Introduction to mathematical philosophy

Introduction to mathematical philosophy (1920)
Author: Russell, Bertrand, 1872-1970
Subject: Mathematics -- Philosophy
Language: English
THIS book is intended essentially as an " Introduction," and
does not aim at giving an exhaustive discussion of the problems
with which it deals. It seemed desirable to set forth certain
results, hitherto only available to those who have mastered
logical symbolism, in a form offering the minimum of difficulty
to the beginner. The utmost endeavour has been made to
avoid dogmatism on such questions as are still open to serious
doubt, and this endeavour has to some extent dominated the
choice of topics considered. The beginnings of mathematical
logic are less definitely known than its later portions, but are of
at least equal philosophical interest. Much of what is set forth
in the following chapters is not properly to be called " philosophy,"
though the matters concerned were included in philosophy so
long as no satisfactory science of them existed. The nature of
infinity and continuity, for example, belonged in former days
to philosophy, but belongs now to mathematics. Mathematical
philosophy, in the strict sense, cannot, perhaps, be held to include
such definite scientific results as have been obtained in this
region ; the philosophy of mathematics will naturally be ex
pected to deal with questions on the frontier of knowledge, as
to which comparative certainty is not yet attained. But
speculation on such questions is hardly likely to be fruitful
unless the more scientific parts of the principles of mathematics
are known. A book dealing with those parts may, therefore,
claim to be an introduction to mathematical philosophy, though
it can hardly claim, except where it steps outside its province,
to be actually dealing with a part of philosophy. It does deal...