ABSTRACT
It is known to-day that the suggestion of Leibniz is only of historic interest. The system of rational metamathematics permits the construction of symbolic representatives of the objects of experience. These symbolic representatives are of the type treated in theoretical physics. This is indeed natural, for the very objects upon which the system depends, namely letters, are just such symbolic objects. However, it should not be forgotten that a whole class of the properties of letters are neglected. In particular there is no way of distinguishing
separate copies of a letter. Clearly then it cannot be expected that rational metamathematics will prove fertile where such objects of experience but not their patterns are concerned. Where investigation of individual objects is begun, where a particular copy of the letter a, a particular automobile, a particular human organism, a particular society is concerned, the system of metamathematics automatically fails to work. However, there is by no means any foundation for a conclusion such as that of Meyerson that reality is irrational and that it can be rationalized only in part.1 There is no reason to think that reality is irrational. Rather it is simply to be confirmed that reality is never given as something completed and that only the patterns of reality are treated. For every pattern there is a correspondent. The farther the process of formaliza tion is carried on, the more complicated will the system be, but it can always be applied to new patterns. The important point is that this process will never be terminated.
