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Adrian and Mr. Weiss,

Thanks for your reply. You and Mr. Weiss are correct, I do not have a clear picture of what Ojectivism is claiming. Therefore, I will do my best to read up on what the core metaphysical beliefs of Objectivism are.

I just have one question for Mr.Weiss: Merriam-Webster defines arbitrary as "existing or coming about seemingly at random or by chance or ...(3b)" By definition you could have included abiogenesis in your list of "arbitrary" examples. Does it fit? Why or why not?

sincerely,

conan

I assume you brought up abiogensis because of this issue:

http://www.talkorigins.org/faqs/abioprob/

I don't agree however that evolution has been "random" - except to the extent that it has not been guided by any kind of "intelligent design" (and certainly not "god(s)"). The seemingly random occurences in nature - and in this instance, evolution - are in fact the result of perfectly natural forces and which, with increasing knowledge, we continue to gain an ever better understanding.

So to answer your question, no I don't consider evolution to be arbitrary. While there is a great deal about it which we are still learning, that evolution occured in some form is absolutely certain, i.e. the evidence for it is massive and overwhelming.

Fred Weiss

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I don't consider evolution to be arbitrary.

I like what Dr. Peikoff said about it once on his radio show. If someone presented us with a suit of clothes we wouldn't say "How strange it is that the measurements of this suit match my body!"

The same thing goes for evolution and wonderfully complex nature of a human being. We shouldn't say, "How strange is it that a human being is so marvellously complex." It's not strange at all. We came from nature which is also wonderfully complex. Through the law of cause and effect, certain definite events in nature occurred which gave rise to the development of human beings with none of these events requiring the intervention of a Creator.

There's nothing random about it. "Randomness," actually, is an incomprehensible psuedo-concept.

The fact that we don't know everything about all the events that produced humans doesn't mean that we can't conclude that this is the way it happened or that we can't make general conclusions about the processes involved.

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I'm saying that we shouldn't view time as if it were some phenomenon detached from objects and events.

Has someone here said otherwise?

Time *is* the objects themselves, in a manner of speaking. More precisely, it is how those objects come into differing spatial relationships amongst themselves--that aspect of reality.
No. The fundamental of time is change of relationship, and spatial relationship is just one kind. For instance, chemical change and change of quantum state can be used for a unit of time measurement and neither of these processes depend on a change of spatial relationship among objects.

Since there are only a finite number of objects in the universe, they can only come into a finite number of rearrangements, hence time is finite.

This assertion and conclusion is very wrong. See Alex S.'s excellent essay at http://www.geocities.com/rationalphysics/U...nded_Finite.htm for explanation. But, regardless, even granting your premise just for argument's sake, and putting aside that your "rearrangements" of spatial relationships exclude many more changes of relationship, you still have completely ignored volition as a causal agent affecting change. No matter how you try to get around it, anytime we measure we will only find a finite duration of time, but the universe is eternal.

Edited by softwareNerd

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I'm trying to say that your conception of the universe being "forever changed" relies on false premises involving the postulated existence of infinite numbers of objects and infinite number of ways that they can inter-relate.

And exactly where did I propose "infinite numbers of objects" or an "infinite number of ways?" That is your creation, not mine, and it comes about because you cannot conceive of any alternatives. As I said before, see Alex S.'s essay at http://www.geocities.com/rationalphysics/U...nded_Finite.htm

Edited by softwareNerd

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This seems to be largely playing with words; if it were possible to travel at an arbitrarily fast speed in a single direction without ever reaching anything which would be called a boundary, then I think this would be what most people mean when they suggest the universe is infinite. It's like me saying that we could start at the number '1' and keep counting through 2, 3, 4 ... and never reach an end, but then claiming that this doesnt mean that there are infinite integers.

The problem is that Alex doesn't actually give a definition of what it would mean for the universe to be infinite, so it's difficult to tell whether he has actually refuted the claim. What he describes certainly seems to me like an 'infinite' universe; are we simply arguing the semantics of what 'infinite' means in this context?

Are all the entities in the universe a quantity? This is the criterion that would have to be filled for one to validly state that there are a finite number of entities in the universe. But, what meaning does a quantity have, if one does not provide any boundaries? After all, the universe must be unbounded.

All quantities must be able to be described by a (finite) number, because all quantities are finite in scope (i.e., extension), whether temporal or spatial. But, the universe as a whole does not encompass a (finite) spatial scope. Does this alleged quantity span out 15 billion light-years? 100 octillion light-years? This amount squared? There can be no answer to this question, because the universe has no bounds, and therefore no extension. To extend is to extend finitely, i.e., in a bounded fashion.

