Hi David,
I would like to detail my assertion that Aquinas is begging the question in the first way.  But first, I hope this post finds you well.  I notice it has been some 5 months since I first started posting here!  Have you been able to consider my words and any of your other sources to revisit your analysis of the First Way?  I realize that academics commonly work on a project for many months, or even years, so I did not necessarily expect a rapid response.  Hopefully at some point in the not too distant future you will be able to find the time to make some thoughtful responses.
 
In your reference [8] you provide a link that was a source for your notation.  At that link I also found this translation that differs slightly from the translation you use in your analysis above.
“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”
 
You outlined this section as follows
 
g.      It follows, therefore, that all that is moved is moved by another.
(3)   If, therefore, that which moves is moved, then it must be moved by another; and this by another [and so on].
(4)   But this cannot proceed to infinity:
a.       Because, in this case, there would be no first mover; and consequently, no thing would move another,
b.      Because second movers do not move unless they are moved by a first mover, in the same way that a cane is not moved unless it is moved by a hand.
(5)   Therefore, it is necessary to arrive at (or come to) a first mover which is not moved:
 
 
Your notation for these items (neglecting 2g which I included in the text from the Francisco Romero Carrasquillo posted translation) seems to me to be exceedingly abbreviated.
 
        C2)      ~ I                 (premise 4)
       CC)     U                    (premise 5)
 
In [8] you cite a reason as “under premises 2 and 4 Aquinas provides support for the content of these premises. Though the support does not belong to the argument as such,” that I must strongly disagree with.
 
To say
Y because X
is to say
X therefore Y.
 
The words “because” and “therefore” are inverted forms of each other.
 
For whatever reason, Aquinas chose the “because” style, which leads to the following relationships:
4 because 4a
4a because 4b
 
4b is logically prior to 4a
4a is logically prior to 4
4 is logically prior to 5
 
Put another way:
4b therefore 4a
4a therefore 4
4 therefore 5
 
Let’s take a closer look at each of these:
4b        second movers do not move unless they are moved by a first mover
4a        in the case of (infinity), there would be no first mover; and consequently, no thing would move another
4          (that which moves is moved, then it must be moved by another; and this by another [and so on]) cannot proceed to infinity
 
Placing the words in more familiar structure using “therefore” we get:
Second movers do not move unless they are moved by a first mover       
therefore
In the case of (infinity), there would be no first mover; and consequently, no thing would move another   
therefore
(that which moves is moved, then it must be moved by another; and this by another [and so on]) cannot proceed to infinity          
therefore
It is necessary to arrive at (or come to) a first mover which is not moved
 
One could argue that 4b should be further subdivided due to the statements regarding second and first movers.  Here the 2 translations I have referenced differ somewhat
“seeing that subsequent movers move only inasmuch as they are put in motion by the first mover”
“Because second movers do not move unless they are moved by a first mover”
 
This could be summarized as
Subsequent movers therefore first mover
or
Second movers therefore first mover
 
If we use the word “second” as the antecedent then “first” is not a proper consequent, rather a mere tautology of definition, since “second” is merely defined to be the next thing after “first”.
 
If we use the word “subsequent” as the antecedent then “first” is again not a proper consequent, merely an assertion of the very thing that the whole argument is attempting to conclude, that a first mover is necessary.
 
So, by either translation 4b is simply an assertion of the first mover
 
4b asserts U (since there is a second mover there is a first mover)
4a asserts that there can’t not be U (there can’t not be a first mover else there would be no things moving other things)
4 asserts not I (the series of motions cannot proceed to an infinite regress)
5 asserts U (a first mover is necessary)
 
4b therefore 4a therefore 4
4 therefore 5
 
U therefore ~~U therefore ~I
~I therefore U
 
Aquinas merely begs the question.  The First Way is logically invalid.

David,
I have developed an argument for another deficiency in the First Way.  Please consider it as you find the time to review the subjects I have raised over recent months.
 
I assert that the language of Aquinas, his terminology, and most importantly his views of the physics of motion implicit in his language is defective when applied to the modern physics of motion.
 
