Thinking takes the same form that your senses provide. — Harry Hindu

What about abstract thought? If you have a pain in your foot and you go to the doctor s/he might tell you that the pain is not really in your foot at all, it is in your brain. Why then, you could ask, does the pain seem to be in your foot? The doctor might go on to say that the brain contextualizes the pain and 'places' it in your foot. But it is not really in your foot...

But this argument can be extended to the mind: the pain is not really in your brain either, it is in your mind. From this it can be argued that the entire physical body is no more than a context; a physical context in which the mind experiences. In fact the entire brain-body-senses context is a physical context in which the mind's experiences are framed. But the mind can also think independently of the bodily context, as The Mad Fool points out.

My position is that the fundamentals can self-exist, because we necessarily have no way of knowing whether the mathematical structure that is identical to our physical universe is dependent on any deeper fundamentally inaccessible structure, so as far as we can tell it does self-exist, and if it can self-exist, there's no reason to suppose that all other mathematical structures don't as well. — Pfhorrest

It is an intriguing idea and, granted, we have not looked deeply enough into reality to go beyond its contingent elements. But I'm sceptical...

The short answer is that numbers aren't the basic elements of math; sets are. Numbers are made of them, as are all other mathematical objects. — Pfhorrest

I know but it doesn't matter how you define these things the question still remains,
how can {0} U {0} = {{0},{0}} have an existence unless it exists in a mind? And if the fundamentals can't 'self-exist' how can the more sophisticated mathematical objects be built on them?

By what means are you aware of your own mind if not by sensing it? What does "perceived" mean? In what manner are you aware of your thinking? What form does thinking and perceiving take to say that you perceive your mind? — Harry Hindu

It seems to me that none of the five senses are required to make us aware of our minds. The mind is conscious over and above the senses. In fact the senses are only a crude imitation of consciousness. Real consciousness is of the mind.

In conclusion, we can be certain of only one thing - the existence of minds - and we can always doubt the reality of the physical world, materialism. — TheMadFool

Matter is not real anyhow. At least not in the naive way our senses lead us to believe. A hydrogen atom is only a geometric condition that energy happens to be in. All that is really there is energy. The physical atom is only an image, a conjuring trick. A sophisticated trick but a trick nonetheless. Likewise with all physical things; they are a condition, not a substance. Reality is energy and mind.

Does anyone know any good resources which talk about what a theory of music is in connection to what a theory in math is or a theory in science is? Bonus points if it references logical positivism or formal first-order logic! — Halley

As an artist I would counter the idea that there can be a theory of aesthetics. I still don't know what art is. It is a mysterious thing. It happens but I don't know how. The poet Bukowski said he writes by a kind of magic. I think any serious attempt to squeeze art into a theory would be counter productive.

If you can’t do something with the “perfect” map that you can do with the territory, then its not really a perfect map. — Pfhorrest

Ok, I'm getting your drift. If the world is really a 'mathematical' abstraction then how is it possible to construct such a world from the atoms and primitive axioms of mathematics?
For example how does 1 + 1 = 2 become 'substantial' enough to evolve into higher and more sophisticated mathematical entities, like group theory etc? Because if mathematics can become something like substance the very atoms of it must also be capable of becoming such. But I don't see how 1 + 1 = 2 can have any reality at all unless it exists in a mind. Abstractions might seem very potent to us but that is because our minds animate them and give them a kind of reality. It seems to me that mind is required to give mathematics any degree of potency. So mind must first exist if abstractions are to exist.

this God of yours is entirely independent of any/all of us and our beliefs, interpretations, daily lives, etc, right? — jorndoe

Our beliefs about God tell us something about God. They may be simple compared to the reality of God but they provide a context in which to comprehend God. George Harrison said "God is not a man with a beard in the clouds - but He is if you want Him to be" In other words, it does not really matter what images we have of God (so long as they are reasonable). What matters is our religious imagery is good enough to form a context into which God can enter.

