Does infinity exist?

That’s like saying we could have something near-infinite.

I attacked this in the OP.

Infinities cannot have beginnings or ends because those are boundaries and we said in the beginning that infinity has no boundaries. We cannot divide infinity in half and say infinity is bounded by this finite location and extends to infinity in that direction; it’s nonsense and breaks our definition of infinity being boundless. Zero is not a boundary, but is just an arbitrary starting point on an infinite number line extending in both directions and we could just as easily started at -2,-1,0,1,2,3,etc or 5,6,7,8,etc. A line that is not infinite is a segment because all lines are defined to be infinite within the construct of mathematics; therefore a line with a beginning (such as a timeline) is not an example of infinity.

You: Here is a road that starts here and goes to infinity.
Me: We could add more road, so it’s not infinite.
You: What do you mean?
Me: Where you’re standing… we could add more road and since we could add more, then it’s not infinite, but bounded by the location where you’re standing. If we could add more road, then the amount of road we have is not infinite.

I don’t know what MEST is.

Yes it does because if there is a place that we could add another apple, then the amount of apples is not infinite. If there are infinite apples, then apples exist in every place there is to exist.

We can divide down to quarks, but to divide a quark pair will create another quark pair from the energy used to divide them. There is no such thing as smaller than a quark because smaller than a quark is smaller than the thing that defines size.

Thanks! I’ve been debating infinity for years and finally decided to consolidate information into one place to avoid rehashing the same old arguments eternally.

Well, I’ve defined infinity as boundless and asserted that what is without boundaries is not a thing neither in reality nor imagination. Just like i (sqrt -1), infinity may have productive uses, but likely it’s indicative of some underlying mechanism that we don’t yet understand.

I’m not sure this is true because we routinely use PI, but never all infinite digits of it.

Right, the concept of “knight” is only relative to the game of chess and the concept of truth is only relative to the duality of the universe.

No, the empty set does not exist unless it contains potential, but then it wouldn’t be empty. I’m saying neither zero nor infinity exists and they are equally absurd.

How is infinity useful? I googled it and here is what I came up with:

[i]We Don’t Need the Infinite
Let’s face it: Despite their seductive allure, we have no direct observational evidence for either the infinitely big or the infinitely small. We speak of infinite volumes with infinitely many planets, but our observable universe contains only about 10^80 objects (mostly photons). If space is a true continuum, then to describe even something as simple as the distance between two points requires an infinite amount of information, specified by a number with infinitely many decimal places. In practice, we physicists have never managed to measure anything to more than about seventeen decimal places. Yet real numbers, with their infinitely many decimals, have infested almost every nook and cranny of physics, from the strengths of electromagnetic fields to the wave functions of quantum mechanics. We describe even a single bit of quantum information (qubit) using two real numbers involving infinitely many decimals.

Not only do we lack evidence for the infinite but we don’t need the infinite to do physics. Our best computer simulations, accurately describing everything from the formation of galaxies to tomorrow’s weather to the masses of elementary particles, use only finite computer resources by treating everything as finite. So if we can do without infinity to figure out what happens next, surely nature can, too—in a way that’s more deep and elegant than the hacks we use for our computer simulations.

Our challenge as physicists is to discover this elegant way and the infinity-free equations describing it—the true laws of physics. To start this search in earnest, we need to question infinity. I’m betting that we also need to let go of it.[/i] blogs.discovermagazine.com/crux/ … 8soKiXwaHs

cs.umd.edu/~gasarch/BLOGPAP … xioms1.pdf

We must have axioms in order to have a foundation for any construct.

To assume infinities is to concede discontinuities exist in nature as if an asymptotic curve could exist in nature and that y=1/x wouldn’t connect at x=0. The truth is far more likely that the Cartesian coordinates are better represented on a sphere rather than infinite plane. Math reflects reality to some degree less than 100%.