For the First Way to be a sound argument today it must be sound in consideration of modern physics.  Perhaps the statements of Aquinas accurately reflected 13th century understandings of physics, but that is not sufficient for the First Way to be a sound modern argument for god.
 
I will reference your OP above for wording locations.
(2)        But, all that is moved, is moved by another.
(2)c.     In fact, to move is nothing else than to bring a thing from potency to act.
(4)b.     in the same way that a cane is not moved unless it is moved by a hand.
 
I realize that “move” is used rather ambiguously by Aquinas, although that is not my core criticism in this argument.  In 2c “move” is defined very generally as a realization of a potential, whereas in 4b “move” is used in the common sense of a change in position.
 
These views are not mutually exclusive when we consider common motion as a change in position.  An object has the potential to move to a new location.  Every time an object changes position it realizes a potential to be in that position.  When an object moves from position a to b to c then upon arrival at b its potential to move to b is realized, and according to Aquinas it must be moved by another to change from position b to realize position c. The language is clumsy, but not strictly erroneous on its face, or so it seems.
 
But what of 2?  When something is moved it is necessarily moved by another.  Well, ok with the example of 4b, when the cane is moved, it is moved by a moving hand.  When the hand stops moving, the cane stops moving.  If one pushes a book across a table the book moves because it is being pushed.  When one stops pushing the book, the book stops.
 
What is my problem then?  You may well ask.  Things seem to be just fine with the First Way.  And on Aristotelian physics, indeed, the language of Aquinas seems to match with simple ordinary object motion like a hand, a cane, and a sliding book.
 
Newton is the problem!  Newton said the cane does not stop when the hand stops and the book does not stop when the pushing stops.  Position keeps changing.  Motion continues.  Each successive new position is being brought into actualization from potency even after the outside causal agent stops pushing.  Thus, for uniform linear motion 2 is violated, since there is no other, yet the object moves from position b (at which point it is only potentially at position c) and then the object realizes this change to position c, yet without another as called for by the A-T language of 2.
 
Aristotle knew of this problem, for example throwing a rock through the air.  Aristotle asserted that a force is continuously applied to the rock from outside the rock even in the air.
 
The language of Aquinas implicitly accepts these assertions of Aristotle, and in fact depends upon them, yet Aristotle was wrong, and therefore the language of Aquinas becomes self-contradictory under modern physics, rendering the First Way unsound.
 
On the definition of motion provided in 2c the assertion of 2 is false in the case of linear uniform motion, thus the First Way is unsound by reason of a false premise in 2.

Above you lay out what you call "the" argument.  However, as I mentioned below, in my view your analysis is abbreviated, and omits certain elements that when properly included make the argument invalid, and therefore unsound.

For example, you write these lines:
                     C2)      ¬ I                 (premise 4)
                     CC)     U                    (premise 5)

But those lines do not fully represent the statements in the text.  A more complete accounting of the text gives us.
                     C1)     U                    (premise in 4a)
                     C2)      U→~I          (4a→4)
                     C3)      ¬ I                 (premise 4)
                     C4)     ~I→U           (begging the question fallacy of 5, since U was a premise in 4a)
                     C5)     U→G             (non sequitur, ad hoc, false dichotomy fallacy of 5a )
                                                        (5a also factually false therefore unsound)
                                                        (G is only a statement of personal understanding, not existence)
                     CC)     G→E             (implied that God exists, because U exists and U is understood to be God)


                Legend:
                  G = U is understood to be God
                  E = God exists

Since you are working toward your PhD I suggest that such an abbreviated approach is not academically sufficient.  Is it not reasonable that the full text should be examined, not a subset of that text?

It is true that by choosing only certain items as a subset an apparently valid (though unsound) argument can be written.  I do not see any academic or analytical value in that approach.  For example, why did you omit G?  After all, these are arguments for God, five ways of arguing for God.  God, very specifically, not an inanimate something, rather, very explicitly God. 

