Proof the universe doesn't exist?

You know, for once you're on to something. This argument is a very potent argument against actualists, who construe possible worlds as maximally consistent sets of propositions. A neo-Cantorian argument is applicable to their position as well.

But, refuting other philosophical positions aside, just because we assume or know that the universe exists does not entail that we have to couch it, ontologically, within a set-theoretic framework. One may take the notion of a world or universe as primitive, that is, it cannot be defined any further. You either know what a world is or you don't.

But you do have something here, which is nice. :-)

Once again, the assumption that we can treat "existence" as understood is the central issue. The "logic" is secondary to that.

The application of logic to ontology is might be likened to trying to stir a hot drink with a spoon made out of ice !

I think we can treat existence as understood; depends on the language game.

The issue is whether we can treat existence and logic as equivalent. Can we treat the entities we are dealing with as, ontologically, mathematical? Seems Pythagorean to me, and it leads to numerous problems, one of which browser pointed out. That's why I'm not an actualist when it comes to possible worlds talk; instead I'm a modal dimensionalist .

I would argue that the entities are not themselves mathematical, but can be "mathematized". A different position, and I believe far more fruitful one.

I think for a proper definition, a Universe is a powerset on itself, you cannot treat it as a simple set...this is why I believe we need a system which is not dynamic, or rather has a simulated dynamic into it...on that regard, dynamics bring no emergent novelty if not from the primitive set...a cyclic dynamic boundless Universe can this way I believe be treated as a powerset and still be qualitatively finite in phenomena even if repeating...

Does this make sense ? (I don't have but a basic intuition on powersets knowledge for tool)

...I very much feel like trying to "box" and contain infinity to render it harmless...

The problem with Cantor's Theorem is that it assumes a finite base set. If the basic set is infinite, it is impossible to have a power set greater , numerically, than infinity.

∞ = ∞ +1 = ∞√ (n² +x²) = ...

Semantics, as according to Cantor there are infinity's bigger then others...

Technically, he only proves that not all infinite sets are equal in infinity. This is assuming linear distribution of parts in a set. The Universe is not a linear model. Where it is true that, on a micro/molecular scale, no object is exactly identical to another, it is also true that no object can exist without space. Another way to think of it is like this:

P(X) = { {a }, { a, b }, { b, c, e }, { a, c }, { e }, . . . }

In your argument, you are assuming X is the universe and P would be the power set of the Universe. In reality, to use set theory to apply to the Universe you must realize that X is a single object in the universe: matter, for instance.

We would need to look at this more like this:

U ≡ (P(X) = { {a }, { a, b }, { b, c, e }, { a, c }, { e }, . . . }) ⁿ < Øⁿ
Where n = ∞

So U is the equivalent of all sets, to the infinite power, less than infinite nothing. The reason for this is that the Universe includes all sets less than infinite nothing as well as the infinite nothing (a measurement of space) in which all sets must exist. Since you cannot have a set of nothing, we are representing nothing (empty space) as a null set.

Cantor's Theorem can only apply to that which can be counted, even infinitely, within a space. Since space cannot be enumerated, it cannot be included in a set as it is the container of all sets and the Universe contains all space.

As I see it the universe is the powerset with all the space time info, a collection of sets of local instants in contact or not, as any object or collection of objects is not just in the here and now but distributed trough vectors of space time...I imagine a motionless ensemble of all space times frames along an axis, a set itself with a circular repeating order...whether it suffices or not...

I feel I may have misrepresented something in my previous post. Allow me to clarify. I am not speaking of distance and motion(space time). I am referring to the space that this measurement is taken in. Space exists without motion while distance does not. Space time frames are still enumerable. Space cannot be observed, thus cannot be enumerated and placed in a set. I imagine space would be the brackets around the set. Not part of the set itself, but a fundamental defining point or key that translates the set for us.

These spoons made of ice are good fun !

Now try observing the observer !

...oh pleeeease...It works like an ocean, Einstein thought of aether at the time, lately some are turning to it again...space is such an empty set is full of energy and virtual pairs of particles coming in and out of existence anywhere even intergalactic space not to mention it can be deformed...but even it was the case you can work spacetime as a function all you need is a set of dynamics correlated with every particle ever existed...in fact you experience reality from a certain layer of code/language programming, from a certain layer of correlated ratios which give rise to correlated ratios of effects which you "observe"/measure...as far as I know the whole thing can be reduced to binary coding in a huge algorithm, matter energy space dark energy dark matter n all the remaining ****...yeah even movement, trajectory's and dynamics, are but a collection of ratios...a collection of "objects"...you are far off and green in your conjectures dude...space is an empty set ? oh dear...

These observers observing observers are good fun!

Now try something less constructivist!

It is true that space is filled with "things". All the time. And those "things" exist and can be classified into sets. What I am talking about is the nothing in which they exist. Space time can be deformed, this is true, but space cannot because there is nothing to deform and no way to measure the deformation. Space time exists within space. Space is the void in which all things exist but is not, in and of itself, a measurable/observable anything. There is no equation for it; no theorem or measurement to define it. It is simply the "place" where all observable actions happen. It is the void in which an infinite number of possibilities occur simultaneously.

In multi-verse theory, it is the void in which all universes simultaneously exist without bumping into each other. The standard model of physics has no true definition for it as the standard model focuses on observable reactions. It's a bit like explaining the color red to a man born blind (verbally, without the assistance of retinal receptor manipulation).

And don't "oh pleeeease" me. It just shows ignorance and unwillingness to consider unconventional ideas and does not further the conversation or provide rational, credible argument. I am trying to be amicable while discussing your ideas. Please return the respect.

I can do one better, I can observe the observer observing.

You see but you are totally wrong as space is a shape around and in between objects as much objects are a shape in space...so there is this shadow geometry between form and its absence, the form of things, and the form which things themselves give to the absence that can be translated in information...through time space, dynamics is dependent on this relations...what is the shape of a void between objects in a given local sequence of space time ? It does matter...I can only think of music to give you an example on voids being important...the whole binary sequencing is yet another one...

the "oh pleeeease" thing was not ill intended only spontaneous as expecting the counter you offer...in fact I believe you reason quite well, even if I disagree...

I believe we are arguing over a definition at this point. Let's see if we can get past semantics and move forward. I think I have a solution. Let's change a few definitions and see what we come up with.

Let us assume that the Universe can be expressed as a set, space and everything in it, just as you say. Still, the universe must exist (or NOT exist) somewhere. That somewhere must have the potential to contain everything and nothing simultaneously in order to provide a platform in which our current observations can hold true.

If we are to assume that this has any physical attributes of any type, we create a paradox and would generally break every model of physics that we have come to understand.

So let us call the platform C, the Universe U, and n will be ∞ as before.

C ≡ (P(U) = { {a}, {b, c} ,...})ⁿ ∈ Cⁿ ∴ C ≡ Øⁿ ∈ Cⁿ

So the "platform" C is the equivalent of infinite power sets of infinite sets of Universe as elements of infinite C and therefore also the equivalent of infinite nothing as element of Infinite C. This is where we create the paradox in that C ≡ Cⁿ ≡ C(C)ⁿ(...). So C is not a set or power set but contains the potential of all sets, no sets, and itself infinitely.

There must be a platform to define potential or there could be nothing, including any experiences.

In short, the potential for something defines the existence of something and potential is constant where observation is possible.

Semantics and definitions seem to create the problems for humans.

Simply put, we're here. Anybody need proof?