More on that here: phys.org/news/2013-09-mathemati … world.html

[i]Derek Abbott, Professor of Electrical and Electronics Engineering at The University of Adelaide in Australia, has written a perspective piece to be published in the Proceedings of the IEEE in which he argues that mathematical Platonism is an inaccurate view of reality. Instead, he argues for the opposing viewpoint, the non-Platonist notion that mathematics is a product of the human imagination that we tailor to describe reality.

This argument is not new. In fact, Abbott estimates (through his own experiences, in an admittedly non-scientific survey) that while 80% of mathematicians lean toward a Platonist view, engineers by and large are non-Platonist. Physicists tend to be “closeted non-Platonists,” he says, meaning they often appear Platonist in public. But when pressed in private, he says he can “often extract a non-Platonist confession.”

So if mathematicians, engineers, and physicists can all manage to perform their work despite differences in opinion on this philosophical subject, why does the true nature of mathematics in its relation to the physical world really matter?

The reason, Abbott says, is that because when you recognize that math is just a mental construct—just an approximation of reality that has its frailties and limitations and that will break down at some point because perfect mathematical forms do not exist in the physical universe—then you can see how ineffective math is.

And that is Abbott’s main point (and most controversial one): that mathematics is not exceptionally good at describing reality, and definitely not the “miracle” that some scientists have marveled at. Einstein, a mathematical non-Platonist, was one scientist who marveled at the power of mathematics. He asked, “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”

In 1959, the physicist and mathematician Eugene Wigner described this problem as “the unreasonable effectiveness of mathematics.” In response, Abbott’s paper is called “The Reasonable Ineffectiveness of Mathematics.” Both viewpoints are based on the non-Platonist idea that math is a human invention. But whereas Wigner and Einstein might be considered mathematical optimists who noticed all the ways that mathematics closely describes reality, Abbott pessimistically points out that these mathematical models almost always fall short.

“I argue that there are many more cases where math is ineffective (non-compact) than when it is effective (compact). Math only has the illusion of being effective when we focus on the successful examples. But our successful examples perhaps only apply to a tiny portion of all the possible questions we could ask about the universe.”[/i]

What do you mean by “be”? How can something be if it has no boundaries?

What do you mean by “prove”? Do you mean arbitrarily define some axioms and then show how a conclusion fits?

Alright, well, my axiom is things are defined by boundaries.

Infinity has no boundary, so by my axiom, it doesn’t exist.

We cannot experience time if there is nothing defining time. We cannot experience time if there is nothing to relate to. Time has absolutely no definition absence of relation. All time means is a relation of one thing to another thing. Time is not fundamental and there is no such thing as objective time. We don’t even need to go before the big bang to see this is true, but merely AT the big bang will suffice since at that theoretical point of “pointness” there was no delineation of things in order to have one thing relating to another thing, but only unity. In fact, it’s still that way since every emission and reception of a photon is a single timeless event meaning that every point in spacetime is still joined as one ( as evidenced by the lack of time and distance between them).

Lack of consensus doesn’t mean anything, but you seem to like consensus, so I figured you’d appreciate the fact that the 4 physicists agree that time is not fundamental. I’m not appealing to the consensus and it wouldn’t bother me if all 4 were in unanimous disagreement with me; it’s beside the point and why I said Btw (by the way).

The infinite is not anything that can exist, so the fact that the universe appears infinite means infinite regression of self-inspection (ie the thing doing the looking is the thing being looked at). There is no other explanation. It’s not an argument from ignorance as if because I can’t think of another explanation, then this one will do. No, it’s that there cannot be another explanation because the actuality of infinity cannot exist. If the universe is infinite, then it is an illusion produced by the universe beholding itself.

You’re bragging that? :smiley: All it means is you didn’t understand it then and 20 years has not helped. Once you get your head around the fact that time is relational and only relational, then everything should fall into place.

No I’m not. I’m working with my own ideas. Sure it may have been their idea first, but I stole it and now it’s mine. I don’t hold their ideas because they said it, but because the ideas made sense to me.