In fact, without G, there is no argument for God.  Aquinas very apparently recognized this, but could not make a logical connection between his asserted U and G, so he simply added a (false) assertion at the end, ad hoc.

Aquinas did not explicitly state his conclusion, the foundational reason for making his 5 arguments or 5 ways, "therefore God exits".  The conclusion "therefore God exits" is left as an implication of a (false) assertion of an ad hoc understanding of U.  Did you omit G and E from your notation in recognition of this exceedingly tenuous link?

Hello David, and best wishes to you,
In this post I would like to take a different approach, in that previous posts focused on logical notation, identification of fallacies, and parsing of words into particular orders.  Such analytical parsing seems to be natural, as you have used the work of  Francisco Romero Carrasquillo in developing your notation, which is typical of how we go about analyzing an argument as to its validity.

Here, however, I will turn to the fundamental worldview of Aquinas (in keeping with your words “in order to properly understand this demonstration”), how the view was embedded into the language of the First Way, how aspects of that worldview have been demonstrated to be incorrect in whole or in part, and how the First Way is thus demonstrably unsound in light of modern understandings of natural existence.

With regard to premise 4 in your notation, ~I, you state, “An essential causal series is a series (cause-effect) in which the cause is simultaneous with the effect, and therefore, is essentially necessary for the continued existence of the effect.[23] A series of changed changers is an essential causal series.”

A Few Definitions
Under A-T thought in an "essential" series cause and effect are viewed as instrumental as well as concurrent, coincident, and simultaneous.  Further, in such an “essential” series the cause is essential to the effect in the common usage meaning necessary as well.  

An ontological cause, in this sense, is also essential in the sense of regarding the essence, or being.  Thus, an ontological cause is a sustaining cause, a cause for the very existence in each moment of the object and of the effect, without which the object would cease to exist and the effect would cease to exist.

Under A-T thought an "accidental" series is a temporal series wherein the prior cause is presently separated from the effect and is no longer instrumental, although it can be essential in the common usage of the word “essential” but not in the A-T sense of the word “essential”.  Since an “essential” or ontological cause is simultaneous with the effect it is not temporal, therefore every temporal causal series is an “accidental” causal series.

On the Notion of Simultaneity
What would it mean for a cause to be concurrent, or simultaneous, with the effect?  Humans tend to assign the title of cause to one object process and the title of effect to another object process. So, one might say that when the cue ball impacts the 8 ball the cue ball is the cause and the motion of the 8 ball is the effect.  Under A-T thought this is considered "accidental" since it is a temporal process such that even if we got rid of the cue ball while the 8 ball was still rolling the 8 ball would continue rolling nevertheless.

If, on the other hand, one uses a stick to continuously push the cue ball along then under A-T thought this is considered an "essential" series because it is imagined that the continuation of rolling is assigned the title of effect, the stick is considered an instrument, and the human pushing the stick is assigned the title of a cause.  In the A-T oriented brain it is imagined that the cause is thus concurrent with the effect.

Such A-T thought hearkens back to centuries past when analysis of cause and effect were limited to simply watching ordinary objects and thinking about them.  What was not appreciated in centuries past is that the continued motion of the 8 ball is not a single effect, nor is the human a single cause, rather, the human is composed of a vast collection of internal causal influences, on the order of some 10^27 atoms organized as some 10^13 cells, all engaged in an enormous set of continual temporal causal sequences.

Similarly, the motion of the cue ball is not only one effect, rather, the cue ball is just as much of an instrument as the stick, transmitting energy to the molecules of the air and the felt in an vast number of temporal causal sequences.

Let's examine one simplified causal series in this vast collection. A single oxygen molecule travels from the outside air, into a lung, through the tissue membrane, and into a red blood cell.  That cell travels through the bloodstream to a muscle where in combination with an organic molecule it transfers a finite amount of energy, enough to move the hand a small increment, say, a nanometer.  The stick then moves a nanometer, which in turn moves the cue ball a nanometer, which in turn bumps into several air molecules, accelerates those air molecules, and transfers that finite amount of energy into kinetic energy of those air molecules. It should be readily apparent that this causal series is temporal and in A-T terms "accidental".

