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Prof. Dr. László Blutman: The Language and Logic of Inquiry: some basic problems *

“Any truth is better than indefinite doubt.” 1

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I. The scope of the paper

Legal thinking is typically manifested in legal texts. An important part of legal work is the analysis of legal texts. The analysis of legal texts is basically done with linguistic and logical tools, with which we can explore the ideas appearing in the texts and their connections. All this carries a lot of uncertainty. Uncertainty is not only linguistic in nature (e.g., what a word or phrase means in a given context) but also is logical. A fundamental problem is how to use the available logical categories to properly describe and evaluate the thinking that appears in legal texts, especially conclusions. For example, anyone who tried to outline a logical map of the reasoning of a judicial decision may have run into many problems. The difficulties begin even with the content of the most basic concepts in question in practical application: e.g. what is a fact, what makes a conclusion deductive, how we can measure or express degrees of probability in an inductive conclusion.

In this paper, I try to illustrate some of the difficulties. For this, I chose a text that is voluminous, tied to one author, well-known, has been analyzed by many, has been the subject of contradictory evaluations, and is aimed at the rational solution of problems, i.e. focused on some kind of inquiry. A usual legal text does not correspond to all this. However, the famous Sherlock Holmes stories may provide proper text and basis for analysis. The attempts to describe the detective’s thinking can be an intermediary for studying some linguistic and logical issues, which could be relevant to the logical analysis of legal texts.

Countless books and articles have been written about Sherlock Holmes' method and thinking. Yet it cannot be said that the thinking of perhaps the most famous detective in world literature has been properly described. I do not attempt to do this either, but I use this literary text to illustrate some of the fundamental logical problems that may also emerge in the evaluation of legal texts.

Is there any definable logical model by which the thinking of Sherlock Holmes (or a detective in general) can be uniformly characterized and understood? Conan Doyle, the father of Sherlock Holmes, has written about the thinking of his master detective in many places, in many ways and sometimes controversially. Perhaps it is worth highlighting where Holmes refers to three important factors in detective work: observation, knowledge (importance of prior knowledge), and “deduction”.2 Sometimes he also adds the power of imagination.3

All of this is quite banal, but it shows that the focus of the method is on deduction. The detective’s prior knowledge (experience) is one of the foundations of inference that can provide one of the premises (major premise). Another basis for the conclusion is observation, which provides the other premise (minor premise). Thus, the pattern of deductive inference, of which the detective was said to be a master, emerges from the general method. In addition to all this, intuition (“imagination” in Holmes’ vocabulary) comes if the logic does not lead to a result.

These three or four factors alone are too abstract to infer the famous and unique method of the detective that stories always refer to. Based on the text of the stories, five specific elements of Sherlock Holmes’ method can be identified:4 (i) observing the little things;5 (ii) the role of deductive inferences;6 (iii) research for unique (unusual) signs during observations;7 (iv) the exclusion procedure;8 (v) the detective thinks of himself as the perpetrator.9 The key to Holmes’ success lies not only in logic, but logic is given a central role.10

According to Conan Doyle, the detective’s logical ability lies primarily in executing successful deductions. Might deduction be the basic model of Sherlock Holmes’ thinking? So, first, some issues of deduction are worth addressing.

II. The deductive model

Much of the literature analyzing Sherlock Holmes’ stories (“holmesology”) considers deductive thinking to be the main method of the master detective.11 However, this is not the case. The detective’s success does not stem from deductive thinking.12

1. The characteristics of deduction

There is no universally accepted definition of deduction as a particular group of inferences. However, we can identify some of its conceptual elements. (i) First, in the case of deductive inferences, if the premises are true, the conclusion is necessarily true. For Aristotle, the necessity of the consequence (conclusion) is a key conceptual element of deductive argument.13 (ii) Second, in the case of deduction, the validity of conclusion is independent of the truth of the premises. A perfect (valid) deduction can also be based on false premises, but then the conclusion will also be false. The basis of the valid deduction is the linguistic-logical structure of the premises. (iii) Third, many authors believe deduction moves from the more general statement to the concrete, it has a constant direction.14 But this view does not leave room for such arguments that run from general to concrete, but are based on probability. Therefore others argue that the direction of an argument is irrelevant. The deductive argument that necessarily leads to a conclusion does not always go from the general to the concrete.15 According to this latter approach, all arguments that have necessary conclusion are deductions, while all probabilistic arguments are inductions.

