abductive

Abductive Inferences and the Structure of ScientificKnowledge

M. D. BYBEE

University of OregonDept. of EnglishCollege of Arts and SciencesEugene 97403-1286, Oregon, USA

ABSTRACT: The received theories of epistemology identify abductive inferences with thecognitive patterns of speculation (hypothesis formation) and insist that they cannot verifyor confirm hypotheses. I criticize various descriptions of abduction, offer a structural analysisof abductive inferences, characterize abduction without alluding to its putative role in inquiry,and then demonstrate that some abductions do provide evidence and that not all scientifichypotheses derive from abductive inferences. This result challenges those notions of scien-tific knowledge that dismiss some central scientific ideas (for example, evolution) as 'meta-physical research programs' or 'just theories' when they are instead well substantiated byabductive evidence.

KEY WORDS: abduction, hypothesis, inquiry, evidence, scientific method

The received account of scientific activity classifies its psychological,sociological, and historical moments, however temporally discontinuous,into discreet categories: observing phenomena, hypothesizing an explana-tion for the phenomena, deducing consequences of the explanation, andchanging conditions to decide between rival explanations (conductingexperiments). Charles S. Peirce, for example, claims that scientific inquiryproceeds through a speculative stage ('hypothesizing'), a stage in whichwe draw out the consequences of our hypothesis, and a confirmationstage ('testing') (7.203). Some attribute to each stage characteristic infer-ential structures: Peirce, for example, claims we use abductive reasoningto speculate, deductive reasoning to draw out the consequences, and induc-tive reasoning to test our hypotheses. These notions gathered power withcommentators (Hanson, 1969) and flourished to the point that some con-fidently partition all inquiry (Sabre).

One might nevertheless question the general notion of whether sciencehas any such architecture, and more specifically, whether speculationproceeds by any inferential pattern and if so, whether that pattern - call itconjecture, intuition, or guessing - can have provenance in other stages ofinquiry. Some prominent philosophers (e.g., Braithwaite, 31f; Popper, 20f;Wisdom, 49) claimed that no logical or cognitive pattern corresponds tothe psychological phenomenon of intuiting a scientific hypothesis, but

Argumentation 10: 25-46, 1996.© 1996 Kluwer Academic Publishers. Printed in the Netherlands.

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others (e.g., Peirce; Hanson, 1959, 1969) argued that scientific specula-tion has a single inferential structure, called 'abduction,' and that abduc-tive inferences cannot 'verify' or 'confirm' a scientific hypothesis.

I think this is mistaken. Accurately describing abductive inferencesshows, first, that they can indeed confirm claims and, second, that notall hypothetical reasoning results from abductive reasoning. Thus, althoughscientific inquiry may exhibit historical or psychological stages, andalthough each stage uses inferential patterns, we cannot restrict one patternto one stage of scientific inquiry, nor may we legitimately bar any patternfrom any other stage, although both these notions figure prominently in theannals of the philosophy of science.

This profoundly challenges the received notions both of scientific knowl-edge and of the nature of scientific evidence.

I. WHAT IS ABDUCTION?

Numerous historical accidents complicate the task of accurately describingabductive inferences. The history of abduction begins with Charles S.Peirce, whose 'writings on this subject are typically fragmentary and, as aconsequence, we find many different views represented' (Fann, 5). Thisplurality of theories derives from Peirce's evolving view of abduction(Anderson), for he himself recognized numerous confusions and mistakesin his explanations (Fann, 7), writing in 1910, for example, that 'in almosteverything I printed before the beginning of this century, I more or lessmixed up hypothesis and induction' (8.227). Thus, we may not rely heavilyor, worse, exclusively on Peirce's work for our understanding of abduc-tive inferences, as do so many.

Moreover, scholars typically characterize abduction solely by its putativerole in inquiry - which begs the question I raise. Peirce used hypothesisand abduction interchangeably (8.227) and describes abduction as 'studyingfacts and devising a theory to explain them' (5.145) or 'the process offorming an explanatory hypothesis' (5.171). Citing Peirce, others describeabduction as a 'type of inference yielding an explanatory hypothesis, ratherthan a result of deductive application of a "rule" to a "case" or establish-ment of a rule by induction' (Runes, 1) or 'the means whereby hypothesesare generated, moving from a particular case to a possible explanation ofthe case' (Reese, 1) or more explicitly, 'The name given by C. S. Peirceto the creative formulation of new statistical hypotheses that explain a givenset of facts' (Flew, 1). Since these definitions equate abduction withconjecture or hypothesis, one might suspect that deductive or inductiveinferences could function 'abductively,' in spite of Peirce's claims to thecontrary (e.g., 5.145).

On the other hand, if abductive inferences constitute a separate kind of

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reasoning from either inductive or deductive inferences, then we are entitledto ask in precisely what ways they differ, and we may also legitimatelyask for citations to or examples of abductive inferences. Unfortunately,scholarly accounts virtually never quote actual abductions, and theirmaterial analyses are vague or (as we shall see) misleading.

If abduction is a third kind of inference, a legitimate alternative to deduc-tion and induction, how may we best explain it such that our answer doesnot beg the question of its role in inquiry and argumentation?

Aristotle, having only syllogistic or class logic, distinguished deduc-tion from induction by claiming that deduction proceeds from generalprinciples to specific cases and that induction proceeds from specific casesto general principles (Posterior Analytics 81a40-b1 ; Topics 105a13). Intel-lectual folklore enshrined this criterion, and ordinary language replicatesit (as various dictionaries report); nevertheless, this uncritically acceptedand dogmatically repeated formula inadequately distinguishes the two infer-ences, for although a few deductive inferences (for example, categoricalsyllogisms) do change their level of generalization, the vast majority simplydo not: modus ponens, modus tollens, disjunctive syllogism, hypotheticalsyllogism, constructive dilemma, destructive dilemma, and so on, all remainat the same level of generalization, however anyone may explain 'gener-alization'. So supposed change in generality do not encompass even alldeductive inferences. And since using this classification makes deductionand induction seem conjointly exhaustive, it certainly cannot help us todistinguish abduction from the other two.

