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.

The subject of mathematical objects comes up here often and they fit well into Universal Form.

So Brain; (what the brain supports)

Becomes,

Brain; (mathematical objects)

The subject of infinities has been covered and can be used as an example.

A little better example is numbers that need to be discovered through mental process like pi or trigonometric ratios. They exist in no form prior the being 'extracted' using mental manipulation.
Since the numbers are ultimately fixed in their form it becomes a process of a brain conforming to a number and not a brain creating a number.

This is an easy application of Universal Form and should be the basis for a philosophy of mathematics.

Since there is some math interest here I thought I'd cover that.

I sometimes see the misperception that these objects have always existed. Without this basic form they actually do not exist.

A lot depends on how close our best models of physics are to the actual real physics.

I asked GPTchat if an unsupported end of a catiliver can support weight. It answered correctly so....
Kind of looking for the line of success and fail.
It did give a textbook page kind of answer.

Most of you have done this but I'm learning.

ChatGPT ....

Okay, not sure what I did.
First time I used it so was following the menu best i could.

No problems though now.
Okay I see send a message so both were listed.
Problem solved.

Okay, I get it.
I tried an email to you for guidance.
Maybe it didn't send.

In the context of Neuroscience this seems very poor curriculum. A historical perspective maybe?

A second try:

The nature of our existence,

[ Brain state]

Expanded,

[ Brain; (mental content)]

Expanded again with specifics,

[Brain; (perception)]

Also,

[Brain; (inference)]

And combined in sequence and relation,

[Brain; (perception, inference)]... I based on P.

And a category in question,

Unperceived existence.....ask about this.... clear as mud??

Edit: Unperceived existence is defined as not perceived so it exists only outside of brain state.

Comment on cup in the cupboard:

The cup exists physically as a physical cup.

The cup exists as brain state,
Brain; (mental representation of cup in cupboard)

Hume fails on this.

This is as far as I have gotten on parsing the question in sentence form:

The nature of our existence leads to what we perceive that leads to what we infer.

The (status of) unperceived existence is in fact a non-existent entity. As we do not perceive it... It does not exist from our personal frame of reference.

This is more for the forum than the homework problem as it may contradict the curriculum.

And it could be parsed in different ways by different people.

Okay, that is relevant.

Take my advice... NOT Jamal's

Try nesting it as a start.

A horribly worded question....
An embarrassment to the university.

You need to parse each word or phrase in a nested set if that is any help.

Looks like four elements.

You probably need to start with your best theory of mind to make any progress.

Just for background on this topic:

Mathematical theories are supported by mathematical proofs.

Physical theories are support by the preponderance of the physical evidence and are subject to revision.

I'm just pointing out a tricky situation you need to think about. The known end point is that physical matter does exist (now). So does some start point of nothing existing have any basis in physical evidence?

As I said, as mathematical objects something does not equal nothing.

I have had some luck in correcting (or guiding) answers. Maybe use the same method you would talking to a person. It doesn't have a bad attitude about trying again.

Nope, tried again and sometimes it gets worse.

If anyone needs a primer on this you can check out my post on Universal Form for trouble shooting philosophy problems.

Less than a week old but it works.

Okay, but I think it's an open question if physical nothing is possible and your own conclusion argues against it.

I'm thinking of starting a DIPSHIT PRIZE that we can nominate for and pass around here.

TDF really isn't that bad. He tries hard. You can be in charge.

Edit: To management...Not serious.

In 13.8 billion years of the universe there has never been a time when a physical nothing has ever existed. Is that right? Are there special cases?

Mentally we can conceive of nothing but that is the only place it ever comes up.

So in the logic of nothing to something you are dealing with two mental abstractions only. Isn't that the only scenario? Is logic expected to work the the same way on mental abstractions as it does on theories of physical matter?

Is there a way to resolve this?

Edit: I'm thinking as a mathematical object only
So this is trivial....nothing does not equal something.

You can have,

Physical nothing

Or

Physical object

And mentally we have,

Brain; (the idea of nothing)

Or

Brain; (the idea of a physical object)

So just what you were saying. But it's different physically and mentally. The physical follows laws of physics and the mental is at will.

Edit: Note the reality of physical nothing may not exist....maybe an open question.

On your post directly above you question if meaning can be reduced to physics. Probably not in the sense we could find out the exact mechanism but it's still a likely guess that holding meaning actually is possible because the physics supports it.

Another question in the same area and I think a little more focused is can our physical brains conform to specific subject matter? I really enjoy the infinity discussions going on here now (other threads) and by that evidence I say yes and we do it very well. The opinions we form don't always agree and often disagree but for individuals it is a problem of matching mental capabilities with an inflexible subject matter. Some do it better than others. In areas of specialty... capabilities are built up over years and years. In other cases insights come quickly.

So meaning doesn't reduce to physics but brains can conform to specific subject matter. More of a reaching out and capturing than a reducing down it appears.

You are too pessimistic. You can have your view and they can have theirs.

You can always declare victory, plant your flag and call it a day. Really, say what you like. I agree there are contradictions and what I brought up about parameters that can be anything your brain can dream up.

Maybe there are real world applications to some of this as has been discussed by those who have actually done it. I assume they use what has proven to work. Math in practice has a precision component, not just theorizing.

This isn't really the place to come to get people to agree with you. I think the math boys really did give you a good amount of feedback that would be hard to get anywhere else. So if you want to run something past us we'll tell you what we think and you can react accordingly. Most of what you say really irks a formally trained mathematician.

To me it seems like arguing about mental fantasies but for someone who has studied it there would be something to defend.

It's been one of the more lively threads here...seems to go on all day.

As far as the math profession I do think you should show some respect because the world runs on the math they do and for some things only a few people per million or billion may be able to do it.

Did you give Philosopher19 the finger or is there real math behind the north pole of the riemann sphere? It would be cool if you meant it both ways.

I can diagram it generally:

My Brain; (the idea of Universal Form)--->My Brain, Muscles physically encoded to matter--->electronically transmitted physical signal (not information as commonly defined)--->Your Eyes, Brain; (decoded and received idea of Universal Form)

My brain holds information in Universal Form and your brain holds information in Universal Form and we both know how to encode and decode by the English language so information is brain internal only. My version of things.

I can expand non-physical for you.

Brain; (non-physical)

Such things as,

Brain; (the future)

Because the future is a known non-physical.

Doing math is manipulating non-physicals.

It took me a while parsing all the words but I think you got my meaning...

Just to make sure ...by universal form I mean such things as the long list I gave at the beginning. Each item conforms to universal form.

The notation is an attempt to show how these items exist in physical reality.

A birdseye view would give,

Physical matter ........................As it exists

AND

Brain; (Physical matter)..........As brain state only

So in troubleshooting you understand there are two options. Of course we really don't have a true birdseye view because we must do this with our brains.

In the list I gave all the items are mental only, not physical objects so it takes some examination.

If I messed that up ask again.

Still.... especially good (or bad) recently.

I like your comment on comic relief.
I think I ended yesterday laughing at all this.
It's not always as good. Maybe a winter pastime for some of us.

In the context of the discussion and the differing opinions I might have been suggesting a while back that the mathematicians here should (occasionally)take their metaphorical pen from the mathematics page to a brain theory of mathematics page.

If you understand that our brains are churning out stand alone theories that work fine in a certain context but don't all work together in every context you will better understand why we disagree.

Is that reasonable? Keep doing what you are doing.