Actual Infinity in Reality?

[GrandizerII]

It's similar to the Watchmaker argument. He's extending what applies to things in this universe to the universe itself.

Been saying that forever 

You have to with such people.

[Amarok]

"Everything has limits. Except for non-physical things [what the fuck does that even MEAN? What the hell is a non-physical thing?!]. Just because." sounds an awful lot like "Everything has a cause. Except God. Just because."

And now they will start throwing things out like  numbers  and logic  or thoughts etc etc. And arguing those things are not physical because because they don't have certain qualities . Of course it's all bollocks .

[SteveII]

The math is based on axioms (assumptions). It is question begging (circular reasoning) to say it is proof that they are logical possibilities. You have assumed an actual infinite in order to do further math with it. So, it gives no help to the argument that an actual infinity can exists. Therefore need we turn to something other than math:

1. You cannot get to infinity by successive addition.
2. You get absurdities when you propose an infinite number of actual objects (Hilbert's Hotel).
3. You get contradictions about how many squares and square roots there must be (Galileo's paradox)
4. Is the vase full or empty in the Ross–Littlewood paradox?
5. Is the lamp on or off in the Thomson's lamp paradox?
6. It seems we cannot traverse even a finite distance in Zeno's paradoxes

These coupled with the fact that we don't have anything in the real world that could be an actual infinite leads a rational person to the believe that an actual infinite of real objects is not possible.

On the contrary, the fact that we do not get inconsistencies from these axioms shows there is no logical problem with them.

We know of many axiom systems that *are* self-contradictory. The theory of infinite sets is not one of them.

Again, question begging. By axiom, you assume something exists. That cannot be then used as proof of that thing existing. You did not get to the assumption by logic, therefore you cannot say that it is logical.  

1. Irrelevant. That isn't the mechanism for getting infinite sets.
2. Not absurdities, just counter to intuition derived from the study of finite things.
3. Not a contradiction. Again, just counter to intuitions derived from the study of finite things.
4. Not well defined. An impossible task due to relativity.
5. Not well defined. Task impossible to do because of relativity.
6. Resolved because both space and time are infinitely divisible: see algebra and calculus.

the lack of coherent arguments against actual infinities and the fact that they are not self-contradictory is enough to show they are *possibilities*. 

Again, whether they are present in the real world is not known. But there is no *logical* issue. Paradoxes because people think in terms of finite sets, yes. But no contradictions.

What?!? Conflicting answers (Hilbert, Galileo), impossibilities (Ross-Littlewood, Thomson), and obviously false (Zeno) is not just "counter to intuition". Your bar is set really, really low for metaphysical impossibilities. Your reasoning is that we don't assume mathematical non-logical axioms--therefore we can't make sense of the paradoxes. That is clearly question-begging. 

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Once again, Steve, you cannot get Graham's number (which is finite) via successive additions for any operations, as fast as they could be, in the current age of the universe.

Do you think Graham's number can exist as a logical possibility?

I have no idea why you might think that Graham's number has a logical problem. It has none at all. Ironically, there are an infinite amount of numbers that could not be counted to in any age of any universe. The fact that you think this is a point is puzzling.

[GrandizerII]

"Everything has limits. Except for non-physical things [what the fuck does that even MEAN? What the hell is a non-physical thing?!]. Just because." sounds an awful lot like "Everything has a cause. Except God. Just because."

And now they will start throwing things out like  numbers  and logic  or thoughts etc etc. And arguing those things are not physical because because they don't have certain qualities . Of course it's all bollocks .

You can't divide by 0, therefore 0 is illogical!!!

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What?!? Conflicting answers (Hilbert, Galileo)

You have been shown several times there are no conflicting answers. Different instances of infinite set are going to yield different results. This is logical, not contradictory.

Same infinite collection - same infinite collection is still 0 (empty collection), and always will be.

It's when you subtract one infinite collection from a different infinite collection that you get other [varying] answers, depending on these collections. It's loosely similar to finite (7) - finity (4) = finity (3) => finity - finity = 3???

And what about 0/0? The answer could be any number, and when we don't know exactly which due to lack of contextual contraints, the answer is that it's indeterminate. Same with infinity - infinity.

[polymath257]

On the contrary, the fact that we do not get inconsistencies from these axioms shows there is no logical problem with them.

We know of many axiom systems that *are* self-contradictory. The theory of infinite sets is not one of them.

1. Again, question begging. By axiom, you assume something exists. That cannot be then used as proof of that thing existing. You did not get to the assumption by logic, therefore you cannot say that it is logical.  

1. Irrelevant. That isn't the mechanism for getting infinite sets.
2. Not absurdities, just counter to intuition derived from the study of finite things.
3. Not a contradiction. Again, just counter to intuitions derived from the study of finite things.
4. Not well defined. An impossible task due to relativity.
5. Not well defined. Task impossible to do because of relativity.
6. Resolved because both space and time are infinitely divisible: see algebra and calculus.

the lack of coherent arguments against actual infinities and the fact that they are not self-contradictory is enough to show they are *possibilities*. 

