Actual Infinity in Reality?

[polymath257]

Not all of them.  Most of them begin as conceptual model which are then described by mathematics so that their construct are made specific enough for any internal contradictions to be made manifest, or their predictions made precise and thereby possible to verify with precision or falsify.

But you’re saying it is true that they are mathematical models before scientists go out into the physical world to tests them, yeah?

The example of Faraday is interesting. He did a lot of the groundwork on electromagnetism, but he was primarily an experimentalist. The mathematical theory came later. So the engineers were able to start making practical objects before we had a mathematical theory. Faraday's conceptual models didn't really go that far. It was his experiments that opened up a whole new area.

[brewer]

The example of Faraday is interesting. He did a lot of the groundwork on electromagnetism, but he was primarily an experimentalist. The mathematical theory came later. So the engineers were able to start making practical objects before we had a mathematical theory. Faraday's conceptual models didn't really go that far. It was his experiments that opened up a whole new area.

Didn't old what's his name do this with two different sized balls in a tilted building?

[Neo-Scholastic]

IMHO logic is prescriptive since what is being described could not be otherwise. It transcends any particular circumstance and applies universally regardless of the type or degree of any particular thing.

That seems a little flip.  Logic can be predictive but I don't see why you'd say prescriptive.  Logic applied correctly and hooked up to solid premises, can yield a correct prediction.  The logic dictates nothing, and its predictive power is entirely dependent upon a correct assessment of the salient factors.  Logic is a tool, nothing more.

I'm referring to the principles of logic not the contents. Kind of like the quadratic equation without any assigned values to the variables.

[The Grand Nudger]

The principles of logic are only as good as how accurately they describe the universe under which we live, Neo.  They're dependent upon them, as well..as all things we know must be.  

Weakness of the system. Just remember not to fall asleep..that's when the night maers get you.

[GrandizerII]

I don't think the B Theory of time solves the underlying problem of having a series of cause/effect relationships. It seems to me that even if all points of time are equally real, they are still ordered by a structure we call cause/effect--a tangible series of objects we can use in thought experiments. [NOTE: I say this to start because there are some here who deny even this].

Like I keep saying, cause/effect relationships are only meaningful to talk about in a certain context (from a temporal perspective). When we're discussing the fundamental nature of reality, especially if we're assuming B-theory of time (and/or eternalism), you have to be willing to accept that it may be logically possible that causality is just an illusion. If there is no time flow, then there is not really change or motion happening. And no causality. Which possibly leaves us with simply an eternal 4D (or higher) static structure of which every time moment is a part of. I'm just saying.

Perhaps a variation of Hilbert's Hotel:

We can conceive of a possible world (much like the one you are proposing) with a beginningless series of discrete successive events of equal duration leading up to the present (real or perceived present). 

[ ...en, ... e5, e4, e3, e2, e1, e0]

We can conceive of another possible world with exactly the same events in the same order, but in between each of those events, another event occurs.

[ ...en, En, ... e5, E5, e4, E4, e3, E3, e2, E2, e1,E1, e0]

In this series, an infinite number of additional events have been added to an already infinite series of events. Are there more events? No. Infinity + infinity = infinity. We can also do the subtraction example from Hilbert, and imagine all the events prior to e3 could have been left out of the chain. 

[e3, e2, e1, e0]

In this series, we have subtracted an infinite number of events from an infinite number of events. Infinity - Infinity = 4.  Alternately, every other event could have been left out:

[ ...en, ... e4, e2, e0]

In this series, we have left out an infinite number of events from an infinite number of events. Infinity - Infinity = Infinity. 

This is not just "counter-intuitive". Actual infinities of real objects leads to absurdities (metaphysical impossibilities). Therefore an actual infinite is not logically possible. 

[Example language from a paper from Wes Morrison - http://spot.colorado.edu/~morristo/EndlessFuture.pdf]

I already addressed this earlier, Steve. Go back a few pages to find my post where I show how inf - inf is indeterminate. You are doing subtractions with different instances of infinite sets. There's no contradiction here.

In the first case of subtraction, you took out everything up until e4 (including e4), so of course you will end up with just 4 events.

In the second case, you took out an infinite set from another infinite set in a way where an infinite set remains (by taking out one event for every two events we go through).