To replace this discredited theory, scholars attempted to distinguishdeduction and induction modally: If a deduction's premises are true, itsconclusion must be true; if an induction's premises are true, its conclusionis only probably true - to some degree of probability. Peirce describedabduction modally: 'Deduction proves that something must be; Inductionshows that something actually is operative; Abduction merely suggests thatsomething may be' (5.171). In other words, nothing in an abduction'spremises contradicts its conclusion. The modal model equates the inferen-tial patterns of deduction, induction, and abduction with necessity, actu-ality, and possibility.

Unfortunately, this distinction also fails: The original modal model ade-quately distinguishes deduction from induction only if 'actually true' means'not certainly false'; thus, it distinguishes deductive inferences only fromnon-deductive inferences, and both induction and abduction would fallunder the latter: If their premises are true, then their conclusions are notcertainly false but would be true to some degree of probability, howeverfirm or remote. So although the modal 'no contradiction' model may super-ficially capture one aspect of abduction, it neither distinguishes it frominduction nor captures abduction's persuasive force.'

Peirce's most rigorous attempt to distinguish abduction from deduction

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and induction claimed that these inferences have different structures.Consider this example (from 2.623):

deduction:

Rule. - All the beans from this bag are white.Case. - These beans are from this bag.

Thus: Result. - These beans are white.

induction:

Case. - These beans are from this bag.Result. - These beans are white.

Thus: Rule. - All the beans from this bag are white.

abduction:

Rule. - All the beans from this bag are white.Result. - These beans are white.

Thus: Case. - These beans are from this bag.

In this scheme, each pattern uses the same propositions as the others butarranges those propositions in a different order. Let me give a differentexample:

sample deduction (a categorical syllogism):All people are mortal.Socrates is a person.

Therefore, Socrates is mortal.

an analogous sample induction:Socrates is a person.Socrates is mortal.

Therefore, all people are mortal.

an analogous sample abduction:Socrates is mortal.All people are mortal.

Therefore, Socrates is a person.

Clearly, then, abductive inferences differ structurally from inductive anddeductive inferences.

Of course, inductions or abductions rarely correspond so precisely tocategorical syllogisms, so those examples grievously mischaracterize thetwo non-deductive inferences. The following better represents an inductionanalogous to the categorical syllogism from which we started:

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Socrates is a person, and Socrates is mortal.Aspasia is a person, and Aspasia is mortal.Plato is a person, and Plato is mortal.Hypatia is a person, and Hypatia is mortal.Aristotle is a person, and Aristotle is mortal.

Diotima is a person, and Diotima is mortal.Therefore, all people are mortal.

That is, real inductions have very many instances, not just one, but all havethe same form, and the persuasive force of an induction increases as thenumber of instances increases.

By the same token, expanding the analogous abduction reveals its infer-ential power:

Socrates is mortal, featherless, wingless, rational, erect,bipedal, omnivorous, ... and mammalian.

All people are mortal, featherless, wingless, rational, erect,bipedal, omnivorous, ... , and mammalian.

Therefore, Socrates is a person.

Inductions analogous to categorical syllogisms attribute two characteris-tics to any number of different instances, whereas analogous abduc-tions attribute any number of characteristics to just two instances. Thus,somewhat more general descriptions of categorical syllogistic inferencesand their inductive and abductive analogues would go something likethis:

a sample deduction (a categorical syllogism):All phi-ers are psi-ers.A is a phi-er.

Therefore, A is a psi-er.

an analogous sample induction:A is a phi-er and A is a psi-er.B is a phi-er and B is a psi-er.C is a phi-er and C is a psi-er.D is a phi-er and D is a psi-er.

Z is a phi-er and Z is a psi-er.Therefore, all phi-ers are psi-ers.

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an analogous sample abduction:A has comparative characteristics alpha, beta, gamma, delta,

epsilon, ... and omega.B has comparative characteristics alpha, beta, gamma, delta,

epsilon, ... ., and omega.Therefore, A and B are the same.

This analysis remains consistent with Peirce's more elaborate structuralmodels (e.g., 2.461).

My point is not, of course, that the last specific structure formalizesall abductive inferences, any more than that the first specific structure (acategorical syllogism) formalizes all deductive inferences; abductions takeas many different structures as deductions. My point is, instead, that abduc-tions are structurally different from deductions and inductions, and thuswe may safely use a structural model to distinguish abductive inferencesfrom deductive and inductive inferences. Before we can discern what char-acterizes all abductive structures, however, we must add another dimen-sion to this model.

Recent critical theory (Domino) suggests that the preceding analysismakes abduction's inferential strength seem to rest solely on the quantityof the predicates two objects share, and that a more adequate account mustconsider the possibility that some predicates are qualitatively more impor-tant than others. For example, in an abduction about whether 'Bob is asuccessful computer consultant,' the common predicates 'breathes air' and'sleeps about eight hours a day' seem less important than the predicate 'ableto answer basic questions about computers' (64), for the first predicatesapply to drug dealers as well as computer programmers and thus do notseem as relevant. 'Lacking a means of prioritizing the predicates, Bybeeaninquirers cannot stop amassing evidence until they have ascertained allrelevant information . . . They cannot legitimately stop at any point lessthan a perfect abduction' (64). Domino advances a 'clincher' model ofabduction, one in which a given abduction rests on 'the predicate that allthe inquirers agree will determine which of the competing claims is correct'(64). In such a model, the inquirers would agree on 'what piece(s) ofevidence would be sufficient to make a reasonable decision' (64).

Amending a strictly quantitative picture of abduction may prove neces-sary on other grounds. Satosi Watanabe's 'Ugly Duckling Theorem' (1969)suggests that any object in the universe has just as many predicates incommon with any second object as with some third object; for example, agiven pencil shares as many predicates with another pencil as it does withan eraser = or a whale or a supernova. Yet, since we do indeed taxono-mize objects, and since we do so on the basis of their predicates, inquirersmust find some more important than others; and a fortiori, we cannot usesimply the number of common predicates to effect classifications or abduc-tive identifications.

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Although I agree that abduction includes a qualitative component, Ihesitate to abandon the quantitative component, for even if we grant thatsome predicates are relevant and some not, the greater the number ofrelevant predicates, the more persuasive we find the abduction. Thus, wemust incorporate some quantitative component in abduction's description.

