Date: Wed, May 6, 1998 12:07 EDT Message-id: <6iq1sd$...@suriname.earthlink.net>
>This seems like a ridiculously inappropriate use of philosophy to describe >the physical world. Can someone please elucidate? I cannot fathom how >objectivism disallows an infinite universe. Anyone???
Philosophy *does* describe the physical world in certain general ways. It insists on identity and causation and non-contradiction. It formalizes and validates the methods used to understand the world. To deliberately think conceptually about the physical world in the first place is to have (at least implicitly) done philosophy first -- to have selected what we take to be a valid method of thinking and a valid set of principles about reality.
Ask what "infinite" -- having no limit -- could physically mean. Taken literally, it means "having features or attributes embodying amount, but at the same time *beyond* any particular amount". This means, having no identity.
If infinity does not name a specific amount, then it isn't a number that can be applied to reality. More precisely, the strategy (discovered by Cantor) that gives it numerical meaning is indulged at the expense of entirely abstracting away the connection to existence that gives numbers their objective status (i.e., their connection to reality). It cannot name any specific amount in reality.
"Infinity" is still a valid mathematical concept, however, so that in a certain non-numerical sense Objectivism *does* allow an infinite universe. Rand said in _Introduction to Objectivist Epistemology_, "An arithmetical sequence extends into infinity, without implying that infinity actually exists; such extension means only that whatever number of units does exist, it is to be included in the same sequence." (This makes "infinity" what her epistemological view calls a concept of method.)
The application of her statement to the physical universe is that "whatever number of existents (or measures of their attributes) exists, it is to be included in the same sequence" of progressively larger numbers.
>Ask what "infinite" -- having no limit -- could physically mean. Taken >literally, it means "having features or attributes embodying amount, but >at the same time *beyond* any particular amount". This means, having no >identity.
Dean, Dean. Since I triggered the post to which you reply I will point out the flaw in your argument. You say "*beyond* any particular amount", this is true. But then you go on to "no identity". But for this to follow the only aspects of identity have to be "amount". Surely you are more than six feet and 180 pounds and 140/80 (whatever the numbers are).
>"Infinity" is still a valid mathematical concept, however, so that in >a certain non-numerical sense Objectivism *does* allow an infinite >universe ... Rand in IOE ... "An >arithmetical sequence extends into infinity, without implying that >infinity actually exists; such extension means only that whatever >number of units does exist, it is to be included in the same sequence." >(This makes "infinity" what her epistemological view calls a concept of >method.)
Who we all live in a concept of method, a concept of method, a concept of method. In the town where I was born, lived a man who failed to see ...
>The application of her statement to the physical universe is that >"whatever number of existents (or measures of their attributes) exists, >it is to be included in the same sequence" of progressively larger >numbers.
What do you think the result of Cantors method would be when applied to the physical universe? - precisely what you wrote. Objectivist just don't like the word "infinity" I think. If the universe is as you describe then it is not finite: How big is it? 1 googol light years? then there is an existent in the sequence beyond a googol, so it is not a googol light years big. The same is true for ANY number you can name.
If the universe is NOT finite, then what is it? Or alternatively if finite does not mean "of some definite size" then what does it mean?
>If the universe is as you describe then it is not finite: >How big is it? 1 googol light years? then there is an >existent in the sequence beyond a googol, so it is >not a googol light years big. The same is true for ANY >number you can name.
>If the universe is NOT finite, then what is it? >Or alternatively if finite does not mean "of some >definite size" then what does it mean?
Ah. But to the best of our knowledge the universe IS finite. It is in the neighborhood of 15 billion light years in radius although its shape is not spherical. This universe had an apparent beginning that places a finite limit on its size. At any particular moment it will be a finite size even if it goes on expanding far beyond heat death.
>Ah. But to the best of our knowledge the universe IS finite. It is in the >neighborhood of 15 billion light years in radius although its shape is not >spherical.
It is spherical. Why do you say otherwise? Do you mean that is it hyperspherical (4 dimensionally spherical)?
