Principia mathematica, by Alfred North Whitehead ... and Bertrand Russell.

INTRODUCTION

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(4) The terseness of the symbolism enables a whole proposition to be
represented to the eyesight as one whole, or at most in two or three parts
divided where the natural breaks, represented in the symbolism, occur. This
is a humble property, but is in fact very important in connection with the
advantages enumerated under the heading (3).
(5) The attainment of the first-mentioned object of this work, namely
the complete enumeration of all the ideas and steps in reasoning employed
in mathematics, necessitates both terseness and the presentation of each
proposition with the maximum of formality in a form as characteristic of
itself as possible.
Further light on the methods and symbolism of this book is thrown by a
slight consideration of the limits to their useful employment:
(a) Most mathematical investigation is concerned not with the analysis
of the complete process of reasoning, but with the presentation of such an
abstract of the proof as is sufficient to convince a properly instructed mind.
For such investigations the detailed presentation of the steps in reasoning is
of course unnecessary, provided that the detail is carried far enough to guard
against error. In this connection it may be remembered that the investigations of Weierstrass and others of the same school have shown that, even in
the common topics of mathematical thought, much more detail is necessary
than previous generations of mathematicians had anticipated.
(/i) In proportion as the imagination works easily in any region of
thought, symbolism (except for the express purpose of analysis) becomes only
necessary as a convenient shorthand writing to register results obtained
without its help. It is a subsidiary object of this work to show that, with
the aid of symbolism, deductive reasoning can be extended to regions of
thought not usually supposed amenable to mathematical treatment. And
until the ideas of such branches of knowledge have become more familiar,
the detailed type of reasoning, which is also required for the analysis of the
steps, is appropriate to the investigation of the general truths concerning
these subjects.