Arguments Against Infinite Quantity

[Grames]

The universe is not infinite. If it were infinite, there would be no discrete areas within in it. If some set is infinite, you are no closer or further from the end at any point. 1 and 10 are the same, as are 1 and 100,000,000,000,000. This can exist on paper, but it cannot be actualized. There are distinct points in the universe. Otherwise, the phrase "You are here and I am over there." would be semantically and metaphysically null. There is no distinct over here and over there in an infinity.

There are no absolute, privileged frames of reference in an infinity. This is oddly congruent with physics since the idea of the aether was discarded and relativity took its place. And yet there are still distinct places.

The question of the thread is "can there be an infinite quantity of finite things?" Is it your argument that the existence of one finite thing entails that the universe is finite?

[Alfred Centauri]

Egoist, where is the center of the universe?

[brian0918]

Egoist, where is the center of the universe?

That question is only relevant to this discussion if TheEgoist must necessarily consider the question absurd. What is the evidence that such a question must be considered absurd?

If you are truly asking where the center of the universe is, I would first ask what the relevance of knowing the answer to the question is, and second ask why our lack of knowledge of the answer has any effect on reality.

Edited August 13, 2010 by brian0918

[dream_weaver]

Just when I thought I was going to find out where to locate my soon to be patented 'Cosmic Cartesian Coordinate Graph Paper', you have to go and blow a hole in the 'argument from omniscience' approach. Just as well. Still have not determined which way to orient the X-Axis.

[Alfred Centauri]

brian0918 (may I call you that?), the question is relevant to the TheEgoists rather confused statement "If some set is infinite, you are no closer or further from the end at any point" which is, evidently, part of this discussion is it not?

Where is the end of an infinite set? Where is the center of the universe?

Do you see any similarity in these questions?

[dream_weaver]

Does the universe even have a center?

[Mindy]

Does the universe even have a center?

Perhaps it has a constantly moving center. Do you conceive of the universe as static in size? I don't.

Mindy

[dream_weaver]

Size implies shape - but is there an 'outside' the universe?

[dream_weaver]

Another thought occurs here.

Every first level percept we integrate, most have no difficulty passing a check that it exists, we are conscious of it existing, and that it is something specific, finite in size, mass, color, etc.

Funny how when it comes to applying this knowledge to the universe, which is eloquently defined as everything that exists, how we choose to expand on this abstraction. The desire to apply infinite to a variety of attributes, that in several cases may be taken for granted.

A primacy of existence point of view confers that 'mater' (in a philosophic sense) has always existed. It is outside of the provence of time in that it is eternal. Many scientist do not appear to accept this premise evidenced by the preface of many of their 'hypothesis'; "When the universe began, . . .", or "How the universe started, . . ." Observation of life's cycles of beginning and ending has conceptual consciousness confering this observation to just about, if not everything.

Observation of the fact that everything that we see has a shape of some sort, a size of some denomination, etc, it appears not to be difficult to induce that because everything we encounter has a size, therefore the universe has a size.

As we expand our grasp of the universe and discover there are atoms, and that entities are comprised of them, we can calculate the quantity of atoms, and delimit the quantity for the things within our perceptual grasp to have a specific quantity.

If there is merit to the universe being "everything that exists", and beyond that to speak of "outside the universe" is meaningless - all attempts to assign the property of shape, size and quantity appear to be similar to the attempt to apply a delimited timeline to its duration.

Are we not more aptly stated, a part of the universe, rather than inside of something, suggesting that an outside be inferred? Are we going to pick and choose the attributes we wish to anthropomorphise in the case of having a beginning or end? Are we going to induce size and shape and extrapolate it to that which has no 'outside'? And then, inducing from the evidence that all that we have encountered to date are indeed finite in quantity as well as their other attributes, choose to disregard that induction in an attempt to apply infinite to attributes that do not appear to fit without contradictions?

My apologies if this is not stated in the clearest, most precise terms.

[Alfred Centauri]

Does the universe even have a center?

