5 o THE SCIENCE OF LOGIC 



case may be) ; therefore the hypothesis is probably true (or cer 

 tainly false, as the case may be).&quot; From this we see that the modus 

 tollens efficaciously disproves, and so eliminates, all hypotheses 

 that are unable to account for the facts under investigation. No 

 single application of the modus ponens, however, can verify the hypo 

 thesis with certitude. Nor, indeed, strictly speaking, could any ac 

 cumulation of them give us certitude about the antecedent, 

 regarding the matter from the point of view of formal inference ; 

 though often, as we shall see, hypotheses are sufficiently verified 

 in this manner (230). We usually try to verify our hypothesis 

 by showing not only that it will account for the facts, but that 

 no other hypothesis will account for them. We may sometimes 

 be able to do this by showing the facts to be such that they 

 necessarily involve the cause supposed in our hypothesis : &quot; If 

 this hypothesis were not true, the facts could not be such and 

 such ; but they are such and such ; therefore, the hypothesis is 

 true.&quot; * It is rarely, however, we can directly show the facts to 

 be such that of their nature they necessarily involve the supposed 

 cause : for the most part we have to be content with showing 

 that they must involve it for the reason that no other conceivable 

 supposition can account for them. That is to say, we verify our 

 hypothesis by eliminating all competing alternatives. Now, this 

 process naturally assumes the form of a mixed disjunctive syl 

 logism in the modus tollendo ponens : 



&quot; The cause of x is either a or b or c or d . . . or z 



J In his admirably clear exposition of Newton s researches on gravitation, Mr. 

 Joseph (Logic, pp. 477-82), illustrating the various stages of the inductive process, 

 says that &quot;the final argument, in which the agreement of the facts with the results 

 of this hypothesis and of no other is shown to require the acceptance of this 

 hypothesis, is inductive&quot; (p. 482). The term &quot;inductive &quot; cannot here be used in 

 a sense opposed to syllogistic, for the argument to which he applies it is a mixed 

 hypothetical syllogism. It is as follows : &quot; Assuming that the continual deflexion 

 of the planets from a rectilinear path is due to an attractive form [force?], their 

 actual motions, if my statement of the law of attraction is true, would be thus and 

 thus ; if it is false, they would be otherwise : but they are thus and thus, and there 

 fore my statement is true&quot; (ibid.). It may be symbolized thus : &quot; If A then C, and 

 if not A then not C ; but C ; therefore A &quot;. The standard syllogism, embodying the 

 axiom applied in this reasoning, and analogous to the standard syllogisms applying 

 the Dictum de omni, etc., in 192, might be expressed thus : &quot; If a supposed cause 

 accounts adequately for any real fact, and is the only cause which can account for 

 it, then that supposed cause is real ; but (by analysis of the facts, through observa 

 tion and experiment) we see that this supposed cause, and it alone, can adequately 

 account tor this real fact ; therefore this supposed cause is real &quot;. The author 

 applies the term &quot; inductive &quot; to reasonings which are not explanatory, which merely 

 convince us that a judgment must be true, without giving us any insight into the 

 reason why it is true. 



