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Consciousness, Literature and the Arts

 

Volume 19 Number 2/3 August/December 2018

(Final Issue)

 

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The Reichenbach Falls of Karl Popper: Singular Cases, Inductive Exceptions, and Arthur Conan Doyle’s “The Red-Headed League”

by

Michael Wainwright

Royal Holloway, University of London

 

Abstract

By the time of Sherlock Holmes’s final case, “The Adventure of Shoscombe Old Place” 1927), Arthur Conan Doyle was preparing to bow out as a professional writer.  By then, the epistemological world appeared to be shifting from inductive reasoning toward critical rationality.  By then, Karl Popper was preparing to bow in as a professional philosopher, adding the finishing touches to a doctoral thesis that would inspire his landmark Logik der Forschung (1934).  In this volume, Popper not only identifies the empirical sciences with logically unsustainable inductive methods, but also posits falsifiability as the deductive alternative to those methods.  The discursive arbiters of literature and science have prorogued the acceptance of his proposition.  This paper, which offers a reading of the singularly Popperian “The Red Headed League” (1891) that at once rejects Hans Reichenbach’s defence of induction, relegates Charles S. Peirce’s concept of abduction, and promotes Sherlock Holmes as an unconscious follower of the principle of falsification, defies that reluctance.  Simply put, “The Red-Headed League” was ahead of its time.

 

The “career” of Arthur Conan Doyle’s (1859–1930) Sherlock Holmes—to all intents and purposes contemporaneous with the publication dates of its defining stories—encompassed forty years from A Study in Scarlet (1887) to The Case-Book of Sherlock Holmes (June 1927).[1]  The span of Holmes’s detective acumen—in A Study in Scarlet, Watson congratulates Holmes for having “brought detection as near an exact science as it ever will be brought” (36), and in the antepenultimate entry in The Case-Book of Sherlock Holmes, “The Retired Colourman” (January 1927), the North Surrey Observer praises the detective’s “intelligence” as a “standing example” (207)—sits, therefore, within a much longer period in which induction dominated the epistemological approach to scientific problems, procedures, and theories.  Literary critics, seemingly reluctant to undertake the necessary interdisciplinary research, have chosen not to address this embedment.  Even The Sign of Three (1983), which boasts contributions by Gian Paolo Caprettini, Umberto Eco, and Thomas A. Sebeok and Jean Umiker-Sebeok as well as the combined editorship of Eco and Sebeok, fails to disavow this neglect: the focus of this compendium, as its subtitle denotes, remains Dupin, Holmes, Peirce; and concerted engagement with the epistemological context of Doyle’s creation is long overdue.

Indeed, three years after Holmes’s retirement, and in the year of Doyle’s death, the philosopher of science Hans Reichenbach (1891–1953) celebrated the preeminence of induction.  Having assumed the editorship of Annales der Philosophie, Reichenbach and Rudolf Carnap rebranded the journal under the name Erkenntnis, with Reichenbach contributing the introduction and two articles, “Kausalität und Wahrscheinlichkeit” and “Die philosophische Bedeutung der modernen Physik,” to the first edition.  In “Kausalität und Wahrscheinlichkeit,” Reichenbach “recognize[s] the central position which belongs to the principle of induction for science: this principle determines the truth of scientific theories” (186).  For Reichenbach, as he attests in “Die philosophische Bedeutung der modernen Physik,” “the principle of induction is unreservedly accepted by the whole of science and no man can seriously doubt this principle in everyday life either” (67).  Induction answers the problem of demarcation between science and nonscience.  Based on the symmetry between verifiability and falsifiability, induction sorts definitively true or scientific statements from definitively false or nonscientific ones.  The abandonment of induction, asserts Reichenbach in “Kausalität und Wahrscheinlichkeit,” “would mean nothing less than to deprive science of the power to decide the truth or falsity of its theories.  Without it, clearly, science would no longer have the right to distinguish its theories from the fanciful and arbitrary creations of the poet’s mind” (186).  What is more, an extended provenance, as Reichenbach makes clear in his posthumously published “Der Lösungsversuch Des Empirismus” (1968), supports this right, with Francis Bacon deserving “historical merit” for “emphatically emphasiz[ing] the importance of the induction term for the empirical sciences” (99).

“Induction,” explains Doyle’s contemporary, the American philosopher and mathematician, Charles S. Peirce (1839–1914), “is where we generalize from a number of cases of which something is true, and infer that the same thing is true of a whole class.  Or, where we find a certain thing to be true of a certain proportion of cases and infer that it is true of the same proportion of the whole class” (2:375).  An inductive inference passes from singular (or particular) statements, which include accounts of observational or experimental results, to universal statements, which amount to judgments, propositions, or theories.  “Induction,” as Kuang Tih Fann summarizes, “may be said to be an inference from a sample to a whole, or from particulars to a general law” (10).  Peirce’s classic example of induction involves white beans in a bag: if “not knowing what proportion of white beans there are in the bag, we draw a handful at random and, finding ⅔ of the beans in the handful white, conclude that about ⅔ of those in the bag are white, we are rowing up the current of deductive sequence, and are concluding a rule from the observation of a result in a certain case” (2:373–74).

Holmes claims induction as his detective rationale—it is a singular claim in Holmes’s canon—at the close of “The Six Napoleons” (May 1904).  He has just smashed a statuette of Napoleon Bonaparte to reveal “the famous black pearl of the Borgias” (195).  “Yes, gentlemen,” he expounds, “it is the most famous pearl now existing in the world, and it has been my good fortune, by a connected chain of inductive reasoning, to trace it from the Prince of Colonna’s bedroom at the Dacre Hotel, where it was lost, to the interior of this, the last of the six busts of Napoleon which were manufactured by Gelder & Co.” (196).  This methodological avowal, which occurs near the middle of the detective’s exacting career in scientific detection, appears to speak for his life’s work, and the titles Watson assigns to Holmes’s cases, as instanced by “The Second Stain” (December 1904), “The Three Garridebs” (January 1925), The Sign of the Four (1890), “The Five Orange Pips” (November 1891), and “The Six Napoleons,” often suggest an inductive base, with repeated singulars appearing to point to universal phenomena.  Titular invocation compounds methodological avowal to imply consonance between Holmes’s logic of detection and Reichenbach’s logic of science.

Yet, as Doyle seems to have realized, prominent figures did challenge the epistemological preeminence of induction.  As early as 1865, in Induktion und Deduktion, Justus von Liebig did not just attack Bacon, but more importantly rejected the inductive method.  At a temporal distance of twenty-two years, Doyle echoes that challenge: deduction is Holmes’s principal method of reasoning in his first case, A Study in Scarlet, as denoted by a second chapter titled “The Science of Deduction”; three years later, The Sign of the Four heightens this sense of methodological preference by employing the same chapter heading for its opening section; a couple of years later, in “The Copper Beeches” (June 1892), Holmes talks not only of “severe reasoning from cause to effect,” but also of “those faculties of deduction” (270); and within nine months, as “The Stockbroker’s Clerk” (March 1893) recounts, Holmes cajoles Watson over the doctor’s interest in their “little deductive problems” (73).