Yes, as near as we can tell from observation the universe (as we know it) is finite in time. Since all hell breaks down at the big bang, beyond that is speculation.
As to finiteness of space, that does not follow from finiteness in time. A thought experiment shows this to be the case: start out on a journey in a starship that accelerates at a nice comfortable 1 gee (9.8 m/sec^2). As you accelerate, you approach the speed of light, your time slows relative to the galaxies so that within your lifetime you will reach a distance of 15 billion light years (I forget the exact number of spaceship years). Within a few more years you pass 30 billion etc. Now it might be the case that the universe is finite and bounded in which case you will hit the boundary evertually whatever that might be. The universe might be finite and unbounded in which case you will find yourself coming back around the universe passing the aged remains of the milky way galaxy that you started from. Or you might continue to pass new galaxies as you speed faster and faster. In this last case the universe could be said to be infinite - what else would you call it?
>This universe had an apparent beginning that places a finite >limit on its size. At any particular moment it will be a finite size even >if it goes on expanding far beyond heat death.
In article <6ispka$cb...@nntp2.ba.best.com>, "Samantha Atkins" <saman...@theLove.org> wrote:
>Ah. But to the best of our knowledge the universe IS finite. It is in the >neighborhood of 15 billion light years in radius although its shape is not >spherical. This universe had an apparent beginning that places a finite >limit on its size. At any particular moment it will be a finite size even >if it goes on expanding far beyond heat death.
The age of the universe only limits how far you can see, not how big it is. Present evidence favors a universe infinite in spatial extent. At the big bang, the curvature parameter of the open universe approaches infinity, but the size is always infinite. Not a very easy thing to picture, but not false because of that..
Bob Renninger wrote in message <6ithlc$...@bgtnsc03.worldnet.att.net>...
...
>The age of the universe only limits how far you can see, not how big it >is. Present evidence favors a universe infinite in spatial extent. At >the big bang, the curvature parameter of the open universe approaches >infinity, but the size is always infinite. Not a very easy thing to >picture, but not false because of that..
Question: What lies beyond that 15 billion light year boundary? Is it something, or is it nothing. Does it meet the definition of "universe", or "existence?
>Question: What lies beyond that 15 billion light year boundary? Is it >something,<BR> >or is it nothing. Does it meet the definition of "universe", or >"existence?<BR>
How could IT be nothing? An IT implies a something. The only thing one can say about non-existence is it doesn't exist.
>... >>The age of the universe only limits how far you can see, not how big it >>is. Present evidence favors a universe infinite in spatial extent. At >>the big bang, the curvature parameter of the open universe approaches >>infinity, but the size is always infinite. Not a very easy thing to >>picture, but not false because of that..
>Question: What lies beyond that 15 billion light year boundary? Is it something, >or is it nothing. Does it meet the definition of "universe", or "existence?
To the best of our knowledge there is nothing beyond the boundary of the universe. It makes no sense within context to even speak of a beyond. There is no conceptual framework to support "beyond".
Bob Renninger wrote in message <6ithlc$...@bgtnsc03.worldnet.att.net>... >In article <6ispka$cb...@nntp2.ba.best.com>, > "Samantha Atkins" <saman...@theLove.org> wrote:
>>Ah. But to the best of our knowledge the universe IS finite. It is in the >>neighborhood of 15 billion light years in radius although its shape is not >>spherical. This universe had an apparent beginning that places a finite >>limit on its size. At any particular moment it will be a finite size even >>if it goes on expanding far beyond heat death.
>The age of the universe only limits how far you can see, not how big it >is. Present evidence favors a universe infinite in spatial extent. At >the big bang, the curvature parameter of the open universe approaches >infinity, but the size is always infinite. Not a very easy thing to >picture, but not false because of that..
This is not so by my understanding. Starting from an event like the Big Bang, relativity strictly limits the size of the universe as expanded from that singularity. There is no theory that gives a result of infinite spatial extent for the universe. Please explain how the size is infinite when at the Big Bang where there is no Space/Time to speak of size at all.