Every so-called "essential" series is in fact "accidental" upon more thorough examination, being made up of a combination of a vast number of minute “accidental” temporal causal sequences.  If a perceived cause and effect are actually composed of many separate causes and effects and each such cause and effect are accidental then the combination of causes and effects must also be “accidental” with the perception of an overarching “essential” cause and effect being illusory and merely a perceptual lumping together of events that are in fact separate and “accidental”.

The assignment of title of cause and effect to whole systems of causes and effects is an approximation of analytical convenience that leads to qualitative analytical errors when the quantity of approximation reduces a vast number to just a few, without due awareness of the pitfalls of such approximations.  The notion of an ongoing motion as an effect is an artifact of the human perception of what is thought of as the present, which is not really the present moment, rather, it is a model in the brain of recent past events and imagined near future events all internally represented as members of a temporally static concept of the present.

To what extent are cause and effect concurrent or simultaneous?  From Newton's fluxions, to Russell’s objections to the infinitesimal, to the definition of calculus by use of limit expressions there is a long and controversial debate about the validity of the notion of an infinitesimal.  The infinitesimal is perhaps loosely described as being infinity small yet not equal to zero.  In calculus it is commonly thought to be what is represented by dx, or dy etc.

In the limit as t2 – t1 goes to 0 we find the only sense in which we can rationally speak of simultaneity, and this is sometimes referred to as the infinitesimal. Simultaneity cannot exist outside this limit or infinitesimal, since any time outside this limit is in the past and thus no longer simultaneous.

Since a causal series is more than one event or a process over some finite time no series can be contained within the limit or infinitesimal, since any 2 events a finite time apart can have their event time difference further divided into an arbitrarily large number of subdivisions, and therefore violate the very definition of what the limit or infinitesimal is.

Thus no causal series is simultaneous or concurrent.  Therefore no causal series is "essential".

Persistence Absent a Changer
The plain text of the First Way clearly calls for an argument based on positional change over time, or more broadly change over time, as first expressed by “It is certain, and evident to our senses, that in the world some things are in motion.” Since all motion and all change that is evident to our senses necessarily occurs over time Aquinas is clearly describing temporal processes.  Aquinas goes on to use the example of a flame, which necessarily moves, as well as describing the heating of wood, which is necessarily a temporal process.  Aquinas describes a hand moving a staff, clearly an example of positional change over time.  So when Aquinas says “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.”  the obvious plain text meaning of this causal series is temporal, since all such cases that are evident to our senses are temporal causal series, in keeping with the sensory evidence basis and examples of the First Way argument.  

However, in spite of the necessity of a temporal regress the plain text language of the First Way demands, it is argued with respect to A-T assertions of a causal series, such as Aquinas describes in his First Way, no attempt is being made to describe the cosmological origins of motion. It is imagined that the true necessity for a first mover is ontological in nature.  That is, the A-T oriented brain imagines a need for an ongoing sustaining cause for both motion and material existence.

It is argued that such an ontological series is "essential" and cannot extend to infinity.  In fact, on the modern sciences of motion and conservation of matter/energy there is no need for any ontological cause or ontological series at all, much less a consideration of an infinite such series to be rejected in favor of a finite series terminating in an imagined first mover.

On conservation of matter/energy to merely persist in existing is no change; therefore no change requires no changer.

On conservation of matter/energy to merely persist in existing is no motion; therefore no motion requires no mover.

On modern science of motion including inertia merely persisting in uniform motion is no change for the object in motion; therefore no change requires no changer.

On modern science the call for a choice between an infinite ontological series versus a finite ontological series in the present moment is a false dichotomy and unnecessary.  No sustaining cause is called for at all.

When things don’t change then things don’t change.  Yes, I realize that is tautological, but that is my point.  The Thomist demands an explanation for this tautology.  We see that persistence of matter/energy is no change, yet the Thomist asserts it would change if there were not something keeping it in existence, a changer that is itself unchanged.  Since this is an asserted changer, the thing being changed is the very thing we observe to not be changing.