Peirce defines deduction with an appeal to the syllogistic.  “The syllogism called Barbara,” he relates, “is as follows: / S is M, M is P; / Hence, S is P” (2:372).  This syllogism “particularly typifies deductive reasoning; and so long as the is is taken literally, no inductive reasoning can be put into this form.”  Barbara is the application of a general rule.  “The so-called major premise lays down this rule; as, for example, All men are mortal.  The other or minor premise states a case under the rule; as, Enoch was a man.  The conclusion applies the rule to the case and states the result: Enoch is mortal.  All deduction is of this character; it is merely the application of general rules to particular cases” (2:373; emphasis original).  While “induction consists in the process of testing hypotheses,” as Fann observes, “deduction explicates hypotheses, deducing from them the necessary consequences which may be tested” (10).  Peirce adds to his classic example of induction to illustrate deduction.  In this case, one knows that two-thirds of the beans in a bag are white, so if “we draw a handful at random and conclude that about ⅔ of the handful are probably white” (2:373), then the reasoning is deductive.  Whereas inductive thought is synthetic, deductive thought is analytic.  “In explicative inference,” writes Fann, “the conclusion follows from the premises necessarily while in ampliative inference the conclusion does not follow from the premises with necessity.  The conclusion amplifies rather than explicates what is stated in the premises” (7).

Peirce himself launched what was in effect another challenge to the epistemological reign of induction with the notion of abduction.  “Peirce first mentioned abduction, or what he called ‘reasoning by hypothesis,’” as Anya Plutynski documents, “in 1866” (228).  This type of inference passes from a result and a rule to a case.  Peirce’s development of this concept occurred over several decades.  Certainly, as its title suggests, Peirce’s paper on “Deduction, Induction, Hypothesis” (1870) separates deductive analysis from inductive and hypothetic synthesis, but some forty years later, as he would admit to Paul Carus, “in almost everything I printed before the beginning of this century I more or less mixed up Hypothesis and Induction” (8:227).  Arthur Wilson Burks’s disinterested retrospection in “Peirce’s Theory of Abduction” (1946) is somewhat more generous, dating Peirce’s consistent and rigorous separation of hypothesis from induction to 1891; Herman Parret confirms this chronology in The Aesthetics of Communication (2012), tracing how “abduction becomes the logic of discovery” (70; emphasis original) in that year; and references hereafter to that logic concern Peirce’s mature reflections.

“Hypothesis,” states Peirce, “is where we find some very curious circumstance, which would be explained by the supposition that it was a case of a certain general rule, and thereupon adopt that supposition.  Or, where we find that in certain respects two objects have a strong resemblance, and infer that they resemble one another strongly in other respects” (2:375).  For Peirce, as Fann relates, “reasoning towards a hypothesis is of a different kind than reasoning from a hypothesis” (4; emphasis original).  Abduction is an insightful procedure of inquiry that adds an original hypothesis to rational thought, and Holmes’s hypotheses in solving his clients’ curious circumstances often reveal the causative rule of criminal practice.

Another addition to his classic example of induction allows Peirce to illustrate abduction.  “Suppose I enter a room and there find a number of bags, containing different kinds of beans.  On the table there is a handful of white beans; and, after some searching, I find one of the bags contains white beans only.  I at once infer as a probability, or as a fair guess, that this handful was taken out of that bag.  This sort of inference,” declares Peirce, “is called making an hypothesis.  It is the inference of a case from a rule and a result” (2:374; emphasis original).  Unlike deduction, which puts known facts into their logical order, or induction, which quantifies known facts according to assumed probability, abduction provides a different sort of fact.  In Peirce’s example, knowledge about colored beans leads to a hypothesis about their bag of origin.

 

Intriguingly, to expand the earlier quote from “The Copper Beeches,” Holmes talks of “those faculties of deduction and logical synthesis” (270; emphasis added), thereby covering what Peirce calls his “trichotomy of all simple arguments into Deductions, Inductions, and Abductions” (2:152).  The challenges mounted to the epistemological preeminence of induction help to recast, therefore, what Caprettini identifies as “Holmes’s imprecision” (141) in categorizing his reasoning processes.  More accurately adduced, Holmes is ahead of his time: throughout his career, as the following argument traces, he places logical analysis before logical synthesis, and while abduction remains crucial to his powers of detection, his deductive inclination actually anticipates the logical denial of induction.  For, as Homes bowed out as a scientific detective at the end of “Shoscombe Old Place” (April 1927), and as Doyle was preparing to bow out as a professional writer, the man who would expose the inductive fallacy, Karl Popper (1902–94), was preparing to bow in as a professional philosopher of science by adding the finishing touches to his doctoral thesis, Zur Methodenfrage der Denkpsychologie.  Popper’s unequivocal disavowal of induction would appear six years after the successful submission of his thesis in Logik der Forschung (1934).

 

Having acknowledged that Liebig “was probably the first to reject the inductive method from the standpoint of natural science” (7n.1), Popper asserts that the “principle of induction cannot be a purely logical truth like a tautology or an analytic statement” (5).  In consequence, “the principle of induction must be a synthetic statement; that is, a statement whose negation is not self-contradictory but logically possible” (5); and this appeal to apriorism constitutes a major objection to the principle of induction.  In addition, as a universal statement, which is neither tautological nor analytical, induction must appeal to induction for corroboration; that demand must call on induction too; and this regressive obligation has no end.  These two major difficulties are insuperable.

 

Beyond fatally undermining the promotion of induction, and so marking the Reichenbach falls of Karl Popper, Logik der Forschung proffers deduction in its stead.[2]  Deduction conforms to the principles of logic.  The deductive approach to scientific problems, procedures, and theories is “directly opposed to all attempts to operate with the ideas of inductive logic.  It might be described as the theory of the deductive method of testing, or as the view that a hypothesis can only be empirically tested—and only after it has been advanced” (6–7; emphasis original).  Popper’s methodological outlook, according to his own suggestion, “might be called ‘deductivism,’ in contrast to ‘inductivism’” (7).  Whereas the criterion of demarcation inherent to induction assumes complementary symmetry, this criterion posits complementary asymmetry in deduction, “which results from the logical form of universal statements.”  Universal statements “are never derivable from singular statements, but can be contradicted by singular statements.”  This form of argument “is the only strictly deductive kind of inference that proceeds, as it were, in the ‘inductive direction’; that is, from singular to universal statements” (19).  Deduction abides by the fact that theories are “never empirically verifiable.”  This consideration further “suggest[s] that not the verifiability but the falsifiability of a system is to be taken as a criterion of demarcation” (18; emphasis original).  In fine, “what characterizes the empirical method is its manner of exposing to falsification, in every conceivable way, the system to be tested” (20).  This method selects the most robust systems at the expense of those that are untenable.