I'm not sure that I can even make sense of this. If I were to ask the question "How many atoms exist at this present time", then the (metaphysical) answer has to be either X (where X is a finite number), or 'infinite'. To claim anything other would be an outright denial of the law of excluded middle - either there an are infinite number of atoms that exist, or there are a non-infinite number of atoms that exist. Edited by softwareNerd

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No. The fundamental of time is change of relationship, and spatial relationship is just one kind. For instance, chemical change and change of quantum state can be used for a unit of time measurement and neither of these processes depend on a change of spatial relationship among objects.

Interesting point!

My premise is that things such as those that you mention are reducible to spatial phenomena plus action. In other words, physics is kinematics. But I am by no means certain about that. You are right to point it out.

Be that as is may, even if they are not kinematic phenomena, there are still only a finite number of states that any existent can be in. In that case, my argument for circular time still stands, mutatis mutandis.

We'll have to wait until physics decides that question, and in the meantime I'll have to express my argument in more general terms.

And exactly where did I propose "infinite numbers of objects" or an "infinite number of ways?"

I'm saying that you are implying such by saying "forever changed." You are claiming (by implication) that there will always be an indefinite number of unique events extending into the future. That would not be possible with only a finite number of objects/existential states in the entire universe, since a finite number of things can only combine to make a finite number of events.

But, regardless, even granting your premise just for argument's sake, and putting aside that your "rearrangements" of spatial relationships exclude many more changes of relationship, you still have completely ignored volition as a causal agent affecting change. No matter how you try to get around it, anytime we measure we will only find a finite duration of time, but the universe is eternal.

I don't understand your point here, if you care to elaborate. How is the volition part of your arguments connected with the fact of measurements being finite?

How have I ignored volition? There are only a finite number if things/states in the universe, and a volitional being therefore can only choose from amongst a finite number of choices each time a choice is made. That fits the framework of my argument.

Also, what is your conception of "eternal"? My guess is that your conception of such is that time is linear, i.e., which would mean that it stretches from an "infinity in the past" towards "infinity in the future." If so, you asserting that the "universe is eternal" amounts to simply asserting that my argument is wrong without providing an argument in support of yours. I don't think that pointing out that all measurements are finite qualifies as an argument for the proposition that time is linear.

My conception of "eternal" is more along the lines of the universe subsuming the phenomenon of time, not that time goes on "forever." This is a word usage problem. The ideal word does not exist, because this is not an everyday topic of conversation. If I were to invent a word, I would call it something like "ultra-temporal" perhaps.

Since there are only a finite number of objects in the universe, they can only come into a finite number of rearrangements, hence time is finite.

This assertion and conclusion is very wrong. See Alex S.'s excellent essay at http://www.geocities...nded_Finite.htm

I'm not too comfortable with it.

I'm not sure I agree that the universe is "a-sizal." Consider, for example, a universe that consists of nothing but a yardstick. One could say that that universe was three feet long. The same thing goes for our (actually existing) universe. You can take a standard inside of it and apply it to the whole thing, operating from within.

You don't have to go outside of the universe to be able to take a measurement of it in its entirety. It can all be done from within. If the universe is simply too large to actually perform the measurement, that wouldn't change the fact that it would still have a size (in the sense that I mention.)

Edited by softwareNerd

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This seems to be largely playing with words; if it were possible to travel at an arbitrarily fast speed in a single direction without ever reaching anything which would be called a boundary, then I think this would be what most people mean when they suggest the universe is infinite.

First off, and as I pointed out in my essay, the proper phrasing of the question at hand is not whether the universe is finite or infinite, but whether the universe's (alleged) size is finite or infinite. We are not discussing the age or density of the universe; we are discussing its spatial extension (size).

Secondly, I agree that most people would think that my ideas amount to claiming that the universe has an infinite size. But, I don't agree that such a popular vote is relevant. My ideas are to an extent original, so of course they will be different from what "most people" believe.

It's like me saying that we could start at the number '1' and keep counting through 2, 3, 4 ... and never reach an end, but then claiming that this doesnt mean that there are infinite integers.
The number series, unlike the universe, is not a metaphysical thing existing "out there"; there are only as many actually existing numbers as the human mind has conceived of. As such, even assuming that we could count indefinitely, there would not be an infinite number of integers. A potential to count indefinitely is just that: a potential, not an actual infinity.

