Cont: Deeper than primes - Continuation 2

[jsfisher]

Great then! I'm glad to be wrong about that.
You are much more educated about Mathematics than I.

Please correct me about this.

But I think your meaning is that this is all irrelevant drivel that is as a matter of course ignored by any Mathematician, and that it doesn't count for anything that would even get mathematics wet by a single drop of spittle.

The problem is that it is not Mathematics. It may be a philosophy of some sort, and it may provide a basis for mathematical development, but it is not Mathematics.

The barber's paradox is simply a self-contradictory statement. The statement, "The barber [a man in the town] shaves every man in the town who doesn't shave himself", appears to have meaning, but doesn't. A less decorated version is "This statement is false". In this form, it's lack of meaning is more apparent.

The loose rules of English let us form self-contradictory statements and give them apparent meaning. However, Mathematics works from well-defined rules that make such statements impossible.

The Bertrand Russell Paradox was significant because it pointed out a flaw in the set theory of the time. Set theory did allow self-contradictory statements. That was a huge problem for Mathematics because set theory stood at the base of Mathematics, and that was a very bad place to find a contradiction.

Russell's paradox has been resolved, and Mathematics' integrity is restored. ZF Set Theory was one approach; it simply prevents self-reference. Mathematics can accommodate many approaches, so there are others. Hierarchical classes is another approach and possibly inline with what you are attributing to Doron.

At any rate, Mathematics isn't constrained to any particular model or philosophical point of view. Doronshadmi's distaste for absolute infinity doesn't in any way forbid Mathematics from having an absolute infinity, or several of them, and they can coexist in harmony with potential infinity.

Philosophic insight may provide a basis for the development of some mathematical system. The glimmer of insight Doronshadmi occasionally exhibits among his contradictions, misunderstandings, and meaningless vocabulary provide the occasional example. Mathematics has room for many such things, even those that contradict others. However, Philosophy does not constrain Mathematics.

 

[Apathia]

The problem is that it is not Mathematics. It may be a philosophy of some sort, and it may provide a basis for mathematical development, but it is not Mathematics.

My first impression was that it was a kind of meta-mathematics, a philosophical underpinning for a new theory of Mathematics. I believe that is still Doron's intention.

The barber's paradox is simply a self-contradictory statement. The statement, "The barber [a man in the town] shaves every man in the town who doesn't shave himself", appears to have meaning, but doesn't. A less decorated version is "This statement is false". In this form, it's lack of meaning is more apparent.

The loose rules of English let us form self-contradictory statements and give them apparent meaning. However, Mathematics works from well-defined rules that make such statements impossible.

The Bertrand Russell Paradox was significant because it pointed out a flaw in the set theory of the time. Set theory did allow self-contradictory statements. That was a huge problem for Mathematics because set theory stood at the base of Mathematics, and that was a very bad place to find a contradiction.

Russell's paradox has been resolved, and Mathematics' integrity is restored. ZF Set Theory was one approach; it simply prevents self-reference. Mathematics can accommodate many approaches, so there are others. Hierarchical classes is another approach and possibly inline with what you are attributing to Doron.

I presented it because Doron uses it as an example of how his framework works in contrast to a Mathematics based on classes. I found it a good opportunity to present Doron's way of thinking.

As far as the English of it goes, I said in an earlier post I find it a deliberate lack of clarity. It's an artificial contrivance not for the sake of communication but maybe good for a joke.

At any rate, Mathematics isn't constrained to any particular model or philosophical point of view. Doronshadmi's distaste for absolute infinity doesn't in any way forbid Mathematics from having an absolute infinity, or several of them, and they can coexist in harmony with potential infinity.

Philosophic insight may provide a basis for the development of some mathematical system. The glimmer of insight Doronshadmi occasionally exhibits among his contradictions, misunderstandings, and meaningless vocabulary provide the occasional example. Mathematics has room for many such things, even those that contradict others. However, Philosophy does not constrain Mathematics.

It appears to me that you can't get to the edifice of Mathematics we have now from Doron's meta-mathematical views. Though if it is the case that a robust structure could be built on it, it would certainly be much different from what we're accustomed to now. Though I suppose there would be some fudging to accommodate some features of higher math that depend on elements contradicting the foundation. But I certainly could be wrong about this and Doron's meta the beginning of a fruitful overhaul.

It certainly could find, as you suggest, a niche in what is already a very creative and still chaotic field.

