## Does infinite sets lead to infinite regress

• 4.4k
Soo,

1) if we have an infinite number of sets, and a set that includes all of them and itself, we have a self consistent system without going off into infinite regress.

2) the only regress is inside the system

3) Sets are controlled by itself

These are the three propositions I set here. Argument is encouraged on them

I want to say something about understanding the infinite. The more platonic thinkers would say we "transcend" sense and individuality, seeing the infinite as in a single set. As anti-nominalists they say we do this with nature's too, but that is a psychological issue and I would rather stay on the question of sets. What do people mean though when the speak of nominalism within mathematics at the turn of the 20th century? Could these mathematicians somehow count eternally without bracketing off infinities into finite groups? That would be amazing

(Trying not to go off an a tangent that only I understand)
• 2.6k
if we have an infinite number of sets, and a set that includes all of them and itself,

If you have a set that includes itself as an element, you're no longer in the realm of standard set theory, in which self-membership is forbidden by the axiom of regularity.

https://en.wikipedia.org/wiki/Axiom_of_regularity

There are in fact sets that contain themselves, but not in standard set theory.

https://en.wikipedia.org/wiki/Non-well-founded_set_theory
• 4.4k
Why not outlaw selfreference then, which is a set container itself anyway. It's almost too easy to throw out Godel then. I don't follow Godel to begin with. Isn't it just Russell's paradox, which as I've said i don't think is a paradox
• 4.4k
Last night and tonight I went over the first propositions of Euclid. I get stuck on proposition 7. He loses me because he makes a lot of assumptions without providing the proof, from what I can see. If infinite regress is possible, it seems to me the ABC triangle could have the same angles with the DEF triangle and not meet at any point. Infinite objects must have a medium just as an infinite regressive system does.
• 366
In which set do you start the system? Is this an important question? Are all sets a moderator of sets therefore?

What is the significance of all sets? How does it imply a self consistent system?

Is the formation of sets spherical or square-form?

So all sets equate each individual set. The fact that it is, is important. Right?

Is this just one perception of all sets?

In this projection are twelve sets in 2D abstract map.

Do you describe all sets as some sort of machine, you say self consistent system?

Does that imply an intelligent user of points (and not sets), set in area formation?

I might agree if you can elaborate.

If someone pressed the programmed sphere it executed it's program.
• 4.4k

You start with THE highest set. There has to be one overarching all the others. I think of them as these: [set] But imagination is not needed for this since it's arithmetic. Infinite regress is not possible without something controlling it. Our reasoning powers are such that they control infinity by finite means. So we can explain all our math by finite means I believe. Logicism was not refuted by Godel
• 366

The skeleton of all sets is set in the perfect position for a perpetual system. It can be rotated as one.

You changed it from all sets to all sets moving.

Does infinity mean increase?

I thought it was forever.
• 4.4k
I would love to know how Frege answered Russell in the extra part added to his book right before it was published. Russell's theory of types just says that sets can't come before objects. That is an opinion. Maybe sets can come first. I have no idea how ZFC answers this, but they might be wrong

I think Newton was wrong to accuse Descartes in his putting of arithmetic higher than geometry. Newton and the Greeks were wrong (except of the Eleatics).

I don't get the step in the 7th proposition (of Euclid) when he says: "Since AC equals AD, therefore the angle ACD equals the angle ADC...Again, since CB equals DB, therefore the angle CDB also equals the angle DCB."

