FALLACIES OF CONFUSION. 



541 



something : if he means anything else, 

 his conclusion is not proved. This 

 fallacy might also be classed under 

 ambiguous middle term : something, 

 in the one premise, meaning some 

 substance, in the other merely some 

 object of thought, whether substance 

 or attribute. 



It was formerly an argiiment em- 

 ployed in proof of what is now no 

 longer a popular doctrine, the infinite 

 divisibility of matter, that every por- 

 tion of matter, however small, must at 

 least have an upper and an under sur- 

 face. Those who used this argument 

 did not see that it assumed the very 

 point in dispute, the impossibility 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 premise does actually seem more 

 obvious than the conclusion, though 

 really identical with it. As expressed 

 in the premise, the proposition appeals 

 directly and in concrete language to 

 the incapacity of the human imagi- 

 nation for conceiving a minimum. 

 Viewed in this light, it becomes a 

 case of the d priori fallacy or natural 

 prejudice, that whatever cannot be 

 conceived cannot exist. Every Fal- 

 lacy of Confusion (it is almost un- 

 necessary 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 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 overflow- 

 ing of logical errors in respect to the 

 foundation of the science, contains 

 the following argument to prove that 

 minus multiplied by minus gives plus, 

 a. doctrine the opprobrium of all mere 

 mathematicians, and which Euler had 



not a glimpse of the true method of 

 proving. He says minus multiplied 

 by minvs cannot give minus ; for 

 minus multiplied hy plus gives mivns, 

 and minus nmltiplied by minus can- 

 not give the same product as minus 

 multiplied by plus. Now one is ob- 

 liged to ask why minus multiplied 

 by minus must give any product at 

 all ? and if it does, why its product 

 cannot be the same as that of minus 

 multiplied by plus ; for this would 

 seem, at the first glance, not more ab- 

 surd than that minus by minus should 

 give the same as jlus by plus, the 

 proposition which Euler prefers to it. 

 The premise requires proof as much as 

 the conclusion ; nor can it be proved ex- 

 cept by that more comprehensive view 

 of the nature of multiplication and 

 of algebraic processes in general which 

 would also supply a far better proof 

 of the mysterious doctrine which Euler 

 is here endeavouring to demonstrate. 



A striking instance of reasoning in 

 a circle is that of some ethical writers, 

 who first take for their standard of 

 moral truth what, being the general, 

 they deem to be the natural or in- 

 stinctive sentiments and perceptions 

 of mankind, and then explain away 

 the numerous instances of divergence 

 from their assumed standard, by re- 

 presenting them as Teases in which the 

 perceptions are unhealthy. Some par- 

 ticular mode of conduct or feeling is 

 affirmed to be unnatural ; why ? be- 

 cause it is abhorrent to the universal 

 and natural sentiments of mankind. 

 Finding no such sentiment in your- 

 self, you question the fact ; and the 

 answer is, (if your antagonist is polite,) 

 that you are an exception, a peculiar 

 case. But neither (say you) do I find 

 in the people of some other country, 

 or of some former age, any such feel- 

 ing of abhorrence : " Ay, but their 

 feelings were sophisticated and un- 

 healthy." 



One of the most notable specimens 

 of reasoning in a circle is the doctrine 

 of Hobbes, Rousseau, and others, 

 which rests the obligations by which 

 human beings are bound as members 



