This argument requires you to first define what a substance even is. You seem to be using substance in the Aristotelian sense of "an individual", but that's not what it always means. Philosophies like naturalism and dualism, for example, are most certainly not referring to individuals when they refer to substances, so I don't think this argument can hold any weight in a debate over them. Furthermore, the idea that the parts are all parts of a whole doesn't really tell you anything. Everything is part of a larger whole. Humans constitute a whole species, which could, by the same argument, be said to be a single substance, as could an ecosystem, the entire planet, the entire solar system, and so on up to the entire Universe. If a substance just means "a whole", the concept is almost meaningless. The only real way to define a "substance" in the sense in which you are using it is to define some type of thing first, say, a whole person or a whole society, and then show how an individual fits a description as that type of substance. I certainly don't see any way such a claim could imply immortality, however.

>At the moment of conception, the newly formed, single-celled zygote contains all the organs needed to keep this new, unbelievably-tiny human being alive.

What? A single-celled zygote doesn't have any organs yet. It's still a single cell. It has the potential to develop organs, but if already having these organs is somehow part of your criterion for being considered a whole substance, it wouldn't be considered one. And it definitely doesn't have everything it needs to keep itself alive. That why it stays inside the mother for nine months.

>That is the reason why everyone is so instinctively certain that he but a single being, with both mind and body, existing as a unified substance interacting with a real physical world.

That's true, and it makes perfect sense if our mind is physical, just like our body. It doesn't make sense that we would feel ourselves as a unified whole if we were in fact both physical and spiritual at the same time. It would require the non-physical to interact with the physical (which is unlikely and has never been empirically observed at best, and an outright contradiction at worst), and to do it so often that a whole can be constituted of both physical and non-physical parts.

>Some reason for the unity of the whole self must be posited. Such a reason, according to Aristotelian-Thomistic philosophy, would be the substantial form, or soul, which animates the entire organism to be and to act as a single substantial unity.

If this is the case, then "the soul" just refers to neurons firing. Psychologists and neurologists have already discovered a great deal about how the brain unifies our experiences (in fact, there is an entire school called "gestalt psychology" which is based on this notion). Our brain receives and unifies all of our sensory input, and it also connects our sense data with the parts of our mind responsible for thinking and action. What more is there to explain? What part of our experience does this leave out?

>The essential insight, as I more fully explain in another Strange Notions article, is that purely physical things can never apprehend the “wholeness” of an experience for the simple reason that physical representations are always extended in space. They always “image” something by having one part represent one part of the object and another part represent another part – with no single part representing (apprehending) the whole.

And so what? I'm not just a single part of my mind - I am my entire mind and body. I'm a unified whole. This is exactly what you already argued for above, but this new argument seems to rely on the exact opposite principle. It would only make sense to argue that you can't have simple unified experiences because your brain is made of smaller parts, like the pixels on a screen, if you were just one of those pixels, if I were just a single neuron. That's exactly the opposite of how the brain works in real life, however. Different parts of the brain are in constant communication with each other. No single part of the brain contains the entire picture, but no single part of the brain is me. I'm the entire screen.

> But, I am saying that what is immaterial is neither extended nor locatable in space.

All you've really proven is that our minds don't occupy a single location in space, since no single part can give rise to the unified experience. You haven't proven that our minds aren't extended objects.

>Some modern materialists are puzzled by “qualia,” properties of experience that are not physically detectable, yet subjectively real. But anything genuinely physical must be locatable in space. Either qualia are locatable or not. If they are, then they are merely material. If not, then immaterial things exist.

Indeed, and qualia are locatable in space. They occur in the cortex.

>But clearly, experiences of “wholes” are not locatable in space, as shown above.

Yes they are. They, too, are located in the brain, but they are extended. They are located in the entire brain, not just a single part of it. Asking, "which part of the brain contains the experiential whole?" is as meaningless as asking "Which part of the body is the human?"

> Aristotle attributes human acts, such as described above, to the form of the substance – the substantial form, which he also calls the soul.

I have no problem accepting Aristotle's "soul", but only because it is very different from the common meaning of the word "soul". Aristotle's soul is simply the form that the matter of the body takes, and this type of soul need not be immaterial, let alone have any spiritual aspect at all.

>So, too, for modern materialists, all knowledge, whether direct sensation or “intellectual” ideas, is merely sensory in nature, and thus essentially mere neural activity and patterns ultimately based in the brain.

This is simply a strawman argument. You can't take Hume as some sort of definitive source for what all non-believers think. Materialists are under no obligation to agree with Hume's position. While I agree that all mental activity occurs in the brain, I disagree that all mental activity, or even all knowledge, is sensory.

>In any event, being radically immersed in matter, they are expressed under conditions of time and space. This means that they are always singular, particular, concrete, and having material qualities, such as shape, color, size, and so forth, which make them imaginable. Thus, one can imagine a horse or triangle, but always with a particular shape, color, size, and so forth.

This confuses the map with the territory. You are assuming that our perceptions of space, time, etc., are the same as actual space, time, etc. I may imagine an object to have a particular color and spatial extent, but that doesn't mean that the image itself actually, physically, has that color or that same spatial extent.

> Indeed, some concepts are directly of spiritual entities which inherently cannot be physically expressed, such as justice, beauty, truth, oneness, and so forth.

I would object to the characterization of any of those things as spiritual. The concepts themselves are abstract, which means they are neither physical nor spiritual, but they certainly can be physically expressed. Justice is physically expressed by a conman having to pay for his crimes. Beauty is physically expressed in the plays of Shakespeare or the artwork of Michelangelo (or, at least, in the brains of people who observe these works, since beauty is in the eye of the beholder). Truth is expressed whenever we say something true, and oneness whenever we have one of something.

