from Memoir 19, Draft E: On Arguments

The nature of argument fully examined in all its aspects. All arguments are either deductions, inductions, abductions, or mixed arguments. My earliest statements were correct in this respect. But in my paper in the Johns Hopkins _Studies in Logic_, overemphasizing formalities, I failed to distinguish between abduction and a previously overlooked or little noticed variety of induction which may be called "abductive induction"; in consequence of which, that paper, although correct as far as it goes, and although fully covering the subject of which it professed to treat, entirely overlooked an indispensable mode of inference, abduction, I myself having previously described the inference correctly. Deduction is necessary inference; but if it is applied to probability, then, while remaining in itself necessary, it concludes a probability. That gives the doctrine of chances. Induction is a totally different sort of inquiry, proceeding, by means of experiment, to obtain an answer to a previously propounded question. It has two species: the extensive, where the question is how much, and the comprehensive, or abductive, where the question is to be answered by yes or no (or else is merely susceptible of a vague answer). Abduction is distinguished from abductive induction in not being, properly speaking, experimental, that is, it makes its observations without reference to any previously propounded question, but, on the contrary, itself starts a question, or problematically propounded hypothesis, to explain a surprising observation. Since I barely escaped error on this matter, I will in this present note illustrate the difference between abduction, abductive induction, and probable deduction.

Suppose, then, that, being seated in a street car, I remark a man opposite to me whose appearance and behavior unite characters which I am surprised to find together in the same person. I ask myself, How can this be? Suppose I find this problematic reply: Perhaps he is an ex-priest. He is the very image of such a person; he presents an icon of an ex-priest. Here is an iconic argument, or abduction of it. Secondly, it now occurs to me that if he is an ex-priest, he should be tonsured; and in order to test this, I say something to him calculated to make him take off his hat. He does so, and I find that he is indeed tonsured. Here at last is an indication that my theory is correct. I can now say that he is presumably an ex-priest, although it would be inaccurate to say that there is any definite probability that he is so, since I do not know how often I might find a man tonsured who was not an ex-priest, though evidently far oftener than he would be one. The supposition is, however, now supported by an inductive induction, a weak form of symptomatic or indexical argument. It stands on a widely different basis from that on which it stood before my little experiment. Before, it rested on the flimsy support of similarity, or agreement in "flavor." Now, facts have been constrained to yield confirmation to it by bearing out a prediction based upon it. Belief in the theory rests now on factual reaction to the theory. Thirdly, while the man's hat is off, I read in the crown of it a name that has been pasted into it. I have no doubt whatever that it is the man's name. I do not go into the question of how I come to be so confident of that. As long as I have no doubt, it matters not how doubt came to be destroyed. I get out of the car, and go to call upon the chancellor of the diocese; and that he will tell me the truth I equally believe implicitly. I ask the chancellor, "Who is Michael Wo-Ling Ptah-Hotep Jerolomon?" (Pardon my nonsense.) He replies, "He is an ex-priest." "Is he the only man of that name?" "No, there are, or may be, fifteen. Fourteen of them reside in this town and are ex-priests. The fifteenth went, twenty years ago, to High Thibet, and has never been heard of since." It thus appears that the name read in the hat, though having no striking "flavor" of ex-priest about it, nor any such causal connection with the man's being an ex-priest as was the tonsure, yet in consequence of this knowledge becomes a symbol of the man's being an ex-priest; for a symbol is a sign which becomes significant simply by virtue of the fact that it will be so interpreted. So, it might conceivably have been an accident that the man was tonsured, but now that the name Michael Wu-Ling Ptah-Hotep Jerolomon signifies for me a probability of more than fourteen to one of being an ex-priest, I must think that the probability on that ground alone is over fourteen to one that he is an ex-priest. There is no escape from that. It is what I consider myself certain of. It is only a probability. Yet now, fourthly, combining the arguments into one mixed argument, and considering, what is logically relevant, that I have no serious stake in the question, I am satisfied to consider the mixed argument as proof, and to dismiss the question until it may acquire more importance. (Although the illustration is silly, it all the better covers the case.)

Mixed arguments are of three kinds. The first consists of those which tend to establish the same conclusion or contradictory conclusions, or to establish two premisses from which, taken together, a conclusion can be inferred; second, arguments consisting of two parts of which one taken by itself lends no support to the conclusion of the other, but tends to establish a fact which makes the other a stronger or weaker argument. For example, I see two men wearing both the same badge going to the polls together talking with great delight over the effect of their vote; and I learn that one of them voted the Democratic ticket. I infer that the other did so, too. But subsequently, I learn that that badge is the symbol of membership of a society which decided that its members should go to the polls in pairs and that one of each pair should vote Democratic and the other Republican. I consequently reverse my previous inference. Under this head come inductions supported by uniformities, of which there are four simple types. The third kind of mixed arguments are those in which the same premisses form two different kinds of arguments. Important subdivisions of induction and deduction will be defined and illustrated.

Courtesy Peirce Telecommunity Project (Texas Tech University)