This volume brings together those papers of mine which may be of
interest not only to various specialists but also to philosophers. Many
of my writings in mathematics were motivated by epistemological
considerations; some papers originated in the critique of certain views
that at one time dominated the discussions of the Vienna Cirele; others
grew out of problems in teaching fundamental ideas of mathematics; sti
II others were occasioned by personal relations with economists. Hence a
wide range of subjects will be discussed: epistemology, logic, basic
concepts of pure and applied mathematics, philosophical ideas resulting
from geometric studies, mathematical didactics and, finally, economics.
The papers also span a period of more than fifty years. What unifies the
various parts of the book is the spirit of searching for the
elarification of basic concepts and methods and of articulating hidden
ideas and tacit procedures. Part 1 ineludes papers published about 1930
which expound an idea that Carnap, after a short period of opposition in
the Cirele, fully adopted; and, under the name "Princip/e of To/erance",
he eloquently formulated it in great generality in his book, Logica/
Syntax of Language (1934), through which it was widely disseminated.
"The New Logic" in Chapter 1 furthermore ineludes the first report
(I932) to a larger public of Godel's epochal discovery presented among
the great logic results of ali time. Chapter 2 is a translation of an
often quoted 1930 paper presenting a detailed exposition and critique of
intuitionism.
