9^ THE SCIENCE OF LOGIC. 



&quot; a plane curve produced by a point so moving that its distance 

 from a fixed line always bears the same ratio to its distance from 

 a certain fixed point &quot;. 



Again, owing to the fact that denotation and connotation 

 influence each other, while the denotation often remains vague 

 because there seem to be no hard and fast lines in Nature 

 Natura non facit saltum, and so we may be doubtful about the 

 boundary lines of our classes, how we are to classify new and 

 doubtful specimens it may and does happen that our class limits 

 fluctuate somewhat and that as a consequence the connotation 

 and definition of our class names may gradually vary. 1 The 

 discovery of new objects always raises the problem of their 

 classification. And this may conceivably disturb the denotation 

 and connotation of some familiar class name. We might illus 

 trate the point by the fanciful supposition that some planets were 

 proved to be inhabited by real rational animals like those en 

 countered by Gulliver in his travels: Would we classify these as 

 &quot; men,&quot; or continue to define men as &quot;rational animals&quot;? 2 



52. LIMITS OF DEFINITION. If definition unfolds the con 

 notation of a term it follows that non-connotative terms (37) 

 have no definition. 



(a) Proper N antes &amp;gt; therefore, cannot be defined. 



(b) Furthermore, not all connotative terms can be defined. So 

 long indeed as the connotation is capable of further analysis into 

 simpler attributes generic and differential definition is possible. 

 But all complex concepts are built up from simpler ones, and 

 analysis inevitably brings us to a multitude of notions those 

 which enter into and compose the self-evident axioms of the 

 sciences which defy further analysis, and therefore cannot be 

 defined. Hence the ten Aristotelian categories or Genera 

 Suprema (71) do not admit of strict definition : because they have 

 no higher genus of which they could rank as species. &quot; Being &quot; is 

 not a genus for them, because it is not differentiated in them by 

 differentiae the concepts of which would differ in intension from 

 that of &quot; Being&quot; itself: no object of any concept is distinct 

 conceptually from the object &quot; Being&quot;. As substitutes for defini 

 tion, recourse is had to explanations and descriptions. Again, the 

 names of simple, unanalysable feelings, such as pain or pleasure \ 



1 Cf. what was said above about generalization and specialization of names, 

 22, 27 ; also VENN, op. cit., pp. 286-7. 

 * Cf. CLARKE, Logic, p. 214. 



