FALLACIES OF CONFUSION. 675 



lacy of Confusion (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 

 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 minus can not give minus; for minus multiplied by plus 

 gives minus, and minus multiplied by mifius can not give the same prod- 

 uct as minus multiplied by plus. Now one is obliged to ask, why minus 

 multiplied by minus must give any product at all? and if it does, why its 

 product can not be the same as that of minus multiplied by plus? for this 

 would seem, at the first glance, not more absurd than that minus by minus 

 should give the same as plus by plus, the proposition which Euler prefers 

 to it. The premise requires proof, as much as the conclusion ; nor can it 

 be proved, except by that more comprehensive view of the nature of mul- 

 tiplication, and of algebraic processes in general, which would also supply 

 a far better proof of the mysterious doctrine which Euler is here endeavor- 

 ing 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 instinctive sentiments and perceptions of 

 mankind, and then explain away the numerous instances of divergence 

 from their assumed standard, by representing them as cases in which the 

 perceptions are unhealthy. Some particular mode of conduct or feeling is 

 affirmed to be unnatural; why ? because 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 

 feeling of abhorrence; "ay, buo their feelings were sophisticated and un- 

 healthy." 



One of the most notable specimens of reasoning in a circle is the doc- 

 trine of Hobbes, Rousseau, and others, which rests the obligations by 

 which human beings are bound as members of society, on a supposed so- 

 cial compact. I waive the consideration of the fictitious nature of the com- 

 pact itself ; but when Hobbes, through the whole Leviathan, elaborately 

 deduces the obligation of obeying the sovereign, not from the necessity or 

 utility of doing so, but from a promise supposed to have been made by 

 our ancestors, on renouncing savage life and agreeing to establish political 

 society, it is impossible not to retort by the question. Why are we bound 

 to keep a promise made for us by others ? or why bound to keep a promise 

 at all? No satisfactory ground can be assigned for the obligation, except 

 the mischievous consequences of the absence of faith and mutual confidence 

 among mankind. We ai'e, therefore, brought round to the interests of so- 

 ciety, as the ultimate ground of the obligation of a promise ; and yet those 

 interests are not admitted to be a sufficient justification for the existence 

 of government and law. Without a promise it is thought that we should 

 not be bound to that which is implied in all modes of living in society, 



