On Sameness and Identity: A Psychological Study: Being a Contribution to the Foundations of a Theory of KnowledgeFullerton, George Stuart
Philosophy
On Sameness and Identity: A Psychological Study: Being a Contribution to the Foundations of a Theory of Knowledge
Fullerton, George Stuart
Knowledge, Theory of
The attempt sometimes made to avoid this difficulty by calling upon
a precisely similar one for aid is of not the least avail. The time
of the motion, it is said, is divisible just as is the space over
which the body moves; the spaces and the times then vary together,
and as the spaces become very small the times become very small;
infinitesimal spaces are passed over in infinitesimal times, and all
these infinitesimals are included in the finite space and finite time
of the motion. But if there be a difficulty in arriving at the end of
an endless series of places or positions, there is surely no less a
difficulty in reaching the end of an endless series of times. If the
series of times to be successively exhausted be truly endless, then
an end of the motion can never be reached. Quibbling over the size
of the members of the series in the case of either space or time is
useless. Whether things are big or little, if the supply of them is
truly endless, one can never get to the end of the supply. The rapidity
with which they are exhausted has nothing to do with the question,
for an increase in rapidity has obviously no effect in facilitating
an approach to what is assumed not to exist, a final term. It is,
then, perfectly clear that, if, in order to move a body, I must come
to the end of an endless series, I may reasonably conclude that I
cannot move a body. Granting the assumption upon which it is based,
Zeno's argument is unanswerable. It is not a question of an ordinary
difficulty, a trifling evil; it is a question of an impossibility, a
flat contradiction; to move an inch, to endure for a minute, one is to
accomplish the feat of reaching the end of the endless. One thing is
quite certain; no rival doctrine can present a greater difficulty.
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