>The fact that the human intellect can form such spiritual entities, demonstrates the spirituality of the human soul, since the less perfect cannot produce the more perfect.

I obviously don't agree since I don't agree that these entities are spiritual in the first place, but I also don't agree with that last part. Less perfect things create more perfect things all the time. That is the basis for biological evolution and for genetic algorithms. Humans, who are imperfect at any task, can create technology that does the same task nearly perfectly, and we are always learning how to make our technology more perfect (and better at more tasks). We humans can also improve ourselves either by surgery (removing malfunctioning or broken parts of our bodies and replacing them with synthetic versions that function better or break less easily) or by instruments that augment our bodies' usual functions (like eyeglasses or telescopes).

>Therefore, the separation of that spiritual soul from the material body at death does not entail the end of life for the human person.

Even if I agreed with everything up to this point - obviously, I don't, I think the argument has many flaws that all compound with each other - this would not follow. You argued earlier that certain mental activities still depend on the material even though they are immaterial. Surely these functions would be lost if the material part of the mind is lost. The only way the soul could completely survive separation from the material body is if it had no material aspects whatsoever, but you already argued against this view. Thus, even if part of the soul survives, that is a crucial part of you that would be lost after death. You would be like a different person. However, there is yet another problem. You haven't actually demonstrated that any part of the soul survives, even if we accept everything up to this point. Even if part of the soul is immaterial, that doesn't mean it MUST survive the death of the body, or even that it can survive this. It simply implies that, in the argument so far, we don't know either way yet. And we certainly don't know whether the soul is immortal.

Just a couple random thoughts here.

First, as I recall, at some point late in his short life, St. Thomas was asked what the next world was really like. I understand that his reply was simply, "Other."

This would not be so surprising to me, since we often forget how tenuous our sources of information about reality really are.

First, all our purely rational knowledge of the spiritual world is indirect. That is, we do not know so much what it is as what it is not. We say it is spiritual. But that means "strictly immaterial." And "immaterial" means what is NOT material. So, we know what is material and we know that something exists which is not it.

So, too, with terms, such as "infinite," meaning Not finite. We know the finite, but then what is NOT finite? So, too, with the entire negative natural theology of concepts that are predicated of God, but without the limits of our direct cognition. Goodness, but without limit. Power, but without limit. Knowledge, but without limit. We know the positive quality that is limited, but have no direct knowledge of what it means to have such a quality without limit.

But do we really have better knowledge of this physical world in which we live? All we know is through the five senses that Plato characterized as mere "peep holes" into the world. What of the rest of the physical world we simply cannot sense, but are convinced is real: gravity (we merely sense its effects, not it), photons, atomic particles too small to be sensed, x-rays, the rest of the universe beyond our instruments range, the universe known only by instruments, not directly by sight, the infrared, the ultraviolet, and on and on.

Do we even know directly five percent of the real physical world we think we know so well?

So, when asking about the nature of reality beyond this physical world, we must realize that its reality is not the problem. It is the absurdly limited range of our knowledge that makes such knowledge beyond the limits of our imagination -- an imagination limited to those five "peep holes."

Important afterthought: I am not a skeptic. I do not limit the range and certitude of our intellectual knowledge. I do not doubt the validity of our proofs for God and the immortal soul. I am just saying that trying to imagine how all this spiritual realm actually exists and would be experienced is not within the range of our human knowledge that must begin with sense experience.

Private revelation is an entirely different matter.

Time is a material thing, not a metaphysical thing; therefore the concept of spending time in purgatory is likely untrue.

It sounds to me like Aquinas himself believed that there was duration in Purgatory, which is difficult (probably impossible) without time or something very much like it:

I answer that, Some venial sins cling more persistently than others, according as the affections are more inclined to them, and more firmly fixed in them. And since that which clings more persistently is more slowly cleansed, it follows that some are tormented in Purgatory longer than others, for as much as their affections were steeped in venial sins.

Reply to Objection 1. Severity of punishment corresponds properly speaking to the amount of guilt: whereas the length corresponds to the firmness with which sin has taken root in its subject. Hence it may happen that one may be delayed longer who is tormented less, and "vice versa.

Of course, just because we cannot imagine or conceive of something does not mean it can't be, nevertheless I would say it is difficult to imagine "cleansing" as something that does not require consciousness of some sort and duration.

Just one other quick correction, in addition to the great suggestions by others. Time is a material thing, not a metaphysical thing; therefore the concept of spending time in purgatory is likely untrue. Time is frequently used as a way to describe the path to heaven much like "time served" or "waiting room". However a better concept is the degree of cleansing to which a soul needs perfecting to enter heaven.

Interesting questions and fascinating topic. First, there is scripture suggesting that all persons will be resurrected at the last judgment, after which some will head in one direction, and others in another. In addition to Rob's book recommendation, you may find these useful: "Death and Immortality" by German philosopher J. Pieper, or French theologian Garrigou-LaGrange's "Life Everlasting." Both are Thomists, Catholic. LaGrange's book is online. Garrigou suggests that eternity differs from our continuous time which we measure by solar movement. He describes eternity as a spiritual moment, or "one unique instant, an immovable eternity, entirely without succession."

According to Frank Sheed in Sanity and Theology, it will be pure love, very similar to the love that exists between the three persons of the Trinity.
I highly recommend that book for you. Also, here is a podcast titled What the Saints Will Do for Eternity.
https://itunes.apple.com/us/podcast/the-thomistic-institute/id820373598?mt=2&i=1000426627750