Does false self = no self?

"However, I still can't make the logical assertion that the self does not exist at all."

That's good because such an assertion would be preposterous and obviously wrong! The Buddha never said the self does not exist at all because of course the self does exist. You and I exist. Persons exist. This is not in dispute by any serious Buddhist that I know of. The question is how we exist. The answer is not at all like how we think we exist :)

"there are multiple versions of the self that pass through time, each of those selves being slightly different than the ones before. So, I am self version 1.0.1, self version 1.0.2, self version 1.0.3, etc".

Can't you divide further? Can't you find self 1.0.0.1? 1.0.0.0.1? 1.0.0.0.0.1? What is the limit to how fine of granularity you can make out? Is this a continuum along the real number line or is it discrete like the integers? Also, when you say "pass through time" do you mean that self at 1.0.0.1 exists for multiple moments or for only one moment? What is the measure of that moment?

"a configuration of energy and matter intersects with the 4th dimension of time over and over again, producing the by product is what we understand as self."

Your matter continually changes over the course of your life. The atoms that make up "you" right now are different than the atoms that made up "you" when you were a baby. Moreover, there are more of them now. And less of them then. So if the matter that makes you up is not "you", what is? You said energy and of course by Einstein's equation we know that matter and energy are related. So, let's say we cooled you down to near absolute zero and let all the energy that is "you" convert into matter. Your body would have zero kinetic or potential energy at that point. Would "you" still be "you" after some new energy was pumped into the system and heated you back up?

"if some version of self did not exist, then the subject of knowledge could not be observed."

Right, Buddhism does not assert that the self does not exist. People exist! Saying otherwise is silly.

Are my assertions correct?

Not all of them. People and selves do exist and asserting otherwise is nonsense. I think your breaking the self down into versions is not very illuminating. I don't think you've yet discovered how persons exist, but it sounds like you are on your way! Keep investigating :)

"Does Buddhist philosophy teach that the self does not exist or merely that it is impermanent?"

I don't know of any orthodox Buddhist philosophy that teaches the self does not exist at all, but you never know who you could find espousing to be a Buddhist and what crazy things they might say :)

It is true that the self is utterly impermanent, but that is not all that one can say about how it exists. The self is not unitary either. It is also completely dependent upon others. It comes from causes and conditions that are themselves impermanent, non-unitary and dependent on other causes and conditions as well. Ultimately, the self is merely a label that we conventionally designate on the illustration of a person. It is not real and it lacks true or inherent existence. This is how the self exists. However, this is deep and subtle and hard to understand. Usually when we hear the above we immediately leap to thinking the self does not exist at all, but that is not what those words mean. The self exists like an illusion, but it does exist.

Here is a really good book that lays out in pretty simple terms the ideas I'm fumbling with above. How to See Yourself As You Really Are by His Holiness the 14th Dalai Lama. To go along with this book I'd highly advise watching Venerable Thubten Chodron who has a series of Youtube videos that follow along as you read.

Hope this helps!

My new understanding (based on this post) is that the self is not permanent and is always changing.

The Pali suttas say the journey starts by listening to the True Teachings made by Worthy Persons (AN 10.61).

However, I still can't make the logical assertion that the self does not exist at all.

The Pali suttas describe the assumption of self (SN 22.81) as the arising of suffering (SN 12.15; SN 5.10); as a disease (Ud 3.10). All that exists is a "disease" and "ignorance & craving", which produces the false idea or assumption of "self". However, since the ordinary person (called "puthujjana") cannot remove the thick covering of ignorance; the ordinary person can't make the assertion that the self does not exist at all. This is the difference between the ordinary person and the enlightened mind. The enlightened mind is very rare in the world (SN 56.47).

At this point, it makes more sense for me to say: "there are multiple versions of the self that pass through time, each of those selves being slightly different than the ones before. So, I am self version 1.0.1, self version 1.0.2, self version 1.0.3, etc".

There are multiple assumptions of self. There are multiples diseases that are named "self" by the sick mind; similar to having influenza; then an infection; then diabetes; then depression; then cancer; etc.

a configuration of energy and matter intersects with the 4th dimension of time over and over again, producing the by product is what we understand as self.

SN 22.81 says the assumption of self is produced from when ignorance clouds the sense bases and craving arises from that. To quote:

Assumes to be the self. That assumption is a fabrication. Now what is the cause, what is the origination, what is the birth, what is the coming-into-existence of that fabrication? To an uninstructed, run-of-the-mill person, touched by that which is felt born of contact with ignorance, craving arises. That fabrication [of self] is born of that.

SN 22.81

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if some version of self did not exist, then the subject of knowledge could not be observed. Example: without a self, there would be no one to respond to this post.

'Self' does not "observe". The element of consciousness observes. Also, the mind thinks and responses to a post, rather than the self.

Are my assertions correct? Does Buddhist philosophy teach that the self does not exist or merely that it is impermanent?

The assertions made are obviously incorrect. Buddhist truth teaches self is a superstitious assumption born from ignorance & craving; that the assumption of "self" is the name the world of the unenlightened gives to a disease or mental illness.

When a mind with mental illness believes it is Alexander the Great or Julius Caesar; it is taken for granted such a mind has a mental illness. Similarly, in Buddhism, any mind that believes it is a "self" has a mental illness. All that exists is mental illness (or "disease") rather than any permanent or temporary self.

This world is burning. Afflicted by contact, it calls disease a 'self.' By whatever means it construes [anything], it becomes otherwise than that. Becoming otherwise, the world is attached to becoming afflicted by becoming and yet delights in that very becoming. Where there's delight, there is fear. What one fears is stressful. This holy life is lived for the abandoning of becoming.

