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Infinite Entities As "concepts"

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manavmehta
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Here is another passage from OPAR that has me stymied....

Chapter 1: Reality > Idealism and Materialism as the Rejection of Basic Axioms, Page 31:

"Is God infinite? '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."

Firstly, how does an entity lose its identity just by being infinite in the extent of its measurements?

Secondly, if the universe is finite, then where does it end? And what is the fabric of reality where the universe ends? (this thought has been numbing my mind for a long time...).

My two questions, above, are related. I canot digest the thought of the universe being a finite entity. And, since I can think of an entity that has identity (the Universe) that I think is infinite, I find it difficult to digest the first argument that an entity loses its identity just because it is infinite!

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Secondly, if the universe is finite, then where does it end? And what is the fabric of reality where the universe ends? (this thought has been numbing my mind for a long time...).

I canot digest the thought of the universe being a finite entity.

I recently discussed this with a friend of mine at U of IL. This was his insight, so I can't take credit.

To grasp the universe being BOTH finite and boundless is tricky. The universe cannot have boundaries since the concept "boundaries" is used to show where one thing stops and another starts.

A great analogy to this is eyesight. Look out your window right now and determine the boundaries of you eyesight. You can't. The reason that you cannot see definite boundaries of your eyesight is because you cannot SEE where you cannot see. Make sense?

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Why do you suppose it ends? If the universe is all that exists, how could it have an end?

I am not saying that the Universe ends. I am just following Peikoff's argument to what I think is its logical end. He states that every entity is finite and this applies to the Universe as well. My question is precisely the same as yours - how can the Universe be finite when it is all that exists?

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I recently discussed this with a friend of mine at U of IL. This was his insight, so I can't take credit.

To grasp the universe being BOTH finite and boundless is tricky. The universe cannot have boundaries since the concept "boundaries" is used to show where one thing stops and another starts.

A great analogy to this is eyesight. Look out your window right now and determine the boundaries of you eyesight. You can't. The reason that you cannot see definite boundaries of your eyesight is because you cannot SEE where you cannot see. Make sense?

So, in other words, the Universe must in logic be finite, but we consider it to be infinite because no living human has ever seen where it ends. Have I correctly understood what you are saying?

Edited by softwareNerd
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I am not saying that the Universe ends. I am just following Peikoff's argument to what I think is its logical end. He states that every entity is finite and this applies to the Universe as well. My question is precisely the same as yours - how can the Universe be finite when it is all that exists?

Actually, my question was rhetorical. What I'd like to ask you is how your last question follows. Why do you think that if the Universe is finite it couldn't be all that exists? I'm just not getting the logic of that.

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Actually, my question was rhetorical. What I'd like to ask you is how your last question follows. Why do you think that if the Universe is finite it couldn't be all that exists? I'm just not getting the logic of that.

I don't know if you and I are using the word 'finite' to mean the same thing. I mean an entity that is limited in its physical dimensions. And in this respect, it is hard to think of the universe as finite.

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I don't know if you and I are using the word 'finite' to mean the same thing. I mean an entity that is limited in its physical dimensions. And in this respect, it is hard to think of the universe as finite.

But I think that's why we shouldn't think of the Universe as an entity in that sense. An "entity," as Aristotle pointed out, is (partially) defined by it's boundaries. The universe is the collection of everything. But, "everything," as such, cannot have boundaries in that primary sense because there is nothing else for it to share a boundary with (since there isn't anything else).

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But I think that's why we shouldn't think of the Universe as an entity in that sense.  An "entity," as Aristotle pointed out, is (partially) defined by it's boundaries. The universe is the collection of everything. But, "everything," as such, cannot have boundaries in that primary sense because there is nothing else for it to share a boundary with (since there isn't anything else).

And this is precisely why I am confused by the passage of OPAR which I quoted. To repeat the key sentence again, "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."

Dr. Peikoff seems to be suggesting that the universe is a finite entity.

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And this is precisely why I am confused by the passage of OPAR which I quoted. To repeat the key sentence again, "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."

Dr. Peikoff seems to be suggesting that the universe is a finite entity.