 

The titles Watson assigns to Holmes’s cases often presume the detective’s use of induction, which the attendant evidence readily demands, but Holmes relies on the asymmetry between verifiability and falsifiability to deny these presumptions.  His deductivism disavows inductivism.  For example, “The Second Stain” concerns a single stain, which has bled through a rug into wooden flooring, but which gives the appearance of two stains because the rug has been inadvertently rotated through 180 degrees.[3]  In another instance, “The Six Napoleons” concerns a single bust of Napoleon, which holds the black pearl, which the thief pressed into its soft clay.  These cases certainly appeal to induction; repeated singulars suggest universal phenomena; and Watson’s tentative answer to the destruction of the statuettes in “The Six Napoleons” illustrates this inductive lure.  His diagnosis of the culprit’s “monomania” confuses a psychological problem with an epistemological one.  Importantly, as Popper makes clear, deductivism necessarily distinguishes “between the psychology of knowledge which deals with empirical facts, and the logic of knowledge which is concerned only with logical relations,” because the appeal to “inductive logic is largely due to a confusion of psychological problems with epistemological ones” (7; emphasis original).  In “The Six Napoleons,” Watson adds to this confusion, taking the repeated smashing of busts to verify a condition that medical science currently verifies by appealing to induction: “there are,” he opines, “no limits to the possibilities of monomania” (179).  This manifold confusion discredits Watson’s reliability as a narrator in “The Six Napoleons”: the report of Holmes’s accreditation of inductive reasoning relies on the accuracy of a reporter to whom the lure of induction undoubtedly appeals.

 

The knowing Doyle carefully exploits this attraction.  In realizing how the lure of induction operates beyond Holmes’s singular cases, Doyle balances the reassurance of familiarity against the danger of repetition at the canonical (or meta-) level.  He answers this requirement both structurally and narratologically.  In structural terms, a Holmes story seemingly follows a standard plot, which witnesses the detective in a state of ennui until presented with a stimulating enigma, which neither the client, the police, nor Watson can fathom, but which the detective triumphantly unravels.  Notwithstanding the success of this groundplot, Doyle is careful to break the pattern on occasion.  Thus, “the best plans of Mr. Sherlock Holmes were beaten by a woman’s wit” (29) in “A Scandal in Bohemia” (July 1891), and in another instance, Watson “give[s] some account” of “The Five Orange Pips,” despite there being “points in connection with it which never have been, and probably never will be, entirely cleared up” (102).  In narratological terms, Watson almost invariably recounts a Holmes story, but “His Last Bow” (September 1917), “The Mazarin Stone” (October 1921), “The Blanched Soldier” (November 1926), and “The Lion’s Mane” (December 1926) provide alternative narrative voices: a third-person narrator relays the first two; Holmes himself recounts the second two, employing his “familiar method of logical analysis” (162), as he remarks in “The Blanched Soldier,” to solve cases, as he declares in “The Lion’s Mane,” “certainly as abstruse and unusual as any which I have faced in my long professional career” (172).

 

Without Doyle’s narrative ingenuity, however, repetitiveness would still have dogged the Holmes canon—and that fault would have ended Holmes’s appeal to the reading public.  This inventiveness, which employs neither induction nor deduction, emerges from what Peirce would have called Doyle’s abductive gift.  Indeed, David Morris turns to “Silver Blaze” (December 1892), in which Holmes solves the case of a stolen racehorse, to illustrate abduction.  “Sherlock Holmes uses abductive reasoning all the time,” avers Morris, “which is what astonishes Watson” (285).  Watson is amazed that Holmes can identify the horse thief from the fact that the dog guarding the stables “did nothing in the night-time” (23).  To Holmes, however, the solution is elementary: the culprit must have been familiar to the dog, which did not bark, and that familiarity points to only one person.  Abduction has provided a different sort of fact: information about a dog has inspired the correct hypothesis about the thief.

 

Fann also draws on Doyle’s Holmes to demonstrate abduction, but this illustration presents a slightly different guise from Morris’s interpretation, pointing to one of Peirce’s conceptual variations.  “A great scientist is always Sherlock Holmes too,” states Fann, “for they are both masters in abductive reasoning.  Holmes, who was a genius at inventing hypotheses, described the process as reasoning ‘backward’” (57).  Holmes’s description of this process occurs in A Study in Scarlet: “Most people, if you describe a train of events to them, will tell you what the result would be.  They can put those events together in their minds, and argue from them that something will come to pass.  There are few people, however, who, if you told them a result, would be able to evolve from their own inner consciousness what the steps were which led up to that result.  This power is what I mean when I talk of reasoning backward, or analytically” (123).  Holmes has already utilized this procedure in concluding that Watson has recently returned from Afghanistan.  “You were told, no doubt,” replies Watson.  “Nothing of the sort,” responds Holmes, “I knew you came from Afghanistan” (20; emphasis original).  Holmes had reasoned thus: “Here is a gentleman of a medical type, but with the air of a military man.  Clearly an army doctor, then.  He has just come from the tropics for his face is dark, and that is not the natural colour of his skin, for his wrists are fair.  He has undergone hardship and sickness, as his haggard face says clearly.  His left arm has been injured.  He holds it in a stiff and unnatural manner.  Where in the tropics could an English army doctor have seen much hardship and got his arm wounded?  Clearly in Afghanistan” (20–21).  Retroduction, therefore, carries the connotations of reasoning backward, as Holmes’s recourse to the word “analytically” suggests, and as Peirce undoubtedly intended too.

 

For Popper, as he makes clear in Logik der Forschung, great scientific discoveries do not emerge from the rational reconstruction that retroduction undertakes.  “Some might object that it would be more to the purpose to regard it as the business of epistemology to produce what has been called a ‘rational reconstruction’ of the steps that have led the scientist to a discovery—to the finding of some new truth.  But the question is: what, precisely, do we want to reconstruct?  If it is the processes involved in the stimulation and release of an inspiration which are to be reconstructed, then I should refuse to take it as the task of the logic of knowledge.”  Popper deems these processes “the concern of empirical psychology but hardly of logic” (8; emphasis original).

 

Fann’s other example of abduction—this one is not from Holmes’s canon—is closer to Peirce’s focus on the conceptual context from which a new hypothesis emerges.  In this instance, a student openly recognizes his tutor in one context, but is completely oblivious to that tutor in a different setting.  The abductive inference in this case alights on the almost impossible possibility of identical twins.  Doyle’s “The Black Doctor” (1919) is, in effect, a precursor to this example, with Dr. Aloysius Lana using the occasion of his brother’s death to disappear from society.  No one knew of Aloysius’s “twin brother Ernest” (150).  Ernest’s dead body at the doctor’s residence will be mistaken for Aloysius’s corpse.  What is more, abduction seemingly provides Aloysius with these ideas: “When I rose from my chair my future movements were finally decided upon without my having been conscious of any process of thought.  It was an instinct which irresistibly inclined me towards one course” (152).  This kind of abduction remarks a rare difference linked to a singular generative point.  “Singular elements already apparent in the experiential field,” as Morris explains, “all of a sudden stand out as in fact being variations in virtue of expressing a concept that for the first time grasps them as variations” (286; emphasis original).

 

Peirce gave this version of abduction a logical form in 1903: “The surprising fact, C, is observed. / But if A were true, C would be a matter of course. / Hence, there is reason to suspect that A is true” (5:189).  Doyle seemingly anticipates this formulation in “The Lost Special” (August 1898).  Doyle’s narrator refers to a letter in The Times.  “It is one of the elementary principles of practical reasoning,” writes the correspondent, “that when the impossible has been eliminated the residuum, however improbable, must contain the truth” (109).  Many literary critics, including Michael Dirda (63) and Nicholas Utechin (111), take this letter, which appears in the paper “over the signature of an amateur reasoner of some celebrity at that date” (92), to be from Sherlock Holmes.  Significant in its irony, however, this suggestion is incorrect.  The “confession of Herbert de Lermac, now under sentence of death” (95)—who admits his guilt in the hope that the possibility of further revelations, which would implicate certain men of high standing, will produce a “reprieve” (95)—exposes the correspondent’s error.

