FALLACIES OP CONFUSION. 465 



if he means anything else, his conclusion is not 

 proved. This fallacy might also be classed under 

 ambiguous middleterrn ; 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, how- 

 ever small, must at least have an upper and an under 

 surface. Those who used this argument did not see 

 that it assumed the very point in dispute, the impos- 

 sibility of arriving 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 

 seern more obvious than the conclusion, although 

 really identical 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 a priori fallacy or natural 

 prejudice, that whatever cannot be conceived cannot 

 exist. Every Fallacy of Confusion (it is almost unne- 

 cessary to repeat) will, if cleared up, become a fallacy 

 of some other sort ; and it will be found of deductive 

 or ratiocinative 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 great merit, 

 but full, to overflowing, of logical errors in respect 

 to the foundation of the science, contains the follow- 



VOL. II. 2 H 



