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Javelin Argument for Infinity

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The universe is finite. This is an application of the 'Law of Identity' applied to the universe as a whole.

In a discussion with a co-worker, the javelin argument is introduced as 'evidence' for infinite space and 'matter'. This appears to be a variation of 'prove existence via non-existence', or 'prove consciousness via non-consciousness'. i.e., Prove identity via non-identity.

Since there is no 'outside' the universe, therefore 'space' and thus - two javelins can continue for eternity along the same vector in opposite directions, infinity is concluded in regard to both the size of the universe and the quanity of matter.

This is challenging my grasp of the Law of Identity applied inductively to the perceptually observable, extrapolated to the universe as a whole.

I hope I have stated this clearly enough. Thanks.

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Okay, I am trying to learn Objectivism, so I think solving these problems might help. Someone make sure that I am right/correctly representing Objectivism.

Here is why your friends argument is wrong.

1. Stolen Concept.

2. Just because to Javelines have the potential to go an infinite distance from one another does not mean that there is an infinite distance between one another.

3. The universe is defined as "Everything which exists". The Javelins do exist and are included in the universe. The distance between one another is a property of the two javelins. As far as I know, what most people think of as space (the "nothingness" "in between" things) is an arbitrary concept, and can not be said to be infinite, because it does not exist, and is there for can not have an identity, including the property of "actualized infinity".

3a. "Space" does not exist in the sense described above because the concept of it relies on the fallacy that someone should say something is there because there is an "in between" distance wise.

It does not follow that there is a thing between your 1-meter separated things A and B. In fact if you claim that there is always a thing (call it X) between A and B, then there must also be a thing between A and X, X'; and then there must be a thing between A and X' (X'') and infinitum. This leads to "actualized infinity", which is wrong.

You have to understand that "between" is an abstraction of method and that if in fact no thing stands between A and B, then there is no "between". Some existent Q is actually "between" A and B if and only if it actually exists and satisfies the appropriate relation "betweenness" (shorthand for some simple math). There is something between two things if and only if there is some thing between them. There is nothing between the two things if and only if there is no thing between them.

4. The Quantity of matter in the universe can in no way be deduced by this thought experiment. That is a question of induction.

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Infinity is not a number and so expressions like "an infinite distance" are not meaningful. Consider the case of the two javelins: for all time, the distance between the javelins is finite. There isn't even a potential to "go an infinite distance". One could properly say (under certain assumptions) that the distance increases without bound, i.e., there is no limit to how large the distance between the javelins may become. However, that distance, no matter how large, will *always* be finite; the distance can never *be* infinite.

Is it proper to speak of a "size" of the universe? I'm not certain that it is. I think that it is instructive to think about the question "how distant can two physical objects be from each other?" Thought about this way, it's clear that the distance in question, no matter how large, is finite. It's also clear (under certain assumptions) that no matter how large the distance is between the objects, that distance could be larger still.

IOW, to say that the universe is finite is, I think, to say that there are no actual infinities. There are no "infinite distances" between physical objects, no "infinite areas" of physical surfaces, no "infinite volumes" of physical containers, etc. That is not the same as saying that these quantities cannot be arbitrarily large, just that they are always finite, i.e., they are always expressible as a number.

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The universe is finite. This is an application of the 'Law of Identity' applied to the universe as a whole.

In a discussion with a co-worker, the javelin argument is introduced as 'evidence' for infinite space and 'matter'. This appears to be a variation of 'prove existence via non-existence', or 'prove consciousness via non-consciousness'. i.e., Prove identity via non-identity.

Since there is no 'outside' the universe, therefore 'space' and thus - two javelins can continue for eternity along the same vector in opposite directions, infinity is concluded in regard to both the size of the universe and the quanity of matter.

This is challenging my grasp of the Law of Identity applied inductively to the perceptually observable, extrapolated to the universe as a whole.

I hope I have stated this clearly enough. Thanks.

