Prof. Dr. László Blutman: The Language and Logic of Inquiry: some basic problems *
The first part can be found here: Language and Logic of Inquiry 1.
“Any truth is better than indefinite doubt.” 1
III. The abductive model
AUTHOR: LÁSZLÓ BLUTMAN - Professor of Law, University of Szeged, Faculty of Law and Political Sciences
More recently, the thinking of a detective has been modelled by many based on abduction
as a form of reasoning.47 The American philosopher Charles Sanders Pierce first used
abduction in its current sense as the third elementary form of inference (in addition to
deduction and induction).48 However, as an elementary schema, abduction is a strange,
weakly relevant, inductive inference that is difficult to begin with. Thus, in Peirce's
writings, abduction later appeared as one of the methodological elements of scientific
thinking, which basically wanted to represent the creation of scientific hypotheses. He
also broke with the elementary, three-member schema, and abduction became more and
more a model of causal, explanatory reasoning, in which thinking about the effect (an
observed phenomenon) traces back to the causes.
Pierce applied this to scientific thinking. The detective's way of thinking only came
incidentally into his field of vision.49 Peirce’s abduction as a general scientific
methodological element was not at first a great success. The concept, on the other hand,
has become popular in some areas since the 1980s.50 This was mainly due to
semioticians (Peirce is the founder of modern semiotics). On this wave, abduction was
also included in the toolbox for the analysis of detective stories (in addition to
semiotics, theory of science, philosophical methodology, etc.).51
That would be fine, but it’s quite confusing what abduction really is. This confusion
can inherently be attributed to Pierce, who wrote about abduction several times in
several ways. According to Chiasson, for example, the philosopher used the term in at
least three different ways.52 Various interpretations were then built on these approaches
in the second half of the 20th century. The uncertainty of the theoretical background
made it difficult to identify abductive conclusions in a specific text. Some common
denominator may be that abduction, by its nature, is a probabilistic inference to explain
a phenomenon.53 Put this way, it seems somewhat banal. Any person does causal
reasoning many times a day. Yet, if we apply this to detective stories to explain
suspicions, observed facts, unusual phenomena, the detective's thinking can be
characterized by it. The detective often has to infer the causes from the effects, in
reconstructing the past from a certain point of view.54 However, abduction is hardly apt to
adequately describe how Sherlock Holmes thought. I see the following reasons for this.
Peirce had fundamental problems in distinguishing between abduction and induction
because both are probabilistic inferences. One of the main differences he saw was that
induction serves to justify or refute an existing idea, a hypothesis, so its starting point is
the already existing hypothesis. In the case of abduction, there is no hypothesis
(explanation) for a group of facts and data yet, the hypothesis is set up by abduction.55
Thus, in a detective story, the pre-abduction phase would be when the detective has
no idea what the explanation might be.56 However, it can be seen that Holmes
sometimes develops an idea or ideas very quickly to explain various unusual facts. Once
such an idea is born, we can no longer talk about abduction, only about the testing and
justification of the idea by the means of deductive and/or inductive inferences. Most of
Holmes’s stories are spent justifying ideas, hypothesis (this becomes clear at the end of
the stories) rather than formulating a hypothesis. The role of abduction in a story is thus
limited to very short, often imperceptible stages in time.
Holmes’ famous method of exclusion, where applicable, almost eliminates the
abduction phase.57 He keeps in mind all possible solutions and gradually filters them
during data collection, testing them with new data and inductive inferences (“my usual
method in logical analysis is to narrow down the range of possible solutions”).58 In
stories where the exclusionary method is well applied, abduction is almost
imperceptible. In The Adventure of the Beryl Coronet Holmes assumed that everyone
who was in contact with the lost jewelry around the time of its disappearance was
suspicious. The suspects were checked one by one, so the client's niece got caught on
the sieve. He then built the story around the client’s niece by gathering more data and
making inductive inferences that explained what had happened.59 In stories with this
pattern, the methodological starting point actually replaces abduction.
In several Holmes stories, the detective starts from a false hypothesis, and then in
checking this, with the new data, the hypothesis is overturned, while the correct solution
unfolds (e.g. Silver Blaze). The erroneous hypothesis can undoubtedly be preceded by
abduction. It is questionable, however, whether any abductive inference plays a role in
the process in which refuting a false hypothesis leads to the correct solution. According
to Peirce, any hypothesis is already tested with inductive inferences. Obviously this is
also the case with the false hypotheses, therefore abduction does not seem to play a
significant role in the development of the correct theory.
