This is how I remember the demonstration. When an object comes into being, there is a change from the not being of that particular object to the being of that particular object. ....We never get to the point of actually describing change, or becoming, by following this manner of logic. Instead, we must simply assume a change, or becoming, which takes the middle position between the not-being and being of an object. — Metaphysician Undercover
This sounds like his discussion of Zeno's paradoxes. But I would say that more generally Aristotle takes the position that nothing comes from nothing. Being begins in potential and actuality is about the move or change from there towards contrary or dichotomous limits. So non-being becomes then a privation or lack of some predicate - a positive kind of absence or negativity! If a horse can be white, it also can be not-white. That is a potential change that can take place, being a complementary and LEM-like crisp possibility.
So in its way, Aristotle's take is the kind of Anaximander/Peirce tale of organic development in which we start with a naked potential or vagueness and then this becomes crisply something by separating towards its own logically dichotomous limits. Change inheres in potentiality in metastable fashion because potentiality is already poised, suspended, between two alternative states of development. The question then is what tips the balance so things move in one direction or the other?
The answer for the process philosophy view is that pure chance can be the initiating spark in this fashion - a fluctuation (as modern theories of spontaneous symmetry breaking explicitly presume). When a river forks, it is a matter of chance where some slight deviation bubbled enough at just the right moment for feedback to cause it to develop into a full-blown bifurcation. As they say about the beating of a butterfly wing, it can cause the storm that appears halfway the other side of the world.
But also - as a world actually does start to develop a history - then a different potential-tipping source of cause comes into play. Instead of pure chance, you now have memory or habit starting to dominate. This is the thesis of pan-semiosis. And it is the flipside of pure chance of course.
If you look at why that particular butterfly caused the storm rather than a billion other butterflies active at the time, now you can say well the world had some particular physical arrangement that determined it to be the case that a chance event right at that point would tip everything else over like a chain of dominoes. Now the world as a whole is seen as being in a state - a state of memory and hence constraint. It was poised in some actual way - a holistic way. So it was awaiting the spark that was inevitably going to happen.
Anyway. The point is that Aristotle's general logical analysis holds. He takes the triadic developmental view that potentiality is metastable, being poised to break in two complementary directions. Nothing can come from nothing. But actuality comes from potentiality as the breaking of its symmetry.
However where Aristotle goes wrong is that he takes reality's basic condition as stasis rather than flux. He was trying to do rigorous physics in an era where it seemed obvious that the basic condition of reality was substantial and material. The world was composed of objects made of stuff, making change the fundamental mystery. The deep question became what could animate this frozen realm of static being?
Today, however, it is quite clear from physics that the mystery is exactly the other way round. The issue is how could stasis emerge from flux.
The most natural state of the universe is that it is a generalised bath of radiation, spreading and cooling, with no action happening at less than the speed of light. So the further symmetry-breaking that created gravitating mass, clumping and blundering about at speeds as slow as "rest", and with temperatures as low as "absolute zero", was the mystery.
And that is why Aristotle's further arguments about things like the prime mover have to understood quite differently to make any sense. In a way, he was quite right to get at the primacy of circular motion as nature's most fundamental kind of symmetry (and so the first symmetry with the potential to be broken). But Aristotle then put this source of change at the fast rotating edge of the physical universe - the outer boundary that causes the largest celestial sphere to spin. Now however, particle physics puts that rotation at the frozen centre of being - point-like quantum spin being the immovable object around which everything else revolves.
:)
Anyway, the better way to understand the ontological story is that the unity of potentially becomes dichotomised actuality via the emergence of stabilising constraints - Peircean habits that regulate spontaneity. So the generality of change that is a potential or a vagueness becomes transformed by a polarisation of the sources of change. We get change now of two crisp kinds - chance and determinism, or freedom and constraint.
Stability then emerges from the balancing of these two opposed species of change. Over time, spontaneity becomes increasingly subject to constraint or memory. The Universe gets larger and so colder. The particles in that Universe thus get more stable in themselves and less disruptive of the spacetime that contains them. Change in the end pretty much vanishes.
Throwing the PSR out the window is not something to be taken lightly. This allows for randomness. Once you allow randomness into your schema, you can't get it out. Then you are left without the means to account for any consistency or coherency in the world. There cannot be a reason for consistency. In other words, any form of apparent consistency in the world would actually be the result of some random, chance occurrence. And this is absurd to think that consistency could emerge from randomness, without any reason. — Metaphysician Undercover
Obviously I take the opposite view. But that is also because I am saying randomness is not opposed to potentiality. It is opposed to determinism or constraint. So it is classed with the crisply emergent and not the vague potentiality from which both the determined and the random arise in complementary fashion.
Randomness in the real world is always the product of some system of constraints. It is not pure freedom. Even "chaos" can be exactly calculated from a description of a system's boundary conditions - a description of the global container within which some measure of stuff is being allowed free rein.
If you have a box of particles, you get one kind of emergent statistics - a Gaussian distribution. If you open the lid of the box and let the particles wander, you get another - a fractal or powerlaw distribution.
So any description of randomness turns out to rely on some crisp set of boundary conditions. There is no such thing as true chaos. An utter lack of order becomes simply the vague - the potentiality that grounds these constrasting kinds of order that we might call the crisply "chaotic" (as in mathematical models of powerlaw distributions) versus the crisply "determined" (as in mechanistic action where the constraints are so fixed, the context so mapped out in terms of a domino-like cascade, that a particle or beating butterfly wing has no choice about the sequence of events it appears to initiate in hindsight - as the principle of sufficient reason likes to demand).