I know a few persons, presumably you do as well. You also claim to know a person you label God. Would this be Knowing by Acquaintance? — jorndoe

Yes. God can be present in whatever form is acceptable to the witness.

how might we differentiate whether (fictional) characters, (imaginary) beings, (hallucinatory) claims are real or not?

In much the same way as you would discriminate between dreams and reality. There is no clear answer. How do you know you are not dreaming right now? Probably because your present state is similar to all other non dreaming states. You are familiar with reality and can tell you are not dreaming. Likewise with questions about the difference between hallucination and vivid reality. It is not possible to give an exact test between the two but one knows in more subtle ways. The reality of mind and thought is more real than physical tables and chairs. Thought is the source of the world and of matter.

Yet the claim is that this God of yours exists entirely independently of us and our interpretations, yes?
Incidentally — jorndoe

Not entirely. God can be known as a person. That is not total knowledge of God, it is an aspect of God that God wants the individual to understand.

I'm not alone in my realization that the Church peddled nonsense to me and I accepted it for years...but although I have broken away completely, there still is that regard for some of the "rigmarole" of the institution despite my resentment of it. — Frank Apisa

I think it is very difficult to frame theism in general in the context of any religion. Most modern religions have permuted many times over the generations. So much so, it is almost impossible to have philosophical discussions in the context of religious particulars - eg. eating meat.

Karen Armstrong argues that the value of religion is not concerned with whether it is 'true' or 'false'. The real value of religion is that it provides a practical context in which people can practice their faith. After all, religion is as practical as it is theological. It seems to me that modern people have difficulty accepting religion because it is wrapped in so much mythological symbolism. Maybe religion in the future will move on to a more direct expression of revelation.

Evidence could be anything. You show, we take a look. — jorndoe

Exactly. Russell said there was not 'enough evidence' for God's existence. But everything is evidence. Every dust mote, every star, planet and galaxy. The question is 'What is it evidence for?. "Evidence for" is subjective. It is how we interpret the evidence.

it is a general feature of mathematics that whatever we find things in reality to be doing, we can always invent a mathematical structure that behaves exactly, indistinguishably like that, and so say that the things in reality are identical to that mathematical structure. — Pfhorrest

In principle yes, but here you are only talking about contingent things. I'm still having great difficulty seeing how there can only be abstractions 'turtles all the way down'. Suppose you have an abstract mathematical idea. Where does that idea exist? In your mind. But is your mind an abstraction? Even in a computer you can't have abstraction only. You have to go the the shop and buy a substantial computer if you want to compute.

But a perfectly detailed, perfectly accurate map of any territory at 1:1 scale is just an exact replica of that territory, and so is itself a territory in its own right, — Pfhorrest

That begs the question; you can grow cabbages on the real territory but not on the map, so there's a difference.

But whatever model it is that would perfectly map reality in every detail, that would be identical to reality itself. — Pfhorrest

See last answer.

Your need for invisible friends is a piece of personal psychology, and not philosophy. — Banno

This is psychoanalysis. Once you go down that road you can make anything true. Like they say Reality is what your shrink tells you it is.

I don't thing there are any good arguments for God's non-existence. I also don't think beliefs are formed that way. Atheists like me got there by questioning our basis for believing in God, and finding it lacking. — Relativist

I don't think a/theists believe or disbelieve on the basis of intellectual machinations - they are post hoc and apologetic, on both sides. The decision for a/theism is more subtle that that.

My point is the arguments for God's existence do not have the power to convince anyone God exists - only Theists accept them. Why bother? — Relativist

The difference between philosophical arguments and mathematical arguments is mathematical truth is demonstrable. Once proven it can't be unproved. Philosophical arguments are not as focused. There is a lot of wiggle room so people can reject these arguments.

The question could be reversed: Arguments for God's [non] existence do not have the power to convince anyone God [does not] exist - only [A]theists accept them. Why bother?

While people strive for objective truth in philosophy, philosophical arguments can be subjectively interpreted.

