An essay on the foundations of geometryRussell, Bertrand
Philosophy
An essay on the foundations of geometry
Russell, Bertrand
Geometry -- Foundations
=186.= This, then, is the kind of externality we are to expect
from space, and our question must be: Would the existence of
diverse but interrelated things be unknowable, if there were not,
in sense-perception, some form of externality? This is the crucial
question, on which turns the apriority of our form, and hence of the
necessary axioms of Geometry.
=187.= The converse argument to mine, the argument from the
spatio-temporal element in perception to a world of interrelated
but diverse things, is developed at length in Bradley's Logic. It
is put briefly in the following sentence (p. 44, note): "If space
and time are continuous, and if all appearance must occupy some time
or space--and it is not hard to support both these _theses_--we can
at once proceed to the conclusion, no mere particular exists. Every
phenomenon will exist in more times or spaces than one; and against
that diversity will be itself an universal[187]." The importance of
this fact appears, when we consider that, if any _mere_ particular
existed, all judgment and inference as to that particular would be
impossible, since all judgment and inference necessarily operate
by means of universal. But all reality is constructed from the
_This_ of immediate presentation, from which judgment and inference
necessarily spring. Owing, however, to the continuity and relativity
of space and time, no _This_ can be regarded either as simple or
as self-subsistent. Every _This_, on the one hand, can be analyzed
into _Thises_, and on the other hand, is found to be necessarily
related to other things, outside the limits of the given object of
sense-perception. This function of space and time is presupposed in
the following statement from Bosanquet's Logic (Vol. I. pp. 77-78):
"Reality is given for me _in_ present sensuous perception, and _in_
the immediate feeling of my own sentient existence that goes with
it. The real world, as a definite organized system, is _for me_ an
extension of this present sensation and self feeling by means of
judgment, and it is the essence of judgment to effect and sustain
such an extension.... The subject in every judgment of Perception
is some given spot or point in sensuous contact with the percipient
self. But, as all reality is continuous, the subject is not _merely_
this given spot or point."
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