I also hesitate to adopt the 'clincher' model for identifying qualitativepredicates. The claim that real inquirers 'cannot legitimately stop [amassingabductive predicates] at any point less than a perfect abduction' (64)seemingly assumes that inquiry's aim is certitude, not belief. Those withan inappropriately high threshold of belief, who require a high degree ofconfidence before assenting (e.g., Hamlet, mathematicians, etc.), may wellhave to restrict themselves to deduction and abandon abduction as a methodof inquiry altogether - but they would, on those same grounds, abandoninduction as well. On the other hand, those whose thresholds of belief arelower and who tolerate a high degree of uncertainty (e.g., Othello, psychics,etc.) would accrue fewer predicates before believing an abduction's con-clusion. Thus, inquirers collect abductive predicates until they reach theirown threshold of belief, whatever that may be. Thus, the insistence thatone needs a perfect abduction is as mistaken as an insistence upon a perfectinduction.

This is not to deny, of course, that some predicates are relevant and someare not, and that some predicates are more relevant than others, which are,I think, the main points of Domino's objection. A mathematical model maymost clearly show the necessity of amassing a quantity of even marginallyrelevant predicates. Take this example (adapted from Domino):

Bob breathes air, has red hair, weighs two hundred pounds,and is left-handed.

The secret computer programmer breathes air, has red hair,weighs two hundred pounds, and is left-handed.

Therefore, Bob is the secret computer programmer.

Suppose that every object in our universe of discourse exhibits the predi-cate, 'breathes air,' but that only thirty percent of that population exhibitsthe predicate, 'has red hair,' twenty percent exhibits, 'weighs two hundredpounds,' and only ten percent exhibits, 'is left-handed.' If each of thesevariables is entirely independent of the others, then the proportion of thosemembers in our universe of discourse that fits this description (Pp) is theproduct of (1) the probability that an arbitrarily selected member of thepopulation breathes air (Pa), (2) the probability that such an object has redhair (Pb), (3) the probability that the object weighs two hundred pounds(Pc), and (4) the probability that such an object is left-handed (Pd):

P = Pa * Pb * P * PdPp = 1.0 * 0.3 * 0.2 * 0.1Pp = 0.006

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This model exposes which predicates (if any) are qualitatively more impor-tant (e.g., left-handedness) and which (if any) we may dismiss out of handas irrelevant (e.g., air-breathing).

An abduction's persuasiveness depends not only on the predicates' quan-titative and qualitative features, however, but also on the size of the universeof discourse. If our domain of choices were small, say, only ten, then wecan be very confident that Bob is the secret programmer. Indeed, a singlepredicate, a 'clincher,' (e.g., left-handedness) might well serve in this case.If, on the other hand, the population numbered a million, then six thousandmembers would have those conjoined characteristics; what served as a'clincher' would do so no longer, and we would need to find furtherrelevant predicates.

This shows we could conceivably have very convincing abductivearguments with no single overpoweringly infrequent characteristic -no 'clincher' in Domino's sense. The persuasive force in such caseswould reside in the large number of common characteristics, even if onlymarginally relevant, and a correspondingly small universe of discourse.More importantly, however, this shows that abductions' inferential powerdepends on both the quantity and the relevance of their comparativecharacteristics.

We clearly may distinguish abduction from deduction and inductionalong these probabilistic, structural lines, but we have yet to characterizethat difference explicitly. What feature distinguishes abductive structuresfrom deductive and inductive structures? Can we now give a general theoryof abductions that does not beg the questions before us?

An exhaustive description of abductive inferences equivalent toAristotle's Organon (for deduction) or Bacon's Novum Organon (for induc-tion) is outside my present scope, but observe the following: No additionalpremise would make a valid deductive inference more conclusive, so deduc-tions, unlike inductions and abductions, do not proceed by amassingevidence. Amassing inductive evidence increases the proportion of theuniverse encompassed by the induction's conclusion; a perfect inductioncomprises every member of its universe of discourse. In abductive rea-soning, however, each comparative condition decreases the proportion ofthe universe that satisfies the abduction. Abductive inferences proceed,then, by the process of elimination, citing comparative conditions that, inconcert, exclude potential satisfactory conclusions until, finally, theaudience reaches its threshold of belief. A perfect abduction eliminatesevery possible alternative to its conclusion. 2

This model of abductive inferences, based on the probabilistic, ramifiedstructural description, incorporates the alternative models of abduction (themodal 'no contradiction' model, the truncated structuralist model, and the'clincher' model) as special cases, and it includes both quantitative andqualitative elements. Moreover, unlike some accounts (e.g., Lanigan), it isnot limited to only those abductive inferences analogous to categorical

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syllogisms, a flaw Peirce ultimately came to recognize in his own work(2.102). Most importantly, we have characterized abduction without refer-ring to its putative role in inquiry, which enables us to address and disposeof the two erroneous beliefs at hand: first, the fanciful notion that abduc-tion cannot provide evidence for a conclusion; and second, the fallaciousbelief that abduction is the only inferential pattern in scientific speculation,hypothesis-formation.

II. CAN ABDUCTION PROVIDE CONFIRMATION?

As we have already seen, the received wisdom limits abduction to thecognitive process by which we create hypotheses and, derivatively, deniesthat it can offer evidence for the truth of any hypothesis that it maygenerate. Although one might suppose that the preceding analysis alonewould establish that abductive inferences can and do provide evidence forconclusions, such a supposition faces potent obstacles.

First, some argue that we must distinguish between the reasons foraccepting a hypothesis and the reasons for suggesting a hypothesis in thefirst place (Hanson, 1959, 22; 1969, 85-92), where (supposedly) the wordreasons refers not to the psychological motives one has for suggesting oraccepting a hypothesis (e.g., greed, fame, assuaging anxiety, etc.) but ratherto the evidence for suggesting or accepting a hypothesis. Were one to grantsuch a distinction, one might believe that a single inferential pattern cannotserve both functions.

Second, the modal 'no contradiction' model of abduction has a widercurrency than any other model, attributing to abduction (supposedly) theweakest modality of the three patterns of inference: If an abduction'spremises are true, we may only legitimately infer that its conclusion ispossibly true.