The notion that the universe is determined fails. — Banno

To prove non determinism it is sufficient to show that mind transcends determinism. If that were the case a mind can choose to do something - like move a stone - now the stone has been influenced by a non deterministic factor.

SO if I have it right, accepting that God exists, for you, involves accepting a a bunch of obscure, somewhat archaic metaphysical notions. — Banno

That is an extreme rhetorical distortion of what I believe. My beliefs are based on many things including reason - see my last few posts - and many other things too. The world is immensely complex and theism is, for me, the best explanation by far, despite the awful distortions in religion. Religion often gives the wrong view of God but it still has truth within it. I believe mythological religion has served its purpose and maybe in the future humanity will have a more purified spirituality.

There is nothing to stop "anything at all" from coming-to-be, etc. ~Atomism (metaphysics) — 180 Proof

Perhaps there is something because it is possible for there to be something. Much the same argument as above...

That's an awful lot of baggage to drag around behind your notion of God. — Banno

See my post here - https://thephilosophyforum.com/discussion/8779/turtles-all-the-way-down-in-physics

But three things at least remain controversial.

Draw a circle in ink. You now have two things, substance/ink and form/circle. If there are two things you can separate them - that is, if the circle, as an abstraction, can exist without substance. But how can you do this? Can you lift the abstraction away from the ink so you can hold up an abstract circle? What would that look like? If there is no substance the universe is an abstraction. But abstractions cannot exist without, at least, a mind to keep them in being.

Space? Space is a positive existence, it is not nothingness.

But learn the differences between belief and reality, what is true and what is supposed. — tim wood

It is not a supposition that form/contingency, must have substance, otherwise the universe is an abstraction.

Is this a definition, or an observation? — Banno

It is a deduction. There can be no properties/contingent things, without substance. The eternal substance that is, is the substance of all contingent things. You cannot have a property/form without substance.

So you hold that God exists, yes? Can you say anything substantive about
that existence? — tim wood

God is substance. One of the most difficult questions in philosophy is why there is something rather than nothing. We don't know why or how but we know there is something. That substance that is, is eternal (otherwise it came from nothing, impossible). This substance is identical with existence. It is existence. Every contingent thing that exists exists because it is in existence/God. Creation is more than existence, it is being; life, consciousness...

As to intelligently designed, as a home? For whom? For creation? Of what?

Matter is contingent so it is made. It is an image of energy. When creation fell away from God it descended into 'veils of matter' (Origen)

Intelligently designed how or for what? — tim wood

By God and as a home for creation.

That - or something equivalent - would be sufficient empirical evidence. Of course it would be most helpful if the giant voice would also tell us the proper religion: — EricH

God is not going to force faith on anyone. To do that would be to destroy free will. There is no need for God to shout, He will be heard by those who listen.

Indeed they have. My point a while ago. But theirs is based in faith, not existence, not knowledge. — tim wood

There are many arguments based on a reasonable assessment of the situation we find ourselves in. Eg the cosmological argument, the fine tuning argument, etc. The argument that the universe seems intelligently designed because it is intelligently designed is not easy to refute - like the man said 'Sometimes a cigar is a cigar'. Sometimes things really are what they seem to be. Positing multiverses and what not is not an answer. That is, for the most part, pulling rabbits out of hats to make the question go away.

As for claims to personal awareness of God. These are brushed aside with baseless accusations of 'Delusion'. That is not an argument.

and that anything goes- young earth creationism, flat earthism, moon landing denial, anti-vaxxism, and so on. — Enai De A Lukal

You cannot seriously compare theism to flat earthism. Some of the best minds in history have presented very reasonably arguments for theism. It is a reasonable viewpoint.

E.g. modern inflationary cosmology posits a cause for the big bang as we know it, but that cause has a cause, and so on, possibly infinitely back. — Pfhorrest

It is not temporal causal relationships that matter. The question 'What came before the beginning of time?' is almost trivial. Physical Time, like any physical object, is a property of the material universe and ultimately a property of energy. The real question here is 'What are the necessary conditions for contingent things to exist?'