Ud 3.10

Does Buddhist philosophy teach that the self does not exist or merely that it is impermanent?

This is not mine, this I am not, this is not my self.

If self exists, then let us rigorously, precisely determine its boundary so that we may understand what is self and what is not self. Is your hair you? And ater a haircut? Pursuing this inquiry near and far, high and low we arrive at the rather odd conclusion that there is watching but not self.

Does Buddhist philosophy teach that the self does not exist or merely that it is impermanent?

In the Self-Doer Sutta (below), the Buddha rubbished the notion that there is no self at all. How could one moving forth and back by his own will, say that there is no self at all?

“So, brahmin, when there is the element of endeavoring, endeavoring beings are clearly discerned; of such beings, this is the self-doer, this, the other-doer. I have not, brahmin, seen or heard such a doctrine, such a view as yours. How, indeed, could one — moving forward by himself, moving back by himself — say ‘There is no self-doer, there is no other-doer’?”

Saying that there is an eternal permanent self is a view of eternalism, while saying that there is no self at all, is a view of annihilationism. This is the message of the Acela Sutta (which is summarized below from here). Instead of resorting to either eternalism or annihilationism, the Buddha prefers to explain using dependent origination.

Again, when the Buddha was asked by the naked ascetic Kassapa whether suffering was of one's own making or of another's or both or neither, the Buddha replied "Do not put it like that." When asked whether there was no suffering or whether the Buddha neither knew nor saw it, the Buddha replied that there was, and that he both knew and saw it. He then said "Kassapa, if one asserts that 'He who makes (it) feels (it): being one existent from the beginning, his suffering is of his own making,' then one arrives at eternalism. But if one asserts that one makes (it), another feels (it); being one existent crushed out by feeling, his suffering is of another's making,' then one arrives at annihilationism. Instead of resorting to either extreme a Tathaagata teaches the Dhamma by the middle way (by dependent origination)" (S. XII, 17/vol. ii, 20).

Is the self impermanent? Everything apart from Nirvana, is considered a sankhara - phenomena which is conditioned by other phenomena, and/or phenomena which is compounded or composed of other phenomena.

How the self comes about is discussed using dependent origination, and is dependent on the five aggregates of form, feeling, perception, mental fabrications and consciousness. As the five aggregates keep changing, one's identity views related to them will also change. One day you may see yourself as young and talented, while many years later, you may see yourself as old and worthless. Yet another day, you might compare yourself to a wealthier person and consider yourself poor.

Another interesting sutta is the Lute Sutta (below) which compares the self to music which arises from the inter-working of the different parts of the musical instrument. Of course if the musical instrument is played differently, different kind of music comes out. But if you break down the musical instrument to its constituent parts, you cannot find music.

The self is like music, the sentient being is like the musical instrument, the five aggregates are like different parts of the musical instrument, and dependent origination is like the mechanism of how the different parts of the musical instrument work together to produce music.

Just as there is no standalone entity called music, there is no standalone entity called self. To say that there is a standalone entity called self is eternalism. To say that there is no self at all is annihilationism. Both are false views.

"Suppose there were a king or king's minister who had never heard the sound of a lute before. He might hear the sound of a lute and say, 'What, my good men, is that sound — so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling?' They would say, 'That, sire, is called a lute, whose sound is so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling.' Then he would say, 'Go & fetch me that lute.' They would fetch the lute and say, 'Here, sire, is the lute whose sound is so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling.' He would say, 'Enough of your lute. Fetch me just the sound.' Then they would say, 'This lute, sire, is made of numerous components, a great many components. It's through the activity of numerous components that it sounds: that is, in dependence on the body, the skin, the neck, the frame, the strings, the bridge, and the appropriate human effort. Thus it is that this lute — made of numerous components, a great many components — sounds through the activity of numerous components.'

"Then the king would split the lute into ten pieces, a hundred pieces. Having split the lute into ten pieces, a hundred pieces, he would shave it to splinters. Having shaved it to splinters, he would burn it in a fire. Having burned it in a fire, he would reduce it to ashes. Having reduced it to ashes, he would winnow it before a high wind or let it be washed away by a swift-flowing stream. He would then say, 'A sorry thing, this lute — whatever a lute may be — by which people have been so thoroughly tricked & deceived.'

"In the same way, a monk investigates form, however far form may go. He investigates feeling... perception... fabrications... consciousness, however far consciousness may go. As he is investigating form... feeling... perception... fabrications... consciousness, however far consciousness may go, any thoughts of 'me' or 'mine' or 'I am' do not occur to him."

The last sutta I would introduce you to, is the River Sutta (below):

At Savatthi. There the Blessed One said, "Monks, suppose there were a river, flowing down from the mountains, going far, its current swift, carrying everything with it, and — holding on to both banks — kasa grasses, kusa grasses, reeds, birana grasses, & trees were growing. Then a man swept away by the current would grab hold of the kasa grasses, but they would tear away, and so from that cause he would come to disaster. He would grab hold of the kusa grasses... the reeds... the birana grasses... the trees, but they would tear away, and so from that cause he would come to disaster.

"In the same way, there is the case where an uninstructed, run-of-the-mill person — who has no regard for noble ones, is not well-versed or disciplined in their Dhamma; who has no regard for men of integrity, is not well-versed or disciplined in their Dhamma — assumes form (the body) to be the self, or the self as possessing form, or form as in the self, or the self as in form. That form tears away from him, and so from that cause he would come to disaster. (and the same applies to the other four aggregates)

What does this mean? When you get hurt, you may say, "I got hurt". This is associating the self with the body. If you are getting old, ageing and dying, then you are suffering. You suffer because you associate your self with that which is getting old, ageing and dying. This shows how associating with the self causes suffering.