Aristotle’s Physics Book VI – Motion and Its Parts
This post is “still” incomplete.
Motion can be divided into species (Book V). But it can also be divided into quantitative parts. It belongs to science of nature to discuss quantitative parts because every mobile being is body.
- 1 Chapter 1 – Movement, Time, and Space are a Continuum
- 2 Chapter 2 – Motion Is Not Continuous Without Its Parts
- 3 Chapter 3 – The Motion of What is Moving and The Rest of What is At Rest Occupies Time.
- 4 Chapter 4 – Two Ways of Dividing Motion. What is codivided with motion.
- 5 Chapter 5 – Only Qualitative Motion Can be Essentially Indivisible – The Now Cannot be Divided
- 6 Chapter 6 – Before every “being moved” is a “having been moved,” and conversely
- 7 Chapter 7 -Finite and infinite are found simultaneously in magnitude, time, mobile, and motion.
- 8 Chapter 8 – No Primary Time at ‘Rest’ or ‘State’
- 9 Chapter 9 – Refutation of Zeno’s Arguments: Dichotomy; Achilles; Tortoise; Arrow; Stadium.
- 10 Chapter 10 – What is indivisible according to quantity is moved only per accidens
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Chapter 1 – Movement, Time, and Space are a Continuum
No continuum is composed of indivisibles. Every magnitude is divisible into magnitudes.
Since whatever is composed of parts is a body and since every mobile being is composed of parts, then every mobile being is a body. Thus mobile beings are partly in act and partly in potency. How many parts are there?
The material definition of a continuum is that which is divisible into what is always further divisible. The formal definition is that whose terms are one.
Material: How do we know the continuum is not made up of indivisibles? Because points, are indivisible because they don’t have parts, and any point that would touch another would totally coincide with that other without ever stretching out beyond it.
Formal: Since the multitude of the parts in a continuum (a line) is not actually infinite, it must be actually finite. (e.g. although the quantity of parts on a line is not actually infinite, there are truly actual parts on such a continuum.). The only way in which the lengthening of a line can be explained is that actual and not merely potential parts are added to the original line; the longer line contains more actual parts than the shorter one.
The actual parts of a (real) line must be distinct in themselves/not overlapping because, they would lose their identity and fail to equal the whole; and they must be distinct from other parts/not compenetrating. Since there can be no comprenetrating, and since they are actual parts, there are indivisibles actually present on a line/continuum. The point is that points on a line, lines in a plane, and planes in a solid are not parts of the line plane and solid because if they were, the continuum would be composed of indivisibles.
So what are the size of the parts and how many are there? We should identify the kind of part we are talking about: proportional, or undesignated parts. In a line 12 inches long, there are twelve undesignated parts – parts that have size only virtually. We cannot apply our metric inch to it – because the minimal part on the line is like the unit in the number system; the unit is not so much a number as a principle of number. Instead of asking how many units are there in 7, its like asking how many units are there in one unit?
Just like one is the principle of number, so the minimal part of line is the principle of the whole. Further, just as a principle contains the effects that issue from it but in a mode differing from the mode of existence these effects shall have as effects, so too that principle of a line which is the minimal proportional part of the line in question is not a line in the same way in which the effect is a line. The material part of the definition bears on potential infinity, the formal definition bears on the actual parts.
The multitude of parts of continuum is infinite in potency. Motion is a successive continuum, while magnitude as such is a simultaneous continuum whose parts are all actual at once and not one after another.
The parts of motion follow the parts of magnitude because the magnitude it traverses is continuous. From the continuity of motion there is evidence of continuity of time.
Chapter 2 – Motion Is Not Continuous Without Its Parts
Time follows magnitude in divisibility and conversely. Since no continuum is indivisible, and since motion is a continuum and therefore motion is not indivisible but made of actual parts. Motion is continuous because magnitude is continuous and time is continuous because motion is continuous. If motion were a series of indivisible moments, a moving being would be at rest in every one of the stages of motion. To reduce motion to a series of nonmotions would really be a denial of motion.
Chapter 3 – The Motion of What is Moving and The Rest of What is At Rest Occupies Time.