- What does the second turtle rest on? — Olivier5

Something I wrote some time ago...

One of the most intractable questions in philosophy is Why is there something rather than nothing? Very little progress has been made in answering this question. But we know there is something; 'I think therefore I am'. So, at least Descartes exists, or at the very least, 'there is thought' (Bertrand Russell). At any rate, we can begin with the assumption that there is something rather than nothing.
The something that is, is existence. Existence is not a verb, it is a noun. It is the substance that is and always has been. Existence is God and is not contingent upon any previous state. Existence is not a property of anything, rather, existence has properties. To show that existence is not a property assume X has the property 'existence'. In this respect we consider X and existence to be distinct entities (otherwise X is equivalent to existence and there is nothing to prove). We now ask the question; Does X exist (as a distinct entity)? There are two answers;

1. X exists.
If this is the case existence, as a property of X, is superfluous since X exists anyhow. Therefore X is equivalent to existence.
2. X does not exist.

It is incoherent to say a non existent X has properties, let alone the property existence.
This means that if existence is not a property, it is not contingent. That is, not dependent on any previous state. All other realities are properties of existence. The universe is a set of properties of existence. Properties of existence 'inherit' their existence. We can say 'This milk bottle exists'. By this we mean that the milk bottle is a property of existence and the substance of it is existence, because existence is the only substance that is.

In principle we can deconstruct the bottle into glass crystals and we can deconstruct the crystals into molecules, atoms and so on until even the atoms are deconstructed into energy because energy is the substance of matter. It may even be possible to deconstruct energy into a deeper form of energy but this deconstruction cannot go on indefinitely; it cannot be 'turtles all the way down'. We must come to some ultimate substance that supports the properties 'atom', 'molecule', 'crystal' 'bottle'. This substance is that which is from the beginning, existence.
Even though philosophy cannot say why existence is or what it is, there are a number of things we can say about it;

1. Existence is.
2. Existence has vast creative potential because it has emerged into a universe and everything in that universe.
3. It has the potential to become life, because life is found in the universe.

The way in which existence made manifest a physical and mental/spiritual universe is very special. It did not just spew out an amorphous blob of matter. It created the universe in a way that optimized the creative potential of matter. Matter, because of the precise way it is made, is capable of great creative transformations. It can become a planet, a crow, a city, an oak tree. If matter had been just a primitive blob it would not have the immense combinatorial possibilities it has. It is the precise balance within matter and energy that gives the universe its vast creative potential. This is the Fine Tuning Argument.
Arguably, the highest point in the creative evolution of matter is the physical image of life and being; physical creatures. But the physical image is just that, an image. Life and being are of the mind which is non physical.

Existence simply is. Being is concerned with life and consciousness; a milk bottle exists, a creature is alive and conscious. Life is plurality and unity. A single mind in isolation is hardly alive. Life is a discourse between minds, between self and not self. When existence becomes manifest as a myriad of minds it emerges into life and being. Life is the union of God and creation. Through creation existence/God emerge into being and God becomes the living God. Egoism is the severance of unity. The mind's consciousness turns inward and the bonds of life are broken. Egoism is counterfeit being and ultimately, spiritual death.

***

It has been suggested that reality can be nothing more than a circular chain of properties or contingencies supporting each other in a never ending circle with no supporting substance. This is an absurdity as it tries to dispose of any real substance in reality.
A property or contingency is perfectly identified with its supporting substance and cannot be divorced from it. Take for example a bronze sphere. Bronze is the supporting substance, and its sphericity is its property which is contingent upon the existence of the bronze. It is also perfectly identified with the bronze.

Now, suppose you try to separate the bronze substance from its property, its contingent sphericity. You could try melting the bronze in the hope that you would end up with pure, abstract sphericity. But all that would happen is the bronze would turn into a molten puddle and the property, sphericity, would vanish. This shows how the property is perfectly identified with its substance; the property sphericity, in terms of substance, is the bronze.