So, in a way, your point is even stronger than what you intended: the universe has a _better_ claim at being infinitely long than the number series, since the universe is an actual, currently existing endless thing. Of course, I have arguments for why I reject that the universe has an infinite size, but they have not been addressed here yet.

The problem is that Alex doesn't actually give a definition of what it would mean for the universe to be infinite, so it's difficult to tell whether he has actually refuted the claim. What he describes certainly seems to me like an 'infinite' universe; are we simply arguing the semantics of what 'infinite' means in this context?

No, I'm not just arbitrarily using words differently; I gave arguments, trying to make a real differenation between infinity and the universe. This is why I did explain in my essay what it would mean for the universe to possess an infinite size (or any infinite attribute). I wrote: "The concept of infinity is metaphysically invalid because it attempts to describe an existent (e.g., an attribute) as existing, but as nothing in particular." For the universe to be infinite, it must have some infinite attribute or characteristic; for an attribute (i.e., size) to be infinite, it must actually exist, but as nothing in particular. To achieve an infinity, the universe must have a size, but have no particular size (which is a contradiction).

My theory is to deny that the universe has either a finite size or an infinite size -- i.e., to reject the claim that the universe has a size in the first place. I see no a priori reason why the universe must possess a size, anymore than I see an a priori reason why the universe must possess an age, density, weight, or shape. What is the arugment that the universe actually possesses any of these characteristics? I would be interested in hearing one.

If I were to ask the question "How many atoms exist at this present time", then the (metaphysical) answer has to be either X (where X is a finite number), or 'infinite'. To claim anything other would be an outright denial of the law of excluded middle - either there an are infinite number of atoms that exist, or there are a non-infinite number of atoms that exist.

Have you stopped beating your wife? After all, either you have stopped beating her or you have not stopped beating her; to claim anything other would be an outright denial of the Law of the Excluded Middle.

In philosophy, one must be very careful not to pass off complex questions as iron instances of the Law of the Excluded Middle. If a question assumes a false premise (and therefore a false context) to begin with, throwing in a negation within this context does not amount to the Law of the Excluded Middle. "Have you or have you not stopped beating your wife?" is an invalid question, because either alternative will assume the false premise that one has beaten one's wife in the past.

Similarly, when you ask whether the universe has an infinite or non-infinite number of atoms, you are obviously assuming that the concept of "number" applies to the universe and its contents to begin with. And this is a premise that I explicitly reject in my essay. I gave arguments for why concepts such as "number," "quantity," and "size" are wholly inapplicable to an unbounded universe, so to just assume that such concepts apply to the universe from the outset does not do justice to my arguments.

-- Alex

Edited by softwareNerd

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Alex,

I enjoy being challenged by your essay, and I agree with many of the statements you make, but not all.

I don't think we have to limit ourselves in using the concept "size" to only those situations where boundaries are present. I think it makes perfect sense to extend the definition to include that one special case of the boundaryless whole that the universe is.

I think you don't think it makes sense, because you are entertaining the possibility of the universe being a Euclidean space, i.e., that one could travel indefinitely in any one direction and never return to the place where one has started. I don't think this is a possibility or that the idea is even comprehensible.

Saying that no matter how far one has traveled, one's path has a definite length, doesn't seem to be an argument that addresses the issue. I'm not sure I can even say it's a non sequitur, because I am not sure that you are actually claiming anything in the positive. I'll have to keep studying it, but your essay seems to be only a critique of other theories, and not a theory in itself. (Like an atheist who is criticizing theistic theories, you are an "asizist." But "asizism" then wouldn't be a theory, just as atheism is not a theory.)

I think that it makes perfect sense to identify the universe as being a hyperspheroid. That's just a general geometrical term for a three-dimensional space that wraps back onto itself. It does not have to be embedded in four spatial dimensions in order for it to be able to "wrap" or "curve" back onto itself. "Curve," would be a very special use of the term where one is analyzing shape only from within the shape. One wouldn't have to go outside of the shape to use the term.

Consider measuring the volume of some part of the universe. We could take three yardsticks oriented at right angles to each other and show how that identifies a volume of one square yard, that that's the size of whatever is in that delimited volume. We can keep adding more and more yardsticks, making our volume bigger and bigger. Eventually the size of what we are measuring would subsume the entire universe (since I don't believe in a Euclidean universe.)

At that point we just assign meaning to what we have done, that we are calling that the "size" of the entire universe. One would not have to go outside of the universe in order to assign meaning to the use of the word "size" in connection with measuring the whole universe. (My argument still holds, even if no human being could actually perform the measurement.)