Philosophy can at times try to oppose certain directions in Mathematics. The Roman Catholic Church vigorously opposed the introduction of Infinitesimals into Mathematics for Theological reasons.

Doron doesn't have a distaste for Absolute Infinity. He's a champion of it. What he vigorously objects to is the kind of mathematical infinity that allows for Infinities manipulated as complete, composed wholes. He objects to any sort of Infinity that can be summed or converged to, or any kind of series that in infinite sequence sums or converges to a finite quantity. He especially objects to Cantor's transfinite infinities.

Others have objected as well, and there are numerous alternatives for these mathematical infinities that build theories and algorithms of Calculus based on potential infinity. However these aren't based on Doron's unique metamathematical views.

Yes, for the time being Doron is presenting philosophy. His work is mostly for illustrating his understanding or the relationship between the Absolute and the contingent and what that means for number and logic. Also its illustrative of his own style of cognition.

Philosophy, Mathematics, and Science are never inseparable. The disciplines profoundly influence each other.


You said that ZF Set Theory avoids paradoxes by preventing self-referential statements. This is roughly similar to what comes of Doron's paradox busting. As seen in my post the bracketing self would not be allowed to bracket itself.

Thanks for following along. I was hoping it wasn't only Doron and I off in a corner.

 

[jsfisher]

My first impression was that it was a kind of meta-mathematics, a philosophical underpinning for a new theory of Mathematics.

Philosophical underpinning of something, ok. New theory of Mathematics, definitely no. There is no theory (singular) of Mathematics; Mathematics has many. Doron may have some non-standard model perhaps, but I am not convinced it is new.

I believe that is still Doron's intention.

Perhaps, and were doronshadmi to hold to that intention, we'd be fine. But the continual "Cantor was wrong", "mathematicians are wrong", "Mathematics is wrong" is tiring at best.

Doron has in the past been encouraged to formalize his notions, and the forum has been very willing to help. The few times Doron has abandoned his blanket condemnation of Cantor, mathematicians, and Mathematics to do this all that was accomplished was exposing fundamental contradiction and a lack of definition.

 

[doronshadmi]

But this is the practice I know and it has helped make me a more graceful person.

This is beautiful, Apathia, you are indeed a graceful person.

 

[doronshadmi]

But the continual "Cantor was wrong", "mathematicians are wrong", "Mathematics is wrong" is tiring at best.

At the moment that one understands that actual infinity is non-composed, one also understands that composed things like infinite collections, are not actual infinity.

Cantor and those who follow after the notion that composed things are actual infinity, are simply miss leaded by their attempt to do mathematics by using only their verbal_symbolic reasoning skills.

By defining actual infinity in terms of the non-composed property of, at least ____ , what is called Russell's paradox does not appear any ware in Mathematics, in the first place.

It means that there is no need to define any mathematical framework in such a way that it will avoid, so called, Russell's paradox.

Doron has in the past been encouraged to formalize his notions,

jsfisher still tries to value http://www.internationalskeptics.com/forums/showpost.php?p=12412827&postcount=3095 and forward, only in terms of verbal_symbolic reasoning skills. He simply refuses to get out of this box.

www.internationalskeptics.com/forums/showpost.php?p=12412832&postcount=3096 demonstrates his way to ignore http://www.internationalskeptics.com/forums/showpost.php?p=12412827&postcount=3095 and forward.

On the other hand, Apathia is a real participator.

 

[doronshadmi]

There is no theory (singular) of Mathematics;

By using visual_spatial AND verbal_symbolic reasoning skills, Mathematics is one harmonious framework, such that its expressions are derived from a single non-composed substance (http://www.internationalskeptics.com/forums/showpost.php?p=12412827&postcount=3095 and forward).

 

[doronshadmi]

Mathematics has room for many such things, even those that contradict others.

jsfisher, You say "Mathematics has" without defining this singular thing (or in your words "There is no theory (singular) of Mathematics").

Since you do not define the single thing called Mathematics, what is the basis of your claim that undefined "has room for many such things, even those that contradict others."?

 

[Apathia]

This is beautiful, Apathia, you are indeed a graceful person.

I like to think I'm aging with Grace. A big part of that is learning to pay
non-judgmental attention and listen.

One of the problems with the elderly mind is that it has consolidated a lot of habitual patterns of thinking. Thank you for the opportunity to recalibrate my mental ears.