The ‘now’ is indivisible in the proper and primary sense (it is a limit). Just as a line is not composed of indivisible points but of lines, so motion is not composed of indivisible moments but of motions.
If time is the measure of motion, and time is a measure applied prior and posterior in motion (magnitude divisible), then motion is thus divisible and time too.
Since the now is indivisble there can be motion in it, and since rest is the contrary the same with it. In an indivisible now, there is no motion or rest.A thing at rest is a thing that remains the same after a period of time.
Chapter 4 – Two Ways of Dividing Motion. What is codivided with motion.
Motion is divisible into
1) the time that it occupies and (time is not composed of indivisible nows, but of smaller times…the now is not divisible.
2) the several parts that are in motion. Since the motion of a thing can never be constituted by the motion of something else, it is the motion of the whole that matters. A thing at rest is a thing that remains the same
It is never proper then to speak of a body or even part of a body as being in a certain place; but it can be strongly argued that a locally moving body according to part of itself is associated more with one part of a trajectory and according to another part of itself with another part of the pathway. Motion transpired between origin and term and so a body shares in some measure in both of them according to different parts of itself…so motion in the strict sense is essentially an affair of parts.
Chapter 5 – Only Qualitative Motion Can be Essentially Indivisible – The Now Cannot be Divided
Since motion is always to something, that which has changed must already at that moment be in that to which it has changed. A primary ‘when’ would be that first unit of time in which a whole nature changed, and hence any change that takes place in stages, with one part os the change taking place in part of the time and another part in another would not have a primary when (it does not change in a primary way when it changes by reason of its parts.
There is no point in time that we cannot find an earlier time. Thus there is no first completion of motion properly speaking. Motion therefore has no primary moment and no primary “when.”
Chapter 6 – Before every “being moved” is a “having been moved,” and conversely
|To get a better understanding of what we mean, it must be considered that just as “point” is a name for the terminus of a line, so “completed motion” is a name for the terminus of a motion. Now, no matter what line or what part of a line you take, it is always true that before the consummation of the whole line, you can take a point according to which the line can be divided. Likewise, before any motion or part of a motion, you can take a “state of completed motion”; because while the mobile is being moved to its terminus, it has already passed a certain stage in respect to which the mobile is said to have been already changed. But just as a point within a line is in potency before the line is actually divided (for a point is the very division of a line), so also the thing called “completed motion” (within a motion) is in potency as long as the motion does not stop there; but if it does stop there, it will be actual. And since what is in act is better known than what is in potency, therefore Aristotle proves his proposition (that what is being continually moved has already been moved) by referring to an equally fast mobile whose motion has already been completed. This is like proving that in a certain line there is a point in potency by showing that a like line has been actually divided.|
Chapter 7 -Finite and infinite are found simultaneously in magnitude, time, mobile, and motion.
A Completion of Motion is Preceded by Motion.Motion is Preceded by a Completion of Motion
Finite Magnitude Passed in finite time, not finite motion in infinite time. Therefore everything that has been moved was previously being moved and everything that is being moved has previously attained some kind of act that we have called the state of having been moved. Both can be true at the same time because motion is a mixed reality, an imperfect act; a thing in motion is constantly other than it was.
Chapter 8 – No Primary Time at ‘Rest’ or ‘State’
Just as there is no first part of motion, there is no first part of rest or first when in which a thing is at rest, because every motion is preceded by a previous motion. Zeno only saw the multiplicity of the continuum and ignored its unity. All of the errors are reducible to this one.
Chapter 9 – Refutation of Zeno’s Arguments: Dichotomy; Achilles; Tortoise; Arrow; Stadium.
One and three were already answered, he answers two and four here, but they involve the same confusion of potential infinity with actual infinity.
Chapter 10 – What is indivisible according to quantity is moved only per accidens
Comparing motion to its completion: 1) in any motion, no matter when we consider the motion, a prior state of having already been changed can be identified. (i think this is why people think determinism).
We can always say that a certain portion of the trajectory has already been covered. Motion is not a mere series of completions of motions or states of having been changed.