I said “If it helps to see a phd in physics and philosophy say the same thing, then watch the video.” If it wouldn’t help, then don’t. I’m not appealing to them, but trying to help you. I tell ya what… don’t watch and instead pretend you already know :wink:

No, we take what works and not because the consensus agrees, but because the idea is sensible. The amount of people in agreement means nothing.

The only authority I appeal to is reason and I’m not sure what you’re on about.

But you just said there is no consensus. If there is no consensus, how do you know many physicists let go of infinity? Doesn’t “many” = consensus?

Does consensus mean more than half? Have more than half the physicists let go of infinity? In that case, there is consensus that the universe is finite.

Does consensus mean 100%? In that case, they’re still clinging to infinity because they aren’t unanimous.

The fact remains that the scientific community (not limited to just physicists) does not like the idea of god, so infinity is an easy way around it and I couldn’t agree that scientists are approaching the problem objectively so long as theists exist in any meaningful numbers, therefore they will always be biased with an affinity towards infinity until there is reason not to be.

Percentages are irrelevant.

You’re skeptical that something without boundaries cannot be considered a thing? Then what could define a thing absent boundaries? Why would you be skeptical without already harboring some alternative view? You must have some conceptualization of a borderless thing in order to assert its plausible existence. IOW, you wouldn’t assert a squared circle without having some idea of how it might exist.

I’ve made them my own… and not because they said it, but because the ideas are sensible. If you don’t want to believe me, then we’ll put you down as disagreement for lack of authority: I don’t have authority to speak, so whatever I said can be disregarded.

So you admit your lack of perception? I agree, so we have consensus that you can’t see :wink:

I dismiss them as authorities yet accept the ideas that seem sensible to me.

Yes, well, be that as it may, I’m not convinced that the audience would come to the same conclusion. If I am reading a series of comments and one guy says the other hasn’t done a good job, it doesn’t sway me a bit; only information sways me.

this is going nowhere, we need less rhetoric and more technical analysis people.

Can you start over, but with in mind what these guys have to say? Then it will be more substantial and involuntary deceit can’t be as big a part. I mean misreadings and stuff. A n n o y I n g .
viewtopic.php?f=4&t=185099&p=2470116

Oh yeah and lets follow definitional logic, so first define what there are supposed to be either infinitely or finitely many of.

SO what Arminius opened up is the idea that whereas we can perceive and thus conceive only finite sets and ranges, this doesn’t mean we have proven the absence of infinity.

If it is about language and grammar then no, infinity doesn’t exist.
Because everything that is defined is finite. Because de-finition.

So if you go on to define infinity as a thing and calculate with it, thats faux because you’re working with a limited thing that is different from something else, so its not actually infinite. Its just a vector with the presumption that it won’t run into a limit. But I think Serendipper is prob right that this sort of infinity is actually a circle.
Even because as the range progresses away from the definer its steps become less significant and thats already a curving.

Also we need to compare infinity to something, its in-finite, it stands opposed to the finite range of some form or something.
It is not a comprehensible idea on its own.

Infinite to what?

(I know that sounds strange but you gotta bend your thought, because thats in the end what its all about. Can the thought of infinity exist together with the though of existence )

According to Spinozas logic here, a substance can only be conceived as infinite, the argument materializes in proving proposition VIII.

[list]"DEFINITIONS.

I. By that which is self—caused, I mean that of which the essence involves existence, or that of which the nature is only conceivable as existent.

II. A thing is called finite after its kind, when it can be limited by another thing of the same nature; for instance, a body is called finite because we always conceive another greater body. So, also, a thought is limited by another thought, but a body is not limited by thought, nor a thought by body.

III. By substance, I mean that which is in itself, and is conceived through itself: in other words, that of which a conception can be formed independently of any other conception.

IV. By attribute, I mean that which the intellect perceives as constituting the essence of substance.

V. By mode, I mean the modifications[1] of substance, or that which exists in, and is conceived through, something other than itself.

[1] “Affectiones”

VI. By God, I mean a being absolutely infinite—that is, a substance consisting in infinite attributes, of which each expresses eternal and infinite essentiality.