 

Peirce’s own concept of abduction remained polyvalent.  Indeed, “in his theory,” as Atocha Aliseda argues, “Peirce recognized not only different types of reasoning, but also several degrees within each one, and even merges between the types” (147).  Despite this amorphousness, and despite the rareness of the differences it remarks or the improbability of the residuum on which it alights, abduction seemed to Peirce to have been remarkably successful.  Scientific advances owed much to this method.  “It is evident,” writes Peirce, “that unless man had had some inward light tending to make his guesses on these subjects much more often true than they would be by mere chance, the human race would long ago have been extirpated for its utter incapacity in the struggles for existence” (qtd. in Sebeok and Umiker-Sebeok, 17).  To illustrate his point, as Plutynski chronicles, “Peirce argues that abductive inference played a role in the discovery of the kinetic theory of gases and Kepler’s positing of an elliptical orbit of Mars” (236).

 

Yet, “Peirce’s treatment of the validity of abduction,” as Fann avers, “is one of the most unsatisfactory features in his theory.”  On the one hand, “Peirce’s appeal to the repeated successes of abduction is inductive.”  On the other hand, “the claim that abduction is necessarily valid in itself is essential to the whole theory (Part II, Section 3), but he seems unable to provide a clear-cut justification for it.  The affinity of mind with nature is an hypothesis which can only be arrived at by abduction and thus must not be used to support the validity of abduction” (54).  From the perspective of epistemological reductionism, Peircean abduction can adopt one of three guises, either the psychology of knowledge, rational reconstruction, or Bayesian inference to the likeliest explanation—the examples of “Silver Blaze,” A Study in Scarlet, and “The Lost Special,” illustrate each guise, respectively—and on the rare occasions when Popper concerns himself with the origin of scientific discoveries, he turns to Henri Bergson’s (1859–1941) method of intuition rather than to Peirce’s theory of abduction.  He expresses his view in Logik der Forschung “by saying that every discovery contains ‘an irrational element,’ or ‘a creative intuition,’ in Bergson’s sense” (8).

 

In critically addressing Edmund Husserl’s (1859–1938) analysis of the flow of variations, Bergsonian intuition avoids not only induction, but also the related appeal to extensive variation.  Husserlian phenomenological reduction insists that objects are solely objects of meditation.  “Transcendency in every form,” he avows in Cartesian Meditations (1931), “is an immanent existential characteristic, constituted within the ego.”  The universe and consciousness of that universe are essentially one.  “If transcendental subjectivity is the universe of possible sense, then an outside is precisely-nonsense.  But even nonsense is always a mode of sense and has its nonsensicalness within the sphere of possible insight” (117).  Husserl’s reduction of phenomena to their conscious immanence means that no object of consciousness ever enjoys full presence.  “The cogitatum qua cogitatum is never present to actual consciousness as a finished datum,” he explains; “it becomes ‘clarified’ only through explication of the given horizon and the new horizons continuously awakened” (82–83).

 

The universal is never present in its entirety, but is indeterminately determinate, appearing as invariance in the flow of variations.  A horizontal distancing, which operates within the flow of experience, and which separates the singular and the universal, facilitates this appearance.  This distancing is distinct, on the one hand, from the verticality associated with transcendence, and on the other hand, from the horizontality associated with induction or iteration.  Husserl’s sense of universal statements, or what he commonly deems universal judgments, emerges from the mind’s reconfiguration of variations from within.  Universal judgment is a matter of intensive variation.  Thus, as Morris concludes, “scientific or forensic discovery is not so much totting up regularities in an existing space of extensive variation, it is seeing existing variations as knitting together a space with a novel intensive structure” (275), which is symptomatic of an alternative phenomenological substrate.  From this perspective, the detective facility of Doyle’s Holmes is not so much his extraction of evidence from crime scenes, witness statements, and suspect behaviors, but his apprehension of these seemingly bewildering data sets as unified spaces of variation from which to elicit the fundamentals of his commissions.

 

Agreeing in the most part with Husserlian variation, Bergson’s method of intuition diverges from that concept on the subject of phenomenological origins.  For Bergson, the intensive variation posited by Husserl can succumb to subjective prejudice, because that variational requirement concerns space within consciousness rather than space within nature.  “Bergsonian intuition helps address this problem,” as Morris explains, “by sinking consciousness into a distance that arises within singular becomings” (272).  For Bergson, as Morris notes, “pure intuition, what is given us in inner or outer experience, is an undivided continuity,” but practical interests encourage the mind “to break up this continuity into elements laid out side by side.”  After this dismantling, the mind seeks to conceptualize and articulate that continuity.  These aims are not achieved “by contacting a transcendent beyond, or by adding a magic dash of universals to experience; what we are seeking is within experience, but at its source, past our usual fragmentation of it” (281; emphasis original).  Bergson’s variational requirement, therefore, concerns space within nature, not space within consciousness.  His method of intuition promotes a return to the nature of experience in which intuitions are at once sensuous and intelligible.  These intuitions form a variable flux, but without the danger of indetermination, because invariant patterns impress themselves on the subject’s consciousness.

 

Whereas concepts arise in the time of free variation for Husserl, they arise in the duration-variation of phenomena for Bergson, who maintains, as Dorothea E. Olkowski remarks, “that it is possible for a consciousness to exist absolutely within the same frame of reference as another phenomena [sic], thus for there to be an experience of simultaneity.  His famous example, that of sugar dissolving in a glass of water, seems to exemplify this.  The consciousness of the observer dissolves along with the sugar.”  That observer’s “frame of reference is, for Bergson, exactly the same as that of the dissolving sugar in the glass.  Rather than existing relative to one another, their lived time is simultaneous” (60–61).  While Husserl’s invariants are static, Bergson’s invariants are dynamic, and preeminent to Bergson among the invariants of variability within nature is the human body.  The body opens onto sense; it is not a singular constituent of action; nor is action the isolated behavior of a single body.  The body functions as a material locus that intersects with other bodies that are similarly functioning.

 

Concepts, as invariants within variant thinking, are reasoning processes for both Husserl and Bergson.  For Husserl, the conceptual process requires variational jumps from one singular to another, rather than alterations of a singular essence.  For Bergson, the conceptual process requires a third type of difference, with the separateness of singularities exhibiting the peculiar combination of pattern and invariance that Morris identifies with repetition: “it is the same thing happening, yet utterly different because it is a repeat.”  This sort of peculiarity runs throughout the Holmes canon.  “Where Husserlian variation freely plays with an example so as to draw out neighboring but different possibilities, in Bergson’s intuition we are given a field of variation in which different things show an affinity in virtue of repeating a common generative point” (284).  Bergson provides the arresting example of the evolutionary origin that has produced the similar yet dissimilar eyes of octopuses and humans.