Third, the only widely-known alternative to the modal description is ahighly-truncated structuralist description, an abductive analogy to modusponens,3 and in that paradigm, serious thinkers easily dismiss abductionas a means by which to provide evidence: Are we to believe, after all, thatSocrates is a Greek, based simply on the facts that Socrates is mortal andthat all Greeks are mortal?

These misconceptions may account for the fanciful ideas many haveabout abduction, for if a given inferential pattern can have only one functionin inquiry, and if abduction can generate only possible conclusions, and ifits structure seems to be wildly speculative (to say the least), then abduc-tions seem to describe nothing more than hunches or guesses and are there-fore inadequate for any task to which a reasonable thinker might apply themexcept speculating, hypothesizing, or conjecturing.

Notice, however, that these reservations apply equally well to induction.Is induction to be constrained to a single function in inquiry? In a world

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demanding certainty, what credence should we give to a conclusion that isonly probable, especially if the degree of probability can include extremeunlikelihood? And who would confidently conclude that all Greeks aremortal based on knowing only that a Greek named 'Socrates' gasped hislast some twenty-five hundred years ago?

We understand inductive reasoning far better than this, of course; weknow that it sometimes requires millions of instances to be persuasive,and that these instances do provide evidence, say, that all people are mortal,although we may grant that a possibility exists (however slight) that someone person (a teenage rock star, no doubt) will live forever. Thus, theaccounts typically used to describe abduction do not even adequatelycapture induction.

The same is true of abduction. Everything the modal and truncated struc-turalist models say about abduction is true, of course, but as we have seen,both fail to say everything; a more sophisticated understanding of abduc-tion would lead scholars to see that abductive inferences do provide ampleevidence for positions, even though such evidence does not provide certi-tude. Consider, for example, the inference in the following anecdote:

Separated from her husband within five years of their marriage, Princess Mathilde hada long affair with Count Niewekerke. The liaison was public knowledge, but because ofPrincess Mathilde's position in the imperial family, no one was supposed to know aboutit. She was entertaining a group of ladies one afternoon when her dog, a miniature grey-hound, came running up to her to be caressed. 'Go away, you naughty dog,' said theprincess, pushing it from her. 'Don't you know you're a disgrace?' Then turning to herguests she complained: 'Last night he kept jumping on the bed all night and I couldn'tget any sleep at all.' A short while later Count Niewekerke joined the party. The littledog ran to fawn on him as well, but he pushed it away. 'You're a very bad dog and I'mnot going to pet you. You kept jumping on the bed all night and I didn't sleep a wink'(de Stoeckl and Edwards).

This inference is abductive: The bed in which Princess Mathilde slept andthe bed in which count Niewekerke slept share a number of characteris-tics, some explicit (e.g., a miniature greyhound jumped on it all night long)and others implicit (e.g., both beds were in the same residence, both existon the same night, the dog not only jumped on both but jumped in the sameway, and with the same results). This plethora of implicit and explicit com-parative characteristics leads us (and the Princess's auditors) to infer thatthose two beds were, in fact, one.

Abductions with a single explicit comparative property occur infre-quently, for as we have seen, as the number of conditions increases, aconclusion's theoretical possibility becomes a practical probability, to thepoint where, with a sufficient number of comparisons, we would find itextremely unlikely (yet still possible) for an abductive conclusion to befalse. Moreover, universes of discourse are rarely so limited. Suppose, forexample, that a department store clerk hears a radio announcer describe theperson who just robbed the corner bank as a red-haired, blue-eyed, left-

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handed, near-sighted, tattooed, overweight, lame adolescent of indetermi-nate sex. If the clerk's customer matched that description, the clerk wouldinfer:

The bank robber was a red-haired, blue-eyed, left-handed,near-sighted, tattooed, overweight, lame adolescent of indeter-minate sex.

My customer is a red-haired, blue-eyed, left-handed, near-sighted, tattooed, overweight, lame adolescent of indeterminatesex.

Therefore, my customer is the bank robber.

In this adventitious abduction, the 'no contradiction' model leads us tobelieve that 'my customer is the bank robber' is highly speculative, onlypossibly true, nothing more; still, the number of comparative conditionsmakes the inference compelling, for they limit the number of conclusionsthat can possibly satisfy the condition set. Consider this skein of reasoning:

In the southwest comer of the Agora there is a large enclosure, almost square in plan,measuring 27 by 31 m; only a single course above the foundations is preserved. It wasapproached by five steps built all along the north side. Within, there were no rooms orinternal divisions or roof in the original period. The building was erected in the 6th centuryBC, perhaps around the middle of the century, to judge from the ceramic evidence. Thereis no known ancient reference to the building, and for its identification we must rely onthe remains alone. The usual function of a large walled temenos is to enclose a sacredarea, but excavations carried down to bedrock within most of the building revealed notrace of an altar or shrine and no trace of votive offerings of the sort commonly foundin sanctuaries. Its large size, early date, and prominent location by the Agora all suggestthat it is a public building; a likely candidate would be one of the lawcourts of the day.We have a great deal of indirect evidence in the literary sources about lawcourts, thoughno certain examples. The basic requirement of a court is that it should be large enoughto contain the hundreds of jurors who made up an Athenian court. The courts segregatedthe jurors, but outsiders could often overhear the proceedings; several courts wereunroofed and open to the sky. All these elements apply to this structure, which shouldtherefore in all likelihood be identified as one of the earliest courts of Athens (Camp,46-47).

Because the two share so many relevant characteristics, which so few otherconclusions satisfy, we infer that the twenty-seven by thirty-one meterenclosure in the southwest corner of the Agora is the ruins of one of theearliest courts of Athens.

Consider another example of abductive reasoning even less speculativethan the last, where the question at issue is which aircraft carrier Lt. Leslie'sdivebombers attacked at Midway:

Leslie's target had many planes on the flight deck; the same was true of the Soryu. Lesliedived with 13 planes; some 12-13 attacked the Soryu. Leslie's last four planes shiftedto other nearby targets; the Soryu's screening destroyer Isokaze was bombed at this time.None of the other squadrons attacked the screening ships, and the only screening destroyerbombed was assigned to the.Soryu (Lord, 294).