Again, whether they are present in the real world is not known. But there is no *logical* issue. Paradoxes because people think in terms of finite sets, yes. But no contradictions.

2. What?!? Conflicting answers (Hilbert, Galileo), impossibilities (Ross-Littlewood, Thomson), and obviously false (Zeno) is not just "counter to intuition". Your bar is set really, really low for metaphysical impossibilities. Your reasoning is that we don't assume mathematical non-logical axioms--therefore we can't make sense of the paradoxes. That is clearly question-begging. 

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Once again, Steve, you cannot get Graham's number (which is finite) via successive additions for any operations, as fast as they could be, in the current age of the universe.

Do you think Graham's number can exist as a logical possibility?

3. I have no idea why you might think that Graham's number has a logical problem. It has none at all. Ironically, there are an infinite amount of numbers that could not be counted to in any age of any universe. The fact that you think this is a point is puzzling.

1. One standard way to show the impossibility of something is a proof by contradiction. If you assume the existence and derive a contradiction, you have established the non-existence. But, in spite of many attempts to show a contradiction in the notion of actual infinities, no such contradiction has ever been found.

2. What conflicting answers? Be specific. There are two notions of size relevant to sets: containment and one-to-one correspondence. They are different ways to describe size and yes, they can give different answers. That isn't a contradiction any more than the fact that volume and mass can give different answers to the question of 'how much?'. All that is required to resolve this 'absurdity' is more precise language.

The impossibilities of Thomson and Ross-Littlewood are not in the notion of infinity, but the fact that the activities required cannot be done because of relativistic effects.

Zeno's paradoxes were *solved* by the introduction of infinities! The infinite divisibility of both space and time nicely solve ALL of the Zeno paradoxes.

3. Well, one of your objections to the notion of an actual infinity is that it cannot be counted to (which is, truthfully, irrelevant). Neither can Graham's number. So why do you accept one as a possibility and not the other?

[RoadRunner79]

Where do you think that the fallacy of composition is being committed here?  It seems to me that this fallacy is often casually thrown in, when such an argument is not being made.

It's similar to the Watchmaker argument. He's extending what applies to things in this universe to the universe itself.

I don't see that in the argument.  The fallacy of compositions would be, that because the things that make up the collection have this property, that that which they compose must have the same property.  For example, a tooth pick is relatively weak, there fore, your bridge made out of many toothpicks is equally weak.  

What is being done here, as far as I can tell, is making a statement about all physical things.   Which if the universe is a physical thing (or collection of things), then it would apply.  You are free to argue with the reasoning behind it.  You can offer arguments against it.   However I believe you hastily and wrongly dismiss it; with the fallacy of composition.

What special reason, would we not apply this reasoning to all other physical things, but not to the universe, if it is a physical thing?

[GrandizerII]

It's similar to the Watchmaker argument. He's extending what applies to things in this universe to the universe itself.

I don't see that in the argument.  The fallacy of compositions would be, that because the things that make up the collection have this property, that that which they compose must have the same property.  For example, a tooth pick is relatively weak, there fore, your bridge made out of many toothpicks is equally weak.  

What is being done here, as far as I can tell, is making a statement about all physical things.   Which if the universe is a physical thing (or collection of things), then it would apply.  You are free to argue with the reasoning behind it.  You can offer arguments against it.   However I believe you hastily and wrongly dismiss it; with the fallacy of composition.

What special reason, would we not apply this reasoning to all other physical things, but not to the universe, if it is a physical thing?

Don't be silly. By your argument, even the example you provided is not an example of a composition fallacy.

[Amarok]

Roads examples are crap . This is still a composition fallacy .

[RoadRunner79]

I don't see that in the argument.  The fallacy of compositions would be, that because the things that make up the collection have this property, that that which they compose must have the same property.  For example, a tooth pick is relatively weak, there fore, your bridge made out of many toothpicks is equally weak.  

What is being done here, as far as I can tell, is making a statement about all physical things.   Which if the universe is a physical thing (or collection of things), then it would apply.  You are free to argue with the reasoning behind it.  You can offer arguments against it.   However I believe you hastily and wrongly dismiss it; with the fallacy of composition.

What special reason, would we not apply this reasoning to all other physical things, but not to the universe, if it is a physical thing?

Don't be silly. By your argument, even the example you provided is not an example of a composition fallacy.

You're not giving much specific here to work with... I would encourage anyone to look it up for themselves.

[Edwardo Piet]

There was a debate ( about 18 months ago) with a Jewish Rabi (Daneil Rowe) and atheist philosopher A.C. Grayling.  One of the parts that interested me, was Rowe's point that physical things cannot be infinite or endless in extent.   This is due to the fact that physical things, are necessarily defined by their limits.  They have properties such as size, weight, position and a number of other qualities that require limits in order to define them.  He described this as being bound (finite) as opposed to being unbound.   I tried searching for this type of thought process, but didn't have much luck; finding others who described it this way.   But I thought it was interesting.

IMO the very idea of a non-physical thing is incoherent.

I mean... not much of a thing is it?