"The concept 'infinity' denotes merely a potentiality of indefinite addition and subdivision." and, "Infinite does not mean large; it means larger than any specific quantity, i.e., of no specific quantity" (these are from OPAR). Its crucial to remember when taliking about 'infinity', we're not talking about a measurement of stuff in "existence". Its not a metaphysical term, its a mathematical concept of method. Metaphysically the concept is invalid, or perhaps "stolen" as Hairnet said because it denies the concept of identity on which it relies. Cosmology has (recently) dicovered through studying the microwave background of the universe, and through gravitational lensing that the universe is in fact expanding at a much higher rate than we expected, and faster than it "should be" based on our scientific knowledge. A form of unknown "dark energy" is likely the cause. If its infinite, how can it be expanding?

j..

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"If it is infinite, how can it be expanding?"

I think the above is a bit confused. The first "it" appears to be referring to the universe while the second "it" appears to be referring to spacetime since, in GTR, it is spacetime that is expanding. But, according to general relativity, spacetime is a dynamic entity, a *part* of the universe that acts on matter, "telling matter how to move" while matter acts on spacetime, "telling spacetime how to curve".

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"If it is infinite, how can it be expanding?"

I think the above is a bit confused.

The question was sort of rhetorical, relating to the OP,but Ill bite....

reply forthcoming.... (I'm at work)

more later...

j.

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I think the above is a bit confused. The first "it" appears to be referring to the universe while the second "it" appears to be referring to spacetime since, in GTR, it is spacetime that is expanding. But, according to general relativity, spacetime is a dynamic entity, a *part* of the universe that acts on matter, "telling matter how to move" while matter acts on spacetime, "telling spacetime how to curve".

This is not quite correct. According to GTR (and Einstein's own words), space is not an independent entity. It is a description of the relationships between massive entities. There is not literally a curved spacetime; the behavior and relationships of massive entities are affected by the presence of other massive entities. There is no background, just entities.

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This is not quite correct. According to GTR (and Einstein's own words), space is not an independent entity. It is a description of the relationships between massive entities. There is not literally a curved spacetime; the behavior and relationships of massive entities are affected by the presence of other massive entities. There is no background, just entities.

Thats kinda how I see it. The expanding universe thing just means that locally everything is getting farther apart, thats my understanding. The stuff I referred to earlier, though, those studies talk a lot about "dark matter" and "dark energy", dark matter as a kind of gravitational scaffolding that "tells matter how to move" as Alfred Centauri said about "spacetime" (hes probably 4.3 lightyears ahead of me on this stuff :D ), and dark energy as the stuff pulling the matter apart (away from other matter in the universe). I digress, the topic at hand is that infinity is a mathematical/cosmological concept of method, and is invalid when referring to real "stuff" in existence.

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There is no a priori reason that the universe cannot be infinite. Suppose the universe is finite. That would imply that there is an object with the greatest distance to the earth. There would be no object that is farther removed than that object. Why should that be the case? There isn't any logical contradiction in the hypothesis that there will be always objects farther removed than any finite distance we can think of.

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This is not quite correct. According to GTR (and Einstein's own words), space is not an independent entity. It is a description of the relationships between massive entities. There is not literally a curved spacetime; the behavior and relationships of massive entities are affected by the presence of other massive entities. There is no background, just entities.

I must disagree. According to GTR, gravitational waves, which carry energy-momentum, exist. While it's true that GTR is background free, this only means that there is no a priori geometry.

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There is no a priori reason that the universe cannot be infinite. Suppose the universe is finite. That would imply that there is an object with the greatest distance to the earth. There would be no object that is farther removed than that object. Why should that be the case? There isn't any logical contradiction in the hypothesis that there will be always objects farther removed than any finite distance we can think of.

In any so-called infinite universe, are any two physical objects separated by an "infinite" distance?

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There is no a priori reason that the universe cannot be infinite. Suppose the universe is finite. That would imply that there is an object with the greatest distance to the earth. There would be no object that is farther removed than that object. Why should that be the case? There isn't any logical contradiction in the hypothesis that there will be always objects farther removed than any finite distance we can think of.

We will assume here that a priori just means metaphysical principles, since Objectivism rejects the a priori/posteriori distinction.