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We infer that Leslie's target was the aircraft carrier Soryu based on the largenumber of shared conditions relative to the small universe of discourse(four possible aircraft carriers).

In that rigorous and yet common-sensical arena of dispute, forensicdebate, abduction reigns under the name, 'comparison.' The Federal Rulesof Evidence, subsection 6824, Rule 901(b)(3) outlines 'comparison by trieror expert witness' this way:

An expert witness and/or the trier of fact may base an opinion as to authenticity upon acomparison between the questioned piece of evidence and an exemplar the authenticityof which has been sufficiently established, Rule 901(b)(3). The process of authentica-tion by comparison rests upon the notion that with respect to a particular item there areso many common identifying characteristics that it is possible by this means to establishthat the exemplar and the item in question have the same origin. Comparison is frequentlyused in connection with ballistics, handwriting, fingerprints, and typewriting. The sametechnique has also been used to authenticate tire tread marks, shoe prints, and otheritems where the presence of sufficient common characteristics is shown.

Although United States federal law leaves what constitutes 'sufficientcommon characteristics' to expert opinion, English law explicitly stipulatesthat exemplar fingerprints and fingerprints in question must exhibit at leastfourteen 'points of comparison.'

Abductive inferences occur virtually everywhere, under any number ofguises, often disguises: For example, the abductive inference analogous tocategorical syllogisms is the limiting case of 'inductive analogy.' Otherwisewell informed thinkers often mistake abductive inferences for induction.4

A skeptic might begrudgingly agree that abduction provides evidencefor a conclusion but still claim that it so serves only in the absence of other,more compelling kinds of evidence. It seems, however, that real inquiry,as opposed to fanciful taxonomies of inquiry, uses all three inferentialpatterns in various roles. Examine again the famous syllogism:

Socrates is a Greek.All Greeks are mortal.Therefore, Socrates is mortal.

Ostensibly a deductive proof provides the strongest form of evidence, forif its premises are true, the conclusion must be true; but as Bertrand Russellpoints out, the premise 'All Greeks are mortal' in this syllogism in factresults from an inductive argument; and we might further notice that oneof the instances in that induction would be Socrates himself! So, Russellobserves, since no deductive conclusion can be stronger than its premises,deductive arguments are in fact no stronger than inductive arguments - andin many cases, perhaps even weaker, for they require more inferences toobtain the same conclusion.

The same is true mutatis mutandis of abductive reasoning and the otherpremise, for what evidence do we have that 'Socrates is a Greek' or thatany object is the member of any class? Naive taxonomical schemes iden-

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tified class members by comparing their characteristics against those whichcollectively constituted the criterion for class membership, supposedly adeductive inference:

Criterion: If X has characteristics alpha, beta, gamma, ...and omega, then X is a member of class Y.

Observation: X has characteristics alpha, beta, gamma, ...and omega.

Conclusion: X is a member of class Y.

'Family resemblance theory' sounded the death-knell for this notion ofclasses, however, for Wittgenstein (17-19) pointed out that objects couldbe considered the members of classes the way people were sometimes iden-tifiably members of the same family: Most members share one character-istic, say, a prominent nose, and most share another characteristic, say, curlyhair, and so on, but no one characteristic extends throughout the family.Thus, members of a class would have a 'family resemblance,' not becausethey shared 'defining characteristics' (properties that all members and onlymembers of that family exhibited), but because they shared a large pro-portion of a set of characteristic properties which, when occurring inconcert, marked someone a family member - and though no single char-acteristic was shared by all! Thus, we must recognize members of classesthe same way we recognize, say, that my customer is the bank robber,abductively:

Observation One: X exhibits characteristics alpha, beta,gamma,..., and omicron.

Observation Two: Members of class Y exhibit many (thoughnot all) of the characteristics alpha, beta, gamma, ... , nu,omicron, pi, ... , and omega.

Conclusion: X is a member of class Y.

Thus, while the deductive premise 'All Greeks are mortal' almost assuredlyresults from inductive reasoning, the other deductive premise 'Socrates isa Greek' results from abductive reasoning.5 And since no conclusion canbe known with greater certainty than any of its premises, the hoary cate-gorical syllogism, paradigm of deduction, cannot provide stronger evidencethan its associated inductive and abductive arguments.

Thus, although deductions ostensibly have a greater modal 'strength,'in actual inquiry, no pattern of inference is superior to any other. In fact,a given abductive argument could even be more conclusive than a givendeductive argument; the strength of an argument does not - cannot - relyon its taxonomy.6

Therefore, not only do actual inquiries use abduction to support con-clusions or confirm hypotheses, but abduction performs this role aswell as induction or deduction. Thus, we may not legitimately limit abduc-

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tion to only some phase or part of inquiry (e.g., speculation), nor maywe preclude abductive arguments from another stage of inquiry (e.g.,confirmation).

III. WHAT IS THE PATTERN OF SCIENTIFIC INQUIRY?

Our second issue concerns whether all scientific speculations follow abduc-tive reasoning or whether some speculations result from either deductiveor inductive reasoning.

The belief that only abduction forms the cognitive pattern of scientificspeculation remains the strongest mythology not only about abduction butalso about how we discover scientific knowledge. Indeed, as we have seen,the word abduction is often identified with or defined by its putative roleas the sole inferential pattern of conjecture. To examine this claim criti-cally and evaluate evidence on its behalf, we can perhaps rely best onNorwood Hanson's account, because it generously acknowledges Peirceas its source, and because it is both the most accessible and the most influ-ential: Nearly every other commentator cites either Hanson directly orthose passages from Peirce and Aristotle that Hanson cites. We shall see,however, the evidence Hanson gives on behalf of this picture of scientifichypothesis is either false or misleading or both.

Following Peirce (5.144), Hanson begins his description of abductionby claiming that Aristotle lists three types of inferences: deductive, induc-tive, and one other called apagoge (85). Aristotle, however, claimed that'every belief comes either through deduction (syllogismos) or from induc-tion (epagoge)' (Prior analytics 6 8b13- 1 4 , cf. 42a3, 6 8 b3 2 -3 7 , Posterioranalytics 71a5-11) or, most emphatically, that 'everyone produces beliefthrough exhibiting either paradigms or enthymemes - and in no other way'(Rhetoric 13 5 6 b6-8, my emphasis). Thus, Aristotle did not by any meansidentify three kinds of inferences.