Samantha Atkins wrote in message <6iviip$m4...@nntp2.ba.best.com>... >Bob Renninger wrote in message <6ithlc$...@bgtnsc03.worldnet.att.net>... >>The age of the universe only limits how far you can see, not how big it >>is. Present evidence favors a universe infinite in spatial extent. At >>the big bang, the curvature parameter of the open universe approaches >>infinity, but the size is always infinite. Not a very easy thing to >>picture, but not false because of that.. >This is not so by my understanding. Starting from an event like the Big >Bang, relativity strictly limits the size of the universe as expanded from >that singularity. There is no theory that gives a result of infinite >spatial extent for the universe. Please explain how the size is infinite >when at the Big Bang where there is no Space/Time to speak of size at all.
The phrase describing the universe's size that I've read in books on cosmology (e.g., Hawking's) is "finite, but unbounded". Regardless, referring to scientific evidence on this can only corroborate, not refute, the fact (from the law of identity) that no actual entity or attribute can be infinite. Philosophy is the foundation of science, not the other way around.
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....) GRADinc <grad...@aol.com> (Tom Clarke) wrote: Date: Thu, May 7, 1998 09:11 EDT Message-id: <1998050713111200.JAA03...@ladder01.news.aol.com>
>>Ask what "infinite" -- having no limit -- could physically mean. Taken >>literally, it means "having features or attributes embodying amount, but >>at the same time *beyond* any particular amount". This means, having no >>identity.
>Dean, Dean. >Since I triggered the post to which you reply I will point out >the flaw in your argument. You say "*beyond* any >particular amount", this is true. But then you go on to >"no identity". But for this to follow the only aspects of >identity have to be "amount". Surely you are more >than six feet and 180 pounds and 140/80 (whatever the >numbers are).
Flaw???? The context is clearly *quantitative* aspects of existence. We're talking about the things that *do* come with numbers, so to speak. Any such thing *not* existing in some particular degree can't be part of any identity.
>>"Infinity" is still a valid mathematical concept, however, so that in >>a certain non-numerical sense Objectivism *does* allow an infinite >>universe ... Rand in IOE ... "An >>arithmetical sequence extends into infinity, without implying that >>infinity actually exists; such extension means only that whatever >>number of units does exist, it is to be included in the same sequence." >>(This makes "infinity" what her epistemological view calls a concept of >>method.)
>Who we all live in a concept of method, a concept of method, >a concept of method. >In the town where I was born, lived a man who failed to see ...
Once you get this jingle out of your head, then, I take it that you'll have no quarrel with the stuff that *isn't* a last-moment parenthetical aside as opposed to the point of the paragraph.
>>The application of her statement to the physical universe is that >>"whatever number of existents (or measures of their attributes) exists, >>it is to be included in the same sequence" of progressively larger >>numbers.
>What do you think the result of Cantor's method would be >when applied to the physical universe? - precisely what >you wrote.
The point is that Cantor's strategy *can't* be applied to the physical universe, except rationalistically and without any comprehension of what would justify it or what it would *mean*. See the parable later on.
>Objectivist just don't like the word "infinity" I think.
Don't be silly. I say it most every day. If we just didn't like it, the onset of every car commercial would drive anxiety through us until we realized it's not for...uh...the I-word. Uh, Coach Rael, can you help?
>If the universe is as you describe then it is not finite:
This is wrong in the sense of literal infinity -- infinity as some number that applies to reality.
>How big is it? 1 googol light years? then there is an >existent in the sequence beyond a googol, so it is >not a googol light years big. The same is true for ANY >number you can name.
It's true of numbers. Not of existents. You're mixing the two. It's in the nature of real numbers that there is no highest. It's in the nature of reality that existents and the measures of their attributes and relations (such as distance) exist in some real, specific amount. If you want to know what the literally infinite *means*....