What does it mean to be an infinite amount of distance away from something? It is tantamount to saying no distance, because infinity isn't any set of boundaries. To speak of distance and infinity together is to combine two things that cannot coexist. Two javelins thrown at light speed in polar opposite directions will always remain a distance from another, even if they somehow (This is rather impossible) passed every single entity that has already existed. You can test this rather easily. Go walk away from a friend of yours. Have him walk away at equal pace. At what point does the distance become infinite?

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What does it mean to be an infinite amount of distance away from something? It is tantamount to saying no distance, because infinity isn't any set of boundaries. To speak of distance and infinity together is to combine two things that cannot coexist.

Bingo. And I assert what TheEgoist just said should be accepted a priori. :D "Any finite distance we can think of", Tensorman, is still subsumed under the concept "universe", (everything that exists), which we deem finite.

j..

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First off, thanks for the interest and responses. I am not trying to open a can of worms, but determine if this individual is actually seeking to understand, or just looking for someone to adopt his point of view.

This has driven me back into the books to try to recollect what was so enrolling 20 years ago.

The points brought up here have are much in line with the anticipated responses, while The Egoist's (This is rather impossible) and Alfred Centauri's (under certain assumptions) have me wondering - I have been essentially arguing finite/actual distance - further apart/potential distance - infinite/concept of method; we seem to come back to the same point. The stumbling block is in the finite: Who/what decided this amount of matter and no more/less - who/what decided gravity/speed of light/etc: appearing to me to be a varient of who/what decided Law of Identity. While he is not an explicit theist, the influence of Christianity is obviously present. This was a major hurdle for myself, and at times it takes a great deal of focus to weed the years of indoctrination through upbringing from my own views to try and keep them consistant.

We have even hit validation vs. proof - which I have now a better grasp of before broaching this with him (to which I am thankful) yet have not been able to posit it in such a way as to generate an 'a-ha' moment. I see in him, the struggle I went thru moving from an implicit primacy of consciousness to an explicit primacy of existence, and would like to be an effective 'roadsign' to help point the way.

Once more, thanks again.

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In any so-called infinite universe, are any two physical objects separated by an "infinite" distance?

No. But that doesn't mean that there cannot be infinitely many physical objects. Take for example the set of integers, and define the distance between two integers as the absolute difference between those integers. For any two integers that distance is always finite. Nevertheless there are infinitely many integers.

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We will assume here that a priori just means metaphysical principles, since Objectivism rejects the a priori/posteriori distinction.

What does it mean to be an infinite amount of distance away from something?

Here is the misunderstanding: I didn't say that there could exist an infinite distance between two physical objects, I said that it was possible that there is no largest distance, i.e. that for any two objects O1 and O2 with distance D1 I always can find an object O3 with distance D2 to O1, with D2 > D1. That also implies that there is then no upper bound on the total number of objects. In other words, the universe could be infinitely large with infinitely many objects, while the distance between any two objects is always finite. "Infinite" is not some point far away, it means that there is no farthest point.

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What's the difference in distance between an infinitely large distance and an infinitely small distance?

I think I've made clear that infinite distances are not relevant for the question whether the universe is infinite, but mathematically this isn't difficult: if there are two points P1 and P2 with distance D, then we can say that D is infinitely small if any sphere with center P1 always contains P2, and that D is infinitely large if there is no sphere with center P1 that contains P2. In those cases D is not a real number.

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The stumbling block is in the finite: Who/what decided this amount of matter and no more/less - who/what decided gravity/speed of light/etc: appearing to me to be a varient of who/what decided Law of Identity.

Ayn Rand said it best "existence exists", or Aristotle if you like "A is A". These types of questions, as you said, show a primacy of consciousness metaphysics. While they are sometomes fun to ponder, any real answers are found in the special sciences. "Why does light travel at 186k miles p/s?" Thats not a question for philosophy to answer. Things are what they are, I know that you know this, but your friend seems not to. Give him a copy of OPAR.

j..

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To what particular writings of Aristotle do you refer?

Its not a direct quote, (as you know), but his work in metphysics got the philosophic ball rolling toward what we know as the law of identity. If it were a direct quote I would have cited a reference. Did you ask because youre genuinely interested, or as a feeble attempt to make me look like I dont know what Im talking about?

j..

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