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3. Key words of Holmes's theory of reasoning
There are several key words when Holmes characterizes his own method of reasoning.
Method by elimination, method of exclusion
(Q3) "By the method of exclusion, I had arrived at this result, for no other hypothesis would meet the facts." [A Study in Scarlet, pt. 2, ch. 7]
(Q4) "You will not apply my precept," he said, shaking his head. "How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?" [The Sign of Four, ch. 6]
[Let me give you a simple example of this method. In the beginning part of The Sign of Four, Holmes surprizes Watson by telling him that Watson went to the post-office in order to send a telegram. His reasoning may be put in the following form:
(1) A v B v C (this is already proved from other sources);
(2) -A (from observational evidence);
(3) -B (from observational evidence);
(4) therefore, C (conclusion).
(Let A, B, C mean, respectively, "Watson went to the post-office in order to send a letter"; or "in order to buy stamps or postcards"; or "in order to send a telegram.")
This seems simple and perfectly all right. But Holmes's eliminative method may not be as simple as this, if we want to take into consideration the link between the three premisses and their evidence, which may be probabilistic. Notice that in (Q4), eliminative method is somehow combined with the consideration of probability or improbability.]
Next, it is interesting to notice that Holmes seldom uses the word "induction," when he speaks of his own method. Instead, he prefers the word "hypothesis."
Hypothesis
(Q5) "I have devised seven separate explanations, each of which would cover the facts as far as we know them. But which of these is correct can only be determined by the fresh information which we shall no doubt find waiting for us." [The Adventure of the Copper Beeches]
(Q6) "Where is he, then?"
"I have already said that he must have gone to King's Pyland or to Mapleton. He is not at King's Pyland. Therefore he is at Mapleton. Let us take that as a working hypothesis and see what it leads us to." [Silver Blaze]
So far, even a layman can understand what Holmes wanted to say. But we need good philosophical knowledge in order to understand the following words:
Analytical reasoning, synthetic reasoning (reasoning backward, reasoning forward)
(Q7) "I have already explained to you that what is out of the common is usually a guide rather than a hindrance. In solving a problem of this sort, the grand thing is to be able to reason backward. That is a very useful accomplishment, and a very easy one, but people do not practise it much. In the everyday affairs of life it is more useful to reason forward, and so the other comes to be neglected. There are fifty who can reason synthetically for one who can reason analytically."
"Most people, if you describe a train of events to them, will tell you what the result would be. They can put those events together in their minds, and argue from them that something will come to pass. There are few people, however, who, if told them a result, would be able to evolve from their own inner consciousness what the steps were which led up to that result. This power is what I mean when I talk of reasoning backward, or analytically." [A Study in Scarlet, pt.2, ch.7]
Comments: As you may well know, Cartesian analysis is a procedure like this: given a problem to be solved, we examine the conditions to be fulfilled, and divide them into simpler conditions which are easier to solve (in Descartes's words, "divide each of the difficulties I was examining into as many parts as possible and as is required to solve them best"). We go backward, so to speak, from the given problem to the simpler and solvable constituents. In the preceding quotation, Holmes explains a similar procedure in terms of cause-effect relations; i.e., given a problem consisting of a number of facts (effects), we go backward in search for their unknown causes. (Presumably, Holmes adopted this way of explanation because this was easier for Dr. Watson to understand!)
[By the way, eliminative method and analysis are closely related. We can show this by means of Jevons's idea of logical alphabets. For example, given three propositions A, B, C, we can form logical alphabets in the following way: for each proposition, there are two possibilities, either affirmation or negation; so let us signify the former by a Capital letter, the latter by a lower case letter. And further, let us understand that juxtaposing two or more letters means a logical conjunction. Then, we can express all the possibilities out of these three propositions by the following eight conjunctions, which are Jevons's logical alphabets in this case:
ABC, ABc, AbC, Abc, aBC, aBc, abC, abc.
And these correspond to Descartes's "as many parts as is required to solve them best." The process of reasoning is essentially eliminative in that, given any information, this information eliminates some of the logical alphabets; and what remains after all premisses are represented, that is the conclusion. This process takes place within the framework of Cartesian analysis.]
We finally come to the most important key word:
Balance of probabilities
(Q8) "Ah,that is good luck. I could only say what was the balance of probability. I did not at all expect to be so accurate."
"But it was not mere guesswork?"
"No, no: I never guess. It is a shocking habit---destructive to the logical faculty. What seems strange to you is only so because you do not follow my train of thought or observe the small facts upon which large inferences may depend." [The Sign of Four, ch. 1]
(Q9) "We are coming now rather into the region of guesswork," said Dr. Mortimer.
"Say, rather, into the region where we balance probabilities and choose the most likely. It is the scientific use of the imagination, but we have always some material basis on which to start our speculation." [The Hound of the Baskervilles, ch. 4]
Scientific use of the imagination
See the last quotation above.
We have to notice that Sherlock Holmes is contrasting his method, which essentially depends on the balance of probabilities, with "mere guesswork," which he despises as destructive to the logical faculty. He is saying that his method is logical and scientific, although it might seem uncertain or unstable to a layman, like Watson or Mortimer.
It should be clear by now, from these examinations of key words, that Sherlock Holmes's method of reasoning has a firmer structure than you might have imagined at first sight. Is there any theory of scientific method which captures all or almost all of these features? Let us next see some of the 19th century methodologists.
June 21, 1998; last modified, April 16, 2006. (c) Soshichi Uchii
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