Eternal Inflation and it's Philospohical implications

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  • #1
heusdens
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As anlternative to some other pre-Big Bang theories (like the Hawking-Turok Instanton pea model) there is a model of Eternal, Chaotic or Open inflation, in which Inflation reproduces itself eternally.
The merit of this model of inflation is that there is no requirement for a "beginning of time". Once inflation starts, it keeps reproducing new space-time bubbles, each inflating space-time bubble representing a new universe coming out of a big bang.
 

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  • #2
Eh
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Eternal inflation is very similar to the old steady state universe, even though proponents of the theory would like to downplay the similarities. Each "bubble universe" is created from a pre-existing space-time, but the universe as a whole may be eternal, as you've said. But the problem is, the pre-existing space itself is expanding. For a universe finite in size, logically it follows that the volume of space would be smaller and smaller the further back in time you look. Eventually at some time in the past, the entire universe (or multiverse, if you will) shrinks down to a point of infinite density. So even an eternal inflation universe would have a beginning. Andrei Linde admits even the self reproducing universe may start off with a primordial singularity.

But with an infinite volume of space, there may indeed be no beginning at all. However, philosophically there is something very unsettling about an infinite volume of space that has been expanding for an infinite amount of time. Maybe it's because there is comfort in the finite, or maybe it's just because infinity is such an ugly concept. Should analysis of the WMAP survey find conlusive evidence that the universe is actually finite, then this model will be in the toilet. That is, unless someone develops a model of inflation based on extra dimensional space that has a minimum of 4 spatial dimensions.

But ignoring WMAP for a moment, try to compare an infinite chaotic inflation universe with the old steady state models. Hoyle invisioned an infinite universe that had been expanding forever, but with matter continously being created from the vacuum to fill in the great voids. Later models dropped the perfect cosmological principle (that idea that the universe looks the same everywhere and at all times) and included the ideas of mini big bangs arising from the vacuum. Though the math and mechanism for these later models were obviously different than inflation, the basic concept is very much alike. They both involved infinite space, and both involved an infinite regress.

At any rate, it seems the issue again comes down to the concept of infinity. Other models such as the cyclic universe, based on M theory also includes a universe that is infinite in space and time, so it seems to be an unavoidable topic these days.
 
  • #3
wuliheron
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At any rate, it seems the issue again comes down to the concept of infinity. Other models such as the cyclic universe, based on M theory also includes a universe that is infinite in space and time, so it seems to be an unavoidable topic these days.

Just as the concept of paradox is increasingly unavoidable. Although, why you think infinity is "ugly" is beyond me. Certainly it is not nice and neat and easily defined, but personally I enjoy abstract art as much as any other kind. :0)
 
  • #4
Eh
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It's probably a mental thing, as the idea of an infinite number of galaxies, infinite stars, etc. is unsettling. Maybe if the damn universe was static it might be easier to swallow, but expansion throws that out the window.

In physics, infinity is often a sign a certain theory is wrong, such as in the case of attempts to formulate a theory of quantum gravity.
 
  • #5
wuliheron
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In physics, infinity is often a sign a certain theory is wrong, such as in the case of attempts to formulate a theory of quantum gravity.

I agree that more often than not that is what it means, but it also means big things are likely in the wind. Newton used infinity to create an incredibly useful theory of motion and calculus. M-theory is now using it to reconcile a rift between mathematics and physics that has grown for over a century. If infinity can't lead to the next big thing in physics it may be that more profound paradoxes are required and that could be a great deal more difficult to resolve. :0)
 
  • #6
Mentat
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M-/string Theory does a pretty good job (IMO) in describing how the universe can continue to expand forever. You see, instead of saying that it will continue to alternate between expansion and contraction, it postulates that it (the universe) is always doing both. It all has to do with forms of measurement, since the measurement of the distance between "wound" strings is inversley proportional to the measurement of the distance between "vibrational" strings.
 
  • #7
heusdens
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Originally posted by Eh
Eternal inflation is very similar to the old steady state universe, even though proponents of the theory would like to downplay the similarities. Each "bubble universe" is created from a pre-existing space-time, but the universe as a whole may be eternal, as you've said. But the problem is, the pre-existing space itself is expanding. For a universe finite in size, logically it follows that the volume of space would be smaller and smaller the further back in time you look. Eventually at some time in the past, the entire universe (or multiverse, if you will) shrinks down to a point of infinite density. So even an eternal inflation universe would have a beginning. Andrei Linde admits even the self reproducing universe may start off with a primordial singularity.