I'm probably making this explanation harder than it needs to be, but here goes:

In the passage you cite, I take Dr. Peikoff's use of "this" to refer the fact that any _existent_ is finite since every individual entity that constitutes the universe is finite. The universe is simply the sum of entities A+B+C -- and since A is finite, B is finite, C is finite -- the sum is also finite.

His use of "this" doesn't imply that the universe is a unique entity unto itself, with its own special set of attributes. There are these chairs, these planets, these electrons, etc....but there is not an entity _in addition to_ all these particulars, called 'the Universe,' that stands apart from them.

The universe is an existent but not an entity -- the universe should be thought of merely as the sum of all physical entities. So the sense in which the universe is finite differs from the sense in which any entity that comprises the universe is finite. As a placeholder for naming the collection of every thing that exists, the word 'universe' refers to a sum that is finite in the general sense of being "not infinite," whereas any particular entity is finite in the more particular sense of being limited in size, shape, any other relevant measurement.

Maybe we should just stop using the word 'universe' since it seems to raise so many confusions?!

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...

As a placeholder for naming the collection of every thing that exists, the word 'universe' refers to a sum that is finite in the general sense of being "not infinite," whereas any particular entity is finite in the more particular sense of being limited in size, shape, any other relevant measurement. 

...

In what sense is the Universe a finite (alright, I won't call it an entity), if not in the sense otherwise used for physical entities (the extent of their dimensions)?

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manavmehta:

In OPAR, page 31, Leonard Peikoff says "'Infinite' does not mean large; it means larger than ANY specific quantity, i.e., of NO specific quantity.".

Maybe in common usage. But in mathematics, Aleph-null (the smallest infinite cardinal number) has a definite meaning. It is the cardinality of the set of natural numbers.

By treating "ANY specific quantity" first as equivalent to "finite quantity" and then as "any quantity (including infinity)", Peikoff is begging the question.

You asked "Secondly, if the universe is finite, then where does it end?".

The universe is probably infinite, but it could be finite. In either case, it is unbounded.

If it is finite, it could be unbounded by being curved back on itself.

Let S1 = a circle (a one-dimensional "Sphere" in a two-dimensional Euclidean space).

Let S2 = a sphere (a two-dimensional "Sphere" in a three-dimensional space).

Let S3 = a hyper-sphere (a three-dimensional "Sphere" in a four-dimensional space).

The universe could have the topology of: S1*S1*S1, or S1*S2, or S3.

Or it could have other topologies which I would rather not try to describe here.

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This is irrelevant, there is no need to delve into topology--the set of existents in the universe is finite, the space surrounding this set is unbounded.

Understand that entities of infinite quality or quantity can't exist, and that "space" is not an entity, not an existent.

Also, keep in mind that people may mean one of two very different things when they say "universe." Some mean it as only a sum of all existents, others mean it as a sum of all existents as well as "space."

When they use the second definition, they necessarily contradict themselves when they make pronouncements on the "size" of the universe, because this second definition now includes entities as well as non-entities (space). You can't talk about the size or extent of a non-entity, and space, or nothingness, does not qualify as an entity.

When I use the word "universe," I use the former, and in this sense I can say the universe is bounded, but space isn't. So it makes no sense to talk about the topology of space--space isn't an entity.

To address the title of this thread, "infinite entities" is a contradiction, but the concept of infinity is perfectly valid, but keep in mind that not all concepts are entities.

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So, in other words, the Universe must in logic be finite, but we consider it to be infinite because no living human has ever seen where it ends. Have I correctly understood what you are saying?

It's not that the edge has never been seen; it's that there is no edge. It is pointless to talk of the the universe (or, in other words, "EVERYTHING") as having an edge or boundary because that concept is meant to separate two entities and there is only one universe.

I might not be sure what you mean by "finite" and "infinite". I use the term "boundless" in regards to the universe because I thought the term infinite has something to do with TIME.

The very definition of "the universe" implies that it is finite. For example, if you could counted/grabbed/whatever EVERYTHING there was, you would have an exact amount of stuff. That finite amount of stuff is the universe.