Explanation—I say absolutely infinite, not infinite after its kind: for, of a thing infinite only after its kind, infinite attributes may be denied; but that which is absolutely infinite, contains in its essence whatever expresses reality, and involves no negation.

VII. That thing is called free, which exists solely by the necessity of its own nature, and of which the action is determined by itself alone. On the other hand, that thing is necessary, or rather constrained, which is determined by something external to itself to a fixed and definite method of existence or action.

VIII. By eternity, I mean existence itself, in so far as it is conceived necessarily to follow solely from the definition of that which is eternal.

Explanation—Existence of this kind is conceived as an eternal truth, like the essence of a thing, and, therefore, cannot be explained by means of continuance or time, though continuance may be conceived without a beginning or end.

AXIOMS.

I. Everything which exists, exists either in itself or in something else.

II. That which cannot be conceived through anything else must be conceived through itself.

III. From a given definite cause an effect necessarily follows; and, on the other hand, if no definite cause be granted, it is impossible that an effect can follow.

IV. The knowledge of an effect depends on and involves the knowledge of a cause.

V. Things which have nothing in common cannot be understood, the one by means of the other; the conception of one does not involve the conception of the other.

VI. A true idea must correspond with its ideate or object.

VII. If a thing can be conceived as non—existing, its essence does not involve existence.

PROPOSITIONS.

PROP. I. Substance is by nature prior to its modifications.

Proof.—This is clear from Deff. iii. and v.

PROP. II. Two substances, whose attributes are different, have nothing in common.

Proof.—Also evident from Def. iii. For each must exist in itself, and be conceived through itself; in other words, the conception of one does not imply the conception of the other.

PROP. III. Things which have nothing in common cannot be one the cause of the other.

Proof.—If they have nothing in common, it follows that one cannot be apprehended by means of the other (Ax. v.), and, therefore, one cannot be the cause of the other (Ax. iv.). Q.E.D.

PROP. IV. Two or more distinct things are distinguished one from the other, either by the difference of the attributes of the substances, or by the difference of their modifications.

Proof.—Everything which exists, exists either in itself or in something else (Ax. i.),—that is (by Deff. iii. and v.), nothing is granted in addition to the understanding, except substance and its modifications. Nothing is, therefore, given besides the understanding, by which several things may be distinguished one from the other, except the substances, or, in other words (see Ax. iv.), their attributes and modifications. Q.E.D.

PROP. V. There cannot exist in the universe two or more substances having the same nature or attribute.

Proof.—If several distinct substances be granted, they must be distinguished one from the other, either by the difference of their attributes, or by the difference of their modifications (Prop. iv.). If only by the difference of their attributes, it will be granted that there cannot be more than one with an identical attribute. If by the difference of their modifications—as substance is naturally prior to its modifications (Prop. i.),—it follows that setting the modifications aside, and considering substance in itself, that is truly, (Deff. iii. and vi.), there cannot be conceived one substance different from another,—that is (by Prop. iv.), there cannot be granted several substances, but one substance only. Q.E.D.

PROP. VI. One substance cannot be produced by another substance.

Proof.—It is impossible that there should be in the universe two substances with an identical attribute, i.e. which have anything common to them both (Prop. ii.), and, therefore (Prop. iii.), one cannot be the cause of the other, neither can one be produced by the other. Q.E.D.

Corollary.—Hence it follows that a substance cannot be produced by anything external to itself. For in the universe nothing is granted, save substances and their modifications (as appears from Ax. i. and Deff. iii. and v.). Now (by the last Prop.) substance cannot be produced by another substance, therefore it cannot be produced by anything external to itself. Q.E.D. This is shown still more readily by the absurdity of the contradictory. For, if substance be produced by an external cause, the knowledge of it would depend on the knowledge of its cause (Ax. iv.), and (by Def. iii.) it would itself not be substance.

PROP. VII. Existence belongs to the nature of substances.

Proof.—Substance cannot be produced by anything external (Corollary, Prop vi.), it must, therefore, be its own cause—that is, its essence necessarily involves existence, or existence belongs to its nature.