But with an infinite volume of space, there may indeed be no beginning at all. However, philosophically there is something very unsettling about an infinite volume of space that has been expanding for an infinite amount of time. Maybe it's because there is comfort in the finite, or maybe it's just because infinity is such an ugly concept. Should analysis of the WMAP survey find conlusive evidence that the universe is actually finite, then this model will be in the toilet. That is, unless someone develops a model of inflation based on extra dimensional space that has a minimum of 4 spatial dimensions.

But ignoring WMAP for a moment, try to compare an infinite chaotic inflation universe with the old steady state models. Hoyle invisioned an infinite universe that had been expanding forever, but with matter continously being created from the vacuum to fill in the great voids. Later models dropped the perfect cosmological principle (that idea that the universe looks the same everywhere and at all times) and included the ideas of mini big bangs arising from the vacuum. Though the math and mechanism for these later models were obviously different than inflation, the basic concept is very much alike. They both involved infinite space, and both involved an infinite regress.

At any rate, it seems the issue again comes down to the concept of infinity. Other models such as the cyclic universe, based on M theory also includes a universe that is infinite in space and time, so it seems to be an unavoidable topic these days.

I can for sure think of uglyer concepts as infinite.

What about a finite space. When a spacetraveller arrives there, he will find the sign "End of space. Stop here, or you'll be nowhere!".

Or things like begin or end of time. What would it be, if all of a sudden the universe would simply stop. Just before that, a big sign would be written in the sky: "End of time", and then everything would come to a halt and ceased to be.

By the way, it is a good thing that the universe as such isn't consciouss about al things that go on in the universe. Else, it would already have ceased to be, or never even have begun to be. For sure!
 
  • #8
Eh
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The beauty of curved space is that the universe can be finite yet be unbounded and have no edges. A traveller could go in straight line forever, and though he pass where he started from several times, he would never reach an edge. So finite space seems a much more pleasant alternative.

Finite time on the other hand, still does not seem so straight forward. However, if time is literally an extra spatial dimension (as with the no boundary proposal) the point is moot. The universe would only seem to have a beginning, while space-time as a whole would be eternal. The past present and future would exist as a 4 dimensional, static eternal universe. This eliminates the need for an infinite regress, and offers to solve the antinomy of both time and space. But this idea is counter-intuitive, and has it's own fair share of problems.
 
  • #9
wuliheron
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So, the singularity of finite time is more attractive than infinite space? Both just sound paradoxical to me.
 
  • #10
Eh
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Carefull with the word singularity here. In physics, it means a point of infinite density with zero volume.

With a 4D universe, everything would literally be space. Time would be an illusion. Unless you find geometry to be paradoxical itself, there doesn't seem to be any problems of that nature here.
 
  • #11
wuliheron
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Carefull with the word singularity here. In physics, it means a point of infinite density with zero volume.

With a 4D universe, everything would literally be space. Time would be an illusion. Unless you find geometry to be paradoxical itself, there doesn't seem to be any problems of that nature here.

I would suggest this is a temporal singularity. Just as occurs with a physical singularity, the passage of time slows to zero when inside and no distinction between either kind of singularity is possible to measure. Thus, by physical standards they are one and the same thing.

No matter what, it definitely qualifies as a paradox. It not only defies experience in much the same manner as Zeno's philosophy, it defies reason and logic. Just where did this "geometry" come from? If cause and effect don't apply because time doesn't apply, then logic and reason most certainly do not.
 
  • #12
Eh
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I don't see how that would be a paradox. Where did it come from would be a non question, since it would be non contingent. Of course it defies experience, and is one of the reasons this idea isn't likely to catch on. But there is nothing paradoxal or logically inconsistent about it, or at least no such problems have been found.

The notion of an uncaused, eternal universe that just IS may sound hard to swallow, but that alone does not make it an illogical or unreasonable proposition. As I've stated before, there is nothing logically inconsistant about something existing without being created by something else. That is, unless you know of something philosophers have missed.
 
  • #13
wuliheron
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The notion of an uncaused, eternal universe that just IS may sound hard to swallow, but that alone does not make it an illogical or unreasonable proposition. As I've stated before, there is nothing logically inconsistant about something existing without being created by something else. That is, unless you know of something philosophers have missed.

To say something is infinite is to say it has no limits, which, in itself is to assert a limit. This is a contradiction philosophers have known about since the invention of philosophy. So absurd has the very idea of infinity been considered that Aristotle himself asserted there is no such thing as an actual infinity, just potential ones. He then successfully banned the use of actual infinities and other paradoxes from academia.
 
  • #14
Eh
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What does infinity have to do with the no boundary proposal?
 