Nevertheless, in the Holmes stories, the abduction situation envisioned by Peirce is
often well observed, for example, in setting up some grounding hypotheses. However,
general problems of abduction also arise here. Let’s take an example. In The Norwood
Builder, Holmes had to explain a writing (a sketch of a last will and testament) in which
the first few lines, the middle of the second page, and one or two lines at the end read
well, while between the readable parts the writing is very ugly, barely readable, in some
places simply illegible.60 What could be the explanation for such a varying quality of the writing? If at first glance we have no idea about the explanation, it is a pre-
abduction state of mind. We mobilize in our memories the patterns (types of situations) in which such writing can occur. Either we get to some explanation, or we don’t. If this
unusual fact can be fitted to a situation, an idea (possible explanation) arises. But in the
moment an idea emerges, the abduction is already over, because in the next step, the test
of the idea (a hypothesis) begins, which is already an induction according to Peirce.
The detective's imagination puts behind the writing image the situation where it may
have arisen. However, this will be an intuitive psychological phenomenon and not an
inference. Here, abduction does not describe thinking, but conceptually indicates a point in
a thought process supported by imaginary, intuitive, and situational patterns stored in
mind and based on prior experience. 61 The explanation will be a description of a situation,
a short story (that is, a hypothesis).62 In retrospect, one can argue for the probability of an
explanation, but finding an explanation can logically hardly be described. Therefore,
Pierce could note that “... abduction is, after all, nothing but guessing.”63
This is not always the case. If the explanation (hypothesis) does not appear as a
story, but in the form of a general statement (rule, regularity) or some general
statements connected to each other, which is primarily characteristic of science, then
abduction can already mean a real conclusion. This is because thinking can consciously
explain an observed phenomenon with a freshly conceived general statement, regularity
(although this can also be intuitive). A distinction must be stated between recognition of
explanatory patterns (which is typically based on analogy) on the one hand, and
explanation of an observed fact or an available data by including them in the scope of a
freshly conceived, general statement. Recognition of patterns is intuitive in nature,
while the latter, subordination, can be intuitive, but can also be a real inference. Peirce
therefore tried to attribute a dual nature (both logical and psychological) to abduction,
which, however, is difficult to defend.
If the abduction is logical in nature, it must be shown that there must be some
description of it. Peirce gave the following formula, which became famous but proved
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.
I can’t deal with the critique of this scheme, many have already done so.65 I would
make only four remarks to support the finding that abduction as an inference (logical
operation) is not characteristic of Sherlock Holmes' thinking. (i) The link between A and
C is “matter of course”, but it is an empty term that cannot explain the relationship.66 (ii)
The formula contains at least one intuitive element: how A gets into the picture. How did
the mind chose A and connected it to C? In the absence of a profound explanation, this is
basically nothing but an intuitive process wrapped in a seemingly logical formula. (iii) In
the example above, it cannot be said that if A is true (the letter was written on a train),
then C would also be true (i.e. some parts of the writing are illegible). C's relationship with
A is not necessary, but is probability-based (it is possible that someone can write legibly
on a train). This relationship would only be necessary if A were a general statement of
universal truth (and not only a hypothesis in the form of a story). (iv) An unusual fact in a
detective's story may arise not only when the detective observes, but also indirectly
becomes aware of facts (data) to be explained.
All this suggests that abduction (as adopting a hypothesis) is simply a psychological
phenomenon. If this is the case, then there are already concepts that express it. For
example, Dr. Watson called it intuition, Holmes imagination. There is no need to
introduce a new concept for all this.
According to Peirce, abduction seeks a theory (while induction seeks for facts to
substantiate an idea).67 This feature of abduction may fit scientific hypotheses because
science typically works with hypotheses appearing in the form of theories. However, it
does not fit those hypotheses that emerge in a criminal investigation. In Holmes stories,
hypotheses in the process of solving a problem appear in the form of explanatory stories
or specific propositions (assumptions that state specific facts as causes). The detective’s
thinking, as opposed to abduction, does not seek a theory but seeks a story (even if
Holmes frequently calls explanations theories). The essence of Peirce's abduction is to
explain unexplained facts with general theorems, in which the unexplained facts are
included in the scope of a general statement or theory (concrete – general relation). In
detective stories, on the other hand, facts are typically explained by a story, which
consists of concrete facts (data); that is, the detective ultimately seeks a specific system of
relations of concrete facts and data (concrete – concrete relation). Based on the
above, abduction plays a smaller role in a detective story than in science and is hardly
suited to properly characterize Holmes’ thinking with it.
