COMMON BASIS OF EMPIRICISM AND RATIONALISM 39 



the mere word of contradicted witnesses? 1 Moreover, if we ask 

 why demonstration is ever required for any judgment whatsoever 

 why a ground must be sought for the predicated connection of its 

 terms is it not because the judgment as it stands appears to be 

 synthetical and cannot be left so? In a word, is not every syn- 

 thetical judgment a standing problem? So Leibniz believed ; and 

 accordingly he sought to reduce even the axioms of Euclid to 

 analytical form. Thus intuitionalistic rationalism assumes a 

 position substantially identical (despite Leibniz's protest) with 

 that of nominalistic Hobbianism ; namely, that all science must 

 be deduced from definitions. But while thus gaining a certain 

 self-consistency, it is lost in that hopeless unproductivity from 

 which Descartes, by means of the assumption of distinct axioms, 

 had sought to save it. 



It has been suggested that a final means of synthesis is to be 

 found in the judgment which denies a simple concept of its 

 negative; as, for example, What is unextended is not extended. 

 Here we remark that Descartes is correct in assuming that the 

 negative of a simple concept, if it be itself a concept at all, must 

 also be a simple concept. For since all definition is by means of 

 genus and differentia, the negative is not definable in terms of 

 the positive as, for example, non-extension is not a species of 

 extension. And if it be suggested that the negative is in every 

 case a species of non-existence, the reply follows, that the positive 

 is then equally a species of existence, and hence equally complex. 

 If, then, unextended is a concept at all, The unextended is not ex- 

 tended is a synthetic judgment; and as such it would appear to 

 be open to much the same criticisms as other supposedly elemen- 

 tary synthetic judgments. Suppose, however, it be said as Des- 



1 Cf . Hobbes's criticism of the dare et distincte (quoted by Mr. Mahaffy) : "This 

 way of speaking, a great clearness in the understanding (as a test of truth), is meta- 

 phorical, and therefore not fitted for an argument; for whenever a man feels no 

 doubt at al! he will pretend to this clearness." Cf. also Kant's explanation of the 

 necessity for a critical deduction of a priori principles, "without it, our assertion 

 might be suspected of being purely gratuitous." Critique of Pure Reason, An- 

 alytic of Principles, Chap II. 