In light of these considerations, it is easy to conclude that deduction is hardly the central element of a master detective’s thinking. In a crime, the basic problem to be solved or explained does not require thinking from the general to the concrete. Merely, an answer has to be given as to who committed the crime, or other mysterious circumstances, events have to be explained. More generally speaking, an effect (a situation) is given and the causes need to be explored. Sherlock Holmes also saw this, noting that “the quick analysis of cause and effect which gives the charm to an investigation.” 16 Elsewhere, it suggests that cause-to-effect reasoning is “the only notable feature” of the investigation.17 In the Holmes stories causal reasoning is horizontal, that is – considering its endpoints – it goes from the concrete (effect) to the concrete (causes).

2. Deduction and inquiry

In A Case of Identity, Holmes deduced that the visiting lady was a typist because just above her wrists, where her hands are usually pressed against the table, he clearly saw a double line on the plush.18 The structure of the detective's inference can be described as follows: there is a concrete observed fact (POF) + there is a more general empirical statement (PGES) + a concrete conclusion as the explanation of the observed fact (CC). In the specific case the inference looks like this:

POF – the visiting lady wearing plush has a double line on the plush just above the wrist, on both arms;
PGES – every typist wearing plush has a double line on the plush just above the wrist, on both arms;
CC – the visiting lady is (probably) a typist.

The conclusion is based on probability. The degree of probability is highly dependent on the proportion of typists and non-typists among all the ladies who wear plush cuff and a double line shows on their plush cuffs just above their wrists. The detective classified an observed concrete situation (fact) under a more general proposition. But it is not a deductive argument, even if we reverse the order of the premises.

PGES – every typist wearing plush has a double line on the plush just above the wrist, on both arms;
POF – the visiting lady wearing plush has a double line on the plush just above the wrist, on both arms;
CC – the visiting lady is (probably) a typist.

If all three conceptual elements of deduction are taken at the same time, this conclusion is not a deduction (the conclusion is not necessary), but neither is induction (because it moves from the general to the concrete). So deduction and induction cannot indicate the direction of reasoning, because in this case the distinction would not have good enough explanatory power. The first two conceptual elements remain, according to which deductive inference (regardless of the direction of reasoning) always gives a necessary result, while inductive inference (regardless of the direction of reasoning) is always probabilistic.19 In our example we only see an inductive reasoning based on probabilities.

It should be emphasized that in such cases it is not a simple causal argument. Detecting a crime requires reverse thinking because it is necessary to infer backwards from the effects (present circumstances) to what happened. A detective has to be able to tell the story leading to the current situation (explanation for a crime). In doing so, of course, deductive conclusions can also play a role. The basic task is, however, to reveal the concrete causes (antecedents) of the concrete situation arisen and logically connect them. Sherlock Holmes made this clear: “In solving a problem of this sort the grand thing is to be able to reason backwards.”20 And this is not the basic scheme of deductive thinking.

The inference from effect to cause, which requires the explanation of an observed fact or situation, does not fit well with deductive thinking anyway. In the example taken earlier, everything started from Holmes’ observation and a probabilistic inference was built upon that regarding the visitor’s profession. Although this can be transformed formally into a deductive inference, but then the situation must also be modified where the conclusion makes sense. A deductive inference – at least in a formal sense – would look like this.

PGES – every typist wearing plush has a double line on the plush, just above the wrist, on both arms;
PRD – the visiting lady is typist wearing plush;
CC – the visiting lady has a double line on the plush, just above the wrist, on both arms.

