind , he notes, a contribution overlooked by the empiricists (a touch of epagoge still?). /85/

But “induction” is not only invention, it is also verification. (In deduction and even to a large extent in induction, to discover is to verify; the fateful distinction between invention (discovery) and verification comes into view only when a third mode of inference is recognized.) A good hypothesis should explain the phenomena already observed, as well as predicting new kinds. Successful prediction is already a measure of truth. But when a “consilience of inductions” occurs, when hitherto unrelated areas of inquiry fall together under a single hypothesis, this can (he suggested) convince us of the truth of the hypothesis. Consilience involves, then, both enlargement of scope and simplification of structure. And it requires the scientist to follow the progress of a theory over time to assess whether its growth has been coherent or ad hoc.

Peirce. Peirce was the first to say straightforwardly that to deduction and induction, we must add a third (which he variously named abduction, hypothesis, retroduction) if we are to categorize properly what it is that makes science. Abduction is the move from evidence to hypothesis; it is

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“the provisional adoption of a [testable] hypothesis.”116 Unlike deduction and induction, it may involve new ideas and thus may require new language as one moves from known effect to unknown (and possibly unobservable) cause. /86/ Unlike many of his contemporaries (Ernst Mach and William James, for example), he had no hesitation about inferring to unobservable entities. Criticizing James, for example, he notes that the sort of positivism which would question the propriety, in general, of such inference is clearly out of touch with the actual practice of physics. “Attempts to explain phenomenally given elements as products of deep-lying entities” (using molecules to explain heat is his example) are entirely legitimate; in fact, this phrase may be said to describe “as well as loose language can, the general character of scientific hypothesis.”117

A number of questions immediately suggest themselves. Is abduction the inventing of the causal hypothesis, the hitting upon a plausible explanatory account? Or does it in some way involve the evaluation of the proposed explanation? In terms of a distinction later made famous in the philosophy of science, ought it be regarded as discovery or as verification? One does not need to ask this in the case of deduction and induction. But there seem to be at least two (or perhaps even a spectrum of ) varieties of abduction, depending on how much stress one puts on the term, “plausible,” when defining it as a move from effect to “plausible” cause. Peirce gave more stress to the inventive side, raising the further question as to why this should be regarded as inference. “I /87/ reckon it as a form of inference, however problematical the hypothesis may be held.”118

There has been a good deal of controversy among Peirce scholars as to how, exactly, in the end he intended abduction to be understood.119

Some of this was prompted by the appearance of N. R. Hanson’s book, Patterns of Discovery in 1958,120 since Hanson made use of Peirce’s term, “retroduction,” in order to make his own point about the manner in which discovery is “patterned” in science. To “discover” a causal hypothesis is already to see certain phenomena as intelligible. He quotes Peirce with approval: “Abduction, although it is very little hampered by logical rules, nevertheless is logical inference, asserting its conclusion only problematically or conjecturally, it is true, but nevertheless having a perfectly definite logical form.”121 Hanson rejects the standard H-D account of causal inference, claiming that (unlike the retroductive one) it leaves the genesis of the hypothesis itself unaccounted for, focusing only on the subsequent testing.

Peirce’s views on the triad, deduction, induction, retroduction, shifted in marked fashion across the course of his long writing career. Early on, he saw them as three more or less independent types of inference. Later, he presents them as three linked phases of the same inquiry, part of a single complex method. Thus, induction in his ear- /88/ lier account is more or less the sort of generalization across particulars that we have already encountered in

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so many guises. It is basically a sampling technique, yielding an empirical law. Whereas in his later writings, induction becomes the means by which abductive hypotheses are tested, i.e., the final phase of inquiry. He is critical of those who confuse abduction and induction, regarding them as a single argument: “nothing has so much contributed to present chaotic ideas of the logic of science.”122 One (abduction) is preparatory, the other (induction) is the concluding step. They have in common that both lead to “the acceptance of a hypothesis because observed facts are such as would necessarily or probably result as consequences of that hypothesis. But for all that they are the opposite poles of reason.” The method of one is, in fact, the reverse of that of the other. Abduction begins from the facts without having any particular theory in view, motivated only “by the feeling that a theory is needed to explain the surprising facts.” Induction, on the other hand, begins from a hypothesis already arrived at and seeks for facts to support that hypothesis.