Hanson justifies identifying the inferential structure that Aristotle callsapagoge with the inferential structure that Peirce calls abduction, first, bypointing out that Jenkinson translated the word apagoge as 'reduction' (200,note 3) and that Peirce renders it 'abduction' or 'retroduction' (85); second,by citing part of Jenkinson's translation of Prior Analytics 69'20-24 (85);and third, by citing in an endnote Whewell's translation of OrganumRenovatum (200). 7

Even a cursory examination discloses that these descriptions of apagogedo not apply to abduction. Ross, in his commentary to the Analytics,explains that apagoge is of two kinds (489-490). The first, apagoge sim-pliciter (Prior analytics 2 8b2 1 , 69a20-36), is the type of deductive proofthat Plato called 'ex hypothesi' (Meno, 86e-87c), known today as condi-tional proof:

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Assume some proposition A (called the 'hypothesis').On the basis of A, derive (through many deductive steps)

proposition B (called the 'consequent').Conclude the conditional proposition 'If A then B.'

The apagoge eis to adunaton (Prior Analytics 2 9 b6 , 5Oa31), a subset ofthe first kind of apagoge, is also known as 'reductio ad impossible' or, inmodern terms, indirect proof:

Assume proposition 'not A' (called a 'hypothesis').On the basis of not A, derive (deductively) proposition 'not

B.'Conclude the proposition 'If not A then not B.'Infer (deductively) the proposition 'If B then A.'

Aristotle discussed apagoge in other contexts (cf. Topics 1 5 9 b8- 2 3 ,160all-14) but invariably understood it (correctly) to be a deductive infer-ence; these patterns are both called ex hypothesi not because they generatea hypothesis but because they begin with a hypothesis as the first step ina lengthy deduction. Since Aristotle refers to these 'hypothetical' argu-ments with the word apagoge, it might seem that ex hypothesi argumentsare abductive inferences, and thus that apagoge refers to abduction. 8

Nevertheless, the reasoning is spurious: Whatever else apagoge may be,however we may wish to translate the word, it describes a variety of deduc-tive inferences, not an alternative to deduction.

Perhaps, however, Aristotle conflated abduction and conditional proofs;if so, then the term apagoge might (mistakenly) refer to both. This wouldbe the case only if Aristotle did not identify and describe abductive argu-ments distinct from apagoge - but he did, under the name, homoiotes,'arguments from likeness' (cf. Topics 156b10-17). Aristotle accuratelyobserves homoiotes resembles induction (epagoge) but is distinct from it.Thus, contrary to Peirce's and Hanson's accounts, Aristotle's apagoge hasno relation to abduction.

This fallacious scholarship does not necessarily mean, however, thatHanson mistakenly characterizes the nature of abduction or its role in thescientific process. Following Peirce closely (see, for example, 5.189),Hanson repeats the standard truncated structuralist description:

The form of the [abductive] inference is this:1. Some Surprising phenomenon P is observed.2. P would be explicable as a matter of course if H were true.3. Hence there is reason to think that H is true (86).

This is, of course, an abductive inference, one commensurate with themodal 'no contradiction' model, not the abductive inference. 9 The questionis, does it adequately capture the nature of scientific speculation?

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Let me put the question differently: Hanson may well be correct thatscientific hypothesis always follows the abductive pattern analogous tomodus ponens, or he may be correct that it always follows the pattern ofconditional proof (apagoge), but both claims cannot be correct, for thetwo contradict one another. The question is, then, what inferential patterndoes scientific hypothesis follow as a matter of historical fact? Do scien-tists form hypotheses on grounds other than abduction?

Once we call into question the received wisdom of attributing certaininferential patterns to certain stages of scientific inquiry and argumenta-tion, we quickly recognize that hypothesizing does not always and every-where proceed abductively, even if we understand abduction according tothe most elastic and forgiving scheme, the 'no contradiction' model. Take,for example, the hypothesis Niels Bohr advanced about atomic structure,that in an atom, the electrons circle a nucleus in a few, discreet orbits.This hypothesis enjoyed widespread acceptance and remains the basis ofnuclear chemistry today; electrons are still given names based on thishypothesis, e.g., 'p-orbital' and 'q-orbital.' Nevertheless, in spite of itsacceptance and its continuing importance in physics and chemistry, Bohr'sconjecture contradicts so many fundamental notions of science that everyphysicist knew when it was proposed and knows now that it could not betrue: If electrons (charged particles) actually orbited a nucleus, they wouldundergo rotational acceleration, and any charged particle that undergoesacceleration emits electromagnetic radiation. Thus, if the Bohr hypothesiswere true, matter would glow!

A more famous example is the Copernician hypothesis that the sun, notthe earth, is the center of planetary rotation. When Copernicus and Galileoproposed it, the heliocentric theory contradicted reigning scientific knowl-edge: If it were correct, then the earth would have to spin on its axis andmove through space, both, and all empirical experiments undertaken tocheck whether the earth moved demonstrated quite the opposite."

In both cases, of course, subsequent refinements modified either the prof-fered hypothesis (in one case) or all of science (in the other): Contemporaryatomic theory, amending Bohr's picture of the atom, no longer proposesthat electrons actually move around a nucleus but instead describes elec-trons as clouds of probabilities. As Galilean dynamics displaced Aristoteliantheories of motion, scientists devised experiments that did reliably checkfor the earth's movement. Nevertheless, scientists proposed both thesehypotheses (and many others) quite apart from the fact that they contra-dicted an enormous body of existing empirical evidence against them; thus,they did not speculate abductively (for, as we have seen, abduction requiresthat nothing in the conclusion contradicts the conditions)."

Skeptics may object that such cases do not exemplify scientifichypotheses, or that this account conflates theories with hypotheses; but bothobjections beg the question, for without the a priori taxonomy of inquirythat I call into question, the attempt to distinguish speculative hypotheses

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from adopted theories on their inferential structures alone seems tenuousindeed, if not wholly vacuous.

Not all conjectures, even scientific conjectures, even conjectures in the'hard' quantitative sciences, result from abduction, even when the leastdemanding 'no contradiction' model is the standard for abduction. Thus,we may dismiss the second of our two concerns, the uncritically acceptedclaim that abductive inferences generate all scientific hypotheses.