I think a lot of confusion comes from the way in which scientists and philosophers use the term 'universe'. Such as "the universe is expanding".

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"I use the term "boundless" in regards to the universe because I thought the term infinite has something to do with TIME." [Dentist85]

I'm not clear what you mean. Do you now think that the term 'infiniite' pertains only to time?

"You can't talk about the size or extent of a non-entity, and space, or nothingness, does not qualify as an entity." [Felipe]

Can we talk about the size of a space?

"[...] there is no need to delve into topology--the set of existents in the universe is finite, the space surrounding this set is unbounded."

Sets , finiteness, space, and boundedness are explicated by mathematics. I don't see why one would want to reject more rigor in explicating assertions as to the finitutde of the universe and the unboundedness of space.

Edited by softwareNerd
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(I added to my post while you were just posting.)

"[...] it makes no sense to talk about the size of "nothing," "non-existence," "blankness," "absence," etc."

What about talking about a particular area (space) that has nothing in it?

Edited by LauricAcid
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I read your posts there. I'm still curious whether you believe it is meaningful to talk about the size of an area of space, or even whether it is meaningful to talk about an area of space, since I don't presume to know what your answer is, even given your remarks in that other thread.

By the way, I'm accepting, for sake of discussion, your definition of 'space' as emptiness, which is not how the terms is used in most mathematics.

Edited by LauricAcid
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It is meaningful to talk about the size of an area of space, but only in a certain way.

Speaking the words "size of an area of space" implies a reference to something of that particular size of area in space. In other words, it is meaningful to talk about "the size of space" only with reference to existents that can fit into that space. To talk about space as apart from entities makes no sense. In effect, when you say "this amount of empty space," you are parenthetically pointing to an existent or existents that fit into that amount of space. Do you understand now?

In mathematics, lets talk about an empty set, the null set, OK? What is the size of the null set? In math they say "the size of the null set is infinite," in other words not subject to measurement. In this way mathematics uses the same definition I'm using here. Emptiness is not measurable without reference to existents that could fit in emptiness.

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"In math they say "the size of the null set is infinite," in other words not subject to measurements. In this way mathematics uses the same definition I'm using here." [Felipe]

You are flat out incorrect that set theory or mathematics states the size of the empty set as infinite. You could not be MORE incorrect about that, since set theory and mathematics state the cardinality of the empty set as being 0. In set theory and mathematics the empty set is very much NOT infinite. By the very definition of infinite, the empty set is not infiinite since it is equinumerous with a natural number.

"[...] in other words not subject to measurement. In this way mathematics uses the same definition I'm using here. [emphasis original]

No, since the empty set is not an infinite set and since the cardinality of the empty set is not an infinite cardinal, you are very much NOT in accord with mathematics in this regard.

Edited by LauricAcid
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You're right, I was reaching far back to when I took abstract math (six years ago), and I'm not a mathematician. Nevertheless, even if its cardinal number is in an element of the natural numbers, 0 is the lack of measurement, it is emptiness, nothing. Having a cardinal number that is an element in the natural numbers does guarantee "finiteness" in mathematics, but this doesn't correlate with the fact that zero is not a measurement. So OK, space is not the same as "null set" in mathematics. But I think the labeling of the null set as finite is a convention, and I wonder if any proofs rest on empty sets being finite.

Do you not see anything weird about labeling an empty set finite? If finite means measurable, what is the measure of an empty set, defining "measure" as the size of something?

Perhaps defining finiteness as having a cardinal number within the naturals is the problem here. It might be an arbitrary convention to include 0 as a cardinal number.

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'measure' is another technical term in mathematics. It's not usually used to talk about the size of sets in the way you are. Nevertheless, in informal terms, set theory does give a size to the empty set. The size of the empty set is 0. In more formal terms, the cardinality of the empty set is 0.

More fundamentally, though, you conflate the empty set with nothing. The empty set is something. It is the set having no members.

Edited by LauricAcid
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Getting back to space (and thank you for your answer), do believe it is meaningful to speak of points in space (or in a space). If so, what is your understanding of a point? If not, then do you consider the mathematics of real and complex numbers to be gibberish?

Edited by LauricAcid
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