But it is not a question of that; it does not suffice to represent _one_
point, it is necessary to represent _a certain_ point and to have the
means of distinguishing it from an _other_ point. And in fact, that we
may be able to apply to a continuum the rule I have above expounded and
by which one may recognize the number of its dimensions, we must rely
upon the fact that two elements of this continuum sometimes can and
sometimes can not be distinguished. It is necessary therefore that we
should in certain cases know how to represent to ourselves _a specific_
element and to distinguish it from an _other_ element.
The question is to know whether the point that I represented to myself
an hour ago is the same as this that I now represent to myself, or
whether it is a different point. In other words, how do we know whether
the point occupied by the object _A_ at the instant [alpha] is the same
as the point occupied by the object _B_ at the instant [beta], or still
better, what this means?
I am seated in my room; an object is placed on my table; during a second
I do not move, no one touches the object. I am tempted to say that the
point _A_ which this object occupied at the beginning of this second is
identical with the point _B_ which it occupies at its end. Not at all;
from the point _A_ to the point _B_ is 30 kilometers, because the object
has been carried along in the motion of the earth. We can not know
whether an object, be it large or small, has not changed its absolute
position in space, and not only can we not affirm it, but this
affirmation has no meaning and in any case can not correspond to any
representation.
But then we may ask ourselves if the relative position of an object with
regard to other objects has changed or not, and first whether the
relative position of this object with regard to our body has changed. If
the impressions this object makes upon us have not changed, we shall be
inclined to judge that neither has this relative position changed; if
they have changed, we shall judge that this object has changed either in
state or in relative position. It remains to decide which of the _two_.
I have explained in 'Science and Hypothesis' how we have been led to
distinguish the changes of position. Moreover, I shall return to that
further on. We come to know, therefore, whether the relative position of
an object with regard to our body has or has not remained the same.
If now we see that two objects have retained their relative position
with regard to our body, we conclude that the relative position of these
two objects with regard to one another has not changed; but we reach
this conclusion only by indirect reasoning. The only thing that we know
directly is the relative position of the objects with regard to our
body. _A fortiori_ it is only by indirect reasoning that we think we
know (and, moreover, this belief is delusive) whether the absolute
position of the object has changed.
Public-domain text, read in full here on John Shaqi.
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