The starting point is then not an observed fact to be explained (POF), but a reported (preliminary) data (PRD). This reasoning requires a situation which is different from the one in the story. Suppose Mrs. Hudson announces to the detective that a lady named Miss Sutherland, who is typist and wears plush, is waiting downstairs at the entrance and wants to consult with him. Holmes is aware of the general empirical observation (PGES; prior knowledge) and also comes to know from Mrs. Hudson what the lady’s profession is and that she wears plush (PRD; antecedent as well). Based on these, he can quickly come to the (necessary) conclusion that when the visitor shows up, a double line will appear on her plush, just above the wrist, on both of her arms. This is a deductive reasoning regarding its form, which is going from cause (practicing a profession and wearing plush) to effect. This new situation does not demand any explanation of observed facts. When Miss Sutherland enters the room, Holmes will be able to ascertain if the conclusion is right.

However, in vain will this deduction be valid. It is not certain that Miss Sutherland’s plush will show double line when she appears in Holmes’ room. The result of the valid deduction can easily be false. In the example, the basic reason for this may be that the general (empirical) statement is not true (in all circumstances). [Of course, the minor premise (PRD) can also be false, for example, Mrs. Hudson misunderstood the young lady's profession or the visitor did not tell the truth in this respect.] The general statement can be false for many reasons. (i) Miss Sutherland might not wear plush when typing. (ii) She might wear another plush when working. (iii) She might have a new plush that she has only used once or twice before the visit and the work has not yet left lines on the material. (iv) There may be typists who have such a hand position that only one line (or possibly none) is visible on their sleeves.

This example also brings another lesson. In some cases, a probabilistic inference can be transformed into a deductive inference, but it will be worthless. This is because the conclusion must be based on a general statement that, as such, will not be true in all circumstances. Changing the linguistic-logical structure of a probabilistic relation does not eliminate the uncertainty of the content.

The above general statement (PGES) “every typist wearing plush has a double line on the plush, just above the wrist, on both arms,” is an ordinary generalization of experience, which could be true in some cases. However, it is not universal truth. Thus, the result of the inference based on it – even in a valid deductive form – will only be more or less likely to be true in specific, individual cases. This is worth noting because in the Holmes stories we may find inferences that are deductive in their logical form. However, if the writer uses them in probability relations (i.e. they are based on general empirical statements) they give uncertain results just like probabilistic inferences would do in the same relations.

There are, of course, many complex, comprehensive arguments in Holmes stories that primarily serve to explain the main mystery or mysteries of a story. The simpler, more transparent retrospective causal arguments, on the other hand, are well exemplified by the recurring elements of the stories when the detective, to entertain Dr. Watson and often independently of the crime to be solved, draws unexpected and not at all obvious conclusions based on tiny signs. For example, from the six tiny scratches on Watson’s shoes to how sloppy Watson’s maid was (A Scandal in Bohemia), from the client’s fingertips to her occupation (The Adventure of the Solitary Cyclist), from the little mud stain on Watson’s shoes to that he recently sent a telegram at the Wigmore Street post office (The Sign of Four) or from a tattoo to that the person in question had been to China (The Red-Headed League). What all of these have in common is that there is an observed fact, a situation (effect), and it must be inferred from the effect the causes that created it (and the circumstances under which it arose.) It also appears that the retrospective causal reasoning that characterizes detective thinking is fundamentally based on probability and not deductive in nature.

Deductive inference requires a general premise on which deduction can be built with certainty (e.g. mathematical truths, scientific laws, or other empirical generalizations on the verge of certainty). However, crimes usually not or rarely can be solved by such general premises. The detective relies mainly on his own experience and knowledge, which has limited validity, no matter how rich it may be. He has to guess, assess the probability of the assumed causal relationships, select the circumstances to consider. However, he only rarely gets assurance. He cannot resort to the chain of deductive inferences that would automatically (necessarily) lead to a solution and at the same time to the truth.

There is another angle that should not be forgotten. Sherlock Holmes is interested in finding out the truth. He wants to know what happened. However, as I have pointed out, flawless deduction does not guarantee truth. The result of a valid deduction can also be false. In this sense, the success of a detective’s work does not lie in deduction itself, but in reaching a true conclusion by applying it. It would be in vain for the detective to be a “master” of deduction if he did not get to the truth. This is only possible if the premises are true. The key issue, then, is not the use of deduction. What really matters is choosing the right premises. Deduction itself (typically the classification of the description of a particular situation under a general statement and drawing a conclusion) is then already a banality. Despite all that, the opinion according to which Holmes was the master of deduction is still standing in the literature.

