Infinitely Powerful

[Tricky]

Aleph-null ([latex]$\aleph_0$[/latex]) is the number of integers and rational numbers.

How is that different from the mathematical concept of infinity?

Marvin Gardner had a book called aha! Gotcha, which had various fun discussions of puzzles and paradoxes. He pointed out that if you add aleph-null to aleph-null, you get aleph-null ([latex]$\aleph_0 + \aleph_0 = \aleph_0$[/latex]), and that if you subtract aleph-null from aleph-null, you get aleph-null ([latex]$\aleph_0 - \aleph_0 = \aleph_0$[/latex]).

Yes, but he is simply renaming infinity as a rational number and then trying to do algabraic math using infinity as a number. The infinity and zero paradoxes are well understood. Giving them another name does not make them any more rational.

Not sure that this has much to do with theology, except perhaps as a reminder that counterintuitive and illogical are not the same thing.

Certainly that much is true. The fact that the earth is roughly sperical is counterintuitive. However, it is strongly supported by evidence. But there is no evidence for infinite anything. In fact, logically, it cannot be a real thing, but only a concept. Try this syllogism

Premise 1: Any real thing can be increased by adding to it.
Premise 2: Infinity is a real thing.
Conclusion: Infinity can be increased by adding to it.

Do you disagree with either of those premises?

 

[Elind]

If he could and chose not to, then it is HIS will, His choice, not yours. If you can only choose what God allows you to choose, then you are not really choosing.

Getting off track here. Who is God?

The problem is, I think, that when any discussion gets into gods, then it becomes meaningless because it doesn't matter how intelligent your philosophy sounds; it's no smarter than the next guy's.

 

[kuroyume0161]

Getting off track here. Who is God?

The problem is, I think, that when any discussion gets into gods, then it becomes meaningless because it doesn't matter how intelligent your philosophy sounds; it's no smarter than the next guy's.

That's my main 'quip' with the efuviant use of 'omnipotent' and 'omniscient'. These are terms used to end logical and rational arguments against the properties of a being that seem contradictory or improbable. IOW - if we can't explain that, then 'omni' this puts a stopper on any further problems.

But it doesn't, does it? It just introduces more problems since assigning a being with infinite properites is as contradictory as the argument that leads to the introduction of such a principle in the first place.

 

[jjramsey]

How is that different from the mathematical concept of infinity?

The Wikipedia article on Aleph-numbers has a pretty good explanation of that. Go read it.

Yes, but he is simply renaming infinity as a rational number and then trying to do algabraic math using infinity as a number.

Aleph-null is a number, but it is not a rational number since it cannot be expressed as the ratio of two integers.

The infinity and zero paradoxes are well understood. Giving them another name does not make them any more rational.

The fact that you just wrote off some advanced abstract mathematics as irrational speaks volumes.

Premise 1: Any real thing can be increased by adding to it.
Premise 2: Infinity is a real thing.
Conclusion: Infinity can be increased by adding to it.

Do you disagree with either of those premises?

Yes, premise 1 is dead wrong. Any real finite thing can be increased by adding to it.

 

[jjramsey]

That's my main 'quip' with the efuviant use of 'omnipotent' and 'omniscient'. These are terms used to end logical and rational arguments against the properties of a being that seem contradictory or improbable.

Considering that philosophical discussion of the implications of omniscience and omnipotence has gone on at least since the Middle Ages, that statement is inaccurate. I remind you of ceo_esq's post on another thread:

http://www.internationalskeptics.com/forums/showthread.php?postid=1226057#post1226057

But it doesn't, does it? It just introduces more problems since assigning a being with infinite properites is as contradictory as the argument that leads to the introduction of such a principle in the first place.

You are begging the question of whether "omnipotence" is inherently contradictory. The discussion of a being with infinite properties can get difficult and abstract, but this is not the same as being contradictory.

 

[Just thinking]

Yes, premise 1 is dead wrong. Any real finite thing can be increased by adding to it.

I must ask if you consider a concept a real thing. Is it? Is it as real as a material quantity, such as matter, energy, a force, etc.? Do you have (require) any qualifiers between the two?

 

[Elind]

But it doesn't, does it? It just introduces more problems since assigning a being with infinite properites is as contradictory as the argument that leads to the introduction of such a principle in the first place.

So why are we still here in the discussion if we are so smart?

 

[jjramsey]

I must ask if you consider a concept a real thing.

That depends on the context. Tricky seemed to be challenging the rationality of Cantor's theories, so I treated aleph-null and other mathematical concepts as "real things," especially since Tricky counted "infinity," another mathematical concept, as a "real thing" in his second premise.

