I'm starting to build my Philosophy of Physics web page which will
include answers to all of Zeno's Paradoxes. I'm posting here my
preliminary argumenst for the first two paradoxes : SPACE and SOUND.
I don't like long posts, so I've broken this down into three parts
Part I References;
Part II The Paradox of Space;
Part III the Paradox of Sound.
This is Part III.
See the web page at <http://home.earthlink.net/~lyttlec/zeno/zeno.html>
"Tell me, Protagoras, said he, does one grain of
millet make a noise when it falls, or does the
ten-thousandth part of a grain? On receiving the
answer that it does not, he went on: Does a measure
of millet grains make a noise when it falls, or
not? He answered, it does make a noise. Well, said
Zeno, does not the statement about the measure of
millet apply to the one grain and the
ten-thousandth part of a grain? He assented, and
Zeno continued, Are not the statements as to the
noise the same in regard to each? For as are the
things that make a noise, so are the noises. Since
this is the case, if the measure of millet makes a
noise, the one grain and the ten-thousandth part
of a grain make a noise." [Faribanks]
Argument 1 :
Aristotle replied (Physics,250b20, that is Book VII,
Chap 5) "Hence Zeno's reasoning is false when he argues
that there is no part of the millet that does not make a
sound; for there is no reason why any part should not
in any length of time fail to move the air that the
whole bushel moves in falling.
Aristotle's reply is wrong for the millet part cannot
move without moving the air it displaces. Even if
Aristotle had correctly answered the specific metaphor,
that does not answer the general question as to whether or
not there are phenomenon not observable by human senses.
Conclusion : Accepted.
correct that there are phenomenon that cannot be
directly observed at a human scale. Likewise, just
because something is observed at a human scale, that
does not mean it is observable at any other scale.
Just as one does not insist on
calculating the motion of a baseball based on quantum
mechanics, there is no justification for insisting that
Newton's laws of motion be observable at a sub-quantum
level. However, insisting that abstracting from
the sub-quantum level to the human level results in a
model at least as good as Newton's.
That's it for now. I think the next in sequence might be Place, then
Plurality, with the better known Motion last.
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