I. Introduction

Informal fallacies are de rigueur for introductory critical thinking courses. Informal fallacies are contrasted with formal fallacies. Formal fallacies make references to argument form whereas informal fallacies do not. Affirming the consequent, for example, is a formal fallacy. A learner has to understand the argument form of modus ponens in order to understand why affirming the consequence is bad reasoning. The bad reasoning in informal fallacies can be explained without reference to argument forms, and so are more accessible to learners who want to sharpen their critical faculty without going into the technicalities of argumentation. In this essay, I give the reader reason to be cautious about dismissing arguments on the basis of applying informal fallacies of inductive inferences.

Consider this unfortunate dialogue between Sherlock Holmes and Mary Morstan.

Sherlock Holmes (SH): You’re a governess.

SH: Your student is a boy of age.

Mary Morstan (MM): Charlie is seven, actually.

SH: Then he’s tall for his age. He flicked ink at you today.

MM: Is there ink on my face?

SH: There are two drops on your ear, in fact. India Blue is impossible to wash off. Anyway, it was impetuous of that boy but you’re too experienced to react rashly, which is why the lady for whom you work lent you that necklace, for the pearls, diamonds, flawless ruby are hardly the gems of a governess. Other jewels you are not wearing tell us rather more.

SH: You were engaged. The ring is gone but the lighter skin where it once sat suggests that you spent some time abroad where you wore it proudly, that is, until you were informed of its true and rather modest worth, at which point you broke off the engagement, returned to England for better prospects. The doctor, perhaps.

MM: Right on all counts, Mr. Holmes, apart from one. I didn’t leave him. He died.[1]

A learner, applying the informal fallacy ‘hasty generalisation’, finds Holmes’ reasoning egregiously defective. He is concluding on the basis of only one observation mixed with speculation. I show that Holmes’ reasoning is defensible as instances of a type of abductive reasoning. Dismissing such arguments on the basis of hasty generalisation denies us the conceptual power to fully describe productive intellectual activity. While I use the Holmes-Morstan dialogue above as my stalking horse, my point generalises. Learners who cognize such ‘bad inference’ by their fit to a template of informal fallacies do not have the wherewithal to be aware that they are misidentifying the form of reasoning, and thereby misevaluate some instances as bad inferences.

II. Inductive inference

An inductive inference moves from premises enumerating instances observed to bear some property, to a conclusion that all instances bear that property. Hence we have the well-worn example:

Swan 1 was observed to be white.

Swan 2 was observed to be white.

Swan 3 was observed to be white.

Swan n was observed to be white.

Therefore, all swans are white.

The standards of goodness of an inductive inference are strength and cogency.[2] The strength of an inductive inference depends on factors like the number of observed instances, the variety of different contexts in which the instances were observed, and the presence of countervailing explanations for the observations. The strength of an inductive inference comes in degrees. A cogent inductive inference is one that is strong and whose premises are true. Unlike a deductive inference, the conclusion of an inductive inference is not truth-preserving. That is, the conclusion can be false even if all the premises are true. Someone in Europe before Willem de Vlamingh’s 1697 discovery of black swans in Australia would, in reasoning as above, be making a cogent inductive inference with a false conclusion.[3]

III. ‘Hasty Generalisation’ in the Holmes-Morstan dialogue

The informal fallacy of hasty generalisation is a fallacy of inductive inference. It charges that one errs in concluding about the general case from premises about insufficient instances or merely one instance. Holmes’ reasoning in the dialogue fits this template. In the context of the narrative, it is the first time he meets Morstan. There were no prior instances on which he can base his conclusions about her, nor is it likely that he’s ever had enough observations regarding flicking of ink on faces or ring tan lines to adequately warrant his inferences. Instead, it is likely that his inferences are based on that one and only instance. However, his inferences appear to meet an essential characteristic of inductive inferences – his conclusions can be false even when they follow from true premises. For example, we can paraphrase his argument, “Morstan’s student is a boy of age because ink that he flicked reached her ear.” Its conclusion, “Morstan’s student is a boy of age,” is false; he was only seven years old. Yet, the premise is true – the ink that he flicked indeed reached Morstan’s ear.

The following table presents the single instances of evidence (Column A) and assumptions (Column C) from which Holmes concludes (Column B).

	A.	B.	C.
	Evidence	Primary Conclusion	Concluded from / Assumptions?
1.	There are two drops of ink on Morstan’s ear.	Morstan is a governess with a student who is of age.	Morstan is too experienced to act rashly upon being flicked.
2.	Morstan is wearing flawless gems that one cannot afford on a governess’ salary.	The gems are loaned by Morstan’s lady employer.	Morstan’s lady employer loaned her the gems because of Morstan’s restraint towards her charge.
3.	There is a ring tan line on Morstan’s ring finger.	Morstan spent time overseas in a sunny location and was engaged.	Morstan called off the engagement and returned to England because of her dissatisfaction with the cheapness of her ring.

IV. Peircean abduction in the Holmes-Morstan dialogue

Peircean abduction is a method of choosing hypotheses. It is the starting point of empirical investigations, not their end – the product of abductions are guesses to be corroborated, not conclusions that are considered to be true.[4] These adventurous moves are instrumental to the progress of science, especially when it comes to breaking out of reigning comprehensive theories. The Peirce scholar, William Mcauliffe, has identified a number of standards of goodness for abduction from Peirce’s writings. I enumerate four that are relevant to evaluating Holmes’ reasoning in the dialogue. In the criteria that follow, ‘hypothesis’ refers to the conclusion of Peircean abduction.