Whether, when induction is formulated in this way, it can so easily be separated from the prior stage of abduction is a matter of debate. In what way, and to what extent, is background /89/ knowledge to be taken into account in the original abduction?123 Does abduction refer to the manner in which a hypothesis is constructed, or the manner in which a plausible hypothesis is selected from among the available alternatives? Are we asking: what hypothesis is more likely to be true, or: which one is more worth considering? Peirce himself had distinctive views on what he called the “economy of research” which led him to hold that one should ordinarily prefer the hypothesis that is more easily tested.124

It is not easy to disentangle the theme of abduction/retroduction from the enormously complex and sometimes idiosyncratic metaphysical and psychological system Peirce labored to build and rebuild. In the closing paragraphs of this essay, we will leave this task aside to focus finally on a relatively simple statement of “the inference that makes science.”

Proposal. The ambiguity we have noted above between the two “sides” of abduction can be dealt with, in part at least, by allowing that there are two quite different modalities to take into account. Let us restrict the term, “abduction,” to the process whereby initially plausible and testable causal hypotheses are formulated. This is inference only in the loosest sense, but the extensive discussions of the logic of discovery in the 1970s showed how far, indeed, it differs from mere guessing. The testing of such hypotheses is /90/ of the most varied sort. It does, of course, involve deduction in a central way, as consequences are drawn and tried out. Some of these may be singular, others may be lawlike and hence involve induction. But we shall not restrict induction to the testing of causal hypotheses, as Peirce came to do. Much of experimental science is inductive, in the sense of seeking interesting correlations between variables; all the

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factors are observable, in the extended sense of “observable” appropriate to sophisticated instrumentation. (Aristotle’s restriction of the starting point of natural science to features that are observable by the human senses has long since been set aside. Virtually none of the properties on which such sciences as physics and chemistry are built today can be perceived by ns, one reason why the patterning involved in perception is such a poor analogue for scientific explanation.) Induction is strictly limited to the observable domain. And it is only in a very weak sense explanatory. Laws may explain singular occurrences, of the sort that the D-N model was devised to handle. But these are the material of history or of engineering, not of such natural sciences as chemistry or physics. Laws are the explananda; they are the questions, not the answers. /91/

To explain a law, one does not simply have recourse to a higher law from which the original law can be deduced. One calls instead upon a theory, using this term in a specific and restricted sense. Taking the observed regularity as effect, one seeks by abduction a causal hypothesis which will explain the regularity. To explain why a particular sort of thing acts in a particular way, one postulates an underlying structure of entities, processes, relationships, which would account for such a regularity. What is ampliative about this, what enables one to speak of this as a strong form of understanding, is that if successful, it opens up a domain that was previously unknown, or less known.

The causal inference here is therefore not the abduction alone, which is still a conjecture, even if a plausible conjecture. It is the entire process of abduction, deduction, observational testing, and whatever else goes into the complex procedure of theory appraisal. Recent philosophers of science have stressed that the virtues to be sought in a good theory do not reduce simply to getting the predictions right. One looks for “natural” explanations, for example, avoiding ad hoc moves even if these latter lead to correct predictions. One looks for “consilience,” in Whewell’s sense, involving both unification and simplification. This issue of the criteria of theory-appraisal is one of /92/ the most actively discussed topics in current philosophy of science.125

Our concern here is not with the detail of this discussion. It is with the process of theoretical explanation generally, the process by means of which our world has been so vastly expanded. This is the kind of inference that makes science into the powerful instrument of discovery it has become. It allows us reach to the very small, the very distant in space, the very distant in past time, and above all to the very different. As a process of inference, it is not rule-governed as deduction is, nor regulated by technique as induction is. Its criteria, like coherence, empirical adequacy, fertility, are of a more oblique sort. They leave room for disagreement, sometimes long- lasting disagreement. Yet they also allow controversies to be adjudicated and eventually resolved.126

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It is a complex, continuing, sort of inference, involving deduction, induction, and abduction. Abduction is generally prompted by an earlier induction (here we disagree with Peirce). The regularity revealed by the induction may or may not be surprising. Deductions are made in order that consequences may be tested, novel results obtained, consistency affirmed. The process as a whole is the inference by means of which we transcend the limits of the observed, even the instrumentally observed. /93/

Let us agree to call the entire process retroduction. We are “led backwards” from effect to cause, and arrive at an affirmation, not simply a conjecture. Retroduction in this sense is more than abduction. It is not simply the initial plausible guess. It is a continuing process that begins with the first regularity to be explained or anomaly to be explained away. It includes the initial abduction and the implicit estimate of plausibility this requires. It includes the drawing of consequences, and the evaluation of the match between those and the observed data, old or acquired in the light of the hypothesis. Tentative in the first abduction, gradually strengthening if consequences are verified, if anomalies are successfully overcome, if hitherto disparate domains are unified, retroduction is the inference that in the strongest sense “makes science.”

