3 o THE SCIENCE OF LOGIC 



universal proposition, the abstract universal, can be reached only 

 by generalization of the abstract judgment which establishes some 

 sort of necessary connexion of attributes between subject and predi 

 cate. Adding parts to parts, to form a natural whole, gives us a 

 collective idea. Considering an object in the abstract, apart from 

 its individualizing characteristics, putting it into relation with its 

 concrete realizations, actual or possible, indefinite in number, 

 seeing that it is predicable of all, is to universalize and to make 

 scientific progress. For &quot; all science is of the universal and 

 necessary&quot;; 1 i.e. it is expressive of necessary, and therefore uni 

 versal, relations between the objects of our thought. The strict 

 universal is no mere actual collection ; it is applicable to an 

 indefinite number of instances. Therefore, this kind of induction 

 does not put us in possession of scientific or necessary truth. 



It assumes, as we have seen, the external form of a syllogism 

 in the&amp;gt; third figure, but it is no more a true syllogistic process 

 than is the apparent syllogism whose premisses contain no true 

 universal, but only collective propositions. In fact it is just the 

 reverse of the process which John Stuart Mill erroneously put 

 forward as the true type of syllogistic reasoning (195). 



To observe successively that each of the planets describes an elliptical 

 orbit around the sun, and then to say that all the planets describe such an 

 ellipse, is simply to group together isolated observations in a formula to aid 

 the memory, but this is not ascending from the particular to the universal. 

 Similarly, to conclude that, because the senses a, b, c, d, e, are each an occasion 

 of error, therefore all the senses are an occasion of error, is certainly not to go 

 through a scientific reasoning process : but rather through an arithmetical 

 process which simply tells us that five times one are five. 



Examples might be multiplied indefinitely. They all point to the same 

 conclusion : that observation pure and simple puts us in possession of par 

 ticular facts, and that the grouping together of those facts in a collective 

 notion may help the memory and abbreviate the expression of thought, but 

 will not lead to scientific knowledge of any necessary truth or law. 



Aristotle distinguished clearly between the formation of an actual whole 

 from its parts and the elaboration of a universal notion ; &quot; Even if we succeeded 

 in showing separately,&quot; he writes, 2 &quot;whether by the same or by separate 

 proofs, that equilateral, isosceles, and scalene triangles have each their in 

 terior angles equal to two right angles, we should not yet have any right to 

 assert the universal proposition ; The triangle, as such, has its interior 

 angles equal to two right angles .&quot; The separate proofs would not neces 

 sarily have given us a universal knowledge ((cafldAov) of the triangle as such. 

 Hence, we should not yet know whether the attribute, &quot; having their interior 



1 H \t.\v bnarriW ta0&amp;lt;$A.ov /coi 5i ivayicalw. ARISTOTLE, Post. Anal., i., 33. 

 * Post. Anal., i. t 5(5-7). 



