ABSTRACT
Language I, with which we have been concerned up to the present, contains only definite concepts; in the domain of mathe matics it contains only the arithmetic of the natural numbers, and that only to an extent which corresponds approximately to a finitist or intuitionist standpoint. Language II includes Language I as a sub-language; all the symbols of I are likewise symbols of II, and all the sentences of I are likewise sentences of II. But Language II is far richer in modes of expression than Language I. It also contains indefinite concepts; it includes the whole of classical mathematics (functions with real and complex arguments; limiting values; the infinitesimal calculus; the theory of aggregates); and in it, in addition, the sentences of physics may be formulated.