 

[Apathia]

The words get in the way. That's why I used Doron's presentation of the Barber Paradox to illustrate the flavor of his cognition and get to something concrete about "visual-spatial thinking."

We are so accustomed to thinking with abstract classes, that we project that onto Doron's discourse. It takes some very basic examples in contrast for us to see that it's something entirely different.

Another telling example Doron has given is about ideas about ideas.
Is a idea about an idea also in the Set of Ideas? We lump it in as such. However we are then using an abstract class rather than a concrete (visual-spatial) idea. As with the Barber example I gave, an idea about an idea brackets the idea as content. The bracket itself is not then to be chucked in as content by membership according to some abstract concept. The idea about an idea is a statement of its own where the bracketing "Idea" is it's own unique thing and not a content in this concrete instance. Visual-spatial thinking doesn't lose the unique and particular for a general, abstract substitute.

If you talk about an idea about ideas about ideas, this is another separate statement where the words "idea" and "ideas" denote particular instances rather than abstract generalities.

This being concrete prevents a paradoxical self-reference. A self cannot speak of itself, for what it speaks of is a different instance from what is being spoken of. The bracketing self cannot be an abstract content.

It's not that a statement such as "I shave myself." is of impossible meaning, but that that "I" can never be merely "myself." The subject can never be merely the object. Doron sees this concrete distinction as another way of putting that the Ultimate I, the SELF, cannot be a finite, single instance or a composition of I instances. The I remains "non-composed."

An interesting thing here is that I is a very abstract concept a mere visual-spatially thinking creature would not arrive at. This is where Doron includes symbolic-verbal thinking with a concept. But beware verbal-symbolic conceptual thinking cannot address the I.

Then is the I a concrete, visual-spatial matter?
Yes. It is apprehended in no-thought, in an altered state of consciousness where the mind is in UNITY.

This is why Doron recommends Transcendental Meditation as the means to obtain his perception and the base of his cognition.

 

[Apathia]

Doron presents for us his "visual-spatial AND verbal-symbolic" cognition. He does have intellectual concepts that he brings to counting and numbers. They are no less abstract and symbolic, but they aren't of the form of classes and categories.

Here is a very simple example of Doron's basic rule of thought:

You work with two binary principles, let's say Emptiness and Fullness. These are the foundations of what we call volume. In everyday life you find a glass of water. This we measure by relative terms of Emptiness and Fullness: Empty as opposed to Full. A glass may be half full, a quarter full, or half empty (if you are the proverbial pessimist). So we generate quantiles of volume by fractions of relation between full and empty.

Speaking in terms of the abstract notion, there's no end to the divisions and fractions you can generate. (Though physically speaking there are a limited number of molecules of H2O.) And were you to try to recombine these fractions while continuing to fracture the fractions, you would never sum up to Fullness. Hence Zeno's complaint that the barkeep can't top off his tankard of ale. If you have a limited number of fractions of volume, you don't spill anything, and there's no evaporation, you can recover by sums whatever volume of water in the glass you began with. However if you assume an all in one fracturing of fractions, you have broken the rule in my previous post of trying to make the bracketing a content of itself. Each fraction must be recombined as an addition own its own. Zeno does not break this rule. This is fine for a real tankard of ale as opposed to a mathematical abstraction where there is a Fullness. The current mathematical abstraction is considered to be a completed infinity composed of infinitesimals. Doron's abstraction is either a non-composed
and unbroken Fullness or a finite, relative volume. So parsed the Doron way, Zeno's paradoxes are busted. You do the finite sums, You don't do infinite sums.

I wasn't planning on going Zeno, but there's how the Binary Principle way of cognition plays out for one of the earliest conundrums in Mathematical speculation and entails a different way of seeing points on lines and numbers.

 

[doronshadmi]

Then is the I a concrete, visual-spatial matter?
Yes. It is apprehended in no-thought, in an altered state of consciousness where the mind is in UNITY.

Please be careful Apathia.

The non-composed is a quality that can't be defined by any composition, whether it is visual_spatial, verbal_symbolic or any composition which is both visual_spatial AND verbal_symbolic.

 

[Apathia]

Please be careful Apathia.

The non-composed is a quality that can't be defined by any composition, whether it is visual_spatial, verbal_symbolic or any composition which is both visual_spatial AND verbal_symbolic.

