Update 11.11.2023: edited some places for clarity.
With all the content in this blog, it is somewhat surprising – even for myself – that I am yet to make an attempt to define a deductive story. After many thoughts, tinkering, and false takes, I think I got one that satisfies me:
A deductive story is a narrative about mysterious events that are, within the plotline, given a correct solution by one or more of the characters using logical means.
Now, let me break it down.
“within the plotline”: I exclude the stories where the solution is only given by the omniscient author or the confessing criminal. Just claiming it could have been solved using logical means is not enough, a sample of particular possible inference within the plotline (that is, an inference that could have been done by a participant, not privy to the totality of data available to the omniscient author) should be present.
“correct”: I exclude stories where the sleuth fails into giving a wholly coherent solution which, by writ of the omniscient author or confession of the criminal, turns out to be wrong; meanwhile, the correct solution had not been reached by anyone using logical means.
“by one or more of the characters”: I don’t demand a single sleuth and also do not force the truth to be revealed to all the characters in the solution, merely that some characters should establish it.
“in a logical way”: that is, no unexplained intuitions allowed. It is not enough to provide a plausible solution to the problem, but a specific way should also be demonstrated to reach it from the facts. Strictly saying, I would prefer the solution ot be also foolproof in the sense of no other solutions being imaginable that fit the facts, but probably this is not compulsory.
As obvious from the abovementioned, I firmly reject the claim to consider And Then There Were None a deductive story. It is, for me, a story, a thriller, a psychological suspense, if you wish, which uses the methodology developed in deductive stories to craft a plot that is nothing of the kind. The reason is in the absence of the “applying logic to solution” part, which is half, and actually the more important half, of deductivity as a concept, the half actually mentioned actually in the title of “deductive story”.
The Detection Collection 
Again I insist, deductive is entirely the wrong term. Even if one could deductively eliminate all other possible solutions (and incidentally, in my nearly 50 years of delving in detective fiction, focusing primarily on puzzle plot writers such as Carr, Christie, Brand, Queen, and Berkeley, I’ve yet to come across a work that has exhaustively done so), the notion of this genre as being fundamentally deductive would deem as inessential most of the clueing that is most frequently cited as being the most compelling and memorable, such as behavioral discrepancies and all indication of motive, because such aspects can never be deductively proven. The choice of murder weapon in THE TRAGEDY OF Y, Louise Bourget’s use of the conditional tense in DEATH ON THE NILE, the reason Isabel Drew is dropped from the balcony in THE DEATH OF JEZEBEL— none of these mean anything if we are to say that the genre is fundamentally deductive in nature. The genre is RETRODUCTIVE: a solution is proposed to account for an observed set of facts or circumstances. Retroduction suggests universal order and causal relationships between incidents, deduction does not.
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The reason I consider the distinction I make above important is that it clears up what we might call the “And Then There Were None problem.” For, by categorizing And Then There Were None as a “thriller” in order to distinguish it from what you refer to as “deductive” stories, you are lumping it together with a wide range of works, from psychological suspense stories to Hitchcockian chases, with which it bears relatively superficial similarities, while overlooking the far more essential kinship it shares with what you call deductive stories. Sure, And Then There Were None thrills, but so do many stories that have solutions arrived at via complex logical explanations.
Fundamentally, however, just like The Problem of the Green Capsule (which I’m offering as an example of the type of work to which I think you’re referring— please correct me if I’m mistaken), And Then There Were None is a puzzle plot, with a solution designed to both surprise (due to devices of deception) and yet seem retrospectively inevitable (due to clueing). (And Then There Were None is a particularly deceptive work in regard to its clueing, as the true clues that provide a sense of inevitability in the solution are never overtly explicated, and are different from the ones that the culprit offers as such in his confession). Another example would be a story like Chesterton’s The Sign of the Broken Sword— a tale that offers a puzzle and significant clueing (indeed, richer clueing than the Christie novel it likely inspired), but no reasoning in it that in any way resembles deduction. The solution makes sense of the odd circumstances provided in the puzzle, but Father Brown does no arrive at that solution by eliminating all (or even any) other possibilities.
Admittedly, there is one major distinction between the likes of And Then There Were None and The Problem of the Green Capsule, which is that only in the latter is the solution arrived at via an explicated process of ratiocination. But that doesn’t demolish their primary common core, it merely makes stories of the Green Capsule type a subset of the larger category of puzzle plot stories. The defining feature of this broader category is the dynamic between a puzzle and a solution that accounts for all elements introduced in it, regardless of the means of arrival at that solution. That dynamic, as present in And Then There Were None as it is in The Problem of the Green Capsule is retroductive in nature. And the more specific quality found in such stories as The Problem Green Capsule— the employment of explicated reasoning to arrive at that solution— is probably best described not as deduction, but with a term such as ratiocination, as not nearly all reasoning in such processes is deductive. The key point is that the fundamental essence of the genre is the relationship between puzzle and solution, not the means by which the solution is arrived at. Recognizing this is not only more inclusive, but provides a stronger understanding of the nature of the genre and its appeal… and explains why people reading such a work as And Then There Were None experience a pleasure similar to that found reading Green Capsule— a pleasure they would not experience reading a take of pure suspense.
