THE DIRECT JUSTIFICATION OF ENTELECHY 303 



We now shall study the theory of the categorical system 

 with special regard to our bio-philosophical purpose. Our 

 task does not require a complete analysis of this system 

 however desirable it might be but will be accomplished 

 by the discussion of two main classes, the categories of 

 relation and of " modality " in the terminology of Kant. 1 



/3. THE CATEGORY OF NECESSITY 



Let us begin with a few words about one category of 

 the latter class, which seems to us to stand at the head of 

 all : necessity or univocal determination, which has been 

 shortly discussed from a narrower point of view on a former 

 occasion. 



All that " is," " is ' of necessity, whether immediately 

 or mediately derived from other necessities. This axiom, 

 expressed in the concept of " function ' ; in its widest, say 

 in its metamathematical meaning and connected in some way 

 with the logical principle of identity, embraces all others. 

 Therefore it is much wider than the axioms of substance- 

 inherence, causality, and so on, in short, than any axiomatic 

 statement with regard to any special kind of relation. 



Vitalism, in what form soever it appears, must be subject 

 to it, as we know already, and need not repeat here. 



The Fundamental Paradox 



But necessity only relates to Givenness. We here reach 

 a very important point, already mentioned in a more general 



1 We do not mean to say that we agree with Kant's system of the 

 categories ; in the first place, we are far from allowing that his four main 

 groups are co-ordinated with one another. But to open up here the problem 

 of the categories as such would complicate our special theme in an un- 

 necessary manner. 