Of course! Unfortunately and fortunately some reference to it is needed for communication. For that we resort to metaphors such as "UNITY," or attempt description so the reader has some idea what we are talking about.
Lao Tsu said that "The Tao that can be spoken of is not the Tao." It isn't. Yet he went on page after page about the Tao." We are talking about shadows. If we wish to avoid the risk of misspeaking about that which cannot be spoken about, we best must do what later Taoists did: Just sit and be silent.

But that's for early morning meditation. Here we aren't going to escape from using words.

My point was that the "non-composed" is not a concept, not even the concept of the "non-composed." As you said some five years ago in this thread, it's a "Direct Perception."

 

[doronshadmi]

My point was that the "non-composed" is not a concept, not even the concept of the "non-composed." As you said some five years ago in this thread, it's a "Direct Perception."

Know about X is not the same as Be X

or more profoundly: Be

or more profoundly:

or more

or

 

[Apathia]

Know about X is not the same as Be X

or more profoundly: Be

or more profoundly:

or more

or

Point most excellently made!

 

[Apathia]

Thousands of posts have gone into this thread where there was so much confusion because we didn't get the skinny of what Doron was trying to say. He'd roll out a new selection of terms and phrases that still didn't bring clarity with them. If you are still one of the few following this thread, I offer a very simple, too simple, description of Doron's chief organizing principle.

You know, basic organizing: putting types of things, categories of things, classes of things in their own labeled, defined boxes. Apples in one crate, oranges in another. This is formalized in Mathematical set theories. But lets go for the less formal, less rigorous organizing of language.

For a dull example let's talk about Male and Female. For some many moments of organization (and many still biased) we collect Male into one class and Female into another. The principle of organizing and membership here is gender. There's a Male class and a Female class. Organization and cognition proceed along this path of manipulating classes.

Here comes the very important point. As Doron presents it, this is not the primary principle of organization, and the making of collections and sets.

He sees this kind of membership by fixed kinds as the root cause of exclusion, separation, and bigotry.

He has an entirely different principle of organization that he considers more fundamental than such.

Recently I've called it, "the Binary Principle" In previous entries to this thread, or at least in my private notes, I called it Biassociation. Earlier than that "X/Y Complementarity"

I'll just apply it here in absence of a decent definition. You have two abstract principles (Or they may be quite concrete) that inform and relate to each other to create a group or collection of things or circumstances. In this example you have Male, Female. Related these organize collections that in part look like membership based on classes, but are not limited to such.

Doron would generate a tree or fractal like image here, but for simplicity I'm just going to list the relevant combinations that are every one items in the collection based on the Biassociation Organizing Principle of Male and Female.

[M,M] (Male males I suppose)
[M,F]
[F,M]
[F,F]
[M,notM]
[notM,notM]
[F,notF]
[notF,notF]
[notM,notF]

(some combos have been left out as not being practically meaningful, but a not Male Female may have some special significance. And again I haven't drawn out the tree to combos such as [F,notF,M], but by the use of the Binary principles it doesn't stop at the first tier of combinations.)

What's significant here (among other things) is best seen in the combo [notM,notF].
Now thinking as we habitually do in terms of classes, one would say, "Of course, that's androgynous!" Well, you aren't wrong, but you don't get how radical this is.

Some years back in this thread, Epix posted a picture of a man and a woman and asked Doron what categories were missing from this male/female collection. Doron answered "Child."
There was much consternation! Epix and others replied that "child" was not a category of gender. They expected something of a class of gender and thought they had Doron in a gotcha moment because there's only two classes of gender: Male and Female (I dispute that, but that's another topic.)

You see if you have the combo of Male and Female, you can get a baby. Note that this is not about cognitive classes. A child is [notM.notF]. It's beside the point that the child may have a sex.

Doron's accounting not only includes what you could definitely identify as being of a certain sexual combination, but by virtue of [notM,notF] uncertainty and ignorance means that nothing can be excluded from the collection.

Cucumber! It's [notM,notF] no matter how you use it.

Triceratops!

OK, I may have carried this farther than Doron would, because he would have it relate in some way to Male/Female, even if that were just that the object could be described as male or female, or was designated with a gender in French. However the answer, "Child," told me everything I needed to know: that it wasn't about organization by classes, and that any collection based on an X/Y association is never complete.

On another occasion I asked him about a collection of all the Beatles albums. He was clear in his reply that the collection could never be complete, not because someone might cut a new compilation disk, but because the collection could not be restricted to just that kind of album.

