An essay on the foundations of geometryRussell, Bertrand
Philosophy
An essay on the foundations of geometry
Russell, Bertrand
Geometry -- Foundations
I cannot hope, however, that no difficulty will remain, for the
reader, in such a deduction, from abstract conceptions, of the
properties of an actual _datum_ in sense-perception. Let us consider,
for example, such a property as impenetrability. To suppose two
things simultaneously in the same position in a form of externality,
is a logical contradiction; but can we say as much of actual space
and time? Is not the impossibility, here, a matter of experience
rather than of logic? Not if the above argument has been sound,
I reply. For in that case, we infer real diversity, _i.e._ the
existence of different things, only from difference of position in
space or time. It follows, that to suppose two things in the same
point of space and time, is still a logical contradiction: not
because we have constructed the data of sense out of logic, but
because logic is dependent, as regards its application, on the nature
of these data. This instance illustrates, what I am anxious to make
plain, that my argument has not attempted to construct the living
wealth of sense-perception out of "bloodless categories," but only to
point out that, unless sense-perception contained a certain element,
these categories would be powerless to grapple with it.
=193.= How we are to account for the fortunate realization of these
requirements--whether by a pre-established harmony, by Darwinian
adaptation to our environment, by the subjectivity of the necessary
element in sense-perception, or by a fundamental identity and unity
between ourselves and the rest of reality--is a further question,
belonging rather to metaphysics than to our present line of argument.
The _à priori_, we have said throughout, is that which is necessary
for the possibility of experience, and in this we have a purely
logical criterion, giving results which only Logic and Epistemology
can prove or disprove. What is subjective in experience, on the
contrary, is primarily a question for psychology, and should be
decided on psychological grounds alone. When these two questions have
been separately answered, but not till then, we may frame theories as
to the connection of the _à priori_ and the subjective; to allow such
theories to influence our decision, on either of the two previous
questions, is liable, surely, to confuse the issue, and prevent a
clear discrimination between fundamentally different points of view.
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