I think that's the right question and I think the answer is "no" as there is no context for the concept "center" w.r.t. the universe. Crucial to the concept "center" is the concept "boundary". But, there can be no coherent concept of a boundary for the universe since the universe is all that there is - there is no meaningful notion of "outside" (on the "other" side of some alleged boundary to) the universe.

[Alfred Centauri]

Are we not more aptly stated, a part of the universe, rather than inside of something, suggesting that an outside be inferred?

I think that is spot on. Well put.

[Alfred Centauri]

So the question is, is it necessarily false that there may be some injective map from the set of natural numbers into some set of physical objects, i.e. can we rule out such a hypothesis without your having to check Wikipedia to see if there is any evidence for or against? We will ask the question of sets of physical objects, such that no two elements in the set share any material parts, thus avoiding some annoying gadflies.

Have you established that the natural numbers form a set?

[Grames]

I don't see why there could not be an infinite number of physical objects. The argument that this is an arbitrary assertion doesn't hold, as its negation "every set of physical objects is finite" is equally arbitrary. It cannot be proved and the question whether there exists infinite or only finite numbers of objects will probably always remain unprovable, as there exist numbers that are so large that we in practice will never be able to determine the difference between such a number and infinity. So this remains an undecidable question, there could be an infinite number of physical objects, but we'll never be able to prove it, nor its negation.

You just explained what arbitrary means, unprovable. So it does hold.

[Mindy]

I don't understand some of this. Why can't the universe have a center? How it could be known is a different question. If by a boundary, you mean a limiting factor, I agree the universe has no boundary, but if by boundry you mean the outer extent of the universe in a given direction from oneself, then the universe, being finite, does have a boundary--(defined that way.)

I think the error in your argument about a universe of finite things is that how many such there are is open.

Mindy

[Grames]

Arguing that the universe if finite therefore it must have a boundary is circular because it simply assumes the conclusion, and it contradicts the earlier conclusion that the universe can have no boundary.

[Mindy]

Arguing that the universe if finite therefore it must have a boundary is circular because it simply assumes the conclusion, and it contradicts the earlier conclusion that the universe can have no boundary.

If that is a response to me, you'll have to say which meaning of "boundary" you are using.

Edit: I'm advised that the proper meaning of "boundary" is that it is the furthest extent of something, so I'm adopting that use.

So, my point is that the universe does have a boundary. That fact is inferred, not observed, of course. The foundation for that belief is that what exists must have identity, and infinite extent is an indefinite attribute.

Mindy

Edited August 14, 2010 by Mindy

[Grames]

If that is a response to me, you'll have to say which meaning of "boundary" you are using.

Mindy

The meaning of a concept is its referent. All contextually differing definitions of boundary must isolate the same referent. If different definitions isolate different referents then they are different concepts.

[Mindy]

The meaning of a concept is its referent. All contextually differing definitions of boundary must isolate the same referent. If different definitions isolate different referents then they are different concepts.

Is that a typing exercize?

Mindy

[Grames]

Is that a typing exercize?

Mindy

The meaning of a concept is its referent. All contextually differing definitions of boundary must isolate the same referent. If different definitions isolate different referents then they are different concepts.

Therefore, the problem with your discussion of boundary is not equivocation but contradiction. Your "meanings" are not consistent with each other by the standard of having the same referent.

[Jake]

1)  The concept of "quantity" precludes infinity.

I have seen no argument to this effect, merely the bald claim.  Even if you have some special notion of what "quantity" means as a term, we may simply look at the definition of "infinite quantity" I gave above.  Can there be an injective map from the set of natural numbers into some set of (disjoint) physical objects?  What is contained in this question which necessitates an answer, "no"?  It is only an answer to this question in which I'm interested, and not any special group jargon about the word "quantity".

Your injective map definition assumes the natural numbers have infinite quantity, so it is circular.

To say that the natural numbers are infinite is to say:

- there is no largest natural number, or

- the natural numbers are unbounded, or

- for any natural number n, n+1 is a natural number, or

- the series of natural numbers is open-ended.

