Resolving the Paradox of Infinity: A Scientific Perspective

[Mentat]

I didn't get to copy my original thread about this, so I will restate my reasoning here:

Wuliheron has repeatedly brought up the "limitlessness paradox", to show that infinity was paradoxical. However, I posit that, since "infinity" does not mean "limitless", this paradox doesn't apply.

Perhaps there is some flaw in my reasoning (and I hope Wuliheron will point it out), but - if my reasoning holds true - the so-called "paradox of existence" may be (at least partially) resolved.

 

[Mentat]

Allow me to explain my understanding of the "limitlessness paradox" (though I believe that Wu Li could do a much better job explaining it):

First let's define "limitless". It means "without limits of any kind".

Second, let's define "limit" (as it is used in discussions of "limitlessness paradox" (a name, btw, that I made up to give quick reference to the concept)). A "limit" is an impossibility. IOW, if something/someone is limited, then there is something that it is impossible for that something/someone to do.

Thus, for something to be "limitless", there can be nothing that is impossible for that thing. And yet, that means that for something to be impossible (with regard to this thing/person) is impossible, and thus the thing/person is limited.

If there is any confusion on this, it is probably my fault, and I would be glad to explain any point that doesn't makes sense to anyone.

 

[drag]

Greetings !

Again (like I said in the original thread), this
may be a conceptual paradox (and a nice word game),
but I fail to see any real paradox associated with
it.

Of course, purhaps wuliheron can explain it better...

Live long and prosper.

 

[RuroumiKenshin]

If there is any confusion on this, it is probably my fault, and I would be glad to explain any point that doesn't makes sense to anyone.

since you asked, I'm sort of confused. (i.e., what you said in red confused me)

 

[wuliheron]

Aleph Aleph is the mathemical infinity of infinity. As some put it, it is infinite in every way. This kind of infinity is utterly paradoxical by the rules of mathematics. However, what you might call lesser infinites (aleph1, aleph2...) still display absurd results like 1=2.

The most popular paradox among logicians, perhaps, is the liar's paradox:

"Everything I say is a lie."

Note that this paradox makes perfect sense to utter if you are a chronic liar. Still, semantically, it contradicts itself and it is only the context that can give it meaning, in this case the context of being a chronic liar.

The paradox of existence presents the distinct possibility that the same thing that allows all those infinities to spout nonsense is existence itself. It also suggests that these are possibly not magical weirdness, but just the limits of human cognition.

Again, I couldn't care less which way, the results are the same for me either way. I exist, and existence can get funky at times. What matters is knowing how to use them as far as I am concerned. That means understanding their limitations if any and how to manipulate them.

Unfortunately in the case of paradoxes and infinities, this means something a bit more personal than how to use a screwdriver. Personal not only in the sense of spirituality, but in the sense that paradoxical statements and poetry for example tend to reflect the mind of the reader. It's similar to what Quantum physicists have to confront today with Shrondenger's Cat, but over a scale that includes everyday events as well as unseen microscopic particles.

 

[CJames]

Results like 1=2 from infinity result from bad use of the concept of infinity, as I understand it. I don't think infinity is a paradox, but I guess I need to see a clear explanation of why you think this to know for sure.

 

[drag]

Greetings !

Cjames has a point there...

Originally posted by wuliheron
The paradox of existence presents the distinct possibility that the same thing that allows all those infinities to spout nonsense is existence itself.

Explain, please.

Originally posted by wuliheron
I exist, and existence can get funky at times.

Existence is absolute but undefinable in such nature -
you have no way of knowing that whatever you mean
by "I" exists.

Live long and prosper.

 

[wuliheron]

C James, Drag,

Existence may be the one thing stranger, more fundamental, and more ineffable than Quantum Mechanics or anything else for that matter. If so, it could be responsible for all the weirdness we perceive in nature and in the human mind for that matter. Unlike Quantum weirdness then, it would apply to every event.

One reason to suspect this is that existence is the only thing known to science that has never been observed to change, yet is responsible for all change. The closer we get to exploring existence as in the case of infinities and other paradoxes, the more strange, bizarre, and ineffable it seems to be.

As for having no way of knowing I really exist, it doesn't matter in the least. I take the pragmatic path and just assume I really exist, even if the exact nature of existence is uncertain.

Additionally, what people call good and bad results such as 1=2 is simply a matter of perspective. Context over rides content.

An example of this is the liar's paradox:

"Everything I say is a lie"

If spoken by a compulsive liar to people who believe them, it makes perfect sense. If used as a joke, it could have some people rolling on the floor and, again, make perfect sense to them. Context is how we give mathematics as well as everything else meaning.

