ABSOLUTE AND RELATIVE POSITION
Some people maintain that position in space or time must be relative
because, if we try to determine the position of a body A, if bodies B,
C, D with respect to which the position of A could be determined were
not present, we should be trying to determine something about A without
having our senses affected by other things. These people seem to me to
be like the cautious guest who refused to say anything about his host's
port-wine until he had tasted red ink.
"Wherein, then," says Mr. Russell,[118] "lies the plausibility of the
notion that all points are exactly alike? This notion is, I believe, a
psychological illusion, due to the fact that we cannot remember a point
so as to know it when we meet again. Among simultaneously presented
points it is easy to distinguish; but though we are perpetually moving,
and thus being brought among new points, we are quite unable to detect
this fact by our senses, and we recognize places only by the objects
they contain. But this seems to be a mere blindness on our part--there
is no difficulty, so far as I can see, in supposing an immediate
difference between points, as between colours, but a difference which
our senses are not constructed to be aware of. Let us take an analogy:
Suppose a man with a very bad memory for faces; he would be able to
know, at any moment, whether he saw one face or many, but he would not
be aware whether he had seen any of the faces before. Thus he might be
led to define people by the rooms in which he saw them, and to suppose
it self-contradictory that new people should come to his lectures, or
that old people should cease to do so. In the latter point at least it
will be admitted by lecturers that he would be mistaken. And as with
faces, so with points--inability to recognize them must be attributed,
not to the absence of individuality, but merely to our incapacity."
Another form of this tendency is shown by Kronecker, Borel, Poincare,
and many other mathematicians, who refuse mere logical determination of
a conception and require that it be actually described in a finite
number of terms. These eminent mathematicians were anticipated by the
empirical philosopher who would not pronounce that the "law of thought"
that A is either in the place B or not is true until he had looked to
make sure. This philosopher was of the same school as J. S. Mill and
Buckle, who seem to have maintained implicitly not only that, in view of
the fact that the breadth of a geometrical line depends upon the
material out of which it is constructed, or upon which it is drawn, that
there ought to be a paste-board geometry, a stone geometry, and so
on;[119] but also that the foundations of logic are inductive in their
nature.[120] "We cannot," says Mill,[121] "conceive a round square, not
merely because no such object has ever presented itself in our
experience, for that would not be enough. Neither, for anything we know,
are the two ideas in themselves incompatible. To conceive a body all
black and yet white would only be to conceive two different sensations
as produced in us simultaneously by the same object--a conception
familiar to our experience--and we should probably be as well able to
conceive a round square as a hard square, or a heavy square, if it were
not that in our uniform experience, at the instant when a thing begins
to be round, it ceases to be square, so that the beginning of the one
impression is inseparably associated with the departure or cessation of
the other. Thus our inability to form a conception always arises from
our being compelled to form another contradictory to it."
FOOTNOTES:
[118] _Md._, N. S., vol. x., July, 1901, pp. 313-14.
[119] J. B. Stallo, _The Concepts and Theories of Modern Physics_, 4th
ed., London, 1900, pp. 217-27.
[120] _Ibid._, pp. 140-4.
[121] _Examination of the Philosophy of Sir William Hamilton_, vol. i.
p. 88, Amer. ed.