I think you are arbitrarily assuming that the term "size" can only have meaning when it applies to *parts* of the universe. But there is no reason why we can't extend the definition of "size" to include the scenario that I present here, namely, so that it could apply in two cases, either to a part of the universe or the whole thing.

Suppose that someone, in the process of developing their cognitive hierarchy, used the term "exist" only in situations where objects had life spans. For example, a certain piece of paper "existed" from the moment it was cut from a sheet at the factory until the time when he burned it and turned it into ashes. That would be a perfectly proper thing to do in using the term in situations like that.

We could say to him, "Why don't you extend the term and use it to apply to the universe as a whole?" Then we could suggest he extend his word usage and use the word "existence" to refer to the universe as a whole.

The same would be allowable in the use of the term "size." We can use it to apply to parts of the universe, or the whole thing, so long as we can show that it makes sense to do so (i.e., creates a meaningful identification), which I believe I have done.

--Adrian

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I'm not sure I agree that the universe is "a-sizal." Consider, for example, a universe that consists of nothing but a yardstick.  One could say that that universe was three feet long. 

In what does the yardstick reside? What is beyond its boundaries?

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I was just using it as as heuristic device to suggest the way to think about the actual universe. I have another post from earlier today up there that elaborates on what I was hinting at.

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Since there are only a finite number of objects in the universe, they can only come into a finite number of rearrangements, hence time is finite. When event E flows into event A, we are not "re-visiting" event A, nor would it be proper to say that it is happening for the "first time" or that in the whole history of the universe it only happens "once." ...

The only thing we can say about event A is: "It is"--not "is" in the present tense, but "is" in an all encompassing way that includes past, present and future....

How have I ignored volition?  There are only a finite number if things/states in the universe, and a volitional being therefore can only choose from amongst a finite number of choices each time a choice is made....

Since there are only a finite number of objects in the universe, they can only come into a finite number of rearrangements, hence time is finite. 

Adrian, let me ask you a question. In this "past, present and future" of your "finite number of rearrangements," was/is/will there be a "me" who does not disagree with you here on OO? Was there a "me" who was a Marxist, and will there be a "me" who accepts physical singularities? Has every "finite number of rearrangements" of "me" already occurred, and will occur again? Have I already had every possible career, married every possible woman, and held every possible idea?

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Adrian,

Your arguments against my essay rest on the supposition that the universe qua "hyperspheroid" is a viable alternative. But, as a fellow thinker, I must confess that I see neither evidence nor meaning in this contention.

To say that the unbounded universe has a "shape" which "curves" or "wraps" back onto itself is to rely on stolen concepts proffered as metaphors. Concepts such as "curve" and "shape" are wholly formed with reference to boundaries, and simply have no meaning apart from them. You refer to the usage of such concepts as a "special case"; I refer it as using concepts which are stolen from their necessary context.

This is why I must spread my hands out in honest disagreement when I hear you describe my position as not even "comprehensible." The universe qua "hyperspheroid" is, in my firm conviction, entirely incomprehensible. A "shape" or "curve" of an unbounded universe is literally just as meaningless and inconceivable to me as motion from point A to point B without traversing the points in between. In contrast, I have no problem comprehending the idea that the unbounded universe is "Euclidean," and nor have I been offered any reason why it is incoherent. It doesn't steal any concepts; it just asserts that the universe is an endless realm of three-dimensional, "Euclidean" space. (True, one cannot imagine an entire "expanse" of it at once, but that's not the standard for comprehensibility.)

The most common impetus among Objectivists for entertaining a notion like a "hyperspheroid" is the claim that it is necessary to avoid the existence of a metaphysical infinity. But, I gave arguments in my essay for why an endless, "Euclidean" universe is finite through and through. Thus, I'm at a loss for finding any reason to regard the "hyperspheroid" hypothesis as anything more than arbitrary.

Adrian, I'm interested in knowing: are your criticisms of my essay based on the supposition that the "hyperspheroid" alternative is correct? Or is the "hyperspheroid" idea attractive to you because every other alternative (mine included) is problematic? I want to go to the fundamental, here, so I can know exactly where you are coming from.

(P.S. -- While you're right that my essay is largely negative in its claims, it is not entirely so. My essay doesn't merely deny size to the universe like atheism denies God to existence. I do deny size to the universe, and further claim that such a denial -- along with positive facts I mention about size, number, quantity, etc. -- is the means to integrating three facts we know about the universe: it is finite, it is unbounded, and it cannot contain an infinite number of entities. Whether this is a theory in the strict sense of the word, I'm honestly not that interested in.)