 

[Just thinking]

That depends on the context. Tricky seemed to be challenging the rationality of Cantor's theories, so I treated aleph-null and other mathematical concepts as "real things," especially since Tricky counted "infinity," another mathematical concept, as a "real thing" in his second premise.

Well, that's really the crux of my asking. Infinity may be nothing more than a concept -- both mathematically and physically. Arguing points of infinity or infinite this or that may be arguing points that don't exist. Anything said to posess the quality of being omnipotent (or omni-anything else) also may very well not exist. And anything outside the boundaries of logic may very well not exist either -- as having the quality of being outside of logic or known physical existance is only a concept.

So I will again ask if concepts are real things -- or must they be given qualifiers that differ them in some way from other real things?

 

[Iacchus]

I must ask if you consider a concept a real thing. Is it? Is it as real as a material quantity, such as matter, energy, a force, etc.? Do you have (require) any qualifiers between the two?

To the degree that "things" affect us, yes they are real ... whether they affect us internally or, externally.

 

[Iacchus]

So I will again ask if concepts are real things -- or must they be given qualifiers that differ them in some way from other real things?

Our id-entity arises from the same place that concepts do by the way. So in that respect concepts are just as real as "we" are.

 

[jjramsey]

Anything said to posess the quality of being omnipotent (or omni-anything else) also may very well not exist.

That is true. The question, however, is whether such an omni-being could not exist on the grounds that the purported omni-qualities lead to contradictions, as kuroyume0161 seems to believe. If the omni-qualities do not lead to contradictions, the existence of such a being may either be ruled out or ruled improbable on other grounds.

So I will again ask if concepts are real things -- or must they be given qualifiers that differ them in some way from other real things?

And I'd still say that the answer to that question depends on the context. "Infinity" is a real thing in the sense that it is a real mathematical concept and can be discussed coherently. Whether anything that is part of the universe can be said to be infinite is another story; AFAIK, the material, physical universe is finite. Whether anything in reality is infinite is yet another story again. If there is an omnipotent God, then obviously something in reality is infinite.

 

[UserGoogol]

Actually, no, you can't. If something is illogical, then it cannot exist in any possible universe, and cannot be imagined at all. One can imagine pigs flying. One cannot imagine a square circle.

If a square circle could not be imagined, then your sentence "One cannot imagine a square circle" would be nonsensical, and would be equivalent to saying "One cannot imagine a flibbery zapdoodle." But they are not equivalent.

People CAN imagine a square circle. Of course, a logical person cannot carefully examine the idea of a square circle without contradicting himself, but the idea exists. Imagine a square. Now say that every point on that rectangle is equidistant from some point. Boom, you just imagined a square circle. Fun, isn't it?

Of course, even logic cannot be timeless. Premises come first, conclusions come after. See why you can't give a logical defense of timelessness?

Depends on what you mean by logic.

Logic as a proccess is of course impossible to exist in a timeless universe. The way most people use logic is to start at some premises and then generate new truths, and this is of course impossible in a timeless world. Proccess requires change, and change implies at least some kind of time, even if the time is completely different from how we see it in our universe.

But logic as an inherent property of propositions does not require time. For example, in a timeless world you might have the propositions "A = 1" and "A * A = 1" floating around in the universe. It would also be true that the two statements are non-contradictory and that the first implies the second. (Given the standard definitions of natural numbers.) Thus, logic can exist in a universe if all you mean by logic are the relationships which exist between propositions. Relationships can exist without time.

Ah, there's the downside of referring to the "laws of logic" as laws at all. It obscures that these laws are not contingent and could not be any other way, unlike the laws of physics.

How do you know that the laws of logic are not contingent?

 

[jjramsey]

Imagine a square. Now say that every point on that rectangle is equidistant from some point. Boom, you just imagined a square circle.

No, you just imagined a square and said something nonsensical about it.

How do you know that the laws of logic are not contingent?

The laws of logic are self-evident, especially the law of noncontradiction. You cannot, for example, argue against the law of noncontradiction without employing the law of noncontradiction. You couldn't even do an experiment to check the validity of the laws of logic, because they are so basic that any experiment must assume their validity. By contrast, the laws of physics, unlike the laws of logic, cannot be determined by pure thought, but only by experiment.

 

[Just thinking]

To the degree that "things" affect us, yes they are real ... whether they affect us internally or, externally.

I believe you are imposing onto the concept the quality of a consequence. In other words, how one reacts to a concept will affect me -- the concept alone cannot. Because this can be a bit confusing (and even seem circular) let me give an example.

