*g6 THE SCIENCE OF LOGIC 



this or that special form of reasoning is based. In so far as such initial 

 conceptions and the reasoning processes dependent on them are, of them 

 selves and apart from their particular subject-matter, liable to be misappre 

 hended or misapplied, they call for notice in a general treatment of logic. If, 

 for instance, I argue that because &quot; a is half of d, and c is half of 6, therefore 

 c is half of a&quot; it is, no doubt, &quot; only a perception of the nature of quantity that 

 reveals . . . the invalidity of the . . . argument &quot; j 1 but this does not remove 

 the fallacy from the jurisdiction of logic, for it is a function of logic to determine 

 what is, and what is not, an axiom or self-evident truth, whatever be the subject- 

 matter in question. The assumption that &quot; things which bear the same quan 

 titative relation to the same thing bear this same relation to one another,&quot; is a 

 misconception of the truth that such things &quot; bear a relation of equality to one 

 another &quot;. It is as much the duty of logic to expose this &quot; undue assumption 

 of axioms &quot; as, for instance, to expose the fallacy of arguing that &quot; because all 

 the angles of a triangle are equal to two right angles, and A B C is an angle 

 of a triangle, therefore it is equal to two right angles &quot; a fallacy which may 

 similarly be resolved into the misconception of an axiom, -viz. the Dictum de 

 omni. 



271. ERROR AND FALLACY. The forms or types of mis 

 leading thought-processes examined in logic are usually compre 

 hended under the general title of Fallacies, But this term has 

 considerable elasticity of meaning : it has been used in all shades 

 of meaning, from the widest sense of &quot; any erroneous judgment or 

 belief,&quot; to the narrowest sense of &quot; the violation of some formal 

 rule of inference &quot;. 



The former usage is too wide. It is not the false judgment or 

 belief itself we should call a fallacy, but rather the causes or 

 sources to which the presence of that error in the mind is due. 

 That something or other, in the origin or progress of the thought- 

 process, which deceived the mind into assenting to a false judg 

 ment that is the fallacy proper. Where the error is reached 

 through a process of inference, it may be due either to the 

 assumption, at some point in the process, of a false premiss, or to 

 the acceptance of a formally inconclusive inference as valid. To 

 restrict the meaning of the termfaHacy to the latter class of cases, 

 is as inconvenient as to restrict the term logic to an exposition of 

 the formal laws of inference, thus making it a science of mere 

 consistency. This usage is too narrow. Besides, the distinction 

 between accepting a false premiss and an inconclusive argument 

 is not fundamental. The mind, which, for one reason or another, 

 accepts a formally invalid inference as valid, is by that very fact 

 assenting to a false proposition as true : for the formal force of an 



1 JOSEPH, op. cit., p. 530. 



