Objections to the possibility of motion
Objections
to the possibility of motion
Parmenides objection to motion
The
philosopher Parmenides was among the first sets is philosophers who objected to
the possibility of any things such as motion. He was born about 510 BC, and
lived most of his life at Elea, southwest of Italy. He rejected the common
sense notion of change by his distinction between appearance and reality.
Change, he said, is the most confusion of appearance with reality and therefore
change is simply an Illusion.[1]
Parmenides
started that motion is a passage from being to non-being and vice versa. He
further stated that, non-being is impossible. Therefore, motion is impossible.
In response, Aristotle argued that motion is a passage from being secundum quid (in a certain sense) to
non-being secundum quid and vice
versa; however, it is not a passage from being simplicitor (in an absolutely sense) to non-being simplicitor and vice versa. He said that
motion is a passage from potential being to actual being. When a thing that is
in potency is moved to act, it receives a new modification of what is in
existence throughout the motion.
Responding further to the objections raised by
Parmenides, Aristotle stated that the existence of non-being simplicitor is impossible, but the
existence of non0being secundum quid
is possible. It is certainly impossible for a substance both to exist and not
to exist at the same time, but it is not impossible to lack a certain form and
hence to be non-being secundum quid.in
a certain respect.[2]
Summarily,
this is Parmenides’ objection: “what is, cannot come to be (since already is);
while nothing can come to be from what is not.”
The idea of this argument seems to be this: it is a
case of coming to be, the resulting object is clearly a being, something that
is. From what initial object doles it come to be? If the initial object is what
is and the resultant object is also what is, we do not really have a case of
coming to be. There is no change or motion. And if the mind object is what is
not, we have another kind of impossibility for nothing can come to be from what
is not.
Aristotle
rejected Parmenides’ dilemma that something comes to be from what is, or from
what is not.[3]
He does so systematically by drawing a distinction between the two senses of
“coming to be.” Is the initial object a being or a non-being: Parmenides asks?
Aristotle answers: in a way it is not a being. And in a way it is not a being
and in a way it is not a non-being. The initial object might be an unmusical
man. This, in one way is a being and in another way a non-being. The initial
object is something (for it is a man) and something that is not (for it is not
musical). Aristotle agrees with Parmenides that nothing comes to be out of
cheer nothingness but he also maintain that, in a sense, things can come to be
in a way. For instance, coincidentally from what is not. Something can come to
be from the privation, which in itself is not, and does belong to the thing.
Note
here that, the ‘music-ness’ comes to be from the compound unmusical man. What
he comes to be from is in one way a non-being, since he comes to be from a
privation, the ‘unmusic-ness’ or unmusical. But in a way, what he comes to be
from is a being as well, for the initial object (man) is something that exists.
Thus Parmenides offers us a false dilemma that the initial object is either being
or not being but since the initial object is a compound, in a way it is both.
Zeno’s objection to the possibility of motion
Zeno was a student of Parmenides.
He was born in Elea about 489 BC. In a bid to defend the position of his master
Parmenides, that motion and change do not occur, he proposed his four
paradoxes.
The first is the dichotomy
paradox. It states that to get to any point, we must first travel halfway, and
to get to that halfway point, we must travel half of that halfway, and to get
to that half of the halfway, we must first travel a half of the half of that
halfway and infinitely, so that, for any given instance there is always a
smaller distance to be covered first. And so, we can never start moving at all.
Aristotle answered that, time can be divided just as infinitely as space, so
that it would have infinitely little time to cover the infinitely little space
needed to get started, therefore there is the possibility of motion.
The second paradox is known as
the Achilles paradox. It states that, supposing Achilles is racing a tortoise,
and gives the tortoise and gives the tortoise a head start. Then by the
time Achilles reaches the point the
started from, the tortoise will have advanced a certain distance and by the
point Achilles covers that certain distance the tortoise will have advance a
bit farther, and so on, so that it seems Achilles will never be able to catch
up with, let alone pass the tortoise. Thus, motion is not taking place.