 

For Bergson, the variational process of life accounts for the differential process behind intuition, and this sort of differentiation also lies behind Peircean abduction.  Both Martin Heidegger and Maurice Merleau-Ponty understand this abductive-intensive variation as the connection between Bergson’s method of intuition and Peirce’s method of abduction.  Accepting the assumption that a concept is not a given, but a reasoning process, and accepting the corollary from this assumption that concepts exhibit abductive-intensive variation, then conceptualization is only possible if nature is abductive.  Popper’s appeal to creative intuition through similitude in Logik der Forschung produces a related conclusion.  “In a similar way,” concedes Popper, “Einstein speaks of the ‘search for those highly universal laws . . . from which a picture of the world can be obtained by pure deduction.  There is no logical path,’ he says, ‘leading to these . . . laws.  They can only be reached by intuition, based upon something like an intellectual love (‘Einfühlung’) of the objects of experience” (8–9).  The metaphysical is undoubtedly valuable to empirical science.  “This sense of abduction which neither calls for nor accepts a ‘reason’ for its existence,” as Arthur F. Stewart writes, “doesn’t seem to be something Popper wanted to dispense with in science” (81).

 

Nor would one wish to dispense with creative intuition in the arts.  At a meta-level, with abductive-intensive variation carefully balancing the reassurance of familiarity against the danger of repetition, Doyle’s tales of Sherlock Holmes admirably illustrate this value.  At a narratological level, one story stands out, not merely speculating on the importance to scientific detection of abduction, but more importantly promoting the detective science of deduction, as if in anticipation of the Reichenbach falls of Karl Popper.  “The Red-Headed League” (1891), published in the year that witnessed Peirce’s decisive separation of abduction from induction, encourages this interpretation with its inductive sense of the singular and its singular sense of induction.  Holmes explodes these senses, effectively rewriting Reichenbach’s assertion from “Kausalität und Wahrscheinlichkeit,” with induction becoming the fanciful and arbitrary creations of the criminally poetic mind.

 

The case of “The Red-Headed League,” as Holmes’s initial remarks adumbrate, engages with, while breaking from, the repetitive, regimented social constructions of its Victorian sociopolitical context: “I know, my dear Watson, that you share my love of all that is bizarre and outside the conventions and humdrum routine of everyday life” (49).  Thus, in supplying the unconventionally conventional, Doylean abduction at once obeys and countermands the epistemological preeminence of induction, with the inductive method more suited to Holmes’s everyday cases, the problems that Watson does not bother to recount, than to his stranger commissions.  “As a rule,” avows Holmes, “when I have heard some slight indication of the course of events, I am able to guide myself by the thousands of other similar cases which occur to my memory” (50).  Where his memory proves deficient, he draws on the back catalogue, or inductive file, that constitutes his self-compiled “index.”  In “A Scandal in Bohemia,” when the Grand Duke of Cassel-Felstein mentions making “the acquaintance of the well-known adventuress, Irene Adler,” Holmes asks Watson to “kindly look her up in my index,” with Watson explaining in an aside that Holmes “had adopted a system of docketing all paragraphs concerning men and things, so that it was difficult to name a subject or a person on which he could not at once furnish information” (12).  Various other tales—including “A Case of Identity” (September 1891), “The Five Orange Pips,” “The Bruce-Partington Plans” (December 1908), “The Red Circle” (March 1911), and “The Creeping Man” (March 1923)—include references to this index.  Crucially, however, this back catalogue never proffers decisive information.  Put succinctly, rule-abiding commissions of the humdrum kind, with their inductive reliance on the uninspired culprits’ psychological motivations, little interest the detective.

 

“For strange effects and extraordinary combinations,” maintains Holmes, “we must go to life itself.”  Nature, with what Bergson would call its invariants of variability, provides the detective’s compelling cases.  “Life,” insists Holmes, “is always far more daring than any effort of the imagination” (49).  Watson takes “the liberty of doubting” (50) this proposition.  The detective determines to change his friend’s opinion—and this determination expresses a form of authorial self-goading, with Holmes, rather than Dr. Watson, expressing Dr. Doyle’s resolve to balance the lure of the familiar against the danger of repetition.  That Holmes defers to induction in stating his determination—“you must come round to my view, for otherwise I shall keep on piling fact upon fact on you until your reason breaks down under them and acknowledges me to be right” (50)—seems to lengthen his chance of convincing Watson.  This deference, however, is particularly sly.  Holmes counts on the inductive predilection in those around him to maintain the aura that surrounds his deductive facility, which the explanation of his deductions might otherwise dispel.

 

Holmes’s deductions about Jabez Wilson, his prospective client in “The Red-Headed League,” and their subsequent explanations illustrate this danger.  To Watson’s prejudicial mind, which interprets the lower-middle class as a social rank that lacks intensive variation, Wilson “bore every mark of being an average commonplace British tradesman, obese, pompous, and slow” (50).  In contrast, Holmes’s self-avowedly “deduce[d]” summation of Wilson—that he has performed “manual labour,” that “he is a Freemason, that he has been in China, and that he has done a considerable amount of writing lately”—is acute.  Yet, Holmes’s explanation of his deductions—“Your right hand is quite a size larger than your left.  You have worked with it, and the muscles are more developed” (51); “You use an arc-and-compass breastpin” (51); the “right cuff so very shiny for five inches, and the left one with the smooth patch near the elbow where you rest it upon the desk” (51); “The fish that you have tattooed immediately above your right wrist could only have been done in China” (51)—are met with Wilson’s laughter: “I thought at first that you had done something clever, but I see that there was nothing in it, after all” (52).  Holmes is left to mourn the wonder initially elicited by his deductions; “my poor little reputation, such as it is, will suffer shipwreck if I am so candid” (52); but the inductive predilection of those around him helps to forestall this foundering.

 

Although mundane emanations cannot help but envelop Wilson, whose “small pawnbroker’s business” (52) embodies the inductive, his unusual predicament emerges as a discrete expression of the strange pattern that characterizes the Holmes canon: the abductive-intensive variation within “The Red-Headed League” shadows the canonical abductive-intensive variation without.[4]  Indeed, this tale is more generous than any other case in its provision of inductive lures, making Wilson’s dilemma an outstanding case in the series of Holmes’s outstanding cases.  The pawnbroker’s narrative “promises to be one of the most singular which I have listened to for some time” (50), and Holmes had already perceived this novelty—“As far as I have heard it is impossible for me to say whether the present case is an instance of crime or not, but the course of events is certainly among the most singular that I have ever listened to” (50)—before the interruption occasioned by Watson’s arrival at 221B Baker Street that morning.

 

Holmes now asks Wilson to “recommence” (50) his “narrative” (50), and this repetition from the narratological beginning helps Holmes to transform the sjuzhet of Wilson’s recount into the fabula of chronological events.  This transformation sets up the deductive cause-and-effect timescale for the flow of intensive variations in the case.  Wilson’s assistant Vincent Spaulding had alerted his employer to the advertisement concerning the League of the Red-Headed Men—to the prejudicial Watson, Wilson’s hair, “his blazing red head” (51), is the pawnbroker’s only impressive feature (or invariant of variability)—but this event necessarily occurred after Spaulding’s appointment, and the fabula immediately reveals not just an inductive cycle, but more especially Spaulding’s role in breaking that sequence.