IV. The puzzle model
The puzzle model is based on that the elements of the story explaining the mystery fit
together, thus reinforcing each other and increasing the probability of each other as well as
the whole story. Some hypotheses are sometimes justified not only by the additional facts
and data revealed, but also by the fact that they fit together.68 Thus, at the end of a
successful investigation, there is a story (no longer as a hypothesis but as a conclusion to
the case) that most likely (or on the verge of certainty) explains or solves the crime or
other unusual event to be explained. The explanatory story unfolds in such a way that the
known facts and data make sense in a single framework and in relation to each other. With
a good story, everything will be verifiable and explainable. Thus, it is obvious that we
perceive the elements of the story as pieces of a jigsaw puzzle, which are patiently
matched to form a final picture where each piece has a place and significance.69
The puzzle model reflects the detective’s thinking well in some respects. On the one
hand, some complex results are to be achieved in both. The detective strives to find a
comprehensive explanatory story, while the puzzle player a detailed picture. On the
other hand, the relationships concerning the details and the whole are similar in both. At
the beginning of the puzzle game, there is no idea for the whole picture (unless, as a
relief, the creator of the game has provided the picture to be assembled). Inserting a
puzzle piece depends on whether it matches the pieces that have already been laid out.
The step-by-step construction, in terms of method, changes slowly as ideas emerge
about what a part of the image or the image as a whole, represents. An emerging idea
will represent a new point of reference, making it increasingly purposeful to find what
puzzle pieces to look for in the process of construction. The investigation by a detective
reveals a similar pattern. At the beginning of the investigation, the individual clues and
data themselves offer the direction of further progress. Later, the threads of the
investigation may be torn apart, the clues must be sought more and more purposefully,
and this will not go without hypotheses about what happened (which corresponds to the
imagined picture or a detail of the picture in the puzzle).
In other respects, the puzzle is far from being able to adequately represent what is
happening in the investigation of a crime or other mystery. I see two significant
differences. On the one hand, the number of individual pieces of the puzzle is finite, the
pieces and their significance are unchanged throughout the game, and they can be
matched in the same way. During the investigation, however, one has to face the fact
that the data representing certain elements of the later explanatory story change. A
partial hypothesis about them is overturned, a witness changes his or her testimony, or a
specific clue takes on a new meaning or is shed new light. If it is a key data, it may
upset the overall hypothesis (if it already exists) and a whole new idea needs to be
sought. The final story is made up of hard facts and soft data subject to change. The
variability of the latter must always be taken into account.
On the other hand, in the case of the puzzle, the picture is already given at the
beginning of the game, which will be laid out by the successful player at the end. You
have all the puzzle pieces, and you just need to find and insert them in the right place
during the game. This is by no means always the case with detective stories. Even after,
an investigation has begun, new evidence often emerges, new crimes or other
mysterious events may occur, and there is a struggle between the detective and suspect
to hide or uncover clues. These new events, data and evidence should be covered by the
investigation, as a satisfactory explanation can only be given together. Detective stories
are in motion. The range of evidence is not given, and due to subsequent events, not
even the story that needs to be found as an explanation is final.
Exceptions, of course, are. In puzzle-like cases like the ones in which Doyle’s hero
investigated, there could in principle be a larger number of stories where events were
closed and the puzzle became static (except for the escape of the perpetrators). For
example, in the short story of The Adventure of the Engineer’s Thumb, this is well
observed (the engineer escaped from the site of the mysterious activity, the perpetrators
set the house on fire and fled). The data had to be collected and put together with regard to
what had happened. On the other hand, Holmes stories often enclose mysteries, often
unrelated to a crime, that are based on protracted or repetitive activity and persist when the
investigation commences (e.g. The Yellow Face, The Creeping Man). In fact, there are
stories when Holmes and Watson began investigation in an ongoing criminal case (The
Adventure of the Speckled Band, The Five Orange Pips). In some stories, they started
investigating in order to solve some mysterious, unusual event, and it turns out that by
solving it, some crime is prevented (e.g. The Red-headed League, The Adventure of the
Speckled Band). It is not always possible to solve a mystery fast enough to prevent
someone’s death (The Adventure of the Dancing Men, The Stock-broker's Clerk). It is also
the case that the commission of another crime does not add much new data to unravel the
criminal mystery in which the investigation was launched (The Five Orange Pips).