3. Various generalizations as premises

The key, then, is to choose the right premises. The data of the specific case, which the detective obtains through observation, testimonies, conclusions, or from other sources, provide one group of premises. Another group of premises is general statements, which help to arrive at more specific data through inferences. It depends on the content of these general statements whether a deductive argument is possible or not. If they contain a general truth (being certain or almost certain), then deduction is possible. If they have only a certain degree of probability, they can serve as a basis for at most inductive argument. For this reason, in what follows, I will deal only with the latter, that is, the general statements that occur in the Holmes stories and serve as the material for the inferences.

In Holmes stories, the direction of inference is typically horizontal regarding its two endpoints: it moves from concrete data to concrete data. More general statements linking them can often go hidden or unnoticed. A crucial question for the thoroughness of the conclusion is the quality and sources of these general statements that make a connection between concrete propositions. In general, it is difficult to typify such more general statements as a basis for conclusions. However, their four groups are noticeably different: (i) mathematical or logical truths, or other truths based on them (they can lead to certainty with valid inference); (ii) scientific regularities or generalizations of scientific experience (valid inference may lead to conclusions that are on the verge of certainty or highly probable); (iii) ordinary generalizations accepted in a narrower or wider human community based on collective experience (making the conclusions probable to varying degrees); (iv) generalizations based on personal experience and thus of limited validity (possibly probable conclusions).

In the arguments that emerge in the Holmes stories, the first two groups have almost no direct role. Mathematical and logical truths do not have a direct, at most ancillary role due to their subject matter. As far as scientific laws are concerned, they do not play a noticeable role in the arguments leading to the resolution of cases.21 The conclusions will typically be based on generalizations filtered out from the detective's personal experience, or generalizations accepted in the smaller or larger communities of contemporary English society (ordinary customs, wisdom, prejudice, social rules, etc.). As Holmes noted, his art is just “systematized common sense.”22

In the story of The Hound of the Baskervilles, an anonymous letter was compiled from the letters of the Times. Since this newspaper “is seldom found in any hands but those of the highly educated” Holmes concluded the letter was compiled by a highly educated man.23 The binder for the argument is the general proposition in quotation marks. It was obviously a collective experience that the Times was read by the more educated social groups, but that is not the point here. According to the statement, the newspaper does not get into the hands of anyone else, which can already be described as a personal generalization by the detective himself. The truth of this statement is difficult to estimate. One should be familiar with the way of life of the time, and assess the situations in which a non-highly educated man could access the newspaper so that he could cut it into pieces with scissors for assembling an anonymous letter without raising suspicion.

The quality of arguments depends to a large extent on such more general propositions as premises (PGES), which reflect prior knowledge, beliefs, opinions, and experiences. Among these are many simple statements that reflect everyday rules, wisdoms — for example, whoever has to deal with a very cunning man must be circumspect.24 The success of reasoning depends on what prior knowledge the detective can mobilize and use as a general premise. Holmes knew this well. He accumulated a large amount of knowledge partly in his mind and partly in his famous card system. He constantly filed and used his filing system: for example, to look at the life story of Irene Adler, 25 Professor Moriarty and Sebastian Moran,26 to keep count of the interesting crimes on the continent,27 to recall his own past cases.28 His motto is, “To remember it – to docket it.”29 This card system was partly the source or the basis of generalizations the detective used in his investigations.

