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49 Sherlock’s Reasoning Toolbox Massimo Pigliucci “It is simplicity itself. . . . My eyes tell me that on the inside of your left shoe, just where the firelight strikes it, the leather is scored by six almost parallel cuts. Obviously they have been caused by someone who has very carelessly scraped round the edges of the sole in order to remove crusted mud from it. Hence, you see, my double deduction that you had been out in vile weather, and that you had a particularly malignant boot-slitting specimen of the London slavey.” So says Sherlock Holmes to a befuddled Dr. Watson in “A Scandal in Bohemia”1 while explaining how he deduced that his old friend had gotten wet and that his servant had been careless—except that this was not an instance of deduction, in the philosophical sense of the term, but rather a form of induction. Understanding the difference between these two basic types of reasoning is fundamental to appreciate how Holmes operates , and it will lead us through a brief tour of logic, science, and the art of fine reasoning. Conan Doyle tells us that Holmes doesn’t know anything about philosophy , which perhaps accounts for why he refers to his logical method as deduction, while it is in fact a complex and highly effective mixture of different kinds of reasoning. Of course, Holmes does not always succeed in his endeavors, as for instance in the case of the scandal in the (now defunct kingdom of) Bohemia mentioned above. In that adventure, he is outfoxed by a woman from New Jersey, Irene Adler, whom he will subsequently always refer to as “the woman.”2 How to Guarantee Truth Let us start our tour with deduction, the foundation of logic and mathematics . Deduction is what philosophers call a truth-guaranteeing type of rea- 50 Massimo Pigliucci soning, meaning that if the premises of a deductive argument are correct, then the conclusion must inescapably be true. Of course, the trick is in that all-important “if” clause. It was Aristotle (384–322 bce) who first explored deductive reasoning, particularly as exemplified in the form of syllogism, arguably the most famous of which is a variant on the following: Premise 1: All men are mortal. Premise 2: Sherlock Holmes is a man. Conclusion: Sherlock Holmes is mortal. The above can be read as follows: If P1 is true, and if P2 is true, then C must necessarily be true—nice and elegant, exactly the sort of reasoning that would appeal to Holmes. In fact, the famous detective often displays a preference for simple and elegant reasoning, particularly if it leads to inescapable conclusions. In several stories, he tells Watson something along the lines of, “How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?”3 In “The Priory School,” he says that “it is impossible as I state it, and therefore I must in some respect have stated it wrong.”4 In both cases, the implication seems to be that a strict logical analysis of the facts leads to one and only one inescapable conclusion—a guarantee of truth. The dream of developing a system of thought on the basis of which one can deduce facts about the world with absolute certainty goes back to Aristotle ’s mentor, Plato (428/427–348/347 bce), and resulted in a long tradition of philosophical thought appropriately known as rationalism. That school arguably had for its last strong champion René Descartes (1596–1650). Descartes was a bold philosopher, most famous for his (ultimately failed) thought experiment known as radical doubt. He acknowledged that both our senses and our faculty of reasoning can be deceived, which means that we can never be sure of anything we say about the world. However, Descartes argued, we can be absolutely sure of at least one thing: I think, therefore I exist (the famous maxim cogito, ergo sum). There is absolutely no possibility of my being mistaken about this very simple but crucial fact. The idea is that even if I am systemically deceived, I have to exist in order to be deceived, so my very thinking that I may well be deceived is incontrovertible evidence of my existence—as a thinking being. I can’t run this same thought experiment about you, nor you me, but you can run it for yourself. Having found this solid anchor, he then tried to logically deduce other facts...

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