You point to time perseption being a problem.
I agree.

If you think of a timeline you have nothing and then physical matter bursting into existence.

Something is wrong with the time model.

Since we have matter now, maybe the best approach is to look at what we can learn from astronomy and particle accelerators. A universal principle of 'then' and 'now' is likely.

It might make sense. Absent any physical theory, logic says non-existent and non-physical things don't have any cause and effect relation.

The only option in which logic applies is two physical entities interacting.

If that's a wrong interpretation LFranc can correct us.

I'm still kicking around the idea of what brains can do and if brains should be considered in our cosmological models as they have some ability to control energy and matter in a way lesser forms of matter do not.

I just got back to looking at this. It just relates to something I came across... retrocausality.

The brain model applies to brains as emergent and affecting matter in the present.

The signal back propagation idea is speculative but if it exists could be relavent to a first cause.

For me it's something to keep in mind.

I don't see how any logic can be applied to the situation if we don't know the physics involved first. It's rather futile to try. Want are you doing? Applying a mental overlay to unknown physics?
It doesn't seem reasonable.

Maybe it's a process of testing ideas. That's fine.

Here's one. We don't know the exact nature of time. An interesting twist is the possibility of retrocausality or back propagation of signals.

The idea is if the present moment has some duration instead of being defined as only an instant, then there is a question of back propagation of signals. This would take the form of a physical remnant of a future state existing in present matter. Very much debated but it's a thing.

Another form of retrocausality is information based. Our brains hold concepts of past, present and future so an anticipated future event can affect the physical present. For example we do things based on future projections like storing food, preparing for storms, launching space probes and preparing for wars. All things not possible without brains so brains can affect matter. Would it be relavent to a first cause? I don't know but it's a mechanism that appears to operate differently than lesser forms of physical matter are capable of.

I use the terms retrocausality and back propagation loosely, as they have different meanings in other contexts.

Good point about not making vocabulary reality.
There are also infinities and mathematical models that are not physical objects but only mental objects.

The thing is..... physical and mental are both handled with our brains/minds so they get commingled.

If you haven't tried story writing using these AI chats you should try it just to get an idea of their capabilities. I only rarely see slipups.

I gave chapter headings for an Appalachian trail hiking story and it pretty much wrote a story for me. Any details you like will be written in.

In one chapter I needed to make mittens out of socks using a sewing kit.

The AI figured on its own to turn the sock inside out, cut the toe off, shape the toe for a thumb, stitch it on and turn it right side out. Repeat for the other mitten. No idea how it could know that.
Maybe there is a sewing database in its system to give basic sewing directions..

The instructions I gave was just to make mittens out of a socks.

I'm not getting this at all. Whether the universe is limited or unlimited is a matter of physical state. If we conclude that its state is unknown then this discussion is just an attempt at a mental overlay that has no bearing whatsoever. Seems like any mental model we can contrive would be the same. Just a speculation.

So the best we can do is examine the universe we do know and base our models on the known. That could lead to reasonable projections of some of unknowns but still would have a physical basis and not mental abstractions.

I'm still having trouble understanding what you mean by the whole. Is it a philosophy term? As the whole is the sum of its parts, the whole universe in the physical sense, mathematics or what I thought at first, a concept of the whole being something limitless or infinite.

I can make some progress on your argument but then the conversation goes in another direction such as the physical universe which was never stated.

I'm thinking if it's the physical universe we can't impose our own mathematical model on it without knowing what it is.

I'm not good at links on my smart phone but go to the main page here and it is listed as:

Is Universal Form a good tool?

The last entry as of now.

The problem I'm seeing with your approach is that you don't identify the whole as a concept. Its origin is a mental abstraction. Limits are mental definitions. If you apply limits to infinity you no longer have infinity.

I covered this in my Universal Form post not long ago if you want to understand why I object to your method.

Okay. Worth exploring. It takes time to understand it.

If the whole is limitless it has no bounds. Then you introduce bounds and impose limits. What?
Maybe I can get it on a second try but why?

Nope, not getting it. W1 is no longer the whole you started with.

You are proving an unlimited whole is not affected by bounds....okay.

Friction loss but it's way off topic.

I don't really design trusses but in addition to course work I made my own collection of scale model trusses of various designs. I still have them in a folder somewhere. Glue and cardboard.

I've had college algebra, trig and calculus.
I can also design trusses and figure pressure loss in pipelines. Doesn't that sound exciting.

What I've written is about as far as I've gotten on a 'theory'.