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As for the wrongness of the tag “deductive”, I choose to strongly disagree. It is normal, and expected, for specific terms to possess different meanings (sometimes simply for some random historical reasons) to express different notions in different branches of knowledge – and surely literature theory is not the same branch of knowledge as philosophical logic! Demanding not to use the tag “deductive” would presuppose that “deductive” has one, primary meaning, that is, the one from philosophy, and all the rest are derived from it, but this is simply not the case and not how the language (especially scientific language) works.
For example, if we consider the closely related term “induction”, in physics it refers to the appearance of electricity under the influence of a magnetic field, which would arguably have not connection to the “philosophical” notion; meanwhile, in ordinary mathematics, it refers to a property of well ordered sets, which can be argued to be akin to the “philosophical” notion but it wholly separate. Even “deduction” occasionally means simply subtraction of one number from the other, and this is mathematics. The Middle English word *deducen* meant nothing more specific than “demonstrate, prove, show”, and the Latin *deducere* has the basic connotation of “to lead away”, nothing more.
It so happened, that, specifically in crime fiction, the term “deduction” happened to develop the meaning “application of logical inference”, and this obviously happen by the accident of Doyle. Nothing can be achieved by trying to replace a well-familiar term, especially as the natural logical thinking used by sleuths is arguably quite far from the formal logical systems.
And this luggage of recognizability is actually the key: by picking “deductive fiction”, I introduce a term that has the property of being immediately understood, without any preparation. Having such a term is an immense boon. You may dislike the term, but you also instantaneously understand what kind of fiction I refer to. Specifically, a kind of crime fiction (obvious by association with the hoary “detective fiction” term), namely, the one focused on “deductions”, or the thing that is commonly called “deductions” in all of the crime fiction, the thing that Sherlock Holmes did. As long as I say “deductive fiction”, the correct connotations form. This is, by the way, experimentally checked by me starting to use the term without warning in talks to people having only a general idea how mysteries are made.
Demanding a more “correct” version could only make the terminology less welcoming. I would personally prefer “inferential fiction” as surely no-one would ever doubt that whatever happens in these works is “doing inference”; but would you purchase a book promoted in a bookshop as “masterpiece of inferential literature”? I’d run away as fast as I could! Meanwhile, you could put “deductive fiction” on the cover right now and be sure it would be correctly understood. In fact, it was occasionally used for over a hundred years now.
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As for the substantive content, I can easily imagine three (light spoilers) type of “borderline deductive fiction” which I strongly feel not to be within the approach:
1. “The ATTWN way”, the problem is being solved perfunctorily and no solution is reached, but the author or the criminal reveals the answer which happens to be logically reachable by the reader;
2. “The Trent way”, the sleuth gives a plausible solution, it happens to be wrong, the correct answer is reached without using logic, including, but not necessarily, by author or criminal,
3. “The Boileau-Narcejac way”, the characters do not bother to solve anything, but the solution is revealed by the author with the explanations of the clues that would allow the characters, if they cared or were logically inclined, to solve it.
My definition filters only the kind of works dedicated to showcasing a series of inferences that can be done by a participant of the plot, without having access to all the data the author or the criminal have and thus choose to show to the reader; in other words, the works dedicated to the everyday, non-meta logical capabilities of the brain.
I concur that there is some interest in charting a somewhat wider net as well, “the works that bring pleasure in a way akin to pure deductive fiction”, which would clearly include the points 1-3 above – but that would not deny that in works with such an approach the principal part is done differently, based on a different ethos, if you wish. ATTWN would be impossible without the luggage of developed deductive fiction – but so would be the psychological suspense, and arguably even the pure hard-boiled, and there is no need to include them as somewhat close, unless they specifically honour the deductive approach.
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I do recognize the ambiguity of language, and also the practical advantage of using familiar terms. And my objection is perhaps largely based on my misunderstanding of the intended use of the term; as a marketing term, “deductive” is indeed a far more useful term than “retroductive,” “abductive,” or “inferential.” I had assumed the discussion was regarding terminology in use for academic (if not scholarly) discussion of the genre. And for the latter, I think we should insist on terminology that emphasizes the common, fundamental essence and appeal of the genre— which I’m convinced is the dynamic between puzzle and solution. That, I believe is the primary distinction between our viewpoints. You refer to “the works that bring pleasure in a way akin to pure deductive fiction,” but I’m convinced that that pleasure IS the root of the genre, and that what you call “pure deductive fiction” is merely one of its subsets— one of the ways by which that pleasure is arrived at. This goes back to the true roots of the genre, which can be found in Greek tragedy, and are so presciently explicated in Aristotle’s poetics. It didn’t start with detection— it started with puzzle. And puzzle, back to Aristotle’s time, provided “sudden retrospective illumination,” but only sometimes included a deductive path to that solution.