  • #15
heusdens
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Originally posted by wuliheron
To say something is infinite is to say it has no limits, which, in itself is to assert a limit.

Don't get that logic. If something has no limit, then it just asserts it doesn't have limit.

Same is the fact that the use of the term "nothing" is not making it into "something".

This is a contradiction philosophers have known about since the invention of philosophy. So absurd has the very idea of infinity been considered that Aristotle himself asserted there is no such thing as an actual infinity, just potential ones. He then successfully banned the use of actual infinities and other paradoxes from academia.

On the other hand the concept of infinity is contradictionary. It is a contradiction f.i. that the infinity exist of finite parts.

"Infinity is a contradiction, and is full of contradictions. From the outset it is a contradiction that an infinity is composed of nothing but finites, and yet this is the case. The limitedness of the material world leads no less to contradictions than its unlimitedness, and every attempt to get over these contradictions leads, as we have seen, to new and worse contradictions. It is just because infinity is a contradiction that it is an infinite process, unrolling endlessly in time and in space. The removal of the contradiction would be the end of infinity. "

[F. Engels, Anti-Duhring (1877). V. Philosophy of Nature. Time and Space]
 
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  • #16
Originally posted by heusdens
Don't get that logic. If something has no limit, then it just asserts it doesn't have limit.

Same is the fact that the use of the term "nothing" is not making it into "something".



On the other hand the concept of infinity is contradictionary. It is a contradiction f.i. that the infinity exist of finite parts.

"Infinity is a contradiction, and is full of contradictions. From the outset it is a contradiction that an infinity is composed of nothing but finites, and yet this is the case. The limitedness of the material world leads no less to contradictions than its unlimitedness, and every attempt to get over these contradictions leads, as we have seen, to new and worse contradictions. It is just because infinity is a contradiction that it is an infinite process, unrolling endlessly in time and in space. The removal of the contradiction would be the end of infinity. "

[F. Engels, Anti-Duhring (1877). V. Philosophy of Nature. Time and Space]



Exactly my response. Bravo.
 
  • #17
wuliheron
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the concept of infinity is contradictionary. It is a contradiction f.i. that the infinity exist of finite parts.

Exactly. In this case, the concept of infinity itself contains the finite within it as well in that it denies it has limits. To say something has no limits is to impose a limit, the limit that it has no limit.

Don't get that logic. If something has no limit, then it just asserts it doesn't have limit.

Same is the fact that the use of the term "nothing" is not making it into "something".

The two terms are not wholly seperate and distinct, but instead, define each other. The finite and infinite, nothing and something, up and down, back and front, inside and outside all define each other. Attempting to speak of one without referring to or at least implying the other leads to semantically meaningless mumbo jumbo.

In the case of infinity, when we do refer to its opposite it leads to contradiction. In other words, paradox. General semantics goes into more detail on this issue. Essentially, to assert infinity is real is to imply an infinitely valued logic in contrast to Aristotle's finite true/false logic.
 
  • #18
Fliption
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Originally posted by heusdens
Don't get that logic. If something has no limit, then it just asserts it doesn't have limit.

Yes, this semantic nightmare has been pointed out many times before in a hundred other threads about Paradox. It is a point that never seems to be understood. I would suggest getting back to the orginal topic of this thread. It was very interesting until it was pulled off track to step on a dead horse.
 
  • #19
wuliheron
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Sorry about that, didn't mean to pop anyone's bubble or derail the conversation. Merely to point out the semantic and aesthetic difficulties people were bringing up. :0)
 
  • #20
Mentat
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I don't understand everyone's confusion with the limit of limitlessness. Do you think it's possible for something that is limitless to have a limit? And yet, if there is something that is impossible for this [limitless] entity, then it has a limit (whatever it is that is impossible for it is it's limit).
 
  • #21
wuliheron
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I don't understand everyone's confusion with the limit of limitlessness.

Don't worry, you are not alone. This has been an infinitely confusing issue for millennia. Just ignore it, it'll go away. :0)
 
  • #22
Mentat
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Originally posted by wuliheron
Don't worry, you are not alone. This has been an infinitely confusing issue for millennia. Just ignore it, it'll go away. :0)

But don't you think it's possible to explain it?

Seriously, what was wrong with my explanation?
 
  • #23
heusdens
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Originally posted by wuliheron
Exactly. In this case, the concept of infinity itself contains the finite within it as well in that it denies it has limits. To say something has no limits is to impose a limit, the limit that it has no limit.

Don't agree on that logic. Not having a limit, means that there isn't a limit, which doesn't impose a limit.