I was thinking there might be an application for this in central banking or distributing resources to competing unlimited wants. Maybe the math is out there in some form already. Wouldn't doubt it.

What about two infinity generating machines that spit out consecutive integers at variable speeds endlessly.
Set a dial and one or the other can go faster or slower or stop. If you have a system like that matched to physical systems that have finite limits it might be an interesting model

I'm in over my head but don't infinities have some rubber band like properties that can be set at will.

My interest is mostly going from brain state to doing the math as a basis for a philosophy of mathematics..... Real simple,. Brain; (math processes)

Don't expect everyone to do it perfectly and in learning math or new skills it's always a process of brain programing.

Fight the cranks all you like. Makes things interesting. It's just philosophy here not pure math.

I'm really sceptical of the idea that there is any one true math to decide these issues of infinity.

To me the best we can do is categorize models of infinity as conceptual mathematical objects.

As such the parameters are arbitrary and their usefulness is in a defined mathematical environment.

Under this categorization scheme, it can be possible that one model can be inconsistent with another and not be false.

Here is my example,
A smaller infinity can reach any finite number that a larger infinity can by freezing the larger infinity and letting the smaller one catch up.
I'm sure there are all kinds of problems with this in the standardized mathematics but in the sense of a conseptual mathematical object it is legitimate. I think I first said it as a bit of a joke but the idea is we can drive the math by abstractions.

It's all word salad to me.

I'm just lost here because I can't follow the math.
I try but it ends up dissolving on me after just a few sentences. Errrr.

The subject interests me though.

Could you or others occasionally comment in non mathematical summaries....dumb it down just a little so I can follow.

I'm wondering about mental representations. I'm thinking you are discussing some model of mental mapping as you mention physicalism.
Is this a reductionist model? Actually what interests me is going the opposite way of reductionism such as mental agency. Things like testing external environments, interactions, real world mental process. If that's out of bounds just explain it simply and I'll try to follow.

Funny you say that. The book room I was talking about was like a holy of holies. You would walk into the main mathematics department building, down a hall to the mathematics library, past a front desk and main room, into a wing and up a back stairway to the third floor. I think math departments might have their own special collections. It kind of seemed like that. The books seemed like the real math that most people wouldn't know exists. Maybe about year 2000 so before everything was on the internet.
Yes. Candy store.

Cataloging mathematical objects,

Mathematical objects take the physical form of,

Brain; (mathematical object)

Some specific types discussed recently are:

Brain; ( fixed mathematical object)
Such as pi, i, e, √2, √3. Discovered by the process of precedence.

Brain; (defined mathematical object)
Such as defined sets.
May exist or not exist as mathematical objects as derived from a definition.
The Russell set is a non-existent mathematical object.
A proposed defined mathematical object can be explored and determined to exist or not exist.

Brain; (conceptual mathematical object)
Such as concepts applied to the various ideas of infinity.

These may or may not be extraneous in performing math operations but may be helpful in some cases. Again, this gives a physical basis for how mathematics exists physically and is built up from brain state.

I used intermediate because there are two questions to this problem based on two phases.

Phase one, discovery,
Does the Russell set exist?
Requires exploration.
No.

Phase two, end point,
Is the Russell set a paradox?
Given: the Russell set does not exist.
Since the Russell set does not exist we now know it cannot be a paradox.

You can say my method is extraneous because you resolve it using your own method.

But you are using the ideas subconsciously.
And you default to 'not a paradox' when you reach your intermediate conclusion (is a contradiction therefore non-existent).

Also, there is word confusion in contradiction and paradox so be careful of that.

A little more.....You have,

A discovery phase where the question is does a proposed mathematical object exist or not exist.

And

An end point phase where you are given the state.... a(n) existent mathematical object or non-existent mathematical object. Is an existent mathematical object a paradox? No. Is a non-existent mathematical object a paradox? No.

So I don't see how a paradox can exist. The contradiction in your intermediate result is only a basis for determining non-existence.

Also the problem is misnamed because no true paradox ever exists. Because the discovery phase is hypothetical.

So sorry you got mixed up about my view of the existence of the Russell set.

We both are saying the Russell set ultimately does not exist. If you missed it I was developing an alternative method using the concept of mathematical objects as proposed, existent or non-existent.

Would it be fair to say your view develops the Russell set as a proposed mathematical object and concludes that it is ultimately a non-existent mathematical object? If so we should have nothing to disagree on.

