analysis of motion and its species
INTRODUCTION
Have
you ever wondered how an airplane moves in the air, how an arrow moves, what
causes an athlete to run faster than other athletes? Have you ever imagined why
it is possible for a bird to fly, and why humans cannot? Why is it possible for
things to be in one position in one moment, and be found in another in the next?
Natural things are either in motion or being in potency to move. Things in
motion can be defined only in the contrary of potency and act. Motion is the basic
property of natural things.[1]Thus,
there exists an intrinsic relationship between nature and motion.
In
this paper, we shall attempt an analysis of motion and its species. To achieve
this, we shall begin with a definition of nature and motion. We shall look at
the necessary factors for motion, Afterwards, we shall look at the objections
to the possibility of motion, as well as Aristotle’s responses .We shall also
consider the responses of some other
philosophers. Thereafter, we shall highlight its modern application, and then
conclude.
DEFINITION
OF NATURE
Nature,
according to Aristotle, is an inner principle or the source and cause of being
moved or being at rest per se and not
per accidens.[2]
This means that nature is that in which it belongs primarily and not in virtue
of concomitant attributes.
Some
people conceived nature as the subject and constitutive part of natural things
but this idea is false if matter is considered as the whole substance. Others
consider nature as form because the actual thing does not come into being until
it receives a certain form. It is the form that gives the thing identity and
actuality. But since the identity of a thing comes more from its act than from
its potency, nature applies more to the form than to the matter even though
both are nature.
DEFINITION
OF MOTION
. Aristotle posits three working definitions of
motion. [3]
First,
motion is defined as the fulfilment of what exists in potency, in so far as it
exists in potency.[4]
Thus, it is neither the potency of a thing existing in potency, for some things
are actually in potency, nor the act of a thing in act. Rather, it is the act
of a thing in potency, where the word “act” designates its relation to a prior
potency, and the words “of a thing in potency” designate its relation to a
further act.[5]
Second,
motion is defined as “the fulfilment of the mobile in as much as it is mobile.”[6]
This definition is a conclusion to the previous one. Since motion is the act of
what exist in potency, in so far as it exists in potency, and we know that
whatever is in potency is mobile.
In
the third instance, motion is defined as the fulfilment or transition of a
thing from one point (real and imagined) to another, either from its qualitative,
quantitative, substantial or spatial form. This possibility of natural things
to change is grounded in the principle of nature (form, matter and privation),
efficient causality and final causality. Hence, to set a thing in motion
implies causing it to transit from potency to act.
It is
pertinent to note that that which has the power of causing motion can only act
in reference to the thing capable of being changed, and that which is capable
of being changed can only suffer change under the action of that which has the
power to change it. Hence, motion cannot exist apart from what moves, for there
is no such thing as motion in abstract. Again, motion is action in the mover
and passion in the moved. The mover (action) is also moved, this is because the
mover sets the subject (passion) into motion by contact.[7]
NECESSARY
FACTORS FOR MOTION
For motion to be possible, certain factors
ought to be responsible. Aristotle posits five factors responsible for motion.
These include:
1. That
which directly causes motion. This we term efficient cause or the mover.
2. That
which is in motion (the mobile or subject of the motion)
3. That
in which motion takes place, namely time.
4. A
starting point or terminal of the motion.
5. That
to which motion proceeds (the end point or terminal of the motion), since every
motion proceeds from something to something.
SPECIES
OF MOTION
Aristotle identified three species of motion;
namely:
1. Qualitative
motion
2. Quantitative
motion
3. Local
motion (motion in respect of place or locomotion).[8]
Motion
is defined in terms of terminals, and these terminals are distinguished
according to generas of the
predicaments or categories. The species of motion must fall within these ten
categories. The categories are: substance, quantity, quality, relation, place, time,
position, state, action and passion.[9]
Among these ten categories, only three admit of motion. These are: quantity,
quality and place (location).[10]
Continuity and contrary extremes of possible motion
can only be found in categories such as: sensible qualities, quantities and
place. Thus, there are three species of motion: qualitative motion,
quantitative motion and locomotion.
Qualitative
Motion: Motion in respect of quality is called alteration (a
general designation that is used to include both contraries). It could also be
said to be motion in respect of sensible qualities. A vivid example is a change
from white to black.
Quantitative
Motion: This has to do with growth or decrease. There is a
minimum quantity at which (the motion) of growing begins, and a maximum at
which it is terminated. Motion in respect of quantity is called increase or
decrease according as one or the other is designated; that is to say, motion in
the direction of complete magnitude is increase while motion in the contrary
direction is decrease.
Motion
in respect of place (Locomotion): This may be designated
by the general name of locomotion. In other words, it is called local motion.
