Zeno and Naagaarjuna on motion(8)
时间:2008-01-22 20:26来源:Philosophy East and West 26, n作者:Mark Sid… 点击:
with nonbeing (nonexistence), However, if we accept
them, as Zeno apparently did, then they do show that
in a continuous universe, motion is impossible.
Thus, on Eleatic terms, no matter what kind of
universe we suppose-continuous or additive no
intelligible account of motion can be given, and
therefore motion is impossible. Although this and
other of their conclusions never achieved wide
acceptance, their arguments had enormous influence,
establishing the rationalist tradition in philosophy
which survives until today.
Before we proceed to a direct examination of
Naagaarjuna's arguments against motion, we should
like to say a few words about the historical
background behind the writing of the
Muula-maadhyamika-kaarika (MMK) , with particular
reference to Indian notions of space and time. While
far less is known about ancient Indian mathematics
and physics than is known about their ancient Greek
counterparts, it is still possible to discern a few
significant tendencies. And these, it turns out, bear
remarkable resemblances to developments in Greece, It
is known, for instance, that the 'Sulba geometers of
perhaps the fifth or sixth century B.C, discovered
the incommensurability of the diagonal of a square
with its sides.(8) Having done so, they then devised
a means for computing an approximate value of ?
Significantly, however, this was perceived as no more
than an approximation, This suggests that they were
aware that ? is irrational, that is, that its
precise value can never be given with a finite string
of numerals; and from here it is but a short step to
the notion of a number continuum. That is, the
mathematician who knows of the existence of
irrationals should soon come to see that there are
infinitely many numbers between any two consecutive
integers, And with this realization comes the notion
of infinite divisibility, While we cannot say for
certain that the 'Sulba geometers were consc iously
aware of infinite divisibility, developments in
Indian physics require some source for the notion,
and the sophistication of the 'Sulba school makes it
seem the likeliest place to look, The developments to
which we refer are the emergence of the curious