Inferring and Explaining

30 InferrIng and exPlaInIng put chalk there when you play billiards, to steady the cue. 3. You never play billiards except with Turston. 4. You told me, four weeks ago, that Turston had an option on some South African property which would expire in a month, and which he desired you to share with him. 5. Your check book is locked in my drawer, and you have not asked for the key. 6. You do not pro- pose to invest your money in this manner. 2 Te beginning of Te Adventure of the Dancing Men begins with a little case study in Sherlock Holmes’s “deductive” method. Holmes’s method, of course, is not deductive in the formal logi- cian’s sense but inductive, or better, abductive. It is an inference to the best explanation. Holmes possesses a fair amount of data. e 1 . Watson had chalk between his left fnger and thumb. e 2 . He uses the chalk when he plays billiards. e 3 . He only plays billiards with Thurston. e 4 . He told Holmes four weeks ago that Thur- ston had an option on some South African property, which would expire in a month. e 5 . Watson’s checkbook is locked in Holmes’s drawer. e 6 . Watson has not asked for the key. Holmes explains all this with the hypothesis that Watson has decided against the investment. Holmes goes on to explicate his reasoning with the metaphor of a chain. You see, my dear Watson . . . it is not really difcult to construct a series of inferences, each dependent on its predecessor and each simple in itself. If, afer doing so, one simply knocks out all the central inferences and presents one’s audience with the starting-point and the conclusion, onemayproducea startling, though possibly a meretricious, efect. Now, it was not really difcult, by an inspection of the groove between your lef forefnger and thumb, to feel sure that you did not propose to invest your small capital in the gold felds. 3 Although I think it is clear that Holmes exag- gerates when he claims that the inferences follow in sequential lockstep, the insight that explanatory reasoning ofen proceeds in steps is important. Here is how I would schematize Holmes’s inference. e 1 . Watson had chalk between his left fnger and thumb. e 2 . He uses the chalk when he plays billiards. e 3 . He only plays billiards with Thurston. t ′ 0 . Watson played billiards with Thurston last night. e 4 . He told Holmes four weeks ago that Thur- ston had an option on some South African property, which would expire in a month. e 5 . Watson’s checkbook is locked in Holmes’s drawer. e 6 . Watson has not asked for the key. t ″ 0 . Watson has decided against the investment. Each of these inferences is to an “alleged” best explanation. t ′ 0 explains the chalk on his hand and is consistent with Holmes’s background knowledge of Watson’s preferences in playing partners. t ″ 0 explains the lack of a request for the key and is consistent with Holmes’s knowl- edge of what Watson told him four weeks ago and the location of the checkbook.