Using your kind of reasoning also one could say that something undifned is self-contradictionary, cause it would be defined (as 'undefined').

But this reasoning is absurd.
 
  • #24
Mentat
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Originally posted by heusdens
Don't agree on that logic. Not having a limit, means that there isn't a limit, which doesn't impose a limit.

Using your kind of reasoning also one could say that something undifned is self-contradictionary, cause it would be defined (as 'undefined').

But this reasoning is absurd.

No it's not, and your illustration is as good as any, for proving Wu Li's point.

I do not, however, approve of Wuliheron's use of the word "infinity" instead of "limitlessness". I agree that there is a paradox, when speaking of something as being "limitless"; but "infinity" in mathematics and physics can just be endlessness in two directions, it doesn't have to imply limitlessness (and rarely, if ever, does).
 
  • #25
wuliheron
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But don't you think it's possible to explain it?

Seriously, what was wrong with my explanation?

Why certainly you can explain infinity, just as you can explain paradox and the irrational. But your explanation needs to address the heart of the issue more directly instead of relying on finite classical Aristotelian logic alone. Heusdens' quote is more on the money:

"Infinity is a contradiction, and is full of contradictions. From the outset it is a contradiction that an infinity is composed of nothing but finites, and yet this is the case. The limitedness of the material world leads no less to contradictions than its unlimitedness, and every attempt to get over these contradictions leads, as we have seen, to new and worse contradictions. It is just because infinity is a contradiction that it is an infinite process, unrolling endlessly in time and in space. The removal of the contradiction would be the end of infinity. "

[F. Engels, Anti-Duhring (1877). V. Philosophy of Nature. Time and Space]

Infinity is a double negative and, thus, a positive as this quote makes clear. It is a logical tautology and as such lends itself better to more poetic expression. The passage above touches on the poetic and the most famous western poetic passage to date on infinity is that of William Blake:

To see a world in a grain of sand
And a heaven in a wildflower
Hold infinity in the palm of your hand
And eternity in an hour

Because infinity is tautological and lends itself to poetic expression, these are widely considered the most satisfying and clear ways to express the concept.
 
  • #26
Mentat
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This is a very wrong use of the word, "infinity". Infinity is not composed of a lot of finites. It is an infinite number of finites. This means that you cannot define infinity by how many finites it has, because the answer to that is "infinity", and you are no closer to understanding infinity than when you started.
 
  • #27
wuliheron
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This is a very wrong use of the word, "infinity". Infinity is not composed of a lot of finites. It is an infinite number of finites. This means that you cannot define infinity by how many finites it has, because the answer to that is "infinity", and you are no closer to understanding infinity than when you started.

Infinity is not a number, all numbers are finite. Thus when you say infinity is an infinite number of finites you contradict yourself. You are saying infinity is a finite (number) of finites.
 
  • #28
Fliption
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Originally posted by wuliheron
Infinity is not a number, all numbers are finite. Thus when you say infinity is an infinite number of finites you contradict yourself. You are saying infinity is a finite (number) of finites.

All your doing here is defining infinity in such a way that it can't exists. Infinity is meant to convey the concept that something is endless.

So if we take any endless thing and try to attach a number to it, we will be forced to say it is infinite. And therefore, by your definition, we cannot use infinity to convey anything of value so we must have a real number which means it must be finite. But from a semantic standpoint I understand perfectly what the sentence "it has an infinite number of things" is trying to convey. Which, by the way, is the only purpose for having a word for it.

You've created contradictions from semantics yet again. You want to talk about poetry and obscure references whenever you are pontificating on this topic in general, but then when it comes to the specific proofs, you want to apply strict rules of if/then logic. And apply them to semantic concepts no less.
 
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  • #29
heusdens
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Originally posted by wuliheron
Infinity is not a number, all numbers are finite. Thus when you say infinity is an infinite number of finites you contradict yourself. You are saying infinity is a finite (number) of finites.

Infinity is not a finite number, but infinity is a number, but which has peculiar properties, that distinguish it from any finite number.
 
  • #30
wuliheron
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Infinity is meant to convey the concept that something is endless.

Duh!

All your doing here is defining infinity in such a way that it can't exists.

No, I'm not defining it in such a way that it can't exist, I'm merely pointing out the difficulty in defining the concept as a "thing" in the first place.

You've created contradictions from semantics yet again. You want to talk about poetry and obscure references whenever you are pontificating on this topic in general, but then when it comes to the specific proofs, you want to apply strict rules of if/then logic. And apply them to semantic concepts no less.