Aristotle responded that the
paradox assumes the existence of an actual infinity of parts between Achilles
and the tortoise. If there were an actual infinity –that is, if Achilles has
had to take account of all the infinite points, he passed in catching up with
the tortoise – it would indeed take infinite account of time for Achilles to
pass the tortoise. However, there is only a potential infinite, of course,
between Achilles and the tortoise, meaning that Achilles can cover the
infinitely many points between him and the tortoise in a finite amount of time
so long as he does not have another account of each point along the way.
The third paradox is called
the Arrow paradox. It states that, an arrow at flight is really at rest. For
every point in the flight, the arrow must occupy a length of space exactly
equal to its own. After all, it cannot occupy a greater length, nor a lesser
one. But the arrow cannot ………this length it occupies. It would need exactly the
same space in which to move and it of course has none. So at every point in its
flight, the arrow is at rest. And if it is at rest at every moment in its
flight, then it follows then that, it is at rest during the entire flight.
Aristotle answered that it
does not follow that the arrow does not move at all. The concept of motion can
simply be understood as occupying different parts of space at different points
in time.[4]
The forth paradox is called
the stadium paradox. It concerns equal bodies which alongside equal bodies in
the stadium from opposite direction- the ones from the end of the stadium, the
others from the middle, at equal speeds. Zeno drew from this that half the time
is equal to its double.
This is a rather obscure
paradox, but Aristotle posited that the fallacy inherent in this paradox
consists in requiring that a body travelling at equal speed travels for an
equal time past a moving body and a body of the same size at rest. He argued
that how long it takes to pass a body depends on the speed of the body.[5]
Conclusion
In this paper, we have
attempted to understand the meanings of nature and motion. We critically analyzed
the meaning of nature and motion, the various categories of motion, the three
species of motion. This paper was aimed at an examination of Parmenides’ and
Zeno’s objections to the possibility of motion and Aristotle’s responses to
these objections.
Thomas
Aquinas, commenting on Aristotle's objection, wrote "Instants are not
parts of time, for time is not made up of instants any more than a magnitude is
made of points, as we have already proved. Hence it does not follow that a
thing is not in motion in a given time, just because it is not in motion in any
instant of that time. [6]
Before 212 BC, Archimedes
had developed a method to derive a finite answer for the sum of infinitely many
terms that get progressively smaller. (See: Geometric
series, 1/4 + 1/16 + 1/64 + 1/256 + · · ·,
The Quadrature of the Parabola.)
Modern calculus achieves the same result, using more rigorous methods (see convergent
series, where the "reciprocals of powers of 2" series, equivalent
to the Dichotomy Paradox, is listed as convergent). These methods allow the
construction of solutions based on the conditions stipulated by Zeno, i.e. the
amount of time taken at each step is geometrically decreasing.[7]
Bertrand
Russell offered what is known as the "at-at theory of motion". It
agrees that there can be no motion "during" a durationless instant,
and contends that all that is required for motion is that the arrow be at one
point at one time, at another point another time, and at appropriate points
between those two points for intervening times. In this view motion is a
function of position with respect to time.[8]
Nick Huggett
argues that Zeno is begging the question when he says that objects
that occupy the same space as they do at rest must be at rest.[9]
Philosophical
Relevance
Contemporary
Import
Despite
the fact that the positions of
Parmenides and Zeno were denying the subject matter of the study of nature,
that is, denying the starting point of the science of nature;
It is also an
undeniable fact that, these objections helped Aristotle to establish a solid
foundation the this same subject matter (motion) and the science of nature as a
whole.
[1] Samuel stumpf, philosophy, history
and problem…………………p. 16-18.
[2] Aristotle, physics, book I, 191, p.232-236.
[3] Aristotle, 191 a 30.
[4] Aristotle, bk vi, 239 b 33-2, 40a 5.
[5] Aristotle, bk.vi, 240.
[7] George B. Thomas, Calculus and Analytic Geometry,
Addison Wesley, 1951.
Boyer, Carl (1959). The
History of the Calculus and Its Conceptual Development. Dover Publications. p. 295. ISBN 978-0-486-60509-8. Retrieved 2010-02-26.
"If the paradoxes are thus stated in the precise mathematical terminology
of continuous variables (...) the seeming contradictions resolve
themselves."
[9] Huggett, Nick (2010). "Zeno's
Paradoxes: 3.3 The Arrow". Stanford Encyclopedia of
Philosophy. Retrieved 2011-03-07.
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