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The Infinite and the Finite

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But the "universe" is defined as all that exists. Not some of what exists. Or what it exists in certain areas of the bulk of a "multiverse". By the way everything that exists is an existent or a "thing" including the universe. Saying that is NOT invoking the fallacy of composition either.

A quark and a gluon are "things"--existents-- and so is a proton or neutron. "Things" made up of the other "things". Protons and electrons are things(I'm dropping the scare quotes now) that make up hydrogen. Hydrogen is a thing that makes up another thing-- a star.

A star is a thing that makes up another thing-- a system.

A system is a thing that make up another thing-- a galaxy.

Galaxies are things that make up clusters of galaxies, clusters--things that make up superclusters.

All of these things make up the universe. The universe is also a thing. The universe is all that exists.

Both of these facts would still remain the same even if were proven that the readily observable universe was just a "brane" floating in a multi-dimensional bulk. Those would still be things and this expanded "multiverse" would actually be what we now normally term as the universe--all that exists.

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No, I distinctly said considered conclusive. By which I meant that cosmologists consider the evidence to strongly favor the Big Bang theory of the origin of the universe over any other theories.
Fine I don't object to a "consideration". I object to the claim about what they actually concluded. They don't consider the Big Bang to be the origin of the universe. I wouldn't bet 25 cents that cosmologists aren't persuaded that there was a "Big Bang", I'm betting that they do not claim that was the origin of the universe, since it would be irresponsible to come to that conclusion based on the observational data.
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Who is the "your" being addressed in this fairly aggressive and seemingly assumptive paragraph?
I was replying to Nyronus' post, who, in that post, said "The Big Bang no more created the universe than ice creates water". I was addressing the guy who thinks I'm "lashing out", who reads non-contradictory statements and concludes "Sounds pretty contradictory", who determined that I "don't like a scientific theory because it disagrees with the words of [my] philosophical mindset" and finds me "dangerously close to a creationist as far as mindsets go", suggesting that I "stop calling [my]self an Objectivist". I'm not a cosmologist, but it's just not responsible to accuse me of "ignorance on both". I am not "really upset about semantics" and I don't have an "irrational hatred of multiple universe theory", but I do care about people actually saying what they mean using words literally, and then backing up those statements. When someone accuse me of ranting by engaging in a thoughtful philosophical discussion, I do have to draw the line.
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All of these things make up the universe. The universe is also a thing. The universe is all that exists.

Both of these facts would still remain the same even if were proven that the readily observable universe was just a "brane" floating in a multi-dimensional bulk. Those would still be things and this expanded "multiverse" would actually be what we now normally term as the universe--all that exists.

It sounds like you're saying that "our universe" - all that we can perceive within our cosmological system - might be part of a larger, imperceptible multiversal universe. This would be consistent with the examples of things you give, in that every thing listed is component to a larger thing. Getting back to the original discussion, the fact of being component to something larger requires the component to be finite. It does not require the larger thing be finite. To assert that the universe is finite because each of its components is finite is as valid as asserting that the universe is a component because each of its components is. Since this latter leads to a contradiction, it invalidates the premise that the universe must be fundamentally the same as its components in any given attribute, including finiteness.

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But the "universe" is defined as all that exists. Not some of what exists. Or what it exists in certain areas of the bulk of a "multiverse". By the way everything that exists is an existent or a "thing" including the universe. Saying that is NOT invoking the fallacy of composition either.

A quark and a gluon are "things"--existents-- and so is a proton or neutron. "Things" made up of the other "things". Protons and electrons are things(I'm dropping the scare quotes now) that make up hydrogen. Hydrogen is a thing that makes up another thing-- a star.

A star is a thing that makes up another thing-- a system.

A system is a thing that make up another thing-- a galaxy.

Galaxies are things that make up clusters of galaxies, clusters--things that make up superclusters.

All of these things make up the universe. The universe is also a thing. The universe is all that exists.