If we examine the Holmes stories from this point of view, we can see that the detective sometimes uses dubious generalizations, the source of which is not even revealed most of the time. To illustrate this, I list some examples of such generalizations that have been part of an argument in some cases: oscillation upon the pavement always means an affaire de coeur; 30 a well-to-do, drifting and friendless woman, though mostly harmless, but she is inevitable inciter of crime in others;31 “a dog reflects the family life”;32 nosebleeds are the most common in ruddy-faced, robust and full-blooded men;33 a woman of Spanish blood does not condone such an injury lightly that her husband tells her he loves someone else;34 by studying the child, we can gain light as to the character of the parent;35 if a man writes on a wall, he will instinctively write about the level of his own eyes; 36 when a woman thinks her house is on fire, she will instinctively rush to the thing she values most. 37 the individual represents in his development the whole procession of his ancestors;38 the criminal propensity is inherited; 39 in hotels, the ink bottle is usually low on ink and the pens are neglected; 40 women are naturally secretive; 41 “men of character always differentiate long letters, however illegibly they may write”;42 who perspires a lot is not in the best of training;43 in an incredible and grotesque case no woman ever sends a reply- paid telegram; she would appear in person to consult the detective.44

Perhaps the list provides a kind of cross-section of what generalizations Holmes typically bases his conclusions on. Anyone can judge the probability of these statements. Obviously, there are some that are not too likely. However, in an argument these propositions, as premises (PGES), largely define the probability of the conclusion.

It is clear, however, that such general propositions are not universal truths or statements on the verge of certainty, so no deductive conclusions can be drawn from them. This is one of the reasons for which deduction is not typical of Sherlock Holmes' thinking.45 The idea is not new that detective stories are not characterized by deductive reasoning, but by a retrospective causal argument inferring from cause to cause, moving from observed concrete facts to other, also concrete facts (causes). The peculiarities of retrospective causal reasoning were already pointed out by Charles Sanders Pierce, the renowned American philosopher, in the second half of the 19th century. He did not even see sufficient forms of reasoning based on traditional induction or deduction to logically describe this. Thus, in addition to these two, he introduced a new, third form of inference, which he called abduction (sometimes – arguably – retroduction), reflecting backward reasoning.46 This gives the following model for describing Holmes’ thinking.

Here is the continuation: Language and Logic of Inquiry 2.

AUTHOR: LÁSZLÓ BLUTMAN - Professor of Law, University of Szeged, Faculty of Law and Political Sciences

© All Rights Reserved.

We would like to thank Professor László Blutman for publishing his study.
Notes can be found below the next image.

László Blutman Sherlock Study


* This article was originally published in FORVM Acta Juridica et Politica (Szeged) XI. 2021/1. pp. 5-21.

