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 w r e 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) : &quot;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.&quot; Cf. also Kant s explanation of the 

 necessity for a critical deduction of a priori principles, &quot;without it, our assertion 

 might be suspected of being purely gratuitous.&quot; Critique of Pure Reason, An 

 alytic of Principles, Chap II. 