IV. CONSEQUENCES

Since abduction 'confirms' hypotheses as capably as any other kind ofinference, and since conjectures derive from other kinds of inferences thanabduction, the standard identification of scientific speculation with abduc-tion is simply false. Thus, genuine inquiry cannot be as some scholarstake it to be, a series of stages or steps, each with its characteristic infer-ential pattern. Both inquiry (trying to find something we do not know onthe basis of what we already know) and argumentation (justifying whatwe do know on the basis of what our audience agrees is true) must insteadbe networks or webs of interlocking inferences, some deductive, someabductive, and some inductive. One premise of a given deduction mighteasily be either suggested by or supported by an abductive argument,another by an inductive argument; some predications in a given inductiveargument might result from deduction, some from abduction. And someabductive comparative conditions might be deductive conclusions andothers result from inductive inferences. Some arguments and some inquiriesproceed as chains of inductions, deductions, or abductions. Actual inquiriesmay even make use of extra-logical appeals as well, e.g., pathos (an appealto the audience's empathy) and ethos (an appeal to the rhetor's moral orintellectual character).

Thus, we cannot legitimately prescribe in advance what kind of infer-ence should theoretically be appropriate for any given point in an inquiryor an argument; we may only describe a given inferential structure oncesomeone has advanced it. Moreover, we may evaluate a given inferenceonly according to its merits, not according to whether it fits the numerousfanciful, preconceived taxonomies of argumentation or inquiry that abound.

Although true of inquiry and evidence in general, this may not applyto more rigorous subsets; as we have seen, many claim adamantly thatscientific inquiry and argumentation is special in that (1) they universallyfollow a single, specific pattern with identifiable stages, however tempo-rally discontinuous, (2) to each of these stages we can legitimately ascribeone and only one inferential structure, and (3) abduction is the inferenceof conjecture and hence cannot legitimately justify conclusions.

From such commitments, a series of positions about the nature ofscientific knowledge follow directly, at least one of which is crucial: Deeply

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influenced by Karl Popper's insights (1959, 1963), many insist that inscience, the usual criterion of 'confirmation' or 'verification' must be aban-doned and replaced by a more esoteric notion, 'lack of falsification':Supposedly we can never provide conclusive evidence that a scientifictheory is true and can only provide conclusive evidence that a scientifictheory is false. Acceptable scientific theories are merely those that experi-mentation has not (yet) falsified.

Having examined the nature of abduction more carefully, we can nowsee that this scheme, from its first a priori assumptions and definitions toits conclusions, rests on a number of uncritical assumptions, including neo-Pythagorean presuppositions about what constitutes conclusive evidence,namely, a belief (call it 'deductio-centricism') that 'conclusive evidence'means little more than 'deductive proof.'

This is absurd, of course. At the most basic level, no one has eitherdeductive or inductive proof that Lt. Leslie's flight bombed Soryu, but onlyperverse Platonists or Cartesians would claim either that we lack 'conclu-sive evidence' that Soryu was his target or that we cannot be said to 'know'that he bombed Soryu. Not all justification is deductive; not all true propo-sitions are necessarily true propositions. Conclusive evidence cannot bereduced to deductive inferences. Knowledge does not consist solely ofnecessarily true, deductively justified beliefs but includes not only induc-tively justified but also abductively justified beliefs.

People performing actual research in the sciences (as opposed perhapsto those same people performing the philosophy of science) know this,albeit not always explicitly. On the one hand, they use the kind of infer-ence I have herein identified as abductive reasoning as a statistical methodof providing evidence for positions (confirming hypotheses), though theynever recognize it as abduction.

On the other hand, scientists (sometimes to their great embarrassment)have no other recourse than to accept theories solely on the basis of over-whelming abductive evidence. Consider modern evolutionary theory andthe objections to it that some raise on behalf of creationism. Duane Gishpoints out that the origin of life and its evolution are not repeatable, con-trollable, or predictable. Moreover, Gish claims (on the authority of KarlPopper) that Darwinian evolution is not a testable scientific theory butsimply 'a metaphysical research program.' And finally, although the theoryof evolution has enormous explanatory power, no direct evidence 'confirms'the theory of evolution; rather, its truth rests solely on a series of infer-ences. Thus, since no deductive or inductive reason exists for acceptingDarwinian evolution over any alternative with the same explanatory power,and since creationism has the same explanatory power - if not more -Gish can apparently advance creationism as a legitimate scientific rival toevolution.

Under the view of scientific argumentation I am urging, however, thephenomena that Darwinian evolution supposedly 'explains' become instead

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a huge number of comparative conditions in an abductive argument,all of which together 'confirm' or 'verify' modern evolutionary theorybeyond any reasonable doubt, scientific or otherwise. Similarly, creationismbecomes an especially weak version of the long-discredited 'argument fromdesign.' Some have attempted to explain this (Gould, Dawkins), but thereceived wisdom concerning science and its epistemology, stemming fromPeirce, Hanson, and Popper, prevents them from making their case aslucidly as they might otherwise.

These remarks apply not only to the theory of evolution, of course, butto all those theories susceptible to objections like those Gish raises, forexample, the Big Bang theory of the universe's origin, Luis Alvarez's theoryof the extraterrestrial cause for the Cretaceous-Tertiary extinctions, and soon. Such theories are examples of 'the problem of the single case,' forwhich no deductive or inductive inferences can provide evidence and which,therefore, have resisted all attempts to analyze the grounds on whichsapients believe or disbelieve them. Such analyses, of course, ignore abduc-tive inferences as evidence. Thus, not only does the received dogmaregarding 'the scientific method' rest on a number of fallacies, but blindacceptance of it materially hinders scientific practice.

This is not to say that scientific hypotheses do not result from abduc-tive reasoning, of course, for they sometimes do, nor that highly specula-tive conjectures are equivalent to well-established scientific theories, forthe former lack the abductive evidence that supports the latter. Nor do Ideny that scientific inquiry has psychological or historical stages orsequences, though Kuhn's and Bazerman's discussions strongly suggest tome that these stages are also fanciful inventions, imposed on inventiveprocesses only in retrospect to make the activity conform to an illusory'scientific method.'