Clueing is indeed essential— it provides the link between puzzle and solution— but the process by which solution is arrived at is of secondary importance, a matter of subgenres. And if we require a term that refers more specifically to the logical process by which a detective figure arrives at the solution, I feel it should be an accurate term that references all of that subgenre. We know that publishers can— and will— continue to sell closed-circle stories as “locked room mysteries,” but that’s no reason we should do so. I feel that the same applies here.
I grant that “deduction” is used casually in conversation as a substitute for “induction,” “abduction,” and “retroduction,” much as “inference” is employed to speak of “implication,” and vice versa:
“From the pants on the floor and the smell of cigars, I deduced you were home.”
But here we are speaking of its use in reference to a genre that emphasizes reason, and most definitions of “deduction” that reference it in that regard indeed have their origin in strict logical deduction. As vague and inconsistent as Sherlock Holmes’s methods actually are, his claim is one of pure deduction:
“Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.”
(Even this, of course, is faulty except in a purely theoretical sense. In practical application, once you have eliminated the impossible, whatever remains consists of a set that INCLUDES the truth).
The root “deducere” does indeed mean “to lead away from,” but is in unfortunate term in that it doesn’t convey to the unfamiliar listener or reader what is being led away from (much as the gradual abbreviation of the term “pianoforte” to “piano” obscures the primary function of the term— that this instrument, unlike others, can play both loud AND soft). In this case, “deduce” meant to lead away from the general (and to the specific), just as induction mean to lead toward the general from the specific. Obviously, the root term here isn’t very useful by itself, but the point is that it was intended to reference strict logical deduction, as opposed to induction.
Again, I find the example of the Father Brown stories extremely illustrative. The solutions of the best Father Brown stories satisfy because they both surprise and “make sense” of the salient incidents and discrepancies that had been earlier related. They are clearly clue-based stories. And yet, Father Brown arrives at the solution via a retroductive or abductive leap rather than through any kind of deduction. He neither eliminates the impossible, proves, nor leads away from any other general possibilities— he merely offers a solution that offers the “best” causal relationship between the related incidents. But is this really any different than Poirot concluding that Louise Bourget was blackmailing the culprit because she employed the conditional tense? There are certainly other possible reasons why she was speaking that way (she was pondering hypothetical possibilities to herself out loud, she was practicing a more sophisticated English tense that she had just recently mastered, etc…), but Poirot’s explanation fits with the rest of the clues— retroduction. Are we to consider such clues inferior simply because they do not eliminate the impossible?
Finally, let’s take And Then There Were None. Quite admittedly, no detective figure arrives at the correct solution via deduction or any other form of reasoning (though that’s not to say the story is bereft of deduction. Maine and Legge conduct a rather thorough process of eliminating possibilities— it’s just that no truth, however improbable, seems to remain). But the key here is that the reader’s primary interest throughout the story is “whodunit?” up to the point where Legge and Maine demonstrate that apparently no one could have, at which point it temporarily becomes an impossible crime story (“how?”). And the solution subsequently offered satisfies because it surprises (due to the culprit’s ingenious alibi) and yet also seems retrospectively inevitable (due to clues that are never overtly stated— that the requirement of a culprit who has the financial wherewithal to orchestrate this elaborate crime scheme, has a very patent interest in law and justice, and has reached an age and state in life where interest in a such a wild scheme might believably outweigh concerns about his future).
Those clues— even if never overtly explicated— provide the sense of “sudden retrospective illumination” that one won’t find in the likes of Hitchcock’s “Shadow of a Doubt” or Buchan’s “The 39 Steps,” or Fleming’s “You Only Live Twice”—thrillers— but will find in Brand’s “Death of Jezebel,” Queen’s “Cat of Many Tails,” or Carr’s “Till Death Do Us Part” (perhaps his “Crooked Hinge” is an even better example as, just as in And Then There Were None, though there is a “deductive” investigation, the solution is only arrived at via culprit confession [though admittedly Fell was much closer to the truth than Maine and Legge were]).
What I’m asking is, does it really makes any sense to lump And Then There Were None with the thrillers of Hitchcock, Buchan, Fleming, etc… rather than with Carr, Brand, Queen, and the rest of Christie? I’ll grant the differences, but ATTWN is fundamentally a whodunit—a puzzle plot— that provides “sudden retrospective illumination” and THAT, I maintain, is the core. There is admittedly an important subset of the puzzle plot story that has the solution arrived at via the detective’s investigation (sometimes, though not always, employing deduction), but— outside of selling a book— why should we call it by an inaccurate and misleading term?
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