284 PROCEEDINGS OF THE AMERICAN ACADEMY 



Hence the formulae are 



Induction. 



S' S" S'", &c. are taken at random as M's, 



S' S" S>", &CC. are P ; 



.'. Any iT/is probably P. 



directing observation. But I have shown above that certain premises will render an 

 hypothesis probable, so that there is such a thing as legitimate hypothetic inference. 

 It may be replied that such conclusions are not hypotheses, but inductions. That the 

 sense in which I have used '"hypothesis" is supported by good usage, I could prove by 

 a hundred authorities. Tlie following is from Kant : " An hypothesis is the holding 

 for true of the judgment of the truth of a reason on account of the sufficiency of its 

 consequents." Mill's definition (Logic, Book III. Ch. XIV. § 4) also nearly coin- 

 cides with mine. Moreover, an hypothesis in every sense is an inference, because it is 

 adopted for some reason, good or bad, and that reason, in being regarded as such, 

 is regarded as lending the hypothesis some plausibility. The arguments which I 

 term hypothetic are certainly not inductions, for induction is reasoning from par- 

 ticulars to generals, and this does not take place in these cases. The positivist 

 canon for hypotheses is neither sufficient nor necessary. If it is granted that hy- 

 potheses are inferred, it will hardly be questioned that the observed facts must 

 follow apodictically from the hypothesis without the aid of subsidiary hypotheses, 

 and that the characters of that which is predicated in the hypothesis, and from which 

 the inference is drawn, must be taken as they occur, and not be picked out in order 

 to make a plausible argument. That the maxim of the positivists is superfluous 

 or worse, is shown, first, by the fact that it is not implied in the proof that hypothetic 

 inference is valid ; and next, by the absurdities to which it gives rise when strictly- 

 applied to history, which is entirely hypothetical, and is absolutely incapable of 

 Tcrifieation by direct observation. To this last argument I know of but two 

 answers : first, that this pushes the rule further than was intended, it being con- 

 sidered that history has already been so verified ; and second, that the positivist 

 does not pretend to know the world as it absolutely exists, but only the world which 

 appears to him. To the first answer, the rejoinder is that a rule must be pushed 

 to its logical consequences in all cases, until it can be shown that some of these cases 

 differ in some material respect from the others. To the second answer, the re- 

 joinder is double : first, that I mean no more by " is " than the positivist by 

 "appears" in the sense in which he uses it in saying that only what "appears " is 

 known, so that the answer is irrelevant ; second, that positivists, like the rest of 

 the world, reject historic testimony sometimes, and in doing so distinguish hy- 

 pothetically between what is and what in some other sense appears, and yet have 

 no means of verifying the distinction by direct observation. 



Another error in reference to hypotliesis is, that the antecedent probability of what 

 is testified to cannot affect the probability of the testimony of a good witness. This 

 is as much as to say that probable arguments can neither support nor weaken one 

 another. Mr. Venn goes so far as to maintain the impossibility of a conflict of 

 probabilities. The difficulty is instantly removed by admitting indeterminate 

 probabiUties. 



