INDUCTION IN ITS VARIOUS SENSES 31 



angles equal to two right angles&quot; belonged to the triangle as such, and, 

 therefore, to all possible triangles. 



Nor, even when we see that the three species, equilateral, isosceles, and 

 scalene, are exhaustive of the genus triangle, can we be said to know scien 

 tifically that the latter as such has the sum of its interior angles equal to two 

 right angles : unless we have proved this attribute to belong to each of the 

 three species, not on different grounds peculiar to each case, but on some 

 common ground inherent in their common nature as triangles : &quot; f i ravrov rfv 

 rptywi/o) tlvcu. KOI IcroirXtvptf rj ecdcm rj iracriv si eadem sit row esse ratio tn- 

 angulo et aequilatero, aut cuique trianguli speciei aut omnibus.&quot; 1 In order 

 that such a conclusion be anything more than an enumerative judgment &quot; it 

 would be necessary to show that the reason for the inherence of P is the same 

 in regard to all the parts of J/&quot;. 2 



But mere enumeration of the individuals of species (or of the species of a 

 genus) cannot of itself reveal to us anything in their common nature to serve 

 as a sufficient and necessary ground for predicating any attributes found in 

 all the examined individuals (or species), about the species (or genus) as such. 



That Aristotle was acquainted with the true method of arriv 

 ing at such a scientific or necessary knowledge of the nature of 

 things we shall presently show (208). That he realized the in 

 ability of an incomplete enumeration as such to prove a really 

 general principle, is manifest from what he says of the so-called 

 &quot; inductive syllogism &quot; described above. When he speaks of it as 

 a way of &quot;proving the major term of the middle by means of 

 the minor&quot; 3 i.e. of proving the universal principle &quot; M is P&quot; 

 11 If anything is M it is P&quot; which stands as major in the demon 

 strative syllogism in the first figure, he does not mean &quot;proving&quot; 

 in the strict sense of demonstration (aVoSet^t?), for strict demon 

 stration is always by syllogisms in the first figure. He only means 

 that the inductive syllogism is a way of illustrating, making 

 clearer by instances or examples (BrjXouv ; TriOavvTepov, &amp;lt;ra&amp;lt;f&amp;gt;eaT- 



1 ibid., (6). 



2 JOYCE, Logic, p. 229. The author observes that Euclid is usually able to do 

 this in cases where he proves successively that something is true of each of all the 

 possible instances of a logical whole. Cf. JOSEPH (op. cit., p. 503) : &quot; The peculiar 

 nature of our subject-matter [here] enables us to see that no other alternatives 

 are possible within the genus than those which we have considered ; and therefore 

 we can be sure that our induction is perfect . The nature of our subject-matter 

 further assures us that it can be by no accident that every species of the genus 

 exhibits the same property ; and therefore our conclusion is a genuinely universal 

 judgment about the genus, and not a mere enumerative judgment about its species. 

 We are sure that a general ground exists, although we have not found a proof by 

 it.&quot; No doubt, if we are assured that the species exhibit the same property, &quot;by 

 no accident,&quot; our conclusion is universal ; but, even then, we only know that it is so, 

 not why it is so : until we can &quot; show that the reason for the &quot; property &quot; is the 

 same in regard to all &quot; triangles. 



&quot; Anal. Prior, ii., 23, (25). 



