As traditionally presented, the argument from motion rarely lists all the assumptions at the beginning. Assumptions such as "motion must be externally activated from potential" and "motion can not be in an infinite chain" get worked into the argument, often by declaring them to be obvious (the very notion of being an assumption). By then end of the argument, there are a fairly good-sized number of assumptions (each distinct argument having its distinct subset).Now, in mathematics, a lemma is a proven statement used as a step in the proof of a bigger theorem. There is no formal difference between a lemma and a theorem -- both follow the same rules of proof -- but there is a material difference. The main interest centers on the matter of the theorem, while the matter of the lemma is of little interest in itself at the moment. In the same manner a carpenter may use a hammer in the construction of a cabinet without any imputation that the hammer is simply assumed, and not itself constructed.
For example, in the proof that two continuous functions from X into a Hausdorff space Y are equal if they coincide on a dense subset of X makes use the lemma that if A is dense in X and Q is open in X then A∩Q is dense in Q. [Example: the rational numbers are dense in the real numbers, so the rational numbers in the interval (0,1) are dense in that interval.] Now, the proof of the lemma is lengthy enough that to insert it into the midst of the proof of the theorem would constitute a digression. But even disregarding length, the proof of the lemma is "another topic" relative to the purpose of the theorem.
With this in mind, let us consider the Unobrower's complaint wrt the Proof from Motion. When life hands you a lemma, make lemma-nade. We have been handed two lemmas, which puts us in a di-lemma.
Definition. The argument from motion does not proceed from local motion only, that is "change of location." The word κινεσις (kinesis) used by Aristotle or motus used by Aquinas is usually translated as "motion" but more precisely means "change." To refute Parmenides and Zeno, who held that change was in illusion, Aristotle developed the notion of Potency and Act, and defined change as a "motion" from potency to act. A green apple changes to a red apple if first of all it was potentially red and then was moved to being actually red. The motion from potency to act was called kinesis, usages preserved to this day in potential energy and kinetic energy.
|Why an apple turns red|
Example, the apple is moved to become red by anthocyanin, which is activated by light in the regions of 3,600 to 4,500 Å. (This is light within the near-ultraviolet, violet, blue and green regions of the spectrum. Whatever absorbs these colors will appear red.) Without light, apples become yellow as they ripen, even if the apple would otherwise normally turns red. Thus the light possesses redness actually (in an eminent sense) and moves the apple to redness.
In a similar manner, we see that the dog walks across the room because the local motion of its parts (the legs) move the whole. (And the legs are moved by the muscles, etc.) Thus the legs possess local motion actually (in a formal sense) and move the dog to local motion.For a more general discussion of this Lemma, especially as regards the usual counterarguments, see the pdf: "Whatever is Changing is Being Changed by Something Else’: A Reappraisal of Premise One of the First Way," David S. Oderberg
|An essentially-ordered series.|
This cannot regress infinitely.
|These are not the first cause of the|
- the auditory cortex in your brain is moved by
- the auditory nerve, which is moved by
- the cochlea, which is moved by
- the bones of the middle ear, which are moved by
- the tympanum, which is moved by
- compression waves funneled by the pinnae and ear canal, which are moved by
- the vibrations of the strings in the piano, which are moved by
- the hammers, which are moved by
- the keys, which are moved by
- the pianist's fingers, which are moved by
- (skipping some intermediaries) an act of will of the pianist
|An accidentally-ordered series.|
This might regress infinitely.
Now, suppose the series were to regress indefinitely. Then there would be no first changer. But then none of the subsequent changers in the series would have any power whatsoever and there would be no change in the world. But there is change, therefore there must be a first mover for any essentially-ordered series.
This is also addressed somewhat in the Odenberg paper linked above.
|Someone once must have come up with|
this without having to be taught it
Mr. Brow concluded by stating "By then end of the argument, there are a fairly good-sized number of assumptions." A fairly good-sized number? But it is not clear that there are more than the two mentioned, the Major and the minor premise, which are not assumptions but lemmas proven independently. (And how many assumptions lie behind the topological theorem mentioned above?)
+ + +
The first and more manifest way is the argument from motion. It is certain, and evident to our senses, that in the world some things are in motion. Now whatever is in motion is put in motion by another, for nothing can be in motion except it is in potentiality to that towards which it is in motion; whereas a thing moves inasmuch as it is in act. For motion is nothing else than the reduction of something from potentiality to actuality. But nothing can be reduced from potentiality to actuality, except by something in a state of actuality. Thus that which is actually hot, as fire, makes wood, which is potentially hot, to be actually hot, and thereby moves and changes it. Now it is not possible that the same thing should be at once in actuality and potentiality in the same respect, but only in different respects. For what is actually hot cannot simultaneously be potentially hot; but it is simultaneously potentially cold. It is therefore impossible that in the same respect and in the same way a thing should be both mover and moved, i.e. that it should move itself. Therefore, whatever is in motion must be put in motion by another. If that by which it is put in motion be itself put in motion, then this also must needs be put in motion by another, and that by another again. But this cannot go on to infinity, because then there would be no first mover, and, consequently, no other mover; seeing that subsequent movers move only inasmuch as they are put in motion by the first mover; as the staff moves only because it is put in motion by the hand. Therefore it is necessary to arrive at a first mover, put in motion by no other; and this everyone understands to be God.The only thing I see missing is an explicit definition of essentially-ordered series, which is implicit in the underlined part. You can translate that as