296 THE SCIENCE OF LOGIC 



formal validity of the syllogism as a process of reasoning : and 

 it is a characteristic not of the syllogism alone, but of all valid 

 forms of cogent logical inference, whether mediate or immediate. 

 It is expressed by the conjunction &quot; Therefore&quot; \_&quot; Ergo&quot;\ which 

 introduces the conclusion, and the function of which is to express 

 that if the premisses are true, and on this assumption, the conclu 

 sion MUST be true. The nature of the syllogism as a process of 

 formally correct reasoning, i.e. a process every step of which is 

 consistent with every other, and with the assumed starting point, 

 consists wholly and entirely in the accuracy of the hypothetical 

 assertion made by the &quot; Therefore &quot; the assertion, namely, that 

 if the premisses are true the conclusion must be true : e.g. that 

 if what develops the mind is educational, and logic develops the 

 mind, then logic is educational (138). 



This hypothetical guarantee that if the premisses or antecedent be true 

 the conclusion or consequent must be true is the only guarantee of truth 

 involved in the formal correctness of the syllogism. Representing premisses 

 and conclusion by A, B, and C, respectively, we may express the formal force of 

 the syllogism by the hypothetical &quot; If A is true and B is true, then C is true &quot;. 

 And, just as we cannot derive from this the inverse &quot; // A or B or both be 

 false C must be false,&quot; but only the worthless inverse that &quot; If A or B or 

 both be false C may be true or may be false &quot; (140) ; so, also, the nature of the 

 syllogism does not authorize us to infer that if one or both premisses be 

 false the conclusion will be false : J it may be false or it may be true. 

 Hence the axiom : Ex f also sequitur quodlibet. For example, from the two 

 false premisses: &quot;All lions are herbivorous; all cows are lions&quot;; we 

 validly draw the true conclusion, &quot; Therefore, all cows are herbivorous &quot;. 

 Similarly, from the premisses, &quot; All good angels are happy ; some men are 

 good angels &quot; a false premiss, we validly draw the true conclusion, 

 &quot; Therefore, some men are happy &quot;. 



These syllogisms are formally valid, because the formal assertion in each, 

 that the premisses, if true, would be a sufficient ground for the truth of the 

 conclusion is itself a true statement. But the syllogism, considered in its 

 formal aspect, does not say whether the premisses are de facto true, nor that 

 they form the only possible ground for the conclusion, nor that this could not 

 be true on other grounds, nor whether it is de facto true at all, but only that if 

 the given premisses be true they form a sufficient ground for inferring the 

 truth of the conclusion. 



It is possible, then, to reach a true conclusion by reasoning validly from 

 false premisses. In assenting to the latter the mind is, of course, assenting 

 to a false judgment or judgments ; but nevertheless, since the reasoning is 



1 We could of course infer this, if the premisses of the syllogism were assumed 

 to give us the only possible ground of the conclusion ; so that the syllogism could be 

 resolved into a reciprocal hypothetical (135). And so of the other inferences in the 

 text. But no such assumption can be made for the syllogism as a form of inference. 



