Original Version of the Text Through Chapter IV

Abstract

From Antiquity — in fact, for millennia — there have been repeated attempts at the analysis of the concepts upon which mathematics is based, of the elementary truths on which it is built up, and of the methods owing, to which it has always stood as the model of rigorously scientific deduction. And this endeavor has not been exclusively one of mathematicians. Rather, it has mainly been metaphysicians and logicians who, out of the plentitude of problems present here, have taken up now this matter, now that, depending upon the particular interest moving them, and have made it the object of special investigation. In fact, these are not problems which are either solely or mainly the concern of mathematicians. A fleeting glance at the history of philosophy teaches one how views with reference to the theoretical character of mathematics have influenced in an essential and often decisive manner the formation of important philosophical Weltanschauungen. In mutual opposition, the most diverse of philosophical schools have each thought that they could invoke the testimony of mathematics: the Rationalists as well as the Empiricists, the Phenomenalists as well as the Realists. Even Skeptics did not shun this battlefield. Especially <290> since Kant, the issues of the philosophy of mathematics have moved ever more forcibly into the foreground.