Thus the Thomistic explanation becomes that when things don’t change an unchanged changer is continuously changing them to not change.  

Those who are not Thomists realize that when things don’t change they continue as they are.

Of course things do change in some respects, for example, acceleration, change in shape, and change in chemical arrangements.  All such changes are necessarily temporal processes, calling for a temporal causal regress, and thus no ontological cause.

Against Any Need for an Ontological Changer
To show that an ontological first mover is unnecessary several conditions are addressed.
1. For objects merely persisting in existing there is no change and therefore no necessity for an ontological cause.
2. For objects in uniform motion there is no change therefore no necessity for an ontological cause.
3. For objects undergoing change all such changes are temporal and thus call for a temporal regress of causes, and therefore there is no necessity for an ontological cause.

In all instances there is no necessity for an ontological cause and therefore the First Way is negated.

Where Aquinas Goes Causally Wrong
Having established that the very notion of a first mover for an “essential” series of causes and effects of motion is unnecessary, it is apparent that the First Way must be not only unsound, but profoundly erroneous to its core.  But where does the Thomistic argument break down specifically?

First, let’s consider the word “simultaneous”, which simply means “at the same time”.  Thus, in a simultaneous series of cause and effect t1 – t2 = 0, and t2 – t3 = 0,…and t(n-1) – tn = 0.  The time between the first cause and the last effect is precisely zero.  In modern causality we know this is not the case.  Causal influences propagate through space no faster than c, the speed of light in a vacuum.  For moving objects causal influences propagate at much lower rates, the speed of the causal object, or the speed of the causal series such as the speed of sound in a particular medium, for example.  

The very notion of an “essential” simultaneous series is false, in light of modern knowledge.  There simply is no such thing as t1 – tn = 0.

A Local Example
Allow me to give you a specific closed system example, one of many such available.  Consider a tank of compressed Argon gas, which is a sealed steel bottle containing a finite number of Argon atoms.  

Inside we find a mad chaos of motion, a crazy beehive of Argon atoms bouncing off each other and bouncing off the walls of the steel bottle.  The pressure against the walls is accounted for by the sum of the impacts of these agitated atoms.  This motion never stops, so long as the bottle remains sealed, further, the sum of this motion remains constant, as long as the temperature of the bottle remains constant.

Please identify in this bottle of compressed Argon
1.    The “essential” series.
2.    The first mover of this series.

Clearly, both 1 and 2 are illusory, and based on Aristotelian concepts of motion long ago shown to be erroneous.  Here is a simplified description of the Argon atoms, “A”, and the sort of series they are in, necessarily a time sequence of events, not simultaneous.
A1 moves A2
A2 later moves A3
…  later moves An
An later moves A1

If that series were a logical argument we would say it is circular.  It is indeed a circular description.  Simply put, all the atoms inside the bottle just keep bouncing off each other over time without end.  On modern knowledge the reasons are that there is no such thing as friction at the atomic level, the natural state of matter is to continue moving as it is unless acted upon, and matter/energy are conserved.

Now, the Thomist may object that this is a closed system, not representative of the universe as a whole.  It remains to be seen whether or not the universe is a closed system, but irrespective, if there is to be an ontological first changer it must be acting in all places and at all times, including inside our Argon filled sealed bottle.  Irrespective of how the gas was placed in the bottle many days ago, the ontological first mover must be keeping all those atoms in existence and moving them about.  Yet no such necessity is in evidence.  The Argon atoms simply continue to exist under conservation of matter/energy because there is no change to the total amount of matter/energy in the bottle, and therefore no necessity for a changer.

Thus, as an argument for an “essential” ontological series, premise 4 is part of a false dichotomy.  Ontologically there simply is no series, since the very notion of any need for a sustaining cause is illusory on inertia and conservation of matter/energy.

