Does infinite sets lead to infinite regress
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)
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)
Comments (23)
Quoting Gregory
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
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.
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
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.
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.
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
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
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?
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.
Then you and I know different infinites. You can stop and resume infinity in your knowledge of it.
You can theorize set-conversion, though.
Interesting
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.
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.
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?
Great observations. Nature is both infinite and finite says Hegel. How to reconcile that is beyond human comprehension