....put yourself with Cantor, standing at his lowest transfinite ordinal (omega-nought), looking back toward the finites. By his own account, in mathematical fact you can't see *any* of them, no matter *how* many have been piled up in an ever-growing sequence. All you can see is the illusion of a point on the horizon where, beyond it somewhere -- infinitely far away, in mathematical fact -- finite numbers keep extending their reach as they come across yet another existent to count, or another Planck-length of distance to measure from Earth...and they *still* don't get *any* closer to you. And heck. Multiply that count of existents by the number of Planck-scale volume units they encompass on average. (Maybe those little Planckons (neologism, copyright 1998) are the ultimate meta-constituents of existence and can qualify as entities themselves.) So the biggest-so-far number just got inflated by more than we care to imagine. *Way* beyond a paltry googol. But from omega-nought's perspective, it's *still* as if the latest big number is *infinitesimal*. There's *still* an infinite distance to cross in number-space. No matter *how* far they get, they haven't even *started* yet.
So ask yourself how Cantor got there at *any* speed. Not in reality. In his dreams. No longer in contact with reality. The only way of escaping a finite, unbounded universe.
In article <6itkdf$gd...@news.inficad.com>, "Tom Scheeler" <tschee...@remove.inficad.com> wrote:
>>The age of the universe only limits how far you can see, not how big it >>is. Present evidence favors a universe infinite in spatial extent. At >>the big bang, the curvature parameter of the open universe approaches >>infinity, but the size is always infinite. Not a very easy thing to >>picture, but not false because of that..
>Question: What lies beyond that 15 billion light year boundary? Is it > something, >or is it nothing. Does it meet the definition of "universe", or "existence?
Someone, say, 100 trillion light years away is living in a part of the universe, or existence, that is similar to our part here. That at least is the easiest thing to assume. (If memory serves, this is a version of the "cosmological principal" - that the universe is in some sense uniform.)
>>>The age of the universe only limits how far you can see, not how big it >>>is. Present evidence favors a universe infinite in spatial extent. At >>>the big bang, the curvature parameter of the open universe approaches >>>infinity, but the size is always infinite. Not a very easy thing to >>>picture, but not false because of that..
>>Question: What lies beyond that 15 billion light year boundary? Is it >something, >>or is it nothing. Does it meet the definition of "universe", or "existence?
>To the best of our knowledge there is nothing beyond the boundary of the >universe. It makes no sense within context to even speak of a beyond. >There is no conceptual framework to support "beyond".
It actually doesn't make sense to talk about a "boundary of the universe". There is no boundary under anybody's theory. Remember, when you look far away, you are essentially looking back in to the past. 15 billion light years away is 15 billion light years old. Looking back as far as you can look, you go back in time to when the universe was so hot and dense that it was filled with a plasma through which light could not propagate.
That is the farthest thing you can see. And what it "looks like" after taking into account the red-shift from the expansion of the universe, is the 3-degrees-Kelvin microwave background radiation.
In article <6iviip$m4...@nntp2.ba.best.com>, "Samantha Atkins" <saman...@theLove.org> wrote:
>>The age of the universe only limits how far you can see, not how big it >>is. Present evidence favors a universe infinite in spatial extent. At >>the big bang, the curvature parameter of the open universe approaches >>infinity, but the size is always infinite. Not a very easy thing to >>picture, but not false because of that..
>This is not so by my understanding. Starting from an event like the Big >Bang, relativity strictly limits the size of the universe as expanded from >that singularity. There is no theory that gives a result of infinite >spatial extent for the universe. Please explain how the size is infinite >when at the Big Bang where there is no Space/Time to speak of size at all.
You are mistaken. In all models, at the time of the big bang the curvature of the universe approaches infinity. In closed-universe models, this infinite curvature translates to infinitesimal size (but unbounded). However in open universes, while the curvature still starts out large, the size is always infinite. Observations currently favor these open models.
To explain this any further, I'd have to go into the mathematics. This unfortunately means that I would have to review my 25-year-old notes from general relativity class! Might be worth doing though, if you're interested.
