Mysticism and Logic and Other EssaysRussell, Bertrand
Philosophy
Mysticism and Logic and Other Essays
Russell, Bertrand
Mathematics; Philosophy; Science
The _prima facie_ difficulties in the way of this view are chiefly
derived from an unduly conventional theory of space. It might seem at
first sight as if we had packed the world much fuller than it could
possibly hold. At every place between us and the sun, we said, there
is to be a particular which is to be a member of the sun as it was a
few minutes ago. There will also, of course, have to be a particular
which is a member of any planet or fixed star that may happen to be
visible from that place. At the place where I am, there will be
particulars which will be members severally of all the "things" I am
now said to be perceiving. Thus throughout the world, everywhere,
there will be an enormous number of particulars coexisting in the same
place. But these troubles result from contenting ourselves too readily
with the merely three-dimensional space to which schoolmasters have
accustomed us. The space of the real world is a space of six
dimensions, and as soon as we realise this we see that there is plenty
of room for all the particulars for which we want to find positions.
In order to realise this we have only to return for a moment from the
polished space of physics to the rough and untidy space of our
immediate sensible experience. The space of one man's sensible objects
is a three-dimensional space. It does not appear probable that two men
ever both perceive at the same time any one sensible object; when they
are said to see the same thing or hear the same noise, there will
always be some difference, however slight, between the actual shapes
seen or the actual sounds heard. If this is so, and if, as is
generally assumed, position in space is purely relative, it follows
that the space of one man's objects and the space of another man's
objects have no place in common, that they are in fact different
spaces, and not merely different parts of one space. I mean by this
that such immediate spatial relations as are perceived to hold
between the different parts of the sensible space perceived by one
man, do not hold between parts of sensible spaces perceived by
different men. There are therefore a multitude of three-dimensional
spaces in the world: there are all those perceived by observers, and
presumably also those which are not perceived, merely because no
observer is suitably situated for perceiving them.
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