 

Wilson had advertised for an assistant; he had received “a dozen” (61) applications; and he had appointed Spaulding.  The process of interviewing is an asymmetric one.  Control lies with the interviewer.  This power leaves the intensive variation of the interviewees vulnerable to the interviewer’s prejudices.  The variation that counts may lay outside the stipulations of the advertised post, with personal motives exaggerating the horizontal distance between the favored applicant and the other interviewees.  That exaggeration posits an outstanding (but fallacious) suitability.  In this case, however, as Holmes reveals, Spaulding perverted the prejudicial dangers of the interviewing process.  “Why did you pick him?” he asks.  “Because he [. . .] would come cheap,” concedes Wilson.  In fact, he came “for half wages.”  This outstanding willingness, which plays on the prejudice occasioned by Wilson’s financial concerns, reverses the usual asymmetry of the interviewing process.  Holmes admits that financial necessity might press an “obliging youth” to accept this condition, but Wilson denies this possibility: Spaulding is “not such a youth.”  In terms of Popper’s deductive method of testing, Spaulding twice breaks (or disbands) the inductive line of applicants: once with his gamesmanship and once in surpassing the limiting condition of age.  Wilson’s prejudices even overcome Spaulding’s subsequent behavior.  “Oh, he has his faults,” relates Wilson.  “Never was such a fellow for photography.  Snapping away with a camera when he ought to be improving his mind, and then diving down into the cellar like a rabbit into its hole to develop his pictures.”  To Holmes, the compound fracture revealed by deductivism, rather than the inductive loop of interviewees of which Spaulding had been a member, mark Wilson’s subordinate for special attention: “I don’t know that your assistant is not as remarkable as your advertisement” (53).  Spaulding must be part of the novel intensive structure to the case, but Holmes cannot yet outline this alternative phenomenological substrate nor decide whether Spaulding’s designs signal criminal or merely mischievous intent.

 

This exceptional, inductive-breaking assistant not only initiates Wilson’s interest in the League of the Red-Headed Men—“Spaulding, he came down into the office just this day eight weeks, with this very paper in his hand, and he says: ‘I wish to the Lord, Mr. Wilson, that I was a red-headed man’” (53)—but also asserts his boss’s certain admission to this order—“Now, if you cared to apply, Mr. Wilson, you would just walk in” (55).  In effect, as Watson’s estimate of that part of Wilson’s body implies, Wilson could emulate Spaulding in being the exceptional, inductive-breaking applicant.  “All red-headed men,” states the advertisement, “who are sound in body and mind, and above the age of twenty-one years, are eligible.”  The limits on repeatability herein stated, which immediately undercut the professed “all” of redheaded eligibility, but to which Wilson attaches no deceit, are immediately apparent to Holmes.  Holmes’s tells neither Wilson nor Watson of this realization, but his own body informs the reader of this awareness: “Holmes chuckled and wriggled in his chair” (52).  That Wilson remains stumped—“What on earth does this mean?” (52)—despite having “twice read” (52) the advertisement helps to sustain Holmes’s reaction.  The advertisement must be part of the alternative phenomenological substrate to which Spaulding belongs.

 

Professionally attuned to the inductively repetitive, Wilson had worried about the “millions of red-headed men who would apply” (54) to the league.  Spaulding had both reassured his employer—“‘Not so many as you might think,’ he answered.  ‘You see it is really confined to Londoners, and to grown men’” (55)—and accompanied him to the selection process—“Spaulding seemed to know so much about it that I thought he might prove useful” (52)—to be conducted by a Mr. Duncan Ross at “the offices of the League, 7 Pope’s Court, Fleet Street.”  Before reaching Ross’s office, however, their journey is arrested.  “From north, south, east, and west,” recounts Wilson, “every man who had a shade of red in his hair had tramped into the city to answer the advertisement.  Fleet Street was choked with red-headed folk, and Pope’s Court looked like a coster’s orange barrow.”  These prospective interviewees—“I should not have thought there were so many in the whole country as were brought together by that single advertisement”—constitute an inductive loop on a different scale to the dozen applicants who had answered Wilson’s advertisement for an assistant, and the magnitude of this difference traumatizes Wilson, who hopes never “to see such a sight as that again” (55).

 

“In traditional induction,” as Morris explains, “consciousness arrives at universal judgments by detecting an invariant property within a collection of variant singulars; the singulars and their properties are distributed in an already established space of variation” (268).  The applicants to the league constitute such a space, and seeing the innumerable men that populate this space almost causes Wilson to withdraw from the selection process: “I would have given it up in despair,” he owns, “but Spaulding would not hear of it” (55).  The two sets of interviewees—those who answer Wilson’s advertisement and those who answer the League’s—produce a peculiar patterns of invariance, which have a repetitive basis in individuals who deem themselves fitted to each respective offer.  Wilson’s tale now boasts two inductive lures.  Husserlian horizontal distancing individuates the queuing redheaded men, yet Spaulding’s success at getting Wilson straight to the front of the line disrupts the orderly separation and sequence of their horizontal separation.

 

This disruption reveals to Holmes the undoubted fictitiousness of the continuity of the League of the Red-Headed Men.  In getting Wilson to the head of the queue, a position that by right belongs to the next person in the line, Spaulding broke that sequence.  “The universe of the detective story,” as Caprettini avers, “shows both incomprehensible discontinuities—a worn-out, loose reality, where mysterious elements shine in isolation—and fictitious continuities—misleading evidence, wrong connections, inadequate hypotheses, seductive fictions, persuasive mistakes” (140; emphasis original).  Holmes, whose continuous awakening to new horizons resonates to the fictitious continuities of Wilson’s narrative, effectively undertakes a Husserlian restructuring of the universals to which standard inductive inference supposedly points.  Moreover, the extensive variation of hair color in this queue—“Every shade of colour they were,” expostulates Wilson, “straw, lemon, orange, brick, Irish-setter, liver, clay” (55)—suggests that Wilson was not definitively ahead of the rest.  Spaulding had reassured Wilson that it was “no use your applying if your hair is light red, or dark red, or anything but real bright, blazing, fiery red” (55), yet this limiting condition, which would have made the job of the league’s “examiner” less arduous, does not appear in the advertisement.

 

Ross meets Spaulding’s announcement of his boss’s candidature with Wilson’s immediate acceptance into the league.  This decision dissolves the inductive loop embodied by the men queuing outside.  This definitive break places Ross alongside Spaulding for Holmes’s attention as partners of a duplicitous sort.  Spaulding and Ross show an affinity in virtue of repeating a common generative point, and Holmes’s insight, which appeals to Bergson’s variational requirement of space within nature, rather than to Husserl’s variational requirement of space within consciousness, immediately sees through Ross’s feint at authenticity.  Ross, whose hair “was even redder than mine,” as Wilson recalls, took the “obvious precaution” in checking for a wig.  “He seized my hair in both his hands, and tugged until I yelled with the pain,” before excusing his actions: “we have twice been deceived by wigs and once by paint” (56).  To repeat, as preeminent amongst the Bergsonian invariants of variability, the body is a material locus that intersects with other similarly functioning bodies.  The interaction between Ross and Wilson is telling.  The excessive redness of Ross’s hair bespeaks a dye.  He has applied this color to produce a bodily correspondence with Wilson.  In short, the general property of deceit is common to the variational complex that constitutes Wilson’s narrative, and this quality, which is hiding in plain sight, is beginning to stand out to Holmes.

 

That realization enables the detective to see through Ross’s second play at authenticity.  Wilson recalls that Ross asked him about family circumstances.  Was he a married man?  More particularly, did he have children?  The answer to each question is “no.”  Ross was “sorry to hear [. . .] that.  The fund was, of course, for the propagation and spread of the red-heads as well as for their maintenance.  It is exceedingly unfortunate that you should be a bachelor.”  As with Spaulding’s addition of a selection clause, this limiting condition does not appear in the advertisement, but unlike the previous addition, Ross soon brushes aside this additional worry.  “In the case of another,” he avers, “the objection might be fatal, but we must stretch a point in favour of a man with such a head of hair as yours.”  Ross’s introduction of a selection clause that he immediately withdraws compounds Holmes sense of duplicity.