Oh, you can go strawberry picking and insist that only strawberries, not rabbit droppings, belong in your basket. But when it comes to the language of thinking, of logic, of Mathematics, Doron insists on something greater than naïve berry picking.

So collections are always inexclusive and open ended. Free Association rules thought.

 

[doronshadmi]

So collections are always inexclusive and open ended. Free Association rules thought.

By using visual_spatial AND verbal_symbolic reasoning skills, one enables to understand that no collection is the non-composed quality of, at least, ___


It is a rigorous visual_spatial AND verbal_symbolic rule.


Finit collections are finitely weaker than this quality.


Infinite collections are infinitely weaker than this quality.


The details are given in http://www.internationalskeptics.com/forums/showpost.php?p=12413510&postcount=3102.

 

[Apathia]

By using visual_spatial AND verbal_symbolic reasoning skills, one enables to understand that no collection is the non-composed quality of, at least, ___


It is a rigorous visual_spatial AND verbal_symbolic rule.


Finit collections are finitely weaker than this quality.


Infinite collections are infinitely weaker than this quality.


The details are given in http://www.internationalskeptics.com/forums/showpost.php?p=12413510&postcount=3102.

Of course, no collection is non-composed.
And because of the rule of visual_spatial AND verbal_symbolic no collection, not even a "finite" one is a finished product whose members are proscribed and exclusive. Finite collectionss remain both finite and never any kind of infinite whole, or even a completed whole.

Infinite collections, wait, what's an "infinite collection?" Isn't that an oxymoron? No collection is
Infinite. Perhaps you are speaking of a potential infinity.

 

[doronshadmi]

Perhaps you are speaking of a potential infinity.

If the non-composed existence of, at least, ____ is defined as Actual Infinity (AI), then a non-finite collection (which is a form of a composed existence) is endlessly weaker than the existence of AI.

In that sense potential infinity is not an existence that becomes closer and closer to AI, but exactly the opposite.

By finitely weaker I mean that there is an end for a collection's existence to become weaker than AI.

By this reasoning, less you composed, more you exist (where the term existence is not restricted to any particular abstract or non-abstract form).

 

[Apathia]

If the non-composed existence of, at least, ____ is defined as Actual Infinity (AI), then a non-finite collection (which is a form of a composed existence) is endlessly weaker than the existence of AI.

OK. there is Actual or Absolute Infinity which is non-composed.
Then you speak of a non-finite collection that is a composed existence. Is this what is called "Potential Infinity?"

In that sense potential infinity is not an existence that becomes closer and closer to AI, but exactly the opposite.

It appears from this that your answer to my question above would be yes.

I get the sense of what you mean about the potential infinity not getting closer to AI. It can't get closer anyway. It's like the horror movie trope of the endless hallway. You run but it keeps stretching out in front of you all the more.
Zeno's classic arrow has a target. The target doesn't run away, but each halve of the distance is smaller, so "weaker."

By finitely weaker I mean that there is an end for a collection's existence to become weaker than AI.

Then it's merely that the finite collection is weaker than AI, because it's finite.

By this reasoning, less you composed, more you exist (where the term existence is not restricted to any particular abstract or non-abstract form).

I'm not understanding this. Existence always implies that something is singled out as a separate subject of discourse. In that sense what is spoken of as existing is finite. The non-composed is Being, but not an existing object.

I think you may be saying something like the existence of a potential infinity collection doesn't get its existence consolidated. It continues to get fractured more and more with more and more pieces in the composition. But a simple finite collection where the fracturing comes to an end has a consolidated existence. Less composition and it stands out more as itself.

(Lurking Friends, this is as you see speaking in terms of quality, so requiring qualitative words such as "weaker.")

As I understand it applying the Principle of Biassociation any collection is open ended. It's still composed and can add contents in a potential infinity sort of way. It's not of course AI.

The less open ended it is, the more defined it is. The greater definition gives more existence. A composed object that takes on more and more distantly related elements as its content becomes hazy of existence. There is less to clearly single out.

So Fruit/Vegetable can collect orange, tomato, berry, nut, grain, seed, progeny, Fruity Pebbles breakfast cereal, Karen Ann Quinlan, and so on. But as it carries out association father and farther it loses distinction and definition. We don't know what we're talking about. We don't know what exists.

If we want to go mushroom hunting, we'd better have some consolidated definition before we throw whatever we found into the pot. Edible/Inedible mushrooms will give us Shitake, Portobello, Peyote, and Death Cap. A little limiting of the field is necessary if we value our existence.