Both of these facts would still remain the same even if were proven that the readily observable universe was just a "brane" floating in a multi-dimensional bulk. Those would still be things and this expanded "multiverse" would actually be what we now normally term as the universe--all that exists.

Quark, gluon, proton, neutron, electron, hydrogen atom, hydrogen molecule, star, star system, galaxy, galaxy cluster, supercluster - all are things - all are bounded, all are aspects of reality.

The universe is not bounded, in an epistemological sense. That is, when one speaks of the universe, one is not speaking of such and such bounded part of the universe, separate and apart from the rest of the universe which, for the moment, one is ignoring. One cannot speak of the universe as a thing, neither in any sense of the word universe nor in any sense of the word thing. There is no metaphysical universe thing, nor an epistemological universe thing. One can speak of the universe as - epistemologically - everything (but not a thing).

Keep in mind that "entity" is actually an epistemological tool, a cognitive tool. The universe is actually an undivided whole - it is we who are observing it who, as our method of cognition, focus on certain aspects at a time and then on other aspects, as we find it necessary.

Furthermore, it is an inversion of logic to speak of predecessor or successor universes, or alternate universes within a multiverse. Such sequences of words do not have any ontological meaning whatever. They have no cognitive status except for "mumbo jumbo." One cannot point to a predecessor, successor or alternate universe. One cannot acquire data from them. One cannot even speculate, because speculation requires a basic minimum of evidence to go on. One can only speak in tongues in a manner which almost, but not quite, sounds like comprehensible English.

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It sounds like you're saying that "our universe" - all that we can perceive within our cosmological system - might be part of a larger, imperceptible multiversal universe. This would be consistent with the examples of things you give, in that every thing listed is component to a larger thing. Getting back to the original discussion, the fact of being component to something larger requires the component to be finite. It does not require the larger thing be finite. To assert that the universe is finite because each of its components is finite is as valid as asserting that the universe is a component because each of its components is. Since this latter leads to a contradiction, it invalidates the premise that the universe must be fundamentally the same as its components in any given attribute, including finiteness.

Your correct about what I'm saying except when it comes the reason why the universe must be finite. As has been explained over and over the "infinite" is only a mathematical tool--an epistomological concept of method and can not and does not exist as a metaphysical reality. Nothing violates the Law of Identity metaphysically including the universe regardless of what one thinks it contains or not.

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Your correct about what I'm saying except when it comes the reason why the universe must be finite. As has been explained over and over the "infinite" is only a mathematical tool--an epistomological concept of method and can not and does not exist as a metaphysical reality. Nothing violates the Law of Identity metaphysically including the universe regardless of what one thinks it contains or not.

The assertion has been made over and over again, without any attempt to address the opposing argument. The argument that "'infinite' is only a mathematical tool--an epistemological concept of method and [therefore?] can not and does not exist as a metaphysical reality" is simply an assertion.

The number 3 is a mathematical tool and a concept of method, but you would be hard-pressed convincing anyone that the number 3 does not exist as a metaphysical reality without breaking the connection between reality and perception. The fact that one can provide many examples of the number 3 but none of infinity does not invalidate this line of argument, because infinity, by definition, defies example; just as does: the universe.

As an example of the logical quandary you run into when you insist that infinity is impossible, or that the universe is a thing, that is, something of which you can provide an example, I point you to a previous post:

Space is finite and unbounded.

??? -- You can't have an unbounded cake and eat it, too.

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You are wrong, but I will respond to this later when I have more time.

From OPAR pages 31-32

"Infinite" does not mean large; it means larger than any specific quantity, i.e., of no specific quantity. An infinite quantity would be a quantity without identity. But A is A. Every entity, accordingly, is finite; it is limited in the number of its qualities and in their extent; this applies to the universe as well. As Aristotle was the first to observe, the concept of "infinity" denotes merely a potentiality of indefinite addition or subdivision. For example, one can continually subdivide a line; but however many segments one has reached at a given point, there are only that many and no more. The actual is always finite.