It indicates change of place or location.[11]
OBJECTIONS TO THE POSSIBILITY OF MOTION
For want of space and time, we
shall consider only two of such objections as proposed by Parmenides and Zeno.
1.
Parmenides objection to motion. Parmenides was
among the first set of philosophers who objected to the possibility of change and
motion. For him, change is nothing but the confusion of appearance with
reality. He saw change as a mere illusion.[12]
This is Parmenides’ objection: “what is, cannot come to be (since
already it is); while nothing can come to be from what is not.” [13]
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 does 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 initial 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.[14] 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 answer is: in a way it is a being, and 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 maintains that,
in a sense, things can come to be in a way. For instance, coincidentally, from
what is not. For 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, as we have shown, the initial object is a compound, in a
way it is both.
2. Zeno’s objection
to the possibility of motion
Zeno was a student of Parmenides. 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 so on infinitely, so that, for any given distance 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 a head start. Then by the time Achilles reaches the point the
tortoise started from, the tortoise will have advanced a certain distance, and
by the point Achilles covers that certain distance, the tortoise will have
advanced 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 take 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 move within 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 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.[15]
The fourth paradox is called the stadium
paradox. Zeno considered bodies of equal length aligned along three
parallel racetracks within a stadium. One track contains A bodies (three A
bodies are shown below); another contains B bodies; and a third contains C
bodies. Each body is the same distance from its neighbors along its track. The
A bodies are stationary, but the Bs are moving to the right, and the Cs are
moving with the same speed to the left. Here are two snapshots of the
situation, before and after.
Zeno points out that, in the time between the before-snapshot and the
after-snapshot, the leftmost C passes two Bs but only one A, contradicting the
common sense assumption that the C should take longer to pass two Bs than one
A. Zeno mistakenly supposes that a moving body passes both moving and
stationary objects with equal speed.
Aristotle argues that how long it takes to pass a body depends on the
speed of the body; for example, if the body is coming towards you, then you can
pass it in less time than if it is stationary.[16]
RESPONSES FROM OTHER PHILOSOPHERS
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. 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.[17]
Moreover, before 212 BC, Archimedes
had developed a method to derive a finite answer for the sum of infinitely many
terms that get progressively smaller. He seems to agree with Zeno that the
amount of time taken at each step is geometrically decreasing.[18]Thirdly,
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.[19]
Fourthly, 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.[20]
Contemporary Usage and Relevance
Concerning the
modern usage of these arguments, more could be said in the fields of
mathematics and physics. One major breakthrough in our contemporary times in
the field of quantum mechanics is the “Quantum Zeno Effect,” which was proposed
by two physicists Sudarshan and B. Misra in 1977. Studying quantum mechanics,
they discovered that motion of a quantum system could be hindered through
observation of the system.
“The Quantum Zeno
Effect refers to a slowing down of the evolution of a quantum state in the
limit that the state is observed continuously.”
It is a phenomenon in quantum physics where observing a particle
prevents it from decaying as it would in the absence of the observation. This discovery in quantum mechanics is based
on Zeno’s arrow paradox. It has led to
the construction of the Quantum computer. Quantum computer is a computer design
which uses the principles of quantum physics to increase the computational
power beyond what is attainable by a traditional computer.
Evaluation and Conclusion. To deny change is to deny motion, to deny motion is to
deny the science of nature and all its constituents.
In
this paper, we have attempted to understand the meanings of nature and motion.
We critically analyzed the meaning of nature and 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.
[1] Cf. Aristotle,
Physics, Book III, part 1.
[2] Cf. Ibid.
[3] Cf. Ibid.
[4] Cf. Aristotle,
Physics, loc. cit.
[5] Cf. Fr. Kenny’s
note on Philosophy of Nature, p. 28.
[7] Cf. Aristotle,
Physics, Bk III, part 2.
[8] Cf. Aristotle,
Physics, Bk III, part 1.
[9]Cf.Omoregbe J., A Simplified History of Western Philosophy (Lagos:
Joja Press Ltd.), p. 50.
[10] Cf. St. Thomas, op. cit., p. 34.
[11] Cf. Aristotle,
Physics, loc. cit.
[12]
Samuel stumpf, philosophy,
history and problem, Mc Graw-Hill Inc pg. 16-18.
[13]
Aristotle, physics, Book I,
190, n 21-25
[14]
Aristotle, Physics, Book 1,
191 a 30.
[15]
Aristotle, Physics Book vi,
239 n 33-240 n5.
[16]
Aristotle, Physics, Book.vi,
240.
[18]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."
[19]Huggett, Nick (2010). "Zeno's
Paradoxes: 3.3 The Arrow". Stanford Encyclopedia of
Philosophy.Retrieved 2011-03-07.
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