>>> "infinite"...t means ... >>> *beyond* any particular amount". This means, having no >>>identity. >>You say "*beyond* any >>particular amount", this is true. But then you go on to >>"no identity". >Flaw???? The context is clearly *quantitative* aspects of existence.
Yes. Flaw. You step outside that context when you say "no identity".
>Any such thing *not* existing in some particular degree can't be part of >any identity.
Why? There is one universe no matter how big it is. There is one pudding no matter how big it is. The universe has lots of other characteristics, density, Hubble constant etc. just as the pudding does. Both have identity without respect to their size.
>Once you get this jingle out of your head, then, I take it that you'll
>have no quarrel with the stuff that *isn't* a last-moment parenthetical >aside as opposed to the point of the paragraph.
If you admit that we might live in a universe whose size is described by a concept of method.
>The point is that Cantor's strategy *can't* be applied to the physical >universe, except rationalistically and without any comprehension of what >would justify it or what it would *mean*. See the parable later on.
And you would be wrong on this point. I think we went round and round about this once before.
>>Objectivist just don't like the word "infinity" I think. >Don't be silly. I say it most every day. If we just didn't like it, >the onset of every car commercial would drive anxiety through us until >we realized it's not for...uh...the I-word.
That's "Infiniti" with an "i".
>>If the universe is as you describe then it is not finite: >This is wrong in the sense of literal infinity -- infinity as some >number that applies to reality.
There's another flaw. Thinking of infinity as a number. It is, if you like, a concept of method. But a concept of method that has many number-like properties.
>It's true of numbers. Not of existents. You're mixing the two.
So how long an existent string would I have to make to encompass the universe. If it is finite then I can do this in principle with an existent string.
>It's in the nature of real numbers that there is no highest.
Not just real numbers, ordinary integers, even Aristotle knew that from Euclid etc. But I don't think this is relevant to the question of how big the universe is.
How big is it? If it is finite then it must have a definite size. We may not know it yet, but it has to be some value.
>....put yourself with Cantor, standing at his lowest transfinite ordinal >(omega-nought), looking back toward the finites.
Sorry can't get there. Omega-0 is the first unreachable ordinal. You can't reach it by a finite number of finite sized moves, that is by moves smaller than itself. Since I am a finite being I can only look at Omega-0 from below and reason about it.
> in >mathematical fact you can't see *any* of them, no matter *how* many have >been piled up in an ever-growing sequence.
I think I just said this in another way.
>So ask yourself how Cantor got there at *any* speed.
He doesn't. He doesn't have to. The universe is what it is. If its infinite then that is what it is. I didn't make it that way, nor did Cantor.
>The only way of escaping a finite, unbounded universe.
All you have proved is that a man cannot make something infinite. That does not prove that an infinite universe cannot exist.
JLH1942 wrote in message <1998050802261100.WAA15...@ladder03.news.aol.com>...
>>Question: What lies beyond that 15 billion light year boundary? Is it >>something,<BR> >>or is it nothing. Does it meet the definition of "universe", or >>"existence?<BR>
>How could IT be nothing? An IT implies a something. The only thing one can >say about non-existence is it doesn't exist.
> >How could IT be nothing? An IT implies a something. The only thing one can > >say about non-existence is it doesn't exist.
If people would bear in mind Korzybski's profound insight that "the map is not the territory," most of these complications would be seen to be unnecessary.
>Depending on the total mass of the universe, there >are three outcomes: >1) Gravity exceeds the expansion, leading to a "Big Crunch". >2) The mass is "just right", so that the universe >reaches a finite, constant size. >3) The universe expands forever. >If 3) is the case, and no other fundamental limit is >reached, then time would be open-ended, and there >would be no upper limit on the size of the universe.