[bold mine]

From ITOE pages 148-149

The same applies to the concept "infinity," taken metaphysically. [Miss Rand referring to it being an invalid concept in response to a question from "Prof. D".] The concept of "infinity" has a very definite purpose in mathematical calculation, and there it is a concept of method. But that isn't what is meant by the term "infinity" as such. "Infinity" in the metaphysical sense, as something existing in reality, is another invalid concept. The concept "infinty," in that sense, means something without identity, something not limited by anything, not definable. Therefore, the measurements omitted here are all measurements and all reality.

My explanation in bold and brackets.

From The Ayn Rand Lexicon--

Infinity

There is a use of [the concept] “infinity” which is valid, as Aristotle observed, and that is the mathematical use. It is valid only when used to indicate a potentiality, never an actuality. Take the number series as an example. You can say it is infinite in the sense that, no matter how many numbers you count, there is always another number. You can always keep on counting; there’s no end. In that sense it is infinite—as a potential. But notice that, actually, however many numbers you count, wherever you stop, you only reached that point, you only got so far . . . . That’s Aristotle’s point that the actual is always finite. Infinity exists only in the form of the ability of certain series to be extended indefinitely; but however much they are extended, in actual fact, wherever you stop it is finite.

Peikoff_t.jpg Leonard Peikoff, “The Philosophy of Objectivism

lecture series (1976), Lecture 3.

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.

introtoobjectivist.gif Introduction to Objectivist Epistemology, 22.

Every unit of length, no matter how small, has some specific extension; every unit of time, no matter how small, has some specific duration. The idea of an infinitely small amount of length or temporal duration has validity only as a mathematical device useful for making certain calculations, not as a description of components of reality. Reality does not contain either points or instants (in the mathematical sense). By analogy: the average family has 2.2 children, but no actual family has 2.2 children; the “average family” exists only as a mathematical device.

theobjectivistforum.jpg Harry Binswanger “Q & A Department: Identity and Motion,”

The Objectivist Forum, Dec. 1981, 13.

That was the "official" Objectivist usage of the term "infinity". If you argue against any of this then what you are arguing against is "the" Objectivist position on the matter. So I hope this completes this thread conclusively.

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...

There's nothing in any of these quotes about the universe being "unbounded but finite," which is not surprising, since these words are antonyms.

Aside from that, if by "universe" you mean the visible cosmic system in which we reside, I would have to agree that it is finite. If, however, you mean all of existence, including anything which may lie beyond the visible cosmic system, I would have to return to the argument that the universe is not something which exists in reality, as it is reality. The universe omits all measurements and "all reality" because it is "all reality." A thing can't be measured in terms of itself, so the universe necessarily defies any measurement. It likewise, can not be limited by anything, and is at least potentially undefinable, at least in terms of measurement. There is no contradiction in saying that the universe is infinite. It is an assertion, but so is the claim that the universe is finite. The extent of the universe is unknowable and indefinable. That is a metaphysical truism.

The only argument you can make wrt to the infinite and the universe is that anything that may lie beyond the visible universe is hypothetical, and therefore does not objectively meet the minimum requirement for "existence." The argument is valid for such concepts as God, but is a little harder to apply to the universe, since we know the universe to exist, but do not know if the extent of the universe is infinite or bounded.

I don't know quite how to address the argument from authority, except to say that Rand never addresses reality itself as infinite, but the things which exist "in reality." Peikoff does, but then he also defines "entity" as something solid, with a definite boundary ("fluids are not entities"), and perceptual in scale. Clearly this denies the universe, that is, all of existence, as an entity. That is a contradiction, which leaves his view of the universe undefined.

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The assertion has been made over and over again, without any attempt to address the opposing argument. The argument that "'infinite' is only a mathematical tool--an epistemological concept of method and [therefore?] can not and does not exist as a metaphysical reality" is simply an assertion.

Indeed, it is an arbitrary assertion which cannot be proved. There isn't any logical contradiction in the hypothesis that there isn't an upper bound to the number of particles in the universe.