The Thomist may further object that changes in “quality” are somehow different than so called “local motion”.  In fact, changes in color, size, temperature, or any other aspect of an object all require “local motion”.  Color changes as molecules move and photons are absorbed differently while they are in motion.  Size or volume or any change in content of a collection of matter/energy requires that objects move into or out of that collection.  A change in temperature requires that the average motion of the atoms in the object changes by various motions.  Thus, to change any sort of “quality” necessarily requires so called “local motion”.

An additional objection sometimes raised is that there must be an ontological first cause not simply for the persistence of matter/energy, but the persistence of “form”.  On this thinking, the structure or shape or arrangement of objects requires something to hold them together and this series cannot go on to infinity.  This is actually an argument for a fundamental physics, reducing god to the 4 known forces of nature or some more fundamental unified force.  There simply is no need for this fundamental physics to be anything other than properties of material existence.  Further, the First Way is an argument from motion, or change, not an argument from form, which ideally is not changing, and therefore requires no first mover, or first changer.

Infinite Regress in Time
Now, one may object that I have limited my discussion to a finite time, leaving open the question of how the motion of this whole system of motion came to be.  Both Aristotle and Aquinas concluded that an eternal universe either was the case or at least could not be logically disproved, so even in this consideration there is no terminus since motion extends back into the past ad infinitum given the A-T notion of an eternal universe.  Thus, in the case of a temporal regress interpretation premise 4 is also false.

In either case, moving objects bouncing off each other ad infinitum, or extending back in time infinitely, there is no call for an ontological mover at all, since the causal series for motion is temporal, not ontological.

Ontologically premise 4 and premise 5 is a false dichotomy because there is no such thing as an ontological series, the very notion being illusory.

Some Key Concepts Covered
1.The notion of an “essential” series is illusory.
2.Simultaneity of cause and effect does not extend beyond the limit as t goes to zero (the infinitesimal).
3.No ontological first mover (sustaining cause) is necessary for persistence of matter/energy on the modern science of conservation of matter/energy.
4.No ontological first mover (sustaining cause) is necessary for persistence of motion on the modern science of conservation of matter/energy.
5. No ontological first mover (sustaining cause) is necessary for persistence of motion on the modern science of inertia.
6.All forms of change require so called “local motion”.
7.Every causal series is a temporal series.
8. No ontological first mover (sustaining cause) is necessary for change on the modern science of motion.
9.No temporal first mover is called for on the assertion of an eternal universe with eternal motion.
10.The assertion in the First Way of “But this cannot go on to infinity” versus “Therefore it is necessary to arrive at a first mover” is a false dichotomy because there simply is no “this” or “it” (ontological series or sustaining cause) necessary.
11.The plain text reading of the series “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” with respect to “It is certain, and evident to our senses, that in the world some things are in motion” is a temporal regress.
12.The assertion “But this cannot go on to infinity” is false on the plain text temporal reading and an eternal universe with eternal motion.

Conclusion
In my previous posts I showed a variety of argumentation defects of the First Way and the analysis provided above including
1.Affirming the consequent to state, “when Aquinas talks about movement he is talking about change, as can be seen from the definition that he gives of change (to move)” since he actually made the converse of your statement
2.Begging the question by arguing U -> ~~U -> ~I -> U.
3.Stating the manifestly false premise that U is what all consider to be God
4.That same premise “this is what all consider to be God” is also an ad hoc assertion, a non sequitur with respect to U, and a false dichotomy even if we grant U.
5.Aquinas fails to even argue that “a divine being exists” as you address in your opening paragraph at some length.  Aquinas only states (falsely) “this is what all consider to be God”, which is a statement of mere human thinking, leaving the actual existence of a God as an implied non sequitur from mere human notions of God.
6.The notation of Francisco Romero Carrasquillo is crucially abbreviated, invalidly omitting 4b, 4a, 5a, and the implied assertion of the existence of god, without which the notation does not even attempt the purpose called out in your opening paragraph, to show “a divine being exists”.

Still, despite the many defects I have pointed out in previous posts and summarized in 1 through 6 above, those defects are potentially repairable with a more careful rewording of Aquinas, although the actual text of Aquinas will remain hopelessly invalid and otherwise unsound.