 

[doronshadmi]

OK. there is Actual or Absolute Infinity which is non-composed.
Then you speak of a non-finite collection that is a composed existence. Is this what is called "Potential Infinity?"



It appears from this that your answer to my question above would be yes.

I get the sense of what you mean about the potential infinity not getting closer to AI. It can't get closer anyway. It's like the horror movie trope of the endless hallway. You run but it keeps stretching out in front of you all the more.
Zeno's classic arrow has a target. The target doesn't run away, but each halve of the distance is smaller, so "weaker."



Then it's merely that the finite collection is weaker than AI, because it's finite.



I'm not understanding this. Existence always implies that something is singled out as a separate subject of discourse. In that sense what is spoken of as existing is finite. The non-composed is Being, but not an existing object.

I think you may be saying something like the existence of a potential infinity collection doesn't get its existence consolidated. It continues to get fractured more and more with more and more pieces in the composition. But a simple finite collection where the fracturing comes to an end has a consolidated existence. Less composition and it stands out more as itself.

(Lurking Friends, this is as you see speaking in terms of quality, so requiring qualitative words such as "weaker.")

As I understand it applying the Principle of Biassociation any collection is open ended. It's still composed and can add contents in a potential infinity sort of way. It's not of course AI.

The less open ended it is, the more defined it is. The greater definition gives more existence. A composed object that takes on more and more distantly related elements as its content becomes hazy of existence. There is less to clearly single out.

So Fruit/Vegetable can collect orange, tomato, berry, nut, grain, seed, progeny, Fruity Pebbles breakfast cereal, Karen Ann Quinlan, and so on. But as it carries out association father and farther it loses distinction and definition. We don't know what we're talking about. We don't know what exists.

If we want to go mushroom hunting, we'd better have some consolidated definition before we throw whatever we found into the pot. Edible/Inedible mushrooms will give us Shitake, Portobello, Peyote, and Death Cap. A little limiting of the field is necessary if we value our existence.

If AI is a non-composed total existence, then the finitely composed existence is finitely weaker than total existence (AI is reachable by finitely many steps) and the infinitely composed existence is infinitely weaker than total existence (AI can't be reached by infinitely many steps, therefore it is called potential infinity).

By the organic view of AI's expressions, AI existence is independent of its expressions, but not visa versa.

For better understanding please carefully observe once more the following 2-valued logical (organic) tree:

                          Potential infinity                         
                                  ...                                 
                                                                       
    0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1   
    \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /   
     0   1   0   1   0   1   0   1   0   1   0   1   0   1   0   1     
     \   /   \   /   \   /   \   /   \   /   \   /   \   /   \   /     
      \ /     \ /     \ /     \ /     \ /     \ /     \ /     \ /     
       0       1       0       1       0       1       0       1       
       \       /       \       /       \       /       \       /       
        \     /         \     /         \     /         \     /       
         \   /           \   /           \   /           \   /         
          \ /             \ /             \ /             \ /         
           0               1               0               1           
           \               /               \               /           
            \             /                 \             /           
             \           /                   \           /             
              \         /                     \         /             
               \       /                       \       /               
                \     /                         \     /               
     bounded     \   /                           \   /     bounded     
                  \ /                             \ /                 
        by         0                               1         by       
                    \                             /                   
   contradiction     \                           /        tautology   
                      \                         /                     
                       \                       /                       
                        \                     /                       
                         \                   /                         
                          \                 /                         
                           \               /                           
                            \             /                           
                             \           /                             
                              \         /                             
                               \       /                               
                                \     /                               
                                 \   /                                 
       _   _   _   _   _   _   _  \ /  _   _   _   _   _   _   _       
...  _/ \_/ \_/ \_/ \_/ \_/ \_/ \_/ \_/ \_/ \_/ \_/ \_/ \_/ \_/ \_ ...
                                                                       
                            Actual infinity

The 2-valued logical tree existence depends on AI existence, but not vise versa.

More generally, AI is the source of any possible expression, and by being non-composed, its existence is independent of any of its composed expressions, including subjective\objective compositions.

So AI can't be defined in terms of subject, object or the possible interactions among them.

AI is the thing among NOthing, SOMEthing, EVERYthing, YESthing, where NO, SOME, EVERY, YES are its expressions, but not vise versa.

If one knows thing during NO, SOME, EVERY, YES expressions, then one is at UNITY awareness.