 

Wilson’s “purely nominal” (57) work for the league at “four pounds a week” (57) fits this understanding, expressing withal an inductive lure that is both temporal and spatial.  The hours of employment—Monday to Saturday from “ten to two” (57)—never vary.  The place of employment—“you have to be in the office, or at least in the building, the whole time.  If you leave, you forfeit your whole position forever” (57)—never varies either.  Another aspect to this lure is the work itself; Wilson must “copy out the Encyclopaedia Britannica” (58); a meaningless exercise that confirms Wilson’s new position as symptomatic of an alternative phenomenological substrate.  Somewhat dumfounded, Wilson “had reasoned” himself “out of the whole thing” by the night of his acceptance; yet, he had not reasoned out the case, and when “everything was as right as possible” during his first week of employment, he simply believed in the legitimacy of his new position.  Being a member of the league meant accepting the inductive lure of the attendant duties.  “This went on day after day, Mr. Holmes, and on Saturday the manager came in and planked down four golden sovereigns for my week’s work.  It was the same next week, and the same the week after” (58).

 

A break in the inductive routine, however, again bespeaks deceit.  “By degrees Mr. Duncan Ross took to coming in only once of a morning, and then, after a time, he did not come in at all.”  That absence presaged the culminating break.  Without warning, “the whole business came to an end,” with a locked office door on which was pinned “a sheet of note-paper” that announced: “THE RED-HEADED LEAGUE IS DISSOLVED.  October 9, 1890” (59).  Failing to pay Wilson for his final week confirms this inductive exception as the definitive mistake.  Sudden, unexpected, and debt incurring, this end to the inductive lure of league membership prompts Wilson to seek Holmes’s advice.  Just as Spaulding had done in securing employment with Wilson, Spaulding and Ross should have bargained on Wilson’s determination “not lose such a place without a struggle” (60).

 

In covering his “as a rule” dictum concerning humdrum cases, Holmes initially considers the inductive possibility of a romantic affair—“had there been women in the house I should have suspected a mere vulgar intrigue”—but Wilson is single, so sexual intrigue “was out of the question” (72).  The breaks in all the phenomenological loops in Wilson’s case must be instances of inductive falsification.  Popper would have approved of Holmes’s deductivism.  Holmes’s identification of a false foreground narrative suggests that a hidden (or deceitful) source has been dictating events.  “It is most refreshingly unusual” (59), he remarks.  “Your case,” he cannot help but repeat, “is an exceedingly remarkable one” (60).  Wilson’s tale has fulfilled its interrupted promise in being a “very remarkable narrative” (72).

 

Wilson’s testimony has already alerted Holmes to Ross’s deceptive body, with its unnaturally red hair, so he asks for a bodily description of Spaulding.  Most of the information Wilson provides is nonspecific—“small, stout-built, very quick in his ways, no hair on his face, though he’s not short of thirty”—but the detail that he “has a white splash of acid upon his forehead” (61) reveals Spaulding’s own bodily deceit.  This slight disfigurement marks the variance within the invariance of the human bauplan by which Holmes recognizes him as “John Clay, the murderer, thief, smasher, and forger,” a criminal whom Holmes has never come face to face with, but with whom he has “had one or two little turns” (67).  In this instance, then, Holmes’s memory (or his mind’s inductive index) provides illumination of a personally stimulating kind.

 

“The Red-Headed League,” with Jabez Wilson, on the one hand, and Sherlock Holmes, on the other hand, hereby illustrates Husserl’s sense of universal judgments.  Deceit is not a noticeable characteristic of either the series of strange occurrences recounted by Wilson or the inner series that comprise these occurrences (Wilson’s applicants, the league’s applicants, the routine of Wilson’s work for the league, and the regularity of his payment for that work).  Wilson, although intrigued by both the league and the events that involve him in that league, fails to reconfigure these spaces of variation from within.  He can generate no universal judgment.  The remuneration for his work for the league, as Clay surely intends, dispels Wilson’s lurking fears.  Such beneficence forestalls thoughts of deception.  Only when one of the inner sequences is inexplicably broken, with the termination of his league work, do Wilson’s suspicions reappear.  Even then, according to his limited judgment, the deceit amounts to “a pretty expensive joke” (61).

 

In contrast, Holmes manages to reconfigure the spaces of variation in Wilson’s narrative from within.  All the variants in the variational complex considered by Holmes, to appropriate Husserl from Formal and Transcendental Logic (1969), “stand in a relationship of synthetic interrelatedness and integral connectedness; more particularly, they stand in a continuous and all-inclusive synthesis of ‘coincidence in conflict.’  But, precisely with this coinciding, what necessarily persists throughout this free and always-repeatable variation comes to the fore: the invariant, the indissolubly identical in the different and ever-again different, the essence common to all, the universal essence by which all variants of the example, and all variants of any such variants, are restricted” (219).  To the insightful, such as Husserl and Doyle’s Holmes, rays of complementary enlightenment pertain between individual variants and their relational invariance.  Universals, as invariant constraints within a variational landscape, are immanent in the flow of consciousness.  Holmes’s inner reconfiguration of variational space identifies the alternative reality that underpins Wilson’s experiences: criminal intent motivates all the deceptions played on the pawnbroker.

 

Even so, the case remains partially unresolved, with this most singular narrative being an exception to another of Holmes’s rule.  “As a rule,” he declares, “the more bizarre a thing is the less mysterious it proves to be,” but the remaining complexities of Wilson’s case constitute “quite a three-pipe problem” (62).  Holmes, as if anticipating Bergson’s advice, awaits intuitive awakening: inductive in outer appearance, with one pipeful of tobacco following another, this inward consideration involves the rational identification of the criminals’ objective.  Wilson has presented Holmes with a variational complex; its different variations show an affinity in virtue of stemming from a common generative point; so the ultimate rationale for inventing the league has spawned a matter that would be an abductive one to Peirce, a Bergsonian one to Popper, but an abductive-intensive one to Holmes.

 

Although the Holmes canon stretches into the modernist period, Doyle never turns to the techniques of free indirection and stream of consciousness to express Holmes’s thoughts, and the detective’s process of rational identification takes place in camera.  Pipe or cigarette smoking often accompanies this secret meditation—the most notable instances occur in “A Case of Identity,” “The Second Stain,” “The Man with the Twisted Lip” (December 1891), The Hound of the Baskervilles (1902), and “Charles Augustus Milverton” (April 1904)—and the closest Watson comes to identifying Holmes’s secret of rational identification in “The Red-Headed League” comes after his friend’s pipe smoking is definitively concluded, as signaled by Holmes’s declaration of the necessary course of action: “Then it was that the lust of the chase would suddenly come upon him, and that his brilliant reasoning power would rise to the level of intuition, until those who were unacquainted with his methods would look askance at him as on a man whose knowledge was not that of other mortals” (65).