The product of retroduction is theory or causal explanation. It is distinct from empirical law, the product of the simpler procedure of induction. (This distinction is not entirely sharp, since the language in which laws are expressed and the procedures by which observations are obtained are likely to be to some degree theory-dependent.) The criticisms leveled against the original Peircean account can be met, since the claims of both “discovery” and “justification” are recognized, and an implausible dichotomy /94/ between them avoided. Even the original abduction with the modicum of assessment it requires (does the hypothesis, in fact, entail the data prompting its creation? is it testable? is it coherent with background knowledge?) can be called retroduction of a preliminary and tentative sort since it already gives some hint of what the cause may be. But, let it be emphasized again, retroduction is not an atemporal application of rule as deduction is. It is extended in time and logically very complex. It is properly inference, since it enables one to move in thought from the observation of an effect to the affirmation with greater or lesser degree of confidence, of the action of a (partially) expressed sort.

The language here is, of course, that of scientific realism. It is because the cause is, in some sense however qualified, affirmed as real cause, that retroduction functions as a distinct form of inference. Anti-realism reduces effectively to instrumentalism; whether the anti-realist believes that theories may in principle make truth-claims or not, if his or her view does not permit one, in practice, to make an existence claim of any kind for theoretical entities, the distinction between this view and instrumentalism is a distinction with- out a real difference. (Many of those who are currently

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called anti-realists are given that label only because they reject the standard arguments /95/ advanced in favor of realism. But most of these critics in practice affirm the existence of the same entities as realists do, with very similar qualifications; the difference is that they do not present arguments, even bad arguments, in support of their realism.)

The instrumentalist account of explanation reduces retroduction to a complicated form of induction, and theory to law. That is why in the positivist tradition the distinctions between retroduction and induction and between theory and law have been glossed over. If theoretical terms are, in effect, no more than devices used to improve the scope and accuracy of prediction, if “acceptance of a theory involves as belief only that it is empirically adequate” (i.e., predicts observable results correctly), in the influential form of anti-realism propounded by Bas van Fraassen,127 then there really are only two sorts of inference after all. So that on the distinction we have been laboring to draw in these pages, much depends. It is not just a matter of logical convention. It is a question of the amplitude of our world.

Conclusion. It is a far cry from the demonstrations of Aristotle to the retroductions of modern theoretical science. Where they differ is, first, that retroduction makes no claim of necessity, and it settles for less, much less, than definitive truth. It can, under favorable conditions, when theories /96/ are well-established, yield practical certainty. Recent discussions of scientific realism show, however, how hedged this assertion must be, since the truth of a theory requires the existence of the postulated cause under the description given in the theory. Second, the inductions that retroduction relies on are systematic and protracted, not simply a noticing of regularity. Third, the observations from which retroduction begins are, for the most part, performed by sophisticated instruments; the limited scope and lack of precision of the human senses would never permit the range of retroduction that is necessary if the “invisible realm,” as Newton called it, is to be opened up. Fourth, abduction often requires the introduction of new concepts and the testing of new language. The necessity for this was not appreciated as late as Newton’s day; his Third Rule of Reasoning postulated that the properties of all bodies would be the same as those of bodies accessible to the human senses, i.e., would be the so-called primary properties, extension, mobility, hardness, impenetrability, inertia. (He needed this restriction of course, in order that induction might be, as he claimed, the all-sufficient method of natural science.)128 Central to retroduction, as we know it, is the imaginative modification of existing concepts or the creation of new ones quite remote from the universals or forms that might be /97/ abstracted from perceptual experience. Finally, though retroduction is, indeed, an act of the intellect, as the epagoge underlying demonstration was asserted to be, it is exceedingly complex, involving a whole series of discrete and

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well-defined operations, like the drawing and testing of consequences, the assessing of anomalies, and so forth. And it is open-ended; it continues for as long as the possibility of new and relevant evidence remains open. It does not terminate in an act of intuitive insight wherein one sees that the nature must be so.

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