-- Alex

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Alex,

Thanks for the extensive reply.

Just as a quick answer for now, I think that you are projecting a conception of Euclidean space onto the universe, which amounts to an attempt to reify the concepts of Euclidean geometry, which are only intended to be methods. In my mind, Euclidean geometry is valid only on the local, but not the global level ("global" meaning the entire universe).

Also, I'm inclined at this point to say that everything other than a hyperspheroid involves the attempt to posit actually existing infinities and is hence contradictory and not meaningful. It doesn't make sense to try to get around that by talking about particular measurements having definite lengths. The issue is that you are positing actual infinities, regardless of whether or not the infinite expanse you posit contains finite parts. That would be like me saying that infinity as a counting number had a reference because on the way towards counting there I had to count out some finite subsequences.

Stephen, no, I don't believe in any of those things that you mention. First of all, the entity that is you now is the only you that will ever be. You are a specific entity that is occupying a specific world line. Any entity that resembles you, however closely, is a different entity occupying a different world line.

And I certainly don't believe, as the theorizers of parallel universes do, that "all possible" this-or-that thing or situation makes sense. That's pure Rationalism. Simply put, it's nonsensical to think that it is "possible" for every object in the universe to come into relationships of any conceivable sort with every other object in the universe. Since the universe has a nature, the number and type of relationships that the entities (and existents) of the universe can participate in are necessarily limited.

--Adrian

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I think that it makes perfect sense to identify the universe as being a hyperspheroid.

For those not familiar with the technical terminology here, let me explain. In geometry, and topology in general, there is a generalization known as a hypersphere. An ordinary sphere has the property of uniform curvature, i.e., it is both homogeneous and isotropic (the same throughout and in all directions), and in a 2-dimensional space the ordinary sphere is referred to as a 2-sphere.

Our ordinary sphere can be generalized to a 3-sphere; we derive a 3-dimensional space of uniform curvature as the surface of 4-dimensional hypersphere. This 4-D hypersphere should not be confused with the talk you hear about time as a fourth dimension; in the world of the 4-D hypersphere, time is a fifth dimension. The hypersphere, then, is in general in an n-dimensional space with dimensions greater than or equal to four, having certain mathematical properties.

Now, as all of you (hopefully) know by now, I am a very big supporter of modern physics, and I revere the 20th century quantum and relatvistic world that took us out of the primitive structural ether world of the 19th century. The geometric and topological concepts that are at the mathematical root of much of modern physics, are perfectly valid concepts of method. I defend these concepts of method against those who rationalistically reject them, whether they are rejected out of ignorance or even for less justifiable reasons. However, when concepts of method are given a physical life of their own, as occurs often in cosmology, I lead the pack in condemnation of such reification.

Alex is entirely correct to reject the universe-as-a-hypersphere notion as being completely arbitrary. And, frankly, as being utterly absurd. To lend philosophical support for such a notion is as bad -- nay, even worse -- than accepting the idea of physical infinities or physical singularities. To infuse our world in a mythical hypersphere is to remove all philosophy and physics from the realm of rationality. Physics, and metaphysics, is not a word game.

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To infuse our world in a mythical hypersphere is to remove all philosophy and physics from the realm of rationality. Physics, and metaphysics,  is not a word game.

First, I'm not saying that the universe is a hypersphere. I'm saying that it is a hyperspheroid. That's a much more general observation which does not make a specific claim as to the exact shape of the universe. The concept "hyperspheroid" includes any type of 3-D "surface" that has a finite volume, i.e., which wraps back onto itself.

I think my loose use of language has also led us to more misunderstanding. I should have said that the universe is "hyperspheroidal," so as not to confuse the method with that to which it refers. For example, a planet could be said to be "spherical," and we would not be saying that it was a "sphere." You're absolutely right, Stephen, on that count. A "sphere" is a concept of method, but when we apply it and use it to describe a planet, for example, we can say that that actually existing thing is "spherical."

I regard identifying the universe as being hyperspheroidal as akin to identifying it is as being a plenum. Saying that the universe is a plenum is not arbitrarily choosing from amongst a number of alternatives. There are no alternatives to the plenum, since a metaphysical vacuum (or any variation involving a vacuum) is a meaningless contradiction.

At this point, I just don't see any alternative to the universe being hyperspheroidal (and remember, that is a very broad identification). Any other proposed alternatives are pseudo-concepts, as I see it at this point, that involve positing the existence of actual infinities.