The idea that there can be a circle of mutually supporting contingencies or properties without substance is suspect.

Let P1, P2,...Pn be a circle of properties. It is asserted that P1 is effectively the supporting 'substance' of P2 and P2 supports P3 and so on until we get to Pn which is the supporting substance of P1, completing the circle. So it goes round in a self supporting circle without any central supporting substance.
But Pn is perfectly identified with Pn-1 in terms of 'substance' (although the substance in this case is not supposed to be actual, it is still assumed to play the part of the supporting substance). Pn-1 is perfectly identified with Pn-2 and so on until we get to-

P2 is perfectly identified with P1.

What this means is that any separation between P1 and P2 is purely conceptual and there is no separation in actuality. Likewise with P2 and P3 etc. In short, P1, P2...Pn all telescope into a single complex property. That is, there can only be primary, not secondary, properties in actuality. That there seems to be secondary properties is only an effect of the abstract conceptual model we make in our minds.

Here is a simple illustration.

Energy is the substance of atoms. P1 = a set of atoms.
Molecules are made of atoms. P2 = a set of molecules.
The cell is made of molecules. P3 = the cell.

Energy is the substance of the whole system because it is the substance of Property 1, a set of atoms. Conceptually we have three levels of properties but working backwards we can see that the cell is a set of molecules. Molecules are a set of atoms. Atoms are energy.
So P1, P2, and P3 can be collapsed into a single complex property, P3, the cell. In real terms P3 is a primary property of energy because the substance of the cell is energy, just as it is the substance of the atom. So, all the in between properties, as such, are just conceptual categories, not actualities. The error in the concept of a circle of a self supporting set of contingencies, without any supporting substance, is that there can be a property without any supporting substance. In other words, the universe is an abstraction, a property, of nothing. But even an abstraction needs a mind to conceive it and keep it in existence.

Even if that was true, which it isn’t, how do you decide where to stop and say “this is the last turtle”? How do you know your God is the last turtle, or that energy or spacetime or the inflation field or something like that isn’t? — Pfhorrest

What matters is that there is an initial substance. Contingent things are properties of that substance. As I said, first steps first. What I'm trying to establish first is that the universe is made/contingent. And it must be contingent upon some ultimate substance.

The question then becomes What is that substance? If it is a 'mind' and is conscious and intelligent then that is close to a definition of the traditional God.

And just because everything comes from something doesn’t mean there is one particular thing from which all other things come; each thing can come from a different thing. — Pfhorrest

That is unlikely because then you would have numerous sources and numerous eternal existences but then why would they be so congruent to each other? All these contingent things are the same in the sense that the are in the same reality and obey the laws of nature. They are made of the same stuff as far as we can tell. Tea cups and stars are made of the same thing, energy. So are mountains and oak trees. On the level of energy the universe is one thing, a field of energy.

But you’ll also say that graphite is contingent, no? — Pfhorrest

Yes, graphite, being a physical substance, is a property or is contingent.

And is that energy contingent or not? — Pfhorrest

Maybe it is. If energy, as we define it, is contingent upon some deeper substance/energy then that deeper substance is the substance of energy. But there may be an even deeper substance and so on for a bit. But only for a bit. The process of deconstruction cannot continue forever. It cannot be 'turtles all the way down'.

A hydrogen atom is a concept or state. As such it is a physical image of energy. All material constructions are images of energy. That is because they are contingent. The Cosmological Argument says that contingent things must have a beginning. Otherwise there are only states without substance and I don't see how that can be.

It's not my argument. And no one claims you cannot know God completely. The argument is that "God" as defined/understood cannot be known at all. — tim wood

Well, if that's the argument it is wrong. Many mystics have known God's Presence.