Concept: There is a poisonous snake just beyond the door.

Consequence: I don't open the door which I was about to walk through.

The concept of danger just beyond the door in and of itself does nothing. I have to understand and believe it to represent something, which will then cause me to alter my behavoir. The concept is a model of reality -- it may be accurate or it may not, but it is not real like the snake. If I walk through the door it will be the snake that threatens me, not the concept of a snake. I may also walk through the door and find no snake, in which case my concept did not model reality. My choosing not to open the door is a reaction to what the concept represents, not the concept itself. I choose to avoid the snake, not the concept of a snake. I can easily conceive of snakes being beyond every closed door -- and so can you. Will that make you not ever open them?

 

[UserGoogol]

The laws of logic are self-evident, especially the law of noncontradiction.

The laws of logic cannot be determined from pure thought, because without logic, you cannot be ensured that your thoughts are valid. But eh, I don't want to pull the conversation too offtopic, so maybe I should just drop it.

No, you just imagined a square and said something nonsensical about it.

Perhaps we mean different things by imagine. I made a mental representation of a square circle. To imagine something means to think about it. Even in thinking the phrase "square circle," I am imagining a square circle.

Suppose some mathematicians were talking in ancient greece. These mathematicians are of the opinion that pi is a rational number. Cannot these people imagine this rational number? They do not know what it is, but they can certainly concieve of the number existing. That is, they can imagine a pair of integers whose ratio is equal to pi. The only difference between a square circle and a rational pi is that the square circle is somewhat more obviously contradictory.

But even in order to realize that a thing is contradictory, you need to at first imagine the thing, then examine your imagining of the thing, and then realize that your imagining is contradictory.

 

[Just thinking]

Our id-entity arises from the same place that concepts do by the way. So in that respect concepts are just as real as "we" are.

Maybe not. Perhaps concepts are just a product of our id-entity -- I would not be so quick as to assign them equal status.

 

[Iacchus]

Maybe not. Perhaps concepts are just a product of our id-entity -- I would not be so quick as to assign them equal status.

Yes, but there are certain folks -- around here even -- that would contest that "I" doesn't even exist. So, which "I" are we referring to then? The one that exists as a concept? Or, the one that exists in the "id?" Of course when referring to the former, we would have to ask how a concept is capable of conceptualizing itself? Very strange. But then again, if both do arise from the same source (the id), that would satisfy the notion of conceptualized "I," as well as the realized "I." In which case we have to ask, however, if there is another continuum, that exists beyond the realm of our senses and, time and space?

Oh, and I spared you the derail here, for those who don't particularly find any relation in what I'm saying, and started another thread ...

 

[kuroyume0161]

I think that my vague (sorry) point has been focused. The concept of infinity is just that. There are no real examples of infinity which can be used to back the concept, just the idealistic representations. This is why I consider omni-things to be logically impossible - not saying that All A is X, but A is All X seems to introduce logical systemic failures. Logically, infinite sets are idealistic models in conceptual space. We can not place them in any empirical space. So, this creates a contradiction - since we cannot bind such concepts to any systemic process which has strict logical consequences. For instance, according to our information on black holes, the singularity is an unknown. The mathematics introduces infinities, which are always a sign of the deficiency of knowledge or ability to accumulate data on such matters. It does not mean that the internal structures of black holes don't exist. It means that they are indeterminable. We can know nothing of a black hole's singularity (pray tell how we can do that?!).

The idea of placing a being outside of the universe (essentially, non-existent) and then placing qualifications upon it seem to be ill-formed. One is extrapolating from one existence to another by adding infinity to compensate. Just because it may have extra dimensions does not exclude it from limitation. The lack of limitations seems to be a byproduct of some of our limited conceptualizations.

ETA: Do I make myself clear? If you introduce infinite qualifications to something, you introduce self-contradiction just by the qualification. This is the time-honored "Can God make a rock so heavy that he cannot lift it" argument. By introducing infinite qualifications, there is a paradox. If God cannot create the rock, he is limited, and if he can, he is limited. 'Limited' takes on two meanings here - one of potential and one of certainty. Either way, a logical inconsistency is introduced - in both situations, God is no longer infinite in that qualification - logically impossible!!!!!!

 

[jjramsey]

Do I make myself clear? If you introduce infinite qualifications to something, you introduce self-contradiction just by the qualification. This is the time-honored "Can God make a rock so heavy that he cannot lift it" argument.

Time-honored, but multiply refuted.

If God cannot create the rock, he is limited

Only if you consider a logical contradiction a meaningful limitation. Since logical contradictions cannot be meaningful at all, they are not meaningful limitations.