I'm not claiming certainty on this. I just don't see any other way to go with it. I'd be more than happy to change my mind if anyone wants to go point by point and lead me somewhere else.

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Stephen, no, I don't believe in any of those things that you mention.  First of all, the entity that is you now is the only you that will ever be.  You are a specific entity that is occupying a specific world line.  Any entity that resembles you, however closely, is a different entity occupying a different world line.

Your basic claim is that time is finite because there are a finite number of objects in the universe and there can only be a finite number of rearrangements of those objects, and the sequence of events is A-B-C-D-E-A, with A encompassing all past, present and future instances of itself.

But, following your logic, I am composed of a finite number of objects (particles) put into a finite number of rearrangements. So, me as a rearrangement will occur as part of all the other rearrangements of all the other finite number of particles that exist, as many times as is finitely possible. So I live my life right now, and then I die. But in the future, as in the past, in this world of finite time, the finite number of particles that I was composed of will again be the particular rearrangement that is me, and there will be a me for all other finite rearrangements of the other remaining finite particles, and that will be all the other people that can be from the finite number of finite rearrangements of the remaining particles. And, for each of these finite rearrangements, the actions I take will be reducible to the finite rearrangements I can make of all the other objects that exist in a finite number of rearrangements. Hence, I will perform all possible actions with all possible people, in the past and in the future.

But, please don't blame me for the logical conclusion of your argument. :P

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First, I'm not saying that the universe is a hypersphere. I'm saying that it is a hyperspheroid. That's a much more general observation which does not make a specific claim as to the exact shape of the universe. The concept "hyperspheroid" includes any type of 3-D "surface" that has a finite volume, i.e., which wraps back onto itself.

All you are doing is fuzzying up the concept, blurring the edges. Where are you getting this stuff from? A computer search of of the mathematics and physics literature, dating back to 1945, shows zero references to "hyperspheroid" out of 27,287,512 papers published in the standard journals. There are, however, hundreds of references to the "hypersphere." Just for fun I did a "JSTOR" search of the available journals going back to the 1600s and found zero reference to the "hyperspheroid."

But, regardless, granting your fuzzy notion of a hyperspheroid, so what? It is even more arbitrary and more absurd than the more specific and realizable notion (as a concept of method) of the hypersphere. Frankly, your use of the term seems like the utterance of a magic word.

I regard identifying the universe as being hyperspheroidal as akin to identifying it is as being a plenum.
You can regard it as anything that you want, but that does not mean it makes even a bit of sense.

At this point, I just don't see any alternative to the universe being hyperspheroidal (and remember, that is a very broad identification). Any other proposed alternatives are pseudo-concepts, as I see it at this point, that involve positing the existence of actual infinities.

I'm not claiming certainty on this. I just don't see any other way to go with it. I'd be more than happy to change my mind if anyone wants to go point by point and lead me somewhere else.

This is very wrong thinking. If you do not have a solution to a problem you do not manufacture an absurdity because you "don't see any alternative." As long as you fill your mind with nonsensical "answers" you are taking up the room where a real answer could reside. If you want a solution to the metaphysical problem -- and, I believe you sincerely do -- the place to begin is to purge your "hyperspheroid" thinking. Whether you accept Alex S.'s solution (I do -- I think it is brilliant), or not, you need to take a fresh look at the problem.

Edited by softwareNerd

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So, me as a rearrangement will occur as part of all the other rearrangements of all the other finite number of particles that exist, as many times as is finitely possible.

That's an interesting question, but I'm not claiming that at all and I don't see how I am implying it.

Setting aside the circular time issue, let's say you had an identical twin that, against all odds, had the precise same structure of your body. He would still be a different entity and wouldn't be you at all, although he resembled you. In order for him to be you, his life would have to be situated in the exact same historical context that you inhabit. And that is impossible due to the Law of Identity. Only one entity can exist in the same place at the same time, or at the same places and same times.

In other words, your identity is more than just the internal structure of the entity that is you. Your identity also includes its entire context.

Also, I'm not sure if particles is all that you are. You might be composed of other things, too. But whatever those other things are, there are only a finite number of states that they can be in.

So I live my life right now, and then I die. But in the future, as in the past, in this world of finite time, the finite number of particles that I was composed of will again be the particular rearrangement that is me [...]

