160 THE SCIENCE OF LOGIC 



when he got it ; and likewise Theagenes at Megara. Both these fall under 

 the same general principle that a man who aims at a tyranny asks for a 

 bodyguard. 1 1 



237. ANALOGY AS UNDERSTOOD BY ARISTOTLE. We have 

 just seen that what is nowadays called the argument from analogy 

 Aristotle called TrapdSeiy/jia. We have now to consider what he 

 understood by an argument from analogy. The term dvaXoyia 

 originally meant identity of relations. Four terms were said to 

 be analogous when the relation of the first to the second was the 

 same as that of the third to the fourth. Now if the relations are 

 identical, and if what is inferred from them depends on this 

 identity alone, the inference is cogent or necessary. And this is 

 pre-eminently the case in mathematics, where the terms, relations, 

 and inferences are purely quantitative. Here, then, the term 

 &quot; analogy &quot; meant equality of quantitative relations or ratios, &quot; lo-6rij&amp;lt;f 

 \6yajv,&quot; 2 and has been translated by the terms &quot; proportio&quot; &quot;pro 

 portion &quot;. 3 If 2 : 4 : : 3 : 6, we can infer that because 2 is the 

 half of 4, 3 is the half of 6 ; and our reasoning is cogent, like any 

 other mathematical reasoning. But the name &quot; dva\oyia&quot; was 

 also applied to cases in which the terms, relations and inferences 

 were not quite, or not all, quantitative. Thus, &quot;.r vibrations of 

 the air : 2 ^ vibrations : : a note : its octave,&quot; where the second 

 relation is not of the same order as the first ; or again, &quot;;r vibra 

 tions of luminiferous ether : y vibrations : : the sensation of red : 

 the sensation of green,&quot; where again the second relation is quali 

 tative, not quantitative, but yet is so connected with the first 

 that it varies with, and can be known from, the latter; or again, 

 to quote Aristotle s example, intellect bears the same relation to 

 the soul as sight does to the body i/oO? : tyvxij : : o-fris : &amp;lt;rw/ia, 4 

 where there is no idea at all of number or quantity, but only of 

 nature or quality. 



Now if what we infer from an identity of quantitative rela 

 tions does not depend exclusively on those relations, our inference 

 is not necessarily valid : I cannot validly infer that it will be twice 

 as expensive to send goods by rail from A to B as from C to D 



1 &quot;Rhet. a ii., 13576, 25-36. To make the inference to Dionysius necessary (of 

 course it is Dionysius I. who is meant), the principle would have to be, that a man 

 who asks for a bodyguard aims at a tyranny ; and that is really what the suspicious 

 citizen of Syracuse would have had in his mind.&quot; JOSEPH, op. cit., pp. 500, 5or, n. 



a ARISTOTLE, Fth. Nich., bk. v., 3 (8). 



3 FOWLER, Inductive Logic, p. 210, n. 4 ; Deductive Logic, p. 71, n. 2. Cf. also 

 WKLTON, op. cit., ii., p. 75 ; JOSEPH, op. cit., pp. 492 sqq. *Eth. Nich., i., 6 (12). 