Whatever the structure of a story may be, in the case of crimes and mysteries in
motion, the detective's thinking cannot be simply paralleled with that of a puzzle
player.70 In such cases, not all the facts are given as a starting point, as some of them
will only occur after the start of the investigation.
V. Concluding remarks
I examined three models used to describe or characterize a detective’s thinking. I have
shown that none of these models adequately reflect Sherlock Holmes’ thinking as it
appears in Conan Doyle’s stories.
The famous detective's inferences are mostly inductive in nature. These are based on
general statements that are not general truths, but are true only in a number of the cases.
Their future occurrence is only to some degree probable, but not certain. Thus, the
conclusions based on these premises are also based on probability. However, the degree
of probability is not well measurable in practice. Thus, it depends on the detective's
subjective conviction, whether to accept a conclusion based on probability as a starting
hypothesis that determines the further direction of the investigation.
Another secret to a detective’s success is intuition. In many cases, success does not
depend on valid arguments, but on what data you use as the premise for these
arguments. The data can come to the detective's knowledge in many ways, such as from
observations, reports (testimonies), and so on. The point is how one evaluates the data
and to which data one attaches relevance. This, in turn, depends on intuition,
experience, and luck, which can no longer be described by logical means.
© All Rights Reserved.
We would like to thank Professor László Blutman for publishing his study.
Sources and comments can be found below the next image.
SOURCES AND NOTES:
* This article was originally published in FORVM Acta Juridica et Politica (Szeged) XI. 2021/1. pp. 5-21.
45 - For such a conclusion, see also BLUTMAN LÁSZLÓ: Bűntény és logika: három tévhit Sherlock Holmes
gondolkodásáról [Crime and Logic: Three Misconceptions about Sherlock Holmes’ Thinking]. Jogelméleti
Szemle 2019/1. pp. 3–21.
46 - The Essential Pierce: Selected Philosophical Writings. Vol. 2. (1893–1913) Indiana University Press.
Bloomington, 1998. p. 205.; see also Encyclopedic Dictionary of Semiotics. Tome 1. de Gruyter. Berlin – New
York, 1994. p. 1.
47 - See especially a 1983 volume edited by Eco and Sebeok; in this high impact publication a series of studies
interpreted Holmes’ thinking in the context of the abduction model, ECO, UMBERTO – SEBEOK, THOMAS A. (eds.):
The Sign of Three. Indiana University Press. Bloomington, 1983. For a similar approach from the recent literature,
see e.g. FOX, MARGALIT: Conan Doyle for the defense. Random House. New York, 2018. p. 79. from the
Hungarian literature e.g. K. HORVÁTH ZSOLT: A barbárokra várva [Waiting for the barbarians]. Korunk 2011/3.
pp. 103–104. or ANGYAL MIKLÓS: Gondolatok a kriminalista bíborszínű dolgozószobájából [Thoughts from the
criminologist's purple study]. Ügyészek Lapja 2015/5. p. 93.
48 - Abduction was also sometimes referred to as retroduction, or simply hypothesis, which sparked controversy over
whether it was the same thought process. Peirce observed that of the three elements of Aristotle’s syllogism (rule,
case, and result), only two are included as logical consequences in the conclusions – the result is in the scheme of
deductive and the rule in the scheme of inductive inference. In the case of abduction, however, the case will be the
logical consequence (conclusion), the end point of the inference, cf. BALÁZS GÉZA: Az abdukció a modern
nyelvtudományban, valamint igazolása Mikszáth Kálmán Új Zrínyiászában [Abduction in modern linguistics and
its proof in Kálmán Mikszáth's New Zrínyiász.] In: BALÁZS GÉZA – H. VARGA GYULA (eds.): Az abdukció
[Abduction]. Líceum Kiadó. Eger, 2008. p. 44.
49 - Sherlock Holmes does not appear in his writings, only the name of Poe's detective (Dupin), cf. Peirce 1998, 550. p.
50 - A conference has been dedicated to abduction in Hungary as well [conference volume: BALÁZS – H. VARGA (eds.)
2008]; a methodological book was also published about it, SÁNTHA KÁLMÁN: Abdukció a kvalitatív kutatásban
[Abduction in qualitative research]. Eötvös Könyvkiadó. Budapest, 2011.
51 - As I see, the 1983 volume of studies on abduction cited above established the new trend. The study of the Sebeok
couple included in the volume was also published in Hungarian in the form of a small book and came to be one of
the most important work in Hungarian holmesology.