1 - The Adventure of the Yellow Face in: DOYLE, ARTHUR CONAN: Sherlock Holmes: The Complete Stories. Wordsworth Editions. London 1996. p. 328. (in the following, the source of the Holmes stories is this volume).
2 - The Sign of Four, The Complete Stories, p. 65.
3 - The Adventure of Silver Blaze, The Complete Stories, p. 300.
4 - Since Sherlock Holmes did not write the great handbook of investigation, as promised in one of the short stories, it is possible to reconstruct his thinking from the description of his adventures, The Adventure of the Abbey Grange, The Complete Stories, p. 713.
5 - E.g. The Boscombe Valley Mystery, The Complete Stories, p. 171.
6 - E.g. The Adventure of Engineer's Thumb, The Complete Stories, p. 230. The Adventure of the Stock-broker’s Clerk, The Complete Stories, p. 332.
7 - E.g. The Adventure of the Lion’s Mane, The Complete Stories, p. 1090. The Adventure of the Blue Carbuncle, The Complete Stories, p. 203.
8 - E.g. The Adventure of the Blanched Soldier, The Complete Stories, p. 1078. A Study in Scarlet, The Complete Stories, p. 61. In applying this method, Holmes, taking into account every conceivable explanation, gradually excludes those that prove impossible.
9 - E.g. The Musgrave Ritual, The Complete Stories, p. 363. 10 See also BLUTMAN LÁSZLÓ: Módszertani zsákutca: miért nem írható le jól egy mesterdetektív gondolkodása? [Methodological Cul-de-sac: why can’t the thinking of a master detective be well described?] Jogelméleti Szemle 2019/3. pp. 123–124.
11 - E.g. BERG, STANTON: Sherlock Holmes: Father of Scientific Crime and Detection. The Journal of Criminal Law, Criminology and Police Science Vol. 61, No. 3, 1970, pp. 446–452. SEEWALD, JACQUELINE: Sleuthing: Yesterday, Today, and Tomorrow. Sherlock Holmes Mystery Magazine Vol. 5. No. 4. July/August 2014. pp. 19– 22. RIGGS, JOE: The Real Sherlock Holmes. MX Publishing. London, 2012. p. 43. WALTERS, CHARLOTTE: 56 Sherlock Holmes Stories in 56 Days. MX Publishing. London, 2012. p. 22. and p. 51.
12 - E.g. CARSON, DAVID: The Abduction of Sherlock Holmes. International Journal of Police Science and Management Vol. 11, No. 2, 2009, pp. 193–202. KRAFT, RORY E.: Watson's a Liar! In: Sherlock Holmes and Philosophy: The Footprints of a Gigantic Mind. (Ed. STEIFF, JOSEF) Carus Publishing Company. Chicago, 2011. pp. 183–184.
13 - Prior Analytics I.1. 24b paras. 18–19.
14 - E.g. POTTER, W. JAMES: Theory of Media Literacy: A Cognitive Approach. SAGE Publications. 2004. 133. p.; FRANKLIN, MARIANNE I.: Understanding Research. Routledge, 2013. p. 233. GREIMAS, ALGIRDAS – COURTÉS, JOSEPH: Sémiotique. Hachette Livre. Paris, 1993. p. 85. and p. 187.
15 - KAHANE, HOWARD: Logic and Philosophy. Wadsworth. Belmont, 1986. pp. 287–288.
16 - A Case of Identity, The Complete Stories, pp. 147.
17 - The Adventure of the Copper Beeches, The Complete Stories, p. 272.
18 - A Case of Identity, The Complete Stories, p. 153.
19 - Cf. KAHANE 1986, p. 288.
20 - A Study in Scarlet, The Complete Stories, p. 61.
21 - This is not to say that Holmes would not have been proficient in certain sciences and would not have kept tremendous knowledge in his mind. In the background, this helped him to analyse a manuscript in an expert way or to recognize from which part of England a piece of mud came from. However, general and truly scientific propositions, principles did not appear in his inferences.
22 - The Adventure of the Blanched Soldier, The Complete Stories, p. 1082.
23 - The Hound of the Baskervilles, The Complete Stories, p. 467.
24 - The Adventure of the Copper Beeches, The Complete Stories, p. 284.
25 - A Scandal in Bohemia, The Complete Stories, pp. 121–122.
26 - The Adventure of the Empty House, The Complete Stories, p. 565.
27 - A Case of Identity, The Complete Stories, p. 153.
28 - The Adventure of the Sussex Vampire, The Complete Stories, p. 1016.
29 - The Adventure of the Six Napoleons, The Complete Stories, p. 661.
30 - A Case of Identity, The Complete Stories, p. 148.
31 - The Disappearance of Lady Frances Carfax, The Complete Stories, p. 816.
32 - The Adventure of the Creeping Man, The Complete Stories, p. 1000.
33 - A Study in Scarlet, The Complete Stories, p. 62.
34 - The Hound of the Baskervilles, The Complete Stories, p. 551.
35 - The Adventure of the Copper Beeches, The Complete Stories, p. 284.
36 - A Study in Scarlet, The Complete Stories, pp. 23–24.
37 - A Scandal in Bohemia, The Complete Stories, p. 128.
38 - The Adventure of the Empty House, The Complete Stories, p. 566.
39 - The Adventure of the Final Problem, The Complete Stories, p. 436.
40 - The Hound of the Baskervilles, The Complete Stories, p. 468.
41 - A Scandal in Bohemia, The Complete Stories, p. 126.
42 - The Sign of Four, The Complete Stories, p. 69.
43 - The Adventure of the Blue Carbuncle, The Complete Stories, p. 204.
44 - A Reminiscence of Mr. Sherlock Holmes, The Complete Stories, p. 745.

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