This is the main point of contention that you seemed to just brush past in the first part of your reply. Why can’t it go on forever? Every contingent thing has a source. Sometimes that source is another contingent thing. Which might in turn be sourced to another contingent thing. Why at some point must it be different? Why not an infinite string of contingent things sourced from other continent things? — Pfhorrest

Contingent things are essentially properties. A property depends on substance to exist. Take a circle. It is a mathematical abstraction. As such you can't hold it up and show it to anyone; it does not exist. To make it exist you need to give it substance; draw it with graphite. Now the graphite is the substance of the concept of a circle and, having substance, the circle is made manifest. Contingent things are essentially properties, they cannot exist without substance and a regression of substanceless properties cannot exist because a property is a condition of some preceding existence. You are saying that reality can be made of a regression of essentially abstract properties without substance.

Besides, a regression of properties, p1, p2, p3, ... is really just one property. For example, you have a substance, energy and a property of energy, matter. This is how it goes:-

Energy -> p1 (atoms)
Energy -> p1 - > p2 (molecules)
Energy -> p1 - > p2 - > p3 (a cell)

But the distinction between atoms, molecules, and a cell is only by way of classification. In real terms there is only one property (p1 U p2 U p3) = P so

Energy -> P (cell)

The cell is just one complex property of energy. As far as contingency and properties are concerned P (cell) is all that is needed.

They reasoned, in brief, that God is unknowable. — tim wood

Faith also teaches that it is possible to know God. So 'unknowable' must be qualified. Faith says that it is possible to know God as a person but that does not mitigate against the argument that God is ultimately unknowable by human beings. In other words, God can be known as a person but not fully knowable by the human mind.

The claim, then, that God exists is for oh, so many reasons an exhibition of ignorance at the very best. — tim wood

Claiming that God exists and claiming that God is (completely) knowable are not the same thing.

What is each contingent thing has as its source some other contingent thing, such that there are no non-contingent things? What then is God? — Pfhorrest

Contingent means there must be a preceding substance. For example, matter cannot exist without the preexistence of energy. It is not possible to have a property (contingent thing) without substance. Properties can only be a property of a substance in the way that matter is (sometimes) a property of energy

If the Big Bang turns out to be the source of all contingent things, and is not a person or in any way at all like a mythical deity, just some impersonal cosmic event, would you call that "God"? I don't think many would. — Pfhorrest

I'm saying that in order to establish an eternal source it is only necessary to argue that that source/substance must exist. Thereafter it is possible to argue that that substance is mind because the universe is mind-like. It is such because it is mathematical. See also The Fine Tuning Argument. Before talking about God it is easier to establish the existence of a necessary substance and work forward from there and ask questions such as:
Is this substance mind?
Is it a person?
Is it possible for this person to relate to humanity?
Can this person be concerned about what his/her creation does or becomes?
etc.

What I'm getting at here is whether you're okay with the notion of a God that is not a person, that doesn't have thoughts or feelings or wills, that can't hear prayers or issue commands, or judge souls after death, etc. It's just some thing that kicked off existence, and nothing more. Is that really enough to count as "God" to you? — Pfhorrest

No. See last answer.

Must it? [be contingent] Explain. — Pfhorrest

Because matter must have a preexisting substance, energy. Matter is not an ultimate substance, it is a condition that energy is sometimes in. The same may be true of what we call energy; it may be contingent on the existence of some deeper energetic reality. But ultimately this process of deconstruction cannot go on forever, there must be a necessary substance to keep contingent realities in existence.

which is why theism is untenable on any rational or empirical basis, and so is only held as a matter of faith — Enai De A Lukal

Theism is not dependent only on faith. It is a reasonable viewpoint.

God has a lot of company - with an exactly equal claim to existence. Flying hippopotami — tim wood

That is only true for non theists. Theists would disagree. So flat-out atheism must assert theists are misguided/deluded and that claim cannot be convincingly defended. Also, things can be argued to exist through pure reason, without general experience of those things. For example, sub atomic particles can be discovered through mathematical physics. Black holes and other astronomical bodies can be deduced to exist by reason alone (black holes were predicted long before they were an empirical reality). The pure atheist cannot reason in the opposite way and declare that God does not exist.