No, if you reread my posts you will see that I am saying that the concept of "again" does not apply. The concept of "again" or "repetition" entails the idea of some similarity existing between what are actually two *different* events. The events are different because their contexts are different, i.e., the universe around the two separate events is different.

When I say that time is circular, I am not claiming that you will live your life over again, or that you will exist again in the future, or that you have existed before in the past. That would be like me orbiting the earth several times and saying that there are more than seven continents because I kept counting "new" ones each time I orbited.

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A computer search of the mathematics and physics literature, dating back to 1945, shows zero references to "hyperspheroid" out of 27,287,512 papers published in the standard journals.

That's interesting, but I'm sure the term has been used before, and its a good one. It shows up on Google.com, although there aren't many hits. That's odd.

It's possible that we need a different term. I'm open to correction. I'm using it, as I said, to describe any 3-D surface that has finite volume, no matter what its exact shape. It's analogous to talking about 2-D surfaces that have finite areas. Spheres have finite areas (surface areas) but planes do not.

As I said before, I don't see that Alex is claiming a positive, since he apparently sees the universe as being Euclidean, or extending out to infinity in all directions, which I regard as being an incomprehensible attempted reification of concepts of method.

If you agree that the universe is a plenum, then I'm assuming that you believe so because there simply aren't any alternatives. It's akin to saying "everything has a nature." There are no alternatives to such kinds of statements.

Similarly, I'm saying that there can't be any alternative to the idea of the universe wrapping back around on itself. That's the only way that a finite number of entities can exist. Whatever label we put on this is not relevant to the argument.

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As I said before, I don't see that Alex is claiming a positive, since he apparently sees the universe as being Euclidean, or extending out to infinity in all directions...

Firstly, I'm explicit in my essay that I'm neither claiming that the universe is infinite nor "extending." My essay draws out my entire argument, and I encourage you to understand it. Disagreeing with it is one thing, but flatly asserting the very thing that I wrote a whole essay to question renders debate impossible.

Secondly, I only claim positives when something positive exists to claim. The universe lacks size and is not a quantity, and it happens to be these facts which allows one to integrate our knowledge about the universe. The fact that my essay makes a lot of negative claims is neither a fault nor my fault. Moreover, I stated in my last post the positive claims I do make in my essay, so to just assert once again that you can't find any positive claims in my essay is, quite frankly, bizarre.

I'm saying that there can't be any alternative to the idea of the universe wrapping back around on itself.  That's the only way that a finite number of entities can exist.

I devote a whole section to my essay to why the universe does not have an finite number of entities -- and why an infinite number is not the alternative. I explain why "number" and "quantity" don't make sense when applied to a whole which lacks boundaries. Again, you may disagree, but you must draw out why you disagree if you want to enable discussion.

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That's an interesting question, but I'm not claiming that at all and I don't see how I am implying it.

Adrian, I feel like I am squeezing a partially full toothpaste tube. I squish one end and the other end just bulges up, and nothing comes out. I really have nothing more to say about this notion of finite time, so I will just leave this part of things at that.

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That's interesting, but I'm sure the term has been used before, and its a good one. It shows up on Google.com, although there aren't many hits. That's odd.

What is truly "odd" is your reliance on a term that has virtually no meaning.

It's possible that we need a different term. I'm open to correction. I'm using it, as I said, to describe any 3-D surface that has finite volume, no matter what its exact shape.
That would be a 4-dimensional hypersurface that had certain restricted mathematical properties. But, again. so what? (!) It is just a mathematical abstraction, not a physical existent, no matter how much you wish it so.

Similarly, I'm saying that there can't be any alternative to the idea of the universe wrapping back around on itself.

That's because you are answering to an invalid question. You missed that point in Alex's essay and you missed it when he told you that here. As I said before, I truly believe you would like to understand this metaphysical issue, but until you purge your mind of this whole framework that you built, I doubt you will be able to see any alternative.

Edited by softwareNerd

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Alex.

Ok I've read your essay again, this time a bit more closely, and yes, I think I misinterpreted you the first time. I'm still not 100% sure that I understand exactly what you are trying to say, so if I've made any further mistakes please correct me.

spatial extension
Firstly, I don't think that most statements of the form "the universe is/has X" actually make sense - the universe itself is not an existing thing; the word universe means "everything that exists". I dont think it makes any more sense to talk about 'the size of everything that exists' than it makes to talk about 'the size of the_apples_in_this_bag'. You can talk about the size of an individual apple and you can talk about the space that the apples are _existing_ in, but you cannot assign properties to 'the_apples_in_this_bag' - it isnt a 'thing', it's a label used to refer a collection of things.