Thus, the very notion of an “essential” series is an error of human perceptual artifacts, while the call for an ontological causal agent or series is without rational merit, rendering the Thomistic worldview irreparably erroneous to its core, owing to the falsity of these foundational principles.

David,
I have developed some additional criticisms of the First Way, and also some comments on portions of your analysis above.  You provided a link in [8] as a source for your work, so I have copied the translation of the full text of the First Way here because I think it offers additional perspectives relevant to my points in this post.
 
You state:
“First, when Aquinas talks about movement he is talking about change, as can be seen from the definition that he gives of change (to move) as: to bring a thing from potency to act.”  That assertion does not follow from the text itself, although you might find support for it in other works of Aquinas.
 
The first line written by Aquinas makes clear “The first and more manifest way is the argument from motion. “  Motion, not more general change.  Motion is, very apparently, a sort of change, but a particular sort of change.  All motion may be change, but it does not follow logically all change is motion (it is, but Aquinas did not know that, and his First Way argument does not support this subatomic fact of physics).
 
Aquinas says “For motion is nothing else than the reduction of something from potentiality to actuality.”  Your assertion that this definition is a definition of general change calls for the converse wording “the reduction of something from potentiality to actuality is nothing else than motion”, which commits the fallacy of affirming the consequent relative to the actual wording.
 
The converse does not follow because there could logically be different sorts of potential and corresponding different sorts of actuality. While motion may be one sort of actuality it does not follow as a logical necessity that all sorts of actuality are motion.
 
Further, Aquinas clearly differentiates between motion and change when he says “, and thereby moves and changes it”.  If move means change then this phrase would read “, and thereby changes and changes it”, which would then suffer from a redundancy.
 
The fact that the word “change” is used separately from and additionally to “move” shows that Aquinas was quite capable of using the words he meant to use, and has no need of others to say “what he really meant was…”.  If he had meant something different he could have said something different.  Additionally, Aquinas said “as the staff moves only because it is put in motion by the hand”, clearly using “move” to mean a physical motion, his argument being predicated at the outset on what is “evident to our senses”, and the staff quite evidently is in physical motion.
 
Moving on to another item I would like to focus on a couple aspects of your analysis.  You say “Therefore, a being exists which is the primary unmoved mover of all movement - the unchanging changer”…” If at any moment this unchanging changer ceased to cause change, then all changing things would cease to exist.”  I find this to be a self-contradictory claim in the first instance, a non sequitur based on a conflation of change with existence, and an archaic Aristotelian worldview.
 
The term “unchanging changer” is directly contradictory to “If at any moment this unchanging changer ceased to cause change”, the second phrase clearly indicating that this asserted changer is engaged in a time sequence of imparting changes.  Thus, at one moment the changer is potentially imparting a particular change, and in the next moment the changer realizes that potential to impart that particular change, the changer thus fulfilling the very definition of change provided elsewhere in your work, and thus not unchanging, rather itself changing. 
 
But, for the sake of argument, let’s suppose this changer is continually imparting various sorts of change to real objects.  If indeed a real object cannot change without being changed by this asserted changer, and the changer ceases to impart change, it does not follow that the real object would cease to exist, rather, it would merely cease to change.
 
This leads into my more general assertion that you are engaging in an archaic, obsolete, and evidently false Aristotelian world view on the assertion that the objects of the world need to be continually be pushed along, as it were, else cease, not only changing, but their very existence.  Newtonian uniform motion evidently discounts this view, as does modern physics. 
 
On the Aristotelian view an object ceases its motion when the external force upon it ceases.  That is why Aristotle asserted that an object thrown through the air continued to be acted upon by forces outside the object in order to sustain its motion.  Aristotle was wrong, so to state ” if at any moment this unchanging changer ceased to cause change, then all changing things would cease to exist” only repeats this ancient and evidently erroneous world view.
 
I’ll end my writing here for now, please enter these points into your collection for consideration as time permits.  I ease my feelings of guilt over such a long post by considering it as only 0.000007GB of data removed from your ISP allotment (assuming one byte per character).
 
