514 FALLACIES. 



It is assumed by all the disputants in the Ve Finibus as the founda- 

 tion of the inquiry into the sumvium bonum, that " sapiens semper 

 beatus est." The idea that wisdom could be consistent with unhap- 

 piness, was always rejected as inadmissible : the reason assigned by 

 one of the interlocutors, near the beginning of the third book, being, 

 that if the wise could be unhappy, there was not much use in jiursuing 

 wisdom. But by unhappiness they did not mean pain or suffering ; to 

 that, it was granted that the wisest person was liable in common with 

 others : he was happy, because in possessing wisdom he had the most 

 valuable of possessions, the most to be sought and prized of all things, 

 and to possess the most valuable thing was to be the most happy. By 

 laying it down, therefore, at the commencement of the inquiry, that the 

 sage must be happy, the disputed question respecting the summum 

 honum was in fact begged ; with the further assumption, that pain and 

 suffering, so far as they can coexist with wisdom, are not unhappiness, 

 and are no evil. 



The following are additional instances of Petitio Principii, under 

 more or less of disguise. 



Plato, in the Sophistes, attempts to prove that things may exist which 

 are incorporeal, by the argument that justice and wisdom are incorpo- 

 real, and justice and wisdom must be something. Here, if by some- 

 thing be meant, as Plato did in fact mean, a thing capable of existing 

 in and by itself, and not as. a quality of some other thing, he begs the 

 question in asserting that justice and wisdom must be something : if 

 he means anything else, his conclusion is not proved. This fallacy 

 might also be classed under ambiguous middleterm ; something, in the 

 one premiss, meaning some substance, in the other, merely some object 

 of thought, whether substance or attribute. 



It was formerly an argument employed in proof of what is now no 

 longer a popular doctrine, the infinite divisibility of matter, that every 

 portion of matter, however small, must at least have an upper and an 

 under sm-face. Those who used this argument did not see that it 

 assumed the very point in dispute, the impossibility of aniving at a 

 minimum of thickness; for if there be a minimum, its upper and under 

 surface will of course be one : it will be itself a surface and no more. 

 The argument owes its very considerable plausibility to this, that the 

 premiss does actually seem more obvious than the conclusion, although 

 really identica,! with it. As expressed in the premiss, the proposition 

 appeals directly and in concrete language to the incapacity of the 

 human imagination for conceiving a minimum. Viewed in this light, 

 it becomes a case of the u j^^iori fallacy or natural prejudice, that 

 whatever cannot be conceived cannot exist. Every Fallacy of Confu- 

 sion (it is almost unnecessary to repeat) will, if cleared up, become a 

 fallacy of some other sort ; and it will be found of deductive or ratio- 

 cinative fallacies generally, that when they mislead there is mostly, as 

 in this case, a latent fallacy of some other description lurking under 

 them, by virtue of which chiefly it is that the verbal juggle which is 

 the outside or body of this kind of fallacy, passes undetected. 



Euler's Algebra, a book otherwise of gi-eat merit, but full, to over- 

 flowing, of logical errors in respect to the foundation of the science, 

 contains the follovdng argument to prove that minus multiplied by minus 

 ^weaplus, a doctrine the opprobrium of all mathematicians who are not 

 philosophers, and which Euler had not a glimpse of the true method of 