 

In comparison, as Watson readily admits, “I tried to puzzle it out, but gave it up in despair” (66).  “With Holmes,” argues Caprettini, “the relationship between the local and the global is always a function of abductive reasoning: to solve the enigma, regularities have to be found.”  “The Red-Headed League,” with its deductive breaking of inductive lures, falsifies the all-inclusiveness of Caprettini’s contention.  In turn, that falsification draws on the asymmetric demarcation demanded by deduction.  Each of Peirce’s triune of deduction, induction, and abduction concerns the relationship between the local (or singular or particular) and the global (or universal), and Holmes employs the combination of reasoning methods demanded by the case at hand.  “The Red-Headed League” also falsifies the assumed all-inclusiveness of Caprettini’s claim that the “‘small facts’ are the key for the local/global relationship in Sherlock Holmes’s strategy” (146) of detection.  Wilson’s case involves a sequence of occurrences (O₁, O₂, … , O_NO) that comprises a number of series.  Each of these individual series consists of a number of constituents.  Examples include the applicants for the post of Wilson’s assistant (A₁, A₂, … , A_NA) and the applicants for membership of the League of the Red-Headed Men (R₁, R₂, … , R_NR).  Each individual constituent, whether at the lower level, such as A_na or R_nr, or at the higher level of O_no, is a small fact, but none is crucially important to Holmes’s detective strategy.

 

Caprettini is on firmer ground when he discusses Holmes’s openness to the deductive method of testing “in not refusing the falsification of a hypothesis.”  In such instances, a small fact, “some unexplained trifle,” as Caprettini avers, can have decisive significance.  Holmes’s “professional honesty [. . .] is also a kind of scientific rigor,” as Caprettini rightly states.  “According to Popper’s theories, Holmes does not refuse to scrutinize his own theories rigorously and he mistrusts the first positive confirmations of the hypotheses” (147).  Holmes’s abductive-intensive awareness matches that of Clay; the complementary positions Holmes and Clay occupy across the lawful–criminal divide mark this correspondence; as such, Holmes realizes that Clay’s scheme is “far more daring than any effort of the imagination” (49) can ordinarily supply.  “The first thing to be done with [a Peircean] hypothesis,” as Fann states, “is to trace out its consequences by deduction” (42), and Holmes certainly subjects the unstated conjecture to which his secret meditation has led him to rigorous testing.  He travels with Watson to Wilson’s shop in Saxe-Coburg Square.  Not identifying himself, Holmes employs the ruse of obtaining directions to the Strand from Wilson’s assistant.  This deceit does not falsify Holmes’s conjecture about the man’s identity: Vincent Spaulding is John Clay.  Holmes’s expedition, which reveals that the pawnbroker’s shop abuts the City and Suburban Bank, also fails to falsify Holmes’s further conjectures: that Clay has invented the league to secure Wilson’s absence so that he and Ross can dig a tunnel; that Clay’s photographic darkroom in the basement of Wilson’s shop is a ruse to facilitate this digging; and that the men’s tunnel targets a building with valuable stock.

 

Subsequent inquiries reveal that an inductive lure has earned the criminals’ specific interest: gold coins (or napoleons).  As Holmes has already related, Clay is not only a murderer and a thief, but also a forger and a smasher.  The term “smasher,” as Richard Lancelyn Green explains, “is thieves’ slang for a person who passes counterfeit money or forged notes” (323n).  The forger and the smasher need their forgeries to pass the test of falsifiability—and, at the highest level of scrutiny, they rarely do.  Official tender has passed certified examination, but even then, serial numbers make banknotes traceable.  In contrast, and unlike the Bonaparte busts in “The Six Napoleons,” the “thirty thousand napoleons” (69) in the vault of the City and Suburban Bank are indistinguishable from one another.  The vault is well protected—“a side door” (68); “a very massive iron gate” (68); “another formidable gate” (68); a final “door” (68) that opens into this space—and only an audacious criminal would attempt to steal these coins, but in Holmes’s estimation, Clay is singular enough to be “the fourth smartest man in London, and for daring I am not sure that he has not a claim to be third” (63).  While the test of audaciousness does not falsify Holmes’s conjecture concerning Clay, the detective no doubt ranks himself more highly on both scales: for Holmes is, as Watson observes, of “singular character” (64).  That singularity is in keeping with the theme of breaking serial events.  So too is Holmes’s desire to deal with Clay for good.  The detective wishes to discontinue his series of “one or two little turns” (67) with this antagonist.  Holmes’s deduction that the theft will be attempted that night—Wilson’s services had been dispensed with that day; the following day is a Sunday; the bank would not discover the theft until Monday; and that delay in detection would favor the criminals’ escape—should ensure that discontinuation.

 

Accompanied by Watson, “Peter Jones, the official police agent” (66), and Mr. Merryweather, a director of the bank, Holmes plans to hold a vigil in the vault.  Merryweather, whose name ironically suggests his gloomy disposition, hates exceptions to his much-loved routine.  On Saturday evenings he usually plays cards—“it is the first Saturday night for seven-and-thirty years that I have not had my rubber” (67)—and Holmes’s plan breaks this custom.  A significant reason hereby terminates another of the tale’s inductive lures.  Nonetheless, multiple doors and gates protect the contents of the vault, and the bank director maintains his confidence in this expression of induction.  “You are not very vulnerable from above,” concedes Holmes.  “Nor from below,” replies Merryweather.  Yet, as Holmes conjectures, Clay’s deductive reasoning has falsified the confidence the bank directors invest in these repeated safeguards, and this singular case requires exceptional action.  “We must put the screen over that dark lantern,” insists Holmes.  “And sit in the dark?” asks Merryweather.  “I am afraid so,” rejoins Holmes.  “Such an absolute darkness,” remarks Watson, “I have never before experienced” (69).  As the only member of this quartet to have anticipated Clay’s actions, Holmes takes charge of the lantern, keeping it covered until Clay has finished digging and has fully emerged from his tunnel.  Holmes springs on the intruder, Jones handcuffs him, and a police officer in Wilson’s shop forestalls Ross’s escape from the other end of the tunnel.  Clay and Ross, partners in crime, and masters of so many inductive lures, fall to Sherlock Holmes, master of the triune of all simple arguments.  For Popper, as he makes plain in prefacing The Logic of Scientific Discovery (1959), the first English edition of Logik der Forschung, “the most important way in which common-sense knowledge grows is, precisely, by turning into scientific knowledge” (xxi).  The history of this growth, therefore, sheds light on the history of scientific thought, and that illumination reveals how Doyle was ahead of his time in anticipating the Reichenbach Falls of Karl Popper in “The Red-Headed League.”

 

[Word count: 10438]

 

ENDNOTES
 

Works Cited

 

 

Aliseda, Atocha.  “Belief as Habit.”  Consensus on Peirce’s Concept of Habit: Before and Beyond Consciousness.  Ed. Donna E. West and Myrdene Anderson.  Cham, Switz.: Springer, 2016.  143–52.

 

Burks, Arthur Wilson.  “Peirce’s Theory of Abduction.”  Philosophy of Science 13.4 (October 1946): 301–6.

 

Caprettini, Gian Paolo.  “Peirce, Holmes, Popper.”  Trans. Roberto Cagliero.  The Sign of Three: Dupin, Holmes, Peirce.  1983.  Ed. Umberto Eco and Thomas A. Sebeok.  Bloomington, IN: Indiana UP, 1988. 135–53.

 

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