It does mean, however, that inquiry and argumentation do not comein scientific, humanistic, or mathematical shapes, forms, or varieties.Empirical science no more has a single identifiable pattern true of itsmethod and of only its method than does, say, theology; science simplydoes not proceed in the inferential steps that some have fantasized it does;instead, like all inquiry and argumentation, it uses any inferential struc-ture at any point of its processes and has no 'method,' apart from the'method' that all sapients use in inquiring about the universe around themand offering evidence to support what they think.

What distinguishes the so-called scientific method from other kindsof inquiry and argumentation is not, then, its inferential patterns or itssequential stages, as some have claimed, but is instead exactly whatdistinguishes it from, say, the mathematical 'method' or from literary,philosophical, or theological 'methods,' or what distinguishes naturalscience from social science: the field or scope of its reflection. Investigatorsconfine the range of scientific inquiry to strictly empirical domains, justas mathematical inquiry examines strictly syntactic realms - and just as

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particular sciences (for example, physics, sociology) encompass differentempirical phenomena.

Most importantly, since confirmation results from abduction as easilyas from deduction or induction, scientific theories are not merely 'meta-physical research programs' or merely esoteric scientific dogmas held asprinciples of faith by an empiricist priesthood, to be dismissed by the oppro-brious, 'just a theory'; instead, such propositions are often among the mostwell substantiated ideas known to the human mind. Indeed, as we haveseen, abductive confirmation is often the only evidence for many centraltheories in science, or in any realm of investigation.

NOTES

It may be helpful to distinguish three senses of the word induction. One refers to a subsetof deductive proofs in mathematics and logic. A second sense (more Aristotelian) refers toall non-deductive logical inferences. The third refers to logical inferences that proceed byamassing cases. Many think the last two notions coextensive, a confusion which enables themto label abductive inferences as inductions (see note 4, below).

We can consider the possibility of alternative non-deductive inferences only after wedistinguish between these last two notions, a reef on which many investigations founder:Aristotle did not ignore abductive inferences but just dismissed them as akin to induction.Modem scholars often consider abductive inferences, but under other names (for example,'inductive analogy') and not as alternatives to deduction and induction.2 Thus, abduction is a kind of intellectual 'natural selection' that eliminates 'less fit' con-clusions, leaving only those that 'survive' the addition of successive relevant observations.This feature may have initially suggested not only abduction but even pragmatism to Peirce,influenced as he was by Darwin's theory of natural selection.3 In fact, the only widely known structuralist account of abduction is the analogue to modusponens that derives from Peirce: 'The surprising fact, F, is observed. If H were true F wouldbe commonplace. Therefore, H is (possibly) true' (Reese, 1; cf., Peirce 5.189; Hanson 1969,86). See note 9, below.4 Uncritically lumping non-deductive inferences under one name occurs frequently. Considerthis quotation:

There is, however, no need to proceed deductively to the conclusion that because theRomans, and particularly Caesar, were an important influence on post-Renaissance armies,then it was probably Caesar who most influenced the way in which military history waswritten from the Renaissance onwards. We can reach the same point by a single induc-tive leap, for the distinctive features of the 'battle piece' will all be found in any ofCaesar's narratives of his own victories that one cares to turn up (Keegan 63).

Keegan proceeds to give evidence structurally identical to Peirce's account of abduction.Thus, his label is accurate when induction means non-deductive but inaccurate when induc-tion means amassing cases (for his inference amasses properties instead).5 Biologists, for whom taxonomy is a fetish, made this same redefinition: Until the early1940's, many envisioned species as static, invariant typologies to which members couldbe assigned when they satisfied morphological criteria; but unfortunately, no criterionsurvived critical examination. Other properties also fail as criteria: Interfertility, for example,is not always transitive: If members of population A are interfertile with those of populationB, and population B with population C, population A is not always interfertile with popula-tion C.

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In 1942, Ernst Mayr cogently argued that biology had to abandon the notion of speciesqua essentialist classes. To define a species typologically 'is just as impossible as to definethe middle stage in the life of man, mature man, so well that every single human male canbe identified as boy, mature man, or old man' (Mayr, 114). Assigning members to speciesthus became an abductive, not deductive, inference. For more on this, see Eldredge, xx-xxi;Gross (1988); and Hull.6 For a more lengthy exposition of this point, see Bybee, 292-299.7 The ellipses in Hanson's quotation of Jenkinson mark the omission of specifics, the inclu-sion of which would have made careful readers suspicious of applying Aristotle's notion ofapagoge to Peirce's notion of abduction.8 For more on the systematic confusion of abduction with conditional proof, see Bybee,290-291.9 Hanson's mistaken claim that this overly truncated description is the abductive inferenceleads many to confuse abduction with the deductive fallacy of 'asserting the consequence,'with which it is (in this guise) structurally identical. This confusion alone leads many tobelieve abduction cannot provide evidence for a conclusion (see Bybee, 289-290).

This does not mean, however, that 'abductions are formally invalid' (Sabre, 67) any morethan that inductions 'all commit the fallacy of affirming the consequent' (Gross 1990, 12);both abductions and inductions are 'formally invalid' deductions, of course, but then, deduc-tions are 'formally invalid' abductions and inductions! Investigations into inquiry andevidence often suffer from this 'deductio-centricism.''° E. A. Burtt's discussion of Copernicianism demonstrates on what grounds inquirersadopted the heliocentric hypothesis even though it contradicted received scientific and meta-physical theories; Feyerabend's study, whatever flaws it might have in other respects, alsooutlines how the heliocentric theory contradicted contemporary scientific experimentation." If not from abduction, then from what kind of inference did these hypotheses actuallyresult? Copernicus based his theory on mathematical derivations and data analyses (reportedin De Revolutionibus Orbium Coelestium Libri IV). Bohr's inference was also deductive, infact, a classical conditional proof: Assume that the Copenhagen interpretation is true andfrom that derive certain results (Bohr, 1913). For the historical and intellectual context thatenabled and encouraged Bohr to make these deductions (as opposed, say, to others), see'Bohr's Theory of the Hydrogen Atom' in Jammer, 69-88.

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