I trust you are settling into your new and long awaited role, no longer the aspiring student, now the accomplished PhD, a tremendous achievement indeed, my repeated congratulations!
 
(From your link in [8])
"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 Argument from Joy/Desire
Presumably this is regarded as an argument for god.  It is based on a stated premise "Creatures are not born with desires unless satisfaction for those desires exists" which is argued invalidly, employing hasty generalization, citing certain examples, but making no logical case that the premise should be considered universal.

"If none of my earthly pleasures satisfy it, that does not prove that the universe is a fraud."  The simplest explanation is that we are capable of irrational thoughts.  There is almost endless evidence for the irrationality of human thought, and thus irrational human desires, desires for things that cannot be.

Rather than invoke this very simple and highly evidenced expiation Lewis chooses to invent a whole unseen and unevidenced world of his imagination! "If I find in myself a desire which no experience in this world can satisfy, the most probable explanation is that I was made for another world"

Somehow, to Lewis, the invention ad hoc of a whole other world of unearthly properties is more probable than the thing we experience and record in enormous volume every day.  All this somehow constitutes an "argument" to Lewis and his admirers.

BTW, I have not noticed any edits to your post
http://philosopherdhaines.blogspot.com/2013/09/a-defense-of-aquinass-first-way.html
or any counter arguments to my assertions that your post contains errors or argumentation and notation.  Congratulations on your PhD, truly a highly admirable achievement.  So far I have found no person both willing and capable of seriously engaging on the subject of my notational corrections to your work or the invalid logic of the First Way I have described, so I would be interested in your views on the subject.

Continuing with some further points, in general, in my view, your listing of premises is abbreviated.  A more complete list of premises illuminates flaws in the First Way including self contradiction, begging the question, and false assertion.

For example, what you show as 2(d) is actually a very important premise.  Aquinas explains by example in addition to his argumentation that a particular kind of change change can only be caused by a thing already changing in the same way.  Only a hot thing can change a potentially hot thing to become a hot thing.  Thus, only a moving thing can cause a potentially moving thing to move.

We see then that the asserted unmoved mover violates at least some premise or combination of premises that Aquinas previously set forth.

Since 2(d) requires that motion is caused only by a moving thing then U was moving when U caused the first motion in our observable universe.

But motion cannot proceed to a past infinity, according to premise (4).  After all, if motion could proceed to a past infinity then I would be the case and therefore ~U would be the case.

So U must have been motionless, and then moved.  Yet premise (2)   asserts  all that is moved, is moved by another, making U not the first mover at all.

So, U must have moved itself, but that is a violation of 2(f).

In summary, Aquinas collapses under his own weight, or is hoisted upon his own petard, or whatever metaphor you prefer, or perhaps you prefer no such metaphor, in which case it is logically apparent that the First Way is invalid by the fallacy of self contradiction, and therefore unsound.

(2)   But, all that is moved, is moved by another.
(5)   Therefore, it is necessary to arrive at (or come to) a first mover which is not moved:
Response- The speculated god would have to have "moved" (changed or altered or undergone some sort of process) in order to be a "mover".  For example if this speculated god made a decision to “move” the substances of existence that decision itself was a “movement”.   If this speculated god was motionless and then made a decision it “moved” itself.  Even if no decision was made, if the speculated god was motionless and then “moved” in any sense it must have “moved” itself.
Thus on a previously motionless god (5) is incompatible with (2).
 
Alternatively, on a god eternally in motion the following is violated:
(4)    But this cannot proceed to infinity:
 
In either case, Aquinas defeats his own argument through self-contradiction.
 
 
a.        and this is what all consider to be God.[13]
Response- False by counter example.  I am part of all and I do not consider this to be god.  Even if the failed logic of the argument could somehow be rescued the first cause, or first mover, or uncaused cause, or unmoved mover could be merely another inanimate state of existent something.  Thus, this assertion is both patently false by counter example and unsound since it suffers from being a false dichotomy.
 
 
There are other defects in the arguments of Aquinas but I will begin with these.