With this in mind, I would say that both the statements "the universe is finite in size" and "the universe is infinite in size" are outright nonsense if taken literally. "The universe" does not have a size, because "all that exists" does not have a size (or spatial boundaries!). From rereading your essay I _think_ that you are in agreement with me on this but are phrasing it differently, and if so then I am in full agreement with you - the question reduces to one regarding spacial boundaries, since thats the only real way in which it can be made coherant. I don't know if it is the place of philosophy to claim that the 'universe' is unbounded (translated as "the space in which everything exists is unbounded") since I'm not entirely sure whether a bounded universe would be a logical impossibility - obviously talking about a bounded universe in the sense of there being something 'outside' the universe would be nonsense, but it may well be possible to formulate the claim in a different way.

But let us assume that you are correct about the universe being unbounded - assume that you can travel as far as you want in any given direction without reaching a boundary. As far as I can tell, you want to maintain this while also claiming that the spatial extention of the universe isnt infinite. But let us consult the dictionary

infinite:

extending indefinitely : ENDLESS <infinite space>

immeasurably or inconceivably great or extensive : INEXHAUSTIBLE <infinite patience>

7 entries found for infinite.

in·fi·nite 

1. Having no boundaries or limits.

If something extends indefinitely (as you claim the universe does) then it _is_ infinite, by the definition of what 'infinite' means. Something cannot both extend indefinitely and not be infinite. If you are asserting that you can travel arbitrarily far in a given direction then many, including myself, would claim that you are asserting that the universe has infinite spatial extent. This is why I asked you to define precisely what you meant by your usage of the term 'infinite' - even if I accept everything you have written in your paper, it can still be claimed that the universe is infinite by this definition of the term. It extends indefinitely and has no spatial boundary. Are you using the word in a different way?

edit: To clarify, when I say that "the universe extends indefinitely" I do NOT mean that there is a thing called 'the universe' which extends indefinitely - as I said above, I think this is an abuse of language. 'The universe' is not an existing thing, and it has no extent whatsoever. I would translate "the universe extends indefinitely" as "it is possible to travel arbitrarily far in any given direction", and I assume that this is what most people mean when they make the claim.

number of entities

I still disagree with you on this however. Assume I get aboard your hypothetical spaceship capable of travelling at octillion light-years a picosecond and decide to count the number of atoms in the universe. Since you are assuming that I could travel as far as I wanted in any particular direction ("the universe is unbounded"), I think it follows that I will never run out of atoms to count. No matter how far I go and how long I count for, I will always be able to go count higher. If I wanted to count 1000 atoms, this would be possible. If I wanted to count 100000000 atoms, this would also be possible (I'd just have to travel out slightly further). Indeed, given any arbitrary integer X, I would be able to count more than X atoms in the universe. In other words, the number of atoms in the universe is greater than any arbitrary finite value. Again, let us consult the dictionary:

Main Entry: 1in·fi·nite

extending beyond, lying beyond, or being greater than any preassigned finite value however large <infinite number of positive numbers>

It certainly seems that the number of atoms IS infinite, going by this usage of the word. Note that it is not being asserted that there is an actual number 'infinity' existing that somehow corresponds to the cardinality of the set of atoms in the universe, it just means that the number of atoms in the universe is greater than any finite value. This does not seem to contradict what you say.

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I assume you brought up abiogensis because of this issue:

Mr Weiss,

I brought up abiogenesis because of this issue.

http://www.creationofuniverse.com/html/equilibrium03.html

Also, most natural-evolutionists I talk to like to divroce evolution from abiogenesis. I really don't see how you can have naturalistic evolution with out it. But I can see why they want to shy away from it.

Without disrupting the current context of this discussion, I was wondering if anyone would like to address Aristotle's "Unmoved Mover", since as I understand it Objectivists are sympathetic to Aristotle.

http://www.abu.nb.ca/Courses/GrPhil/PhilRel/Aristotle.htm

conan

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Conan,

The last link you provided contains this statement:

"Since everything is moved by something and since motion is eternal, Aristotle concludes that there must be something that imparts motion without itself being moved; otherwise, there would be an infinite regress of movers, the moved and instruments of moving, which is unacceptable (Physics 8.5)."

I disagree with the "otherwise, there would be an infinite regress of movers" conclusion, for the same reason a gave above, in an early post, for their not being a first cause. A mover is really the same thing as a cause, if I am understanding this properly, so my initial response is that it is the same question just using different language. Right?

Adrian

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