I understand how the proof goes in the sense that he shows that at first an angle seems to be larger than another, then equal, and thus there is a contradiction. IDN though, there is something missing here for me. He sets up what is an impossible situation given his geometry and thus when he tries to prove its wrong, doing it from his geometry, even though the setup in not in his geometry

Geometry starts from wrong principles, because space is inherently contradictory.
• 4.4k

We are strictly talking about static sets and numbers in what you are referring too. The power of the ultimate set is a mathematical force, not mechanical. That doesn't mean we can't mechanize our thoughts, because our thoughts lead to the mathematical force, which is the object of our thoughts
• 4.4k
No set needs to include itself. That was a philosophical idea inserted into Frege's system illegally. But any one in the series can.
• 366
I think implying a set is primary is fine, but that you're explaning it as the primary mover, an expanding set, and that is a measure of it's infinity - it's movement. Which also implies your thought is mechanical.
• 4.4k

My thoughts are mechanical, but without motion. I think you are in contradiction in thinking motion and mechanical thinking can go together

Whitehead was a Spinozian. The latter said that God does not love us, yet we are him. So he doesn't love himself. The ultimate action for Spinoza is thought, not love. Whitehead took this ultimate Intelligence and tried to add other stuff, but it gets tangled with stuff from Aquinas, so I don't know if it's valid to go into those areas. Interestingly, Whitehead wrote stuff in the 20's on wholes and parts which are now considered wrong.

I think we can mechanize out thoughts because we are matter, all along guided by the set that contains itself
• 366
taming the wind.

A moving object spins if it collides with a special object.

There is not always regress, there can be harmonious groups of individual sets.

What's to stop all sets in a sphere of sets, becoming a ringed sphere - doesn't infinity imply separating?

No individual set needs to include itself but all sets must take on some form of shape; all sets of infinity is a point in infinite growth?
• 4.4k

It doesn't matter how your imagination sees the set. This is straight arithmetic, not geometry. There cannot be pattern in infinity if you go from 1 to infinity, obviously. If you add on infinities than you have patterns, but only if you believe in patterns. I don't believe in patterns, and also I am a materialist. There is only one infinity, there is only one thing to think about ultimately. It is not a person.
• 366

Then you and I know different infinites. You can stop and resume infinity in your knowledge of it.

You can theorize set-conversion, though.
• 4.4k

Interesting
• 4.4k
An infinity is simply the highest thing possible. I know I am using a philosophical argument here, but there can't something higher than the higher. Call the latter the highest and move on. I don't think a set has to be infinite in order to contain itself. So the higher thought is infinity, and sets lead you there
• 4.4k
When calculus brings the infinity into the finite, we can say maybe that the One of Parmenides is the infinite. Or we know nothing about what makes the infinite finite. Kant calls it the noumena
• 626
I want to say something about understanding the infinite.

Infinity can not be realized, it can not exist, except potentially through repetition, so no “unique” infinity can exist. There is a simple proof having to do with a digital photograph and number of possible pictures it can contain.
• 366
Cycling a figure of eight an infinite amount of times is seemingly a possibility because of it's cycle shape.

It's a fallacy however.

You can plot infinity on the figure of eight(saying yes to it can be infinite) but you can not concieve it(saying yes to what amount of cycles that is.)

Forever gets boring and repetitive.

Yes we've had this figure 8 simulation going on for a while now, it's all the same. What other simulations are possible that can go on forever?

We're the tireless imps and if we keep goin' we can keep the figure 8 in continuum.
• 4.4k
To go from San Francisco to Bakersfield, you have to go half of the space, otherwise your there. And half that, otherwise your there. There is a difference between an infinite regress and simple infinity. The universe is infinite. Spinoza asked "if God is infinite, he must be the world". That has to do with ontology, but in math it is true. Calculus can make the infinite finite although this is a contradiction. I believe the medium this procedure is done is in different from what calculus can describe
• 4.4k
There is nothing that stops an infinity of subdivision of space. There is also nothing in the human tool box to explain how infinite space can have a beginning and end
• 366
There has to be a great turning effort to keep anything infinite in continuum.

Infinity is always something, but this something dies with the user of that something.

Greater quality comes in finite supply, how do we make finite things infinite?
• 4.4k

Great observations. Nature is both infinite and finite says Hegel. How to reconcile that is beyond human comprehension
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