It's been a loooong time since I took in ABHoT (I actually watched the video rather than read the book). Still, in al of this discussion of the universe expanding and shrinking, one thing strikes me as odd. If everything that exists, by definition, exists within the universe, then how is it possible to conceive of a variable size of the universe at all; what does it expand into? In a previous, brief post, I hypothesised (similarly to what Samantha is saying) that there IS no "beyond" the boundary of the universe because what is beyond is nothing, in the most absolute sense of the word, necessitating the boundary of the universe to be a dimensionless point. I suppose that you could envision a stretching of the internal space, such that this hypothetical boundary point remains fixed, but the deistance from that point, back around to itself becomes greater. This is about the point where my visual modelling faculty goes "pop" and I lose the coherence of my model. Thoughts?
Mark Peter's writes: >The phrase describing the universe's size that I've read in books on >cosmology (e.g., Hawking's) is "finite, but unbounded". Regardless, >referring to scientific evidence on this can only corroborate, not refute, >the fact (from the law of identity) that no actual entity or attribute can >be infinite. Philosophy is the foundation of science, not the other way >around.
Assuming that one's philosophy is in fact correct. However, mistakes could have been made at any stage of philosophical reasoning beyond the base axioms. Thus the actual evidence found in reality through science is an important check. Remember, reality is always the final arbiter. Your philosophy cannot chuck out reality without invalidating itself. Reality is the foundation of philosophy, not the other way around.
>Mark Peter's writes: >>The phrase describing the universe's size that I've read in books on >>cosmology (e.g., Hawking's) is "finite, but unbounded". Regardless, >>referring to scientific evidence on this can only corroborate, not >>refute, the fact (from the law of identity) that no actual entity or >>attribute can be infinite. Philosophy is the foundation of science, >>not the other way around.
>Assuming that one's philosophy is in fact correct. However, >mistakes could have been made at any stage of philosophical reasoning >beyond the base axioms. Thus the actual evidence found in reality >through science is an important check. Remember, reality is always >the final arbiter. Your philosophy cannot chuck out reality without >invalidating itself. Reality is the foundation of philosophy, not >the other way around.
Oh, what a mouthful there...thank you! Believe it or not, that's about ALL I've been trying to say for about two years now, at least on the topic of why I think the ARI has abandoned Objectivism. You've said it far more clearly, with about 1/100,000 the verbiage and none of the caustic bite.
Objectivism as a philosophy MUST adhere (adjust, conform) to reality, or it automatically invalidates itself. What a concept...nice job!
Les Cargill writes: >If 3) is the case, and no other fundamental limit is >reached, then time would be open-ended, and there >would be no upper limit on the size of the universe.
There is indeed no upper limit. The universe is whatever size it is. I don't know how large that is, and maybe there's no one else who knows, but it _is_ whatever size it is. I.e. it is _not_ infinite.
Dreweg wrote in message <1998050923300100.TAA12...@ladder03.news.aol.com>... >There is indeed no upper limit. The universe is whatever size it is. I don't >know how large that is, and maybe there's no one else who knows, but it _is_ >whatever size it is. I.e. it is _not_ infinite.
This presupposes that the concept of size is applicable to the entirety of existence. Clearly it is applicable to particular entities but I've recently become unconvinced that concepts of finitude are applicable to "all of existence". Time, space, and all other concepts are induced _inside of_ existence. Just as we can't speak reasonably of a "beginning of time", speaking of the "finitude of existence" itself may be logically meaningless.
In article <1998050923300100.TAA12...@ladder03.news.aol.com>,
Dreweg <dre...@aol.com> wrote: >Les Cargill writes: >>If 3) is the case, and no other fundamental limit is >>reached, then time would be open-ended, and there >>would be no upper limit on the size of the universe.
>There is indeed no upper limit. The universe is whatever size it is. I don't >know how large that is, and maybe there's no one else who knows, but it _is_ >whatever size it is. I.e. it is _not_ infinite.
Scientists are not going to buy this unless you can demonstrate that the assumption of infinite size contradicts what we observe. As long as we have a model that assumes infinite size and is consistent with all observations, while models that assume finite size conflict with observations, you will have trouble persuading people that the cosmos has to be finite.
|
