The investigations contained in this volume were first prompted
by studies in the philosophy of mathematics. In the course of an
attempt to comprehend the fundamental conceptions of mathematics
from the point of view of logic, it became necessary to analyse more
closely the function of the concept itself and to trace it back to its
presuppositions. Here, however, a peculiar difficulty arose: the
traditional logic of the concept, in its well-known features, proved
inadequate even to characterize the problems to which the theory
of the principles of mathematics led. It became increasingly evident
that exact science had here reached questions for which there existed
no precise correlate in the traditional language of formal logic. The
content of mathematical knowledge pointed back to a fundamental
form of the concept not clearly defined and recognized within logic
itself. In particular, investigations concerning the concepts of
the series and of the limit, the special results of which, however,
could not be included in the general exposition of this book, con-
firmed this view and led to a renewed analysis of the principles of the
construction of concepts in general.

The problem thus defined gained more general meaning when it
became clear that it was in no way limited to the field of mathe-
matics, but extended over the whole field of exact science. The
systematic structure of the exact sciences assumes different forms
according as it is regarded in different logical perspectives. Thus
an attempt had to be made to advance from this general point of view
to the forms of conceptual construction of the special disciplines,--
of arithmetic, geometry, physics and chemistry. It did not accord
with the general purpose of the enquiry to collect special examples
from the particular sciences for the support of the logical theory,
but it was necessary to make an attempt to trace their systematic
structures as wholes, in order that the fundamental unitary relation
by which these structures are held together might be revealed more
distinctly. I did not conceal from myself the difficulty of carrying
out such a plan; I finally resolved to make the attempt only because
the value and significance of the preliminary work already accom-
plished within the special sciences became increasingly evident to me.

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