52 - CHIASSON, PHYLLIS: Abduction as an aspect of retroduction. The Commens Encyclopaedia, http://www.
commens.org/encyclopedia/article/chiasson-phyllis-abduction-aspect-retroduction (2020.12.28.); there is author
who distinguishes five interpretations, see PAAVOLA, SAMI: Deweyan Approaches to Abduction? In
ZACKARIASSON, ULF (ed.): Action, Belief and Inquiry – Pragmatist Perspectives on Science, Society and Religion.
Nordic Pragmatist Network. Helsinki, 2015. p. 235. For amendments of Pierce’s position, see e.g. BURCH,
ROBERT: Charles Sanders Pierce. Stanford Encyclopedia of Philosophy; source: https://plato.stanford. edu/
53 - In some places Peirce understood it in such a simple form, see PEIRCE 1998, p. 441. Today's philosophical
conceptions of abduction are already sharply different from Peirce's approach, l. DOUVEN, IGOR: Abduction.
Stanford Encyclopedia of Philosophy; source: https://plato.stanford.edu/entries/abduction/ (2020.12.28.)
54 - Vö. BÁNKI ÉVA: A bűn nyelvét megtanulni [To learn the language of sin]. Napkút Kiadó. Budapest, 2014. p. 16.
55 PEIRCE 1998, p. 106 and p. 205.
56 - The state of blank mind, when the detective refrains from forming any idea due to the lack of data, cf. The
Cardboard Box, The Complete Stories, p. 313.
57 - Pl. The Disappearance of Lady Frances Carfax, The Complete Stories, p. 824.
58 - The Adventure of the Blanched Soldier, The Complete Stories, p. 1078.
59 - The Adventure of the Beryl Coronet, The Complete Stories, p. 270.
60 - The Norwood Builder, The Complete Stories, pp. 573–574.
61 - The basis of finding an intuitive explanation is the mass of situation patterns stored in the detective’s prior
knowledge. It is no coincidence that Holmes knew countless specific crimes (and thus many patterns of crime); he
also filed in his file system the crimes of which he became aware, see e.g. A Case of Identity, The Complete
Stories, p. 153. See also K. HORVÁTH 2011, p. 91.
62 - Holmes’ explanation was that the document had been written on a train: the readable parts at stations when the
train was standing and the illegible parts of the writing scribbled as the train passed through railway switches.
Moreover, it may have been a suburban line because there has been a quick succession of switches.
63 - PEIRCE 1998, p. 107.
64 - PEIRCE 1998, p. 231.
65 - DOUVEN 2020. The unsustainability of the formula is the reason why the inference to the best explanation (or
some version of it) is now considered more under abduction, which is contrary to Peirce’s idea. In his view, this is
already within the stage of testing a hypothesis.
66 - In the example above, Sherlock Holmes did not even attempt to explain how a man travelling by train is logically
connected to a partially unreadable writing held in his hand.
67 - PEIRCE 1998, p. 106.
68 - Gehrke clearly thinks in a puzzle model, GEHRKE, CONSTANZE: Schema und Variation in den Sherlock-Holmes-
Stories von Arthur Conan Doyle. Dissertation (2003/2004) Rheinisch-Westfälischen Technischen Hochschule.
Aachen, pp. 174, 187, 281. source: http://publications.rwth-aachen.de/record/59476/files/59476.pdf (2020.12.29.)
Bonfantini and Proni just point out that one simply needs to find a hypothesis that fits all known data, and this is
perceived as a kind of combination puzzle; BONFANTINI, MASSIMO A. – PRONI, GIAMPAOLO: To Guess or Not to
Guess? In ECO – SEBEOK 1983, pp. 127–128. The crime is considered to be a jigsaw puzzle by the famous German
critic Helmut Heißenbüttel, or also by Isidore Ducasse and Roger Caillois; cf. PRILL, ULRICH: Mir ward alles Spiel.
Königshausen & Neumann. Würzburg, 2002. 84. p. and GEHRKE 2003/2004, p. 11. For this approach in the
Hungarian literature, see DECZKI SAROLTA: Rejtélyes irodalom [Mysterious literature]. Új Forrás 2010/7. p. 37.
69 - Cf. Watson’s note: “I clearly perceived that Holmes was weaving it [i.e. the fact that Mr. Smith had been out for a
walk the morning before] into the general scheme which he had formed in his brain.” The Adventure of the Golden
Pince-Nez, The Complete Stories, p. 693.
70 - Cf. BLUTMAN 2019, pp. 141–147.
The Science Of Deduction