Only when people attempt to use infinity as if it is a classically proven concept in order to prove something else. There is absolutely no accepted logical or scientific evidence infinity exists. It is one of those boarderline concepts that is so popular among the religious especially, who have attempted to use it to prove the existence of god and how many angels you can fit on the head of a pin as I am sure you are well aware. At least poets acknowledge this and don't usually pretend it is indisputable evidence crop circles explain the meaning of life, the universe, and everything!

Infinity is not a finite number, but infinity is a number, but which has peculiar properties, that distinguish it from any finite number.

See what I mean, this defies accepted mathematical theory. OK, I give, just what "number" is infinity then? 666? Go ahead, you can tell me, I won't tell anybody else.
 
  • #31
C0mmie
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I dont know if its my taste buds talking, but I find the idea of a "donut shaped" universe (or many of them for that matter) much more comforting than and infinite universe.
 
  • #32
Fliption
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Originally posted by wuliheron

No, I'm not defining it in such a way that it can't exist, I'm merely pointing out the difficulty in defining the concept as a "thing" in the first place.

See what I mean, this defies accepted mathematical theory. OK, I give, just what "number" is infinity then? 666? Go ahead, you can tell me, I won't tell anybody else.

My only point is that the word infinity conveys meaning when someone writes the sentence "this thing stretches to infinity". But it is meaningless IMO to then take that statement, combine it with some other semantic premise like "infinity is not a number", to then conclude infinity is a contradiction. That's just semantic funtime.
 
  • #33
wuliheron
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My only point is that the word infinity conveys meaning when someone writes the sentence "this thing stretches to infinity". But it is meaningless IMO to then take that statement, combine it with some other semantic premise like "infinity is not a number", to then conclude infinity is a contradiction. That's just semantic funtime.

I'm sorry, but words either have meaning or they don't. Mathematicians don't consider infinity to be a number because it cannot be written down completely, has no clear definition, etc. Therefore we either create clear boundaries as to how it can be dealt with logically or we invite meaningless babble.

What's the meaning of life, the universe, and everything.....Infinity!
Who killed the Kennedys..... Infinity.

This is a scholarly website, not one devoted to meaningless babble.
Everyone here knows what the concept of infinity refers to, but I say again it is an illogical, irrational, and unscientific concept. It also just happens to be one of the most useful ones ever devised. To treat it otherwise is to invite meaningless babble.

Of course, you can argue that this is just semantic funtime, but unlikie some of you I have the philosophical and scientific community to back up my assertions. Either we emphasis semantic funtime or we emphasis anything-goes-funtime (Oh, did I spoil someones fun? Did I tell an unpleasent truth? Too bad.)
 
  • #34
C0mmie
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Mathematicians don't consider infinity to be a number because it cannot be written down completely

You can't write down the square root of 2 completely, or pi, or e, or the square root of -1 (i), but they are still numbers, and to the best of my knowldedge infinity is too.
 
  • #35
Fliption
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1
Originally posted by wuliheron
I'm sorry, but words either have meaning or they don't.

I agree with this completely. But I have yet to understand how something that has no meaning can be useful.

Just because a scientists doesn't know how to write it down on a piece of paper and therefore attach the word "number" to it(if this is even true), doesn't mean that you can then insert the word "finite" into every sentence that uses "infinity" and claim it as proof of contradictions.
What's the meaning of life, the universe, and everything.....Infinity!
Who killed the Kennedys..... Infinity.

I agree these statements make no sense. Infinity has nothing to do with the Kennedy's. Just wanted to point that out in case someone is actually tempted to believe this extreme depiction of the opposing view.

This is a scholarly website, not one devoted to meaningless babble.
Which is exactly why I suggested that we get this thread back on track and stop discussing this concept in this way. Let's keep the meaningless babble in the paradox threads.

Of course, you can argue that this is just semantic funtime, but unlikie some of you I have the philosophical and scientific community to back up my assertions.

Where are the scientific and mathematical sources? Just claiming they exists isn't sufficient. You can see many people here disagree with your mathematical premise. And if these sources do exist, it would be good if you can find some from this century. Alot has happened in the last hundred years or so.

Either we emphasis semantic funtime or we emphasis anything-goes-funtime (Oh, did I spoil someones fun? Did I tell an unpleasent truth? Too bad.) [/B]

Nonsense. We don't have to do either of these time wasting things. We can recognise that the imperfections of language are not proof of more fundamental imperfections in the universe. Once we do this we can attempt to have a philosphical conversation without getting bogged down in these imperfections. It is a common criticism of philosphy that it is nothing but debate over semantics. While I try to avoid this as much as I can, the reason why these people make this claim is all over this forum.
 
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