THE NEW LOGICS. 163 



III. 



Could these principles be considered as disguised 

 definitions? That they should be so, we should 

 require to be able to demonstrate that they involve 

 no contradiction. We should have to establish that, 

 however far we pursue the series of deductions, we 

 shall never be in danger of contradicting ourselves. 



We might attempt to argue as follows. We can 

 verify the fact that the operations of the new logic, 

 applied to premises free from contradiction, can only 

 give consequences equally free from contradiction. If 

 then, after n operations, we have not met with contra- 

 diction, we shall not meet it any more after n+i. 

 Accordingly, it is impossible that there can be a 

 moment when contradiction will begin, which shows 

 that we shall never meet it. Have we the right 

 to argue in this way? No, for it would be making 

 complete induction, and we must not forget that 

 tve do not yet know tJie principle of complete induction. 



Therefore we have no right to regard these axioms 

 as disguised definitions, and we have only one course 

 left. Each one of them, we admit, is a new act of 

 intuition. This is, moreover, as I believe, the thought 

 of Mr. Russell and M. Couturat. 



Thus each of the nine undefinable notions and 

 twenty undemonstrable propositions (I feel sure that, 

 if I had made the count, I should have found one 

 or two more) which form the groundwork of the 

 new logic — of the logic in the broad sense — pre- 

 supposes a new and independent act of our intuition, 

 and why should we not term it a true a priori syx\\\\Q.\\c 

 judgment ? On this point ever)'body seems to be 



