OP ARTS AND SCIENCES : APRIL 9, 1867. 283 



S' for ^' S' and P' for U' P' we obtain formula} of probable in- 

 ference. This reasoning gives no determinate probability to these 

 modes of inference, but it is necessary to consider that, however 

 weak synthetic inference might have been at first, yet if it had 

 the least positive tendency to produce truth, it would continually 

 become stronger, owing to the establishment of more and more 

 secure premises. 



The rules for valid induction and hypothesis deducible from this 

 theory are as follows : — 



1. The explaining syllogism, that is to say, the deductive syllogism 

 one of whose premises is inductively or hypothetically inferred from 

 the other and from its conclusion, must be valid. 



2. The conclusion is not to be held as absolutely true, but only 

 until it can be shown that, in the case of induction, S' was taken from 

 some narrower class than J/, or, in the case of hypothesis, that P' was 

 taken from some higher class than 31. 



3. From the last rule it follows as a corollary that in the case of 

 induction the subject of the premises must be a sum of subjects, and 

 that in the case of hypothesis the predicate of the premises must be a 

 conjunction of predicates. 



4. Also, that this aggregate must be of different objects or qualities 

 and not of mere names. 



0. Also, that the only principle upon which the instanced subjects 

 or predicates can be selected is that of belonging to M.* 



* Positivism, apart from its theory of history and of the relations between the 

 sciences, is distinguished from other doctrines by the manner in which it regards 

 hypotheses. Almost all men think that metaphysical theories are valueless, be- 

 cause metaphysicians differ so much among themselves ; but the positivists give 

 another reason, namely, that these theories violate the sole condition of all legiti- 

 mate hypothesis. This condition is that every good hypothesis must be such as 

 is certainly capable of subsequent verification with the degree of certainty proper 

 to the conclusions of the branch of science to which it belongs. There is, it seems 

 to me, a confusion here between the probability of a hypothesis in itself, and its 

 admissibility into any one of those bodies of doctrine which have received distinct 

 names, or have been admitted into a scheme of the sciences, and which admit only 

 conclusions which have a very high probability indeed. I have here to deal with 

 the rule only so far as it is a general canon of the legitimacy of hypotheses, and not 

 so far as it determines their relevancy to a particular science ; and I shall, therefore, 

 consider only another common statement of it; namely, "that no hypothesis is 

 admissible which is not capable of verification by direct observation." The positivist 

 regards an hypothesis, not as an inference, but as a device for stimulating and 