If the Big Bang turns out to be the source of all contingent things, and is not a person or in any way at all like a mythical deity, just some impersonal cosmic event, would you call that "God"? — Pfhorrest

But the big bang must be contingent. You have to go back further, into eternity, the get to the source.

To start with, the definition of God as the source of all contingent things is sufficient for 'belief in God' and sufficient for a simple definition of God.

As for pure atheism, I don't think it can be defended. We are not in a position to say 'God does not exist'. Such a position, I believe, cannot be defended. Ultimately, agnosticism is the only non theist position.

Physics has shown us the universe has many laws or rules by which it operates; gravitational constant, conservation laws, uncertainty principle, thermodynamics etc — Benj96

The so called laws are not separate from nature. They are merely a description of nature. The electron is not obeying a law that is imposed on it from outside. The law is the electron; it is its nature. Nature is consistent - as far as we can tell - so we formulate this consistency in terms of abstract laws. But there is only nature; it is natural for the electron to behave as it does and what we call law is intrinsic to the electron, it is its nature.

In the beginning there was the inflaton field, and it was without form, and void. — Pfhorrest

There is a difference between nothing and no-thing. Nothingness is just that, no space or time or energy or God or creation. No-thing is no formed thing or no contingent thing or thing that can be defined. This is the void which is the source. The void is existence, in the simplest definition of existence: that which is, necessarily.

Existence is not a property of anything. Contingent realities* are properties of existence.

*Things that are made or dependent on a previous, necessary state.

I really recommend you check out the book I mentioned in my first post. It is actually quite good and the first few chapters are quite approachable. — Tommy

I'll definitely check that one out. Thanks.

Russell suggested we consider the collection "the set of all sets which are not subsets of themselves". Note that, by Frege's abstraction principle, this is necessarily a set. Asking that we, in effect, look the other way and consider instead another set, as you've proposed, doesn't prevent us from considering Russell's set. — Tommy

If I understand you correctly, you are saying "the set of all sets which are not subsets of themselves" is necessarily a set. But it turns out that it is a pathological set or not really a set at all. My argument is that it is an entity of some kind and I'm attempting to define what this entity is. It seems that there can be things that are not simple sets but are infinities of sets. Maybe all sets are really subsets of infinite sets...

Ah, so this is not the correct notation...
Note that we cannot redefine X and that this set is quite distinct from itself. — Tommy

Yes, this is the difficulty with notation but it is really just a notational wrinkle. You can rename the set X' and you have it. All that is required is a set without X as a subset but with all the other sets. The same logic can then be applied to X'₂ and so on. It is really a question of getting the notation right but the concept seems to be coherent.

Well, Russell himself use Type Theory and basically Zermelo-Fraenkel Set Theory (ZF) was made basically to avoid Russell's paradox. If you find your ideas resembling theirs, you can be proud of yourself. — ssu

There are immense complexities with infinite sets so I'm very unsure if my logic holds...

Your definition requests that we posit an object which is logically contradictory, and then remove X from it. — Tommy

I've had great difficulty in this thread with notation but the concept I'm trying to define is simple, namely X\X.

Suppose set A = {a, b} the subsets of this set are:

{{0}, {a}, {b}, {a, b}} Now redefine set A as:

A\A. That is, A\{a, b}

Now the subsets of A are:

{{0}, {a}, {b}}

This is what I mean by X\X.

What's the difference to Russell's Type theory? — ssu

I don't know enough to say but as far as I can see this question can be resolved with simple set theory alone - if my ideas are coherent that is. The problem is with the way the paradox is stated: "The set of all sets that are not members of themselves." Why assume it is a set? Because it turns out that 'The set' is not a set at all. But we can intuitively grasp the concept of 'All sets...etc'. It must be something so what is it if it is not a set? Seemingly it is an infinite collection of sets.
This is similar to Russell's types because there is also a hierarchy of types, each containing the ones below it. So why not just frame the whole thing in terms of sets alone?