“[T]he hypothesis should be experimentally verifiable.”[5]
“[T]he hypothesis should, if true, explain the facts in question.”[6]
“[S]cientists should pay attention to signs indicating that a certain hypothesis is true.”[7]
1. ‘Instinctive’ signs: “[T]hose that “naturally recommend themselves to the mind” and have value because of the human capacity to devise plausible theories.” [Or]
1. ‘Reasoned’ signs: Those “hypotheses [that] have supportive background evidence.”[8]
“[U]nless it be very solidly grounded, likelihood [that a hypothesis is true] is far better disregarded” in favour of “potentially fertile hypotheses.”[9]

Criteria I and II are conditions that have to be met by a good instance of Peircean abduction. Criteria III and IV are guidelines for choosing better hypotheses. If we gave Criterion I a broader interpretation to the effect that we can verify the hypothesis, the four points serve to validate Holmes’ reasoning with respect to his primary conclusions (Column B) in the table above, and to reject the points in Column C.

Without actual countervailing considerations, the points in Column C appear to explain the corresponding points in the Column A, meeting Criterion II. All three resultant explanations can be verified by responses from Morstan when apprised of them, or by directly asking her about their truth. This meets Criterion I. Criterion III appears to be met because the inferences appear to come immediately to Holmes’ mind. To infer that Morstan is a governess via the route of her charge flicking ink at her face is tenuous because there are many possible countervailing considerations. An example would be that Morstan was writing a letter and flicked ink on herself accidentally while trying to swat a fly. However, Criterion IV favours the ‘fertility’ of a hypothesis over its likelihood. Interpreting ‘fertility’ as ‘ability to generate true hypotheses’, Criterion IV is met by the point in Cell 1B of the table (henceforth ‘1B’) because it, in conjunction with 2A, generated 2B. Judging from Morstan’s lack of negative response to the implication of 2C that her employer loaned her the gems, 2B is likely to be true.

1C and 3C both fail to satisfy the condition presented by Criterion II: they do not explain the facts in question, namely, the points in Column A of the table. 1C, that Morstan is experienced with children and does not respond rashly to misbehaviour, does not explain why there are two drops of ink behind her ear without further complicated rationalisations. 1C thereby fails to meet Criterion III. 3C, that Morstan called off the engagement and returned to England because of her dissatisfaction with the cheapness of her ring, does not explain why there was a tan line on Morstan’s ring finger without further complicated rationalisations. 3C also fails to meet Criterion III.

2C attributes a reason to Morstan’s employer for loaning the gems to Morstan, namely, that it’s because of Morstan’s restraint towards her charge. By this attribution, 2C implies that Morstan’s employer loaned her the gems, which, as pointed out above, is likely true. About the reason that is attributed, however, there is not enough information to come to a judgement. On one hand, the reason that Holmes attributed to the employer may be unrelated to any of the evidence in Column A, except by complicated rationalisations. This would violate Criterion III. On the other hand, Holmes could have picked up subtle cues from Morstan’s comportment indicating to him that she is a person of restraint in general. This information serves to weaken the judgment that Criterion III is violated by way of satisfying IIIb. If so, then the judgement that 1C violates Criterion III is similarly weakened.

V. Conclusion

The conclusion of the exercise in the previous section shows that Holmes’ reasoning in the dialogue and his arguments that express them should not be rejected wholesale on the basis of applying the fallacy of hasty generalisation. There are other modes of reasoning, incompatible with the standards of inductive inference, which are essential to fully describing productive intellectual activity. As we have seen from the above analysis, by applying standards of Peircean abduction instead of inductive reasoning, we can appreciate the acceptability of some of Holmes’ inferences in the dialogue. A critical thinking course that presents only deductive and inductive inferences to its students and offers informal fallacies as a sufficient template to identifying bad inferences misleads its students.

From disciplines as disparate as science and criminal investigations, we require the characterisation of some mode(s) of reasoning that enable(s) us to cast aside the deductive strictures of truth preservation and the inductive strictures of adequate sampling, in order to break out of extant dominant understandings of the case at hand. Yet, these adventurous hypotheses are not lucky guesses. They come with standards of goodness that determine whether the inferences that generated them are better or worse ones. Working out what these standards are can help to regiment and produce guidelines for increasing the likelihood of producing adventurous true hypotheses.

[1] Guy Ritchie, Sherlock Holmes (CA: Warner Bros. Pictures, 2009), motion picture. Transcribed from https://www.youtube.com/watch?v=388-rOzD9SM (accessed: 3 May 2020).

[2] Wikipedia, “Argument,” https://en.wikipedia.org/wiki/Argument (accessed: 3 May 2020).

[3] Wikipedia, “Willem de Vlamingh,” https://en.wikipedia.org/wiki/Willem_de_Vlamingh (accessed: 3 May 2020).

[4] William Mcauliffe, “How did Abduction Get Confused with Inferences to the Best Explanation?” Transactions of the Charles S. Peirce Society, vol. 51, no. 3 (2015), p. 301.

[5] Ibid., p. 303.

[6] Ibid.

[7] Ibid.

[8] Ibid., pp. 303-304.

[9] Ibid., p. 304.