An essay on the foundations of geometryRussell, Bertrand
Philosophy
An essay on the foundations of geometry
Russell, Bertrand
Geometry -- Foundations
=203.= Let us consider what this empty space is. (I speak of "empty"
space without necessarily implying the absence of matter, but only
to denote a space which is not a mere order of material things.)
Stumpf regards it as given in sense; Kant, in the last two arguments
of his metaphysical deduction, argues that it is an intuition, not
a concept, and must be known before spatial order becomes possible.
I wish to maintain, on the contrary, that it is wholly conceptual;
that space is given only as spatial order; that spatial relations,
being given, appear as more than mere relations, and so become
hypostatized; that when hypostatized, the whole collection of
them is regarded as contained in empty space; but that this empty
space itself, if it means more than the logical possibility of
space-relations, is an unnecessary and self-contradictory assumption.
Let us begin by considering Kant's arguments on this point.
Leibnitz had affirmed that space was only relations, while Newton
had maintained the objective reality of absolute space. Kant adopted
a middle course: he asserted absolute space, but regarded it as
purely subjective. The assertion of absolute space is the object of
his second argument; for if space were mere relations between things,
it would necessarily disappear with the disappearance of the things
in it; but this the second argument denies[196]. Now spatial order
obviously does disappear with matter, but absolute or empty space may
be supposed to remain. It is this, then, which Kant is arguing about,
and it is this which he affirms to be a pure intuition, necessarily
presupposed by spatial order[197].
Public-domain text, read in full here on John Shaqi.
Reviews
Reviews
No reviews yet
Be the first to share your thoughts on this work.
Elsewhere in the archive
Join the Discussion
Join the discussion
Sign in to leave a comment or review.
Sign InorCreate an account