Note that what we choose to call a context and what we choose to call a result or whatever, again, just depends upon our point of view. Thus, the paradox of existence remains.

 

[CJames]

Maybe my mind just doesn't work right but I can't understand what you are trying to say WuLi.

One reason to suspect this is that existence is the only thing known to science that has never been observed to change, yet is responsible for all change. The closer we get to exploring existence as in the case of infinities and other paradoxes, the more strange, bizarre, and ineffable it seems to be.

What is paradoxical about existence being the only thing known to change? Existence is the only thing known to exist. I'm puzzled by your reasoning. Sorry. I agree with you sometimes but not always.

 

[wuliheron]

Existence is known by some to exist, while others know it does not exist. Just depends upon who you know and ask. I just take the pragmatic course as I said and assume I exist. If you can't understand what I'm saying, check out my thread on the paradox of existence.

 

[Mentat]

Originally posted by MajinVegeta
since you asked, I'm sort of confused. (i.e., what you said in red confused me)

I'll try and explain it better. For something to be "limitless", there can be nothing outside it's grasp. If this is so, then being in the state of having something that is outside of it's grasp, is outside of it's grasp. IOW, the fact that it is definitely without limits is a limit. (It limits it from having limits).

 

[Mentat]

Originally posted by drag
Greetings !

Again (like I said in the original thread), this
may be a conceptual paradox (and a nice word game),
but I fail to see any real paradox associated with
it.

Of course, purhaps wuliheron can explain it better...

Live long and prosper.

You are, of course, correct. It is a mainly semantic argument. However, my point is that (even just within the realm of semanticism) it doesn't apply to infinities, even though Wu Li has repeatedly applied in this way. Just take a look at his thread on the Paradox of Existence - which is otherwise a well-made argument (even if I don't happen to agree with it).

 

[chosenone]

The one infinite paradox you have'nt mentioned is that if the universe is infinite without end,how can there be no end without a beggining,because it could'nt have just been and always was if is infinitly traveling into infinitely if the big bang happened and there was a beggining!

 

[Mentat]

Originally posted by chosenone
The one infinite paradox you have'nt mentioned is that if the universe is infinite without end,how can there be no end without a beggining,because it could'nt have just been and always was if is infinitly traveling into infinitely if the big bang happened and there was a beggining!

I don't know what it is, but for some reason I have difficulty understanding a lot of the points that you try to make, chosenone. I apologize for this.

Actually, I never believed (and still don't believe) that the universe is infinite. I think that there is too much evidence of BB theory. However, I also don't think that your idea of a paradox of infinity holds - or at least what I understood of your idea. You see, you asked "how can there be no end without a begining". This is simple, if it had no begining, then why would it have an end. In fact, if there was not begining, there could not be an end

 

[chosenone]

well infinity is a concept man created to represent something with no end,just like zero mean no value, or nothing,same thing.people try to come up with all types of things to debate infinity.sometiimes you can read to much into it or not enough,there are all types of paradoxes.so reason says because they exist to be said, as a truth or just exist at all you can 't ignore it or get rid of it.so people debate infinity,to prove whether or not its true or not,deos it exist or doesn't it.so ask your self,can you say that if you counted numbers would you ever reach the last number you can count(dont come back with what if you died)or anything for that matter along thoughs lines, that can keep going on indefinitly,to interprete,something with no end.or infinity that defines that statement,can you truly say infinity soes'nt exist!

 

[Mentat]

Well, I you are entitled to your opinion, chosenone. However, I have to wonder if "0" is really just a man-made concept. I mean, let's take an example: How many things are outside the universe - answer: zero.

 

[drag]

Greetings !

Chosenone, what you discribe is not a REAL
paradox, just our limmitation - to prove or
disprove infinity.

Wu Li, you said a lot... But, none of it even
remotely explains what this thread is about
and what I (and others) asked you to explain.

"Does dice play God ?"

Live long and prosper.

 

[Mentat]

Originally posted by drag
Greetings !

Chosenone, what you discribe is not a REAL
paradox, just our limmitation - to prove or
disprove infinity.

This is a very important point, drag. The difference between "paradoxical" and "not understood/understanable" needs to be recognized, or else one could construe all scientific theories as paradoxical - and, more importantly, any discussion of paradox can be ruined by such misunderstandings.

 

[RuroumiKenshin]

...and also, things that "don't make sense" should be added to your list, Mentat.

 

[wuliheron]

Wu Li, you said a lot... But, none of it even
remotely explains what this thread is about
and what I (and others) asked you to explain.

Be specific, I'll try again. Paradox is a slippery concept and often requires more than one glance and more than one explanation.