Also, as relates to the philosophy of mathematics, my view reaches back fully to physical brain state. So for me it was an exercise in exploring that and as a simple result I got the same answer you did.

I am relying on your intermediate conclusion that the Russell set does not exist to go straight to the final conclusion that the Russell set does not exist....a paradox does not exist

I'm not at all saying the Russell set shouldn't be explored. How else would you know?.

Summary,
The Russell set does not exist.
Based on the proposed defined mathematical object failing by contradiction.

Additionally,
In defining the Russell set, two or more (known to exist) defined mathematical objects are used to define the Russell set and produce a failed defined mathematical object (non-existent).....Which I think is an interesting result

Reference,
I covered mathematical objects as brain state 4 days ago in my post on Universal Form.

I'm very far removed from any formal mathematics community. Maybe good and bad so I have my own way of doing things.

You have a good overview. Really, I think the people in math have their own view on how things should evolve.

..........off topic a little,
I used to visit our state university math library and there was this little room on the top floor with all their best books. Maybe 20 by 50 feet of shelves. Still lots of books. I would check random books just to see what was out there. Just amazing.

Okay. I'll go over and sit in the corner and read some set theory textbooks.

Finally, yes, that is what I was getting at.

It's my first look at anything in set theory so I don't have background.

But we are trying to dispell the contradiction, not prove it.

If the Russell set doesn't exist there is no contradiction.

You accept that than the Russel set exists and is legitimate. I don't think it has a sound basis. It's based on definition and that's not proof of existence. You have a burden of proof.

You suggest the Russell set exists only based on the process of defining it.

I'm saying it does not exist.

Which is it.

In my development of the issues these are mathematical objects that don't exist outside of brain state.
One method of establishing existence is predication such as for fixed mathematical objects.

Defined mathematical objects are not based on predication....because we set the definition process. I'm saying for an object to be a legitimate mathematical objects it needs to pass an existence test. Creating paradoxes is a failure of an existence test.

Defined mathematical objects can be subdivided:

Proposed defined mathematical object
Confirmed defined mathematical object...exists
Rejected defined mathematical object ... non-existent

So the Russell set as a rejected defined mathematical object does not exist and cannot be a paradox.

Someone commented just a few days ago about how much new math research is being published.
As a bunch they are really productive.

I think they could do better in philosophy of mathematics.....foundational things like knowing how mathematics exists physically and training the profession accordingly. Especially as we interface with A. I.

Okay.

You seem to be arguing for the paradox after the paradox has been dismissed.

And you can't have a paradox if the defined mathematical object does not exist.

The math procedes in a way that assumes an ultimate set will exist.

I'm saying ultimately the Russell set does not ultimately exist.

Edit: rather never exists and ultimately does not exist...

Never had the set in the first place.

I looked at Russell's paradox again and am thinking the problem is in the use of defined mathematical objects.

I would classify the Russell set as a defined mathematical object. That means it is subject to a determination of if it exists or does not exist. The fact that paradoxes develop means it is a defined mathematical object that does not exist.

This is basic theory of predication. Fixed mathematical objects are determined by predication. Defined mathematical objects are arbitrary and defined by rules and ultimately may not exist.

In short....the Russell set never exists as the defining process procedes and once the problems are discovered the conclusion should be the Russell set is non-existent.

It is useful to know the difference between a fixed mathematical object and a defined mathematical object.

Fixed would be things like pi, e, i, √2, √3.....

Defined would be things like variables, parameters, objects by unrestricted definition.

Infinity should always be regarded as a defined object and never a fixed object.

Mathematical objects exist as brain state.

Brain; (mathematical objects)

These come in different forms with specific properties.

Like fixed,

Brain; (fixed mathematical objects)

Things like pi, i, e, trig functions, √2, √3.

Or defined,

Brain; (defined mathematical objects)

Like defining sets, setting parameters, variables in functions.

Not sure if this will help with Russell's paradox but in general, applying universal form and understanding mathematical objects will work in understanding paradoxes or contradictions

I might give it a try later.

I cover the basics of mathematical objects in my post on universal form. There is an example of the contradictions in time perseption given.

I described to ChatGPT a rope tied to a tree branch at one end and a rock at the other.

It volunteered that this would be a pendulum and if you pushed it, it would swing. Success.

I asked if the rope was a greater length than the height of the tree branch what would happen?

It said the lowest point on the arc of the swing would now be at the height of the tree branch.
Kind of funny. Fail.

The fails are more interesting.