In the addition case, you seem to be missing some important assumptions here, so I'm not going to comment on that until I get a clearer picture of what you mean by "discrete" and such.

Ok, so about the addition case, I'm assuming that there are gaps in between the initial moments into which you can insert the extra moments. So correct me if that's not the case.

Either way, again, you have to keep in mind that just because you have derived the equation inf + inf, doesn't mean that you are adding two instances of the same infinite set to get a totality which is equal to that same infinite set.

In such a case, you have the original infinite set + an additional infinite set to get a newly updated infinite set.

This is a loose analogy, but it's like almost saying that finity + finity (in the form of 3 + 4) = finity (7), rather than 3 + 3 = 3. So there's no contradiction. Infinity is just a confusing concept to those who don't take the time to understand what it's really referring to. And it's counter-intuitive for most (if not all) of us, no question.

[Neo-Scholastic]

The principles of logic are only as good as how accurately they describe the universe under which we live, Neo.  They're dependent upon them, as well..as all things we know must be.  

Weakness of the system. Just remember not to fall asleep..that's when the night maers get you.

You intentionally conflate ontology with epistemology because it suits you. It is similar to how there are natural laws that govern the universe and there are formulas describing/modeling those laws. Saying that something is descriptive implies some other thing being described.

[GrandizerII]

The principles of logic are only as good as how accurately they describe the universe under which we live, Neo.  They're dependent upon them, as well..as all things we know must be.  

Weakness of the system.  Just remember not to fall asleep..that's when the night maers get you.  

You intentionally conflate ontology with epistemology because it suits you.  It is similar to how there are natural laws that govern the universe and there are formulas describing/modeling those laws. Saying that something is descriptive implies some other thing being described.

I assume, and I think we should all assume (for the sake of rationality!), that the laws of logic hold unconditionally in this Existence, that there are logical absolutes regardless of how we arrive at them, or whether or not we ever do.

But then again, Existence doesn't owe us jack shit. If there's no logical sense to this Existence, then there just isn't, and we're all doomed. Logic is the best we can do, and it's not reasonable to not rely on it, but at least if logically problematic stuff does occur, then God can create square circles, and ain't that a good thing!

[Mr.Obvious]

I noted i don't have an opinion. I'm not a physicist and The idea of both a finite as Well as an infinite universe are hard for me to grasp. I often imagine The universe as a growing bubble in a complete and utter void. With The expanding universe being finite, yet vast, and The void being neverending yet unreachable because it does not really exist yet. But i have no good reason to assume it is so. This is simply how i cope while i live my little life trying not to let The weight of The Universe crush me and allow me to focus on The things that matter to me.

Wouldn't it be a kicker if it turned out not to be finite or infinite, but both? Or neither?

[GrandizerII]

I noted i don't have an opinion. I'm not a physicist and The idea of both a finite as Well as an infinite universe are hard for me to grasp. I often imagine The universe as a growing bubble in a complete and utter void. With The expanding universe being finite, yet vast, and The void being neverending yet unreachable because it does not really exist yet. But i have no good reason to assume it is so. This is simply how i cope while i live my little life trying not to let The weight of The Universe crush me and allow me to focus on The things that matter to me.

Wouldn't it be a kicker if it turned out not to be finite or infinite, but both? Or neither?

Yeah, who the hell knows really. I lean towards infinite because logic itself compels me to (note I haven't made any logical argument for infinity in this thread, but just saying).

But suppose infinite universe/cosmos makes no sense. In such case, even a finite universe itself is bizarre and counterintuitive as well. Why this specific universe and not something else? It doesn't matter if God willed it or not (if he exists), the question would still remain: why this, not that?

[Goosebump]

I just read your opening post. I don't know what has been presented.

You ask if something can exist "something concrete (not abstract)". -edit- that is infinite.

The theory of a Black-hole is just that. Is there an end to how dense a singularity can get? No. Theoretically it can continue to be more and more dense. At infinitude. There is nothing more "concrete" then matter its self. A black-hole is that mater condensed and can theoretically continue to condense more and more.

If you mean something that is proven beyond theory, then the idea of numbers. One can always count higher. There is no end to numbers. Count and count and count on. You'll always have another number to go to.