It does not mean that there are an infinite number of natural numbers. In fact such a statement isn't even valid.

It is incorrect to smuggle in the idea of infinity as a number rather than a concept of method which denotes an open-ended iterative process or unbounded set.

The concept of "quantity" refers to the amount of something, which is determined by counting the units which comprise it. This is not a "special notion." The idea of "infinite quantity" is invalid because the Law of Identity demands that whatever the final count of units is, it is that count. If the counting process is open-ended, the counting is never complete: there is no final count; there is no quantity.

Infinity is not a number, or in the words of my high school math teacher: "Infinity isn't a place you can visit."

[Alfred Centauri]

Arguing that the universe if finite therefore it must have a boundary ...

is flawed. Finiteness doesn't entail a boundary. The surface area of a sphere is finite but that surface has no boundary and thus no center.

[Plasmatic]

is flawed. Finiteness doesn't entail a boundary. The surface area of a sphere is finite but that surface has no boundary and thus no center.

Absolutely rediculous. The place where one thing ends and another begins is a boundary."Surface" of what? You are divorcing the attribute from the entity and asking "where is the center".

[Alfred Centauri]

Absolutely rediculous. The place where one thing ends and another begins is a boundary."Surface" of what? You are divorcing the attribute from the entity and asking "where is the center".

(1) Where is the center of the surface of the Earth?

(2) If the universe has a boundary, what is it that is ending and what is it that's beginning?

[Plasmatic]

Arguing that the universe if finite therefore it must have a boundary is circular because it simply assumes the conclusion, and it contradicts the earlier conclusion that the universe can have no boundary.

First, the argument for boundedness and finitness are based on the axiom of identity.

Second, boundedness is implicit in finiteness.

What, then, is the meaning of the concept "man"? "Man" means a certain type of entity, a rational animal, including all the characteristics of this entity (anatomical, physiological, psychological, etc., as well as the relations of these characteristics to those of other entities)—all the characteristics already known, and all those ever to be discovered. Whatever is true of the entity, is meant by the concept.

It follows that there are no grounds on which to distinguish "analytic" from "synthetic" propositions. Whether one states that "A man is a rational animal," or that "A man has only two eyes"—in both cases, the predicated characteristics are true of man and are, therefore, included in the concept "man." The meaning of the first statement is: "A certain type of entity, including all its characteristics (among which are rationality and animality) is: a rational animal." The meaning of the second is: "A certain type of entity, including all its characteristics (among which is the possession of only two eyes) has: only two eyes." Each of these statements is an instance of the Law of Identity; each is a "tautology"; to deny either is to contradict the meaning of the concept "man," and thus to endorse a self-contradiction.

A similar type of analysis is applicable to every true statement. Every truth about a given existent(s) reduces, in basic pattern, to: "X is: one or more of the things which it is." The predicate in such a case states some characteristic(s) of the subject; but since it is a characteristic of the subject, the concept(s) designating the subject in fact includes the predicate from the outset. If one wishes to use the term "tautology" in this context, then all truths are "tautological." (And, by the same reasoning, all falsehoods are self-contradictions.)When making a statement about an existent, one has, ultimately, only two alternatives: "X (which means X, the existent, including all its characteristics) is what it is"—or: <ioe2_101> "X is not what it is." The choice between truth and falsehood is the choice between "tautology" (in the sense explained) and self-contradiction.

In the realm of propositions, there is only one basic epistemological distinction: truth vs. falsehood, and only one fundamental issue: By what method is truth discovered and validated?

Edited August 14, 2010 by Plasmatic

[Alfred Centauri]

First, the argument for boundedness and finitness are based on the axiom of identity.

Second, boundedness is implicit in finiteness.

I suspect from the above that you are failing to distinguish between the words "bounded" and "boundary". A thing can be both bounded and boundary-less. Consider a circle, an example of a closed curve. Where is the boundary? Where is the beginning of the curve? The end?

Finiteness does not entail a boundary.

Edited August 14, 2010 by Alfred Centauri