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Indeed, it is an arbitrary assertion which cannot be proved. There isn't any logical contradiction in the hypothesis that there isn't an upper bound to the number of particles in the universe.

But the lack of an upper bound--unbounded-- and "infinite" are two totally different things. One's possible and the other is a metaphysical immpossibility. This is not an "assertion" ,because to claim otherwise is a violation of the Law of Identity since a metaphysical "infinity" is by definition undefined.

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But the lack of an upper bound--unbounded-- and "infinite" are two totally different things. One's possible and the other is a metaphysical immpossibility. This is not an "assertion" ,because to claim otherwise is a violation of the Law of Identity since a metaphysical "infinity" is by definition undefined.

No, the lack of an upper bound is the definition of infinity, they are exactly the same things. So we can for example prove that there are infinitely many prime numbers by showing that the hypothesis that there is a largest prime number (i.e. the set of prime numbers has an upper bound) results in a contradiction.

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  • 2 weeks later...
No, the lack of an upper bound is the definition of infinity, they are exactly the same things. So we can for example prove that there are infinitely many prime numbers by showing that the hypothesis that there is a largest prime number (i.e. the set of prime numbers has an upper bound) results in a contradiction.

"A" definition, not "the" definition. A non empty set A is infinite if and only if it has a proper non empty subset B such that there exists of mapping f from A -onto- B which is one to one. This is a standard definition used in set theory.

Example: Let A be the set of integers. Let B be the set of even integers. Let f be the mapping from A onto B given by

f: n -> 2*n

So the set of integers is infinite by this definition.

ruveyn

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  • 3 years later...

In Peikoff's book Objectivism page 104, he writes that one "can proceed to discover an unlimited knowledge about the entity" using one mental unit. What exactly does "unlimited" mean in this context? is "unlimited" "infinite"?

You need to step back in the quote to the mathematical analogy established by endless series. The units that are integrated by the mental entity "man" in this case, would be every man that exists, has existed, and will exist, without specifying the specific quantity. It also apply to the knowledge integrated about man under the concept of "man" which would include all the knowledge known about man and all the knowledge yet to be discovered about man, again, without specifying the scope of that knowledge. This is what gives allows concepts to expand the range our scope of awareness beyond that which is just perceptual.

Edited to add.

Edited by dream_weaver
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"A" definition, not "the" definition. A non empty set A is infinite if and only if it has a proper non empty subset B such that there exists of mapping f from A -onto- B which is one to one. This is a standard definition used in set theory.

Example: Let A be the set of integers. Let B be the set of even integers. Let f be the mapping from A onto B given by

f: n -> 2*n

So the set of integers is infinite by this definition.

ruveyn

Could this be considered 'rigging' the problem? Instead of observing an auditorium to see if every seat is filled, and there are no people standing, which may not be do-able if the lights are dimmed, we 'rig' the problem to state that there are two legs for every body that is present. The set of two legs for every body is a given (presuming of course normal, un-maimed bodies). The set of even integers to the set of all integers is by its nature definitional 1:2.

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The following link explains in detail what I am talking about. It was written by a former member of this forum and he personally gave me permission to link to it.

http://www.geocities.com/rationalphysics/U...nded_Finite.htm

There is never a need to obtain permission to provide a link to something published on the internet.

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The link to the essay on Geocities about "unbounded" and "finite" is broken. Would someone please mind clearly defining "bounded/unbounded" and "finite/infinite" and their differences? This distinction seems to have several participants confused or at odds.

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Bounded means "finite in one sense". So, the set of real numbers between 0 and 1 is bounded in that the difference between any two numbers in the set is less than or equal to 1. The set is infinite, in that you can always describe a number between any 2 numbers in the set. IMO, calling the universe "finite and unbounded" is misleading. In that case, "finite" refers to the fact that there is a maximum value of the metric (the distance between any two entities), and "unbounded" refers to the fact that you can travel in one direction forever. By definition, if the universe is finite in any respect then it is bounded. So it would be more correct to say the universe is "finite, but unbounded for linear travel" (or something along those lines).

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