PROP. VIII. Every substance is necessarily infinite.

Proof.—There can only be one substance with an identical attribute, and existence follows from its nature (Prop. vii.); its nature, therefore, involves existence, either as finite or infinite. It does not exist as finite, for (by Def. ii.) it would then be limited by something else of the same kind, which would also necessarily exist (Prop. vii.); and there would be two substances with an identical attribute, which is absurd (Prop. v.). It therefore exists as infinite. Q.E.D. " — Ethica

I don’t know what can be gained with that thread because the only one who really asserted anything was James and he was wrong. We know from experimentation that we can’t split quark pairs without creating new quarks from the energy put into splitting them, so there is no way to cut down to a smaller size and certainly no way to see it since we can’t use electrons to look at things smaller than electrons.

Loss of significance seems like a good theory to me.

If we stick to the definition of the infinite as unbounded, then the opposite is the bounded.

What’s the definition of existence?

Existence is an awareness of a being of everything apparent and conceivable.

Since it is realized through living, that existence is only a partial appearance of that everything conceivable, and even that is only a part of a totality of all, that becomes manifest, that totality is an unreachable absolute.

It is through the door of perception , that absolute manifests from birth to death.

It is that absolute that we as humans have to traverse into incarnation and re-incarnation. Every existence is another manifestation of that Absolute.

I’ve already given you examples of bounded infinite sets. The closed unit interval [0,1] is infinite and bounded. It also happens to contain its upper and lower limit points, 0 and 1. Even its cardinality is bounded (a point you are confused about in your earlier reply to me), since its cardinality is that of the reals, which is strictly smaller than the cardinality of the powerset of the reals by Cantor’s theorem.

Why do you insist on using a definition that’s demonstrably wrong? You can’t fall back on,“Oh it’s in the dictionary,” since the dictionary is not authoritative on technical matters. You enjoy making up your own definitions, but that convinces no one other than you.

S - If you dont know what existence is you have no business discussing infinity. First things first. But you knew that. So…

I guess I’ll take your refusal to engage this short argument by Spinoza on the grounds that you dont understand the term “existence” as admissal of trolling.

That was easy.

Which leaves us no one to argue against the existence of infinity. I think this closes the case, which had indeed been closed since Spinoza. He is great.

Seems like you’re saying existence is relationship because in order to be aware, you must relate somehow. James said if something has no affect, then it doesn’t exist and I think relationship is saying the same thing. Objective existence is therefore not existence as if there could exist a sole thing in absence of everything else.

Something can only exist in relation to something else and if it has no relation to anything else, then it can’t be said to exist lest anything be said to exist, including this pink elephant sitting next to me that I can’t detect.

No you haven’t. What you have accomplished is demonstrating your inability to differentiate between boundaries of categories and boundaries within categories. If I say there are infinite apples, I am not placing boundaries on the number of apples, but that doesn’t mean there are also infinite oranges and the fact there are not infinite oranges doesn’t mean I’ve placed boundaries on apples. Due to some suspected cognitive impairment you’re suffering from, you’re having difficulty making this completely obvious differentiation and are running about patting yourself on the back for being totally blind. :laughing:

Clearly you’re suggesting there are unlimited numbers of numbers between 1 and 0, right? Right? Is anybody home, McFly? :violence-stickwhack:

Because that’s what infinity means… unlimited, unbounded numbers of things. The only bound that exists is the category of identity… which is defined by 1 and 0 per your axiomization.

So you’ve defined a category and stated that within that category there are an unbounded number of things.

I would feel sorry for you if you weren’t so damn arrogant.

I can use whatever definition I want and it’s total within my discretion to define terms in order to communicate. The important thing is I have defined my terms so people know what I’m talking about, unlike you who can’t seem to muster a definition after repeated pleadings for you to do so, yet you continue to use a word that you can’t define.

I have my definition of existence articulated at the top of the OP because “first things first and I knew that”.

The question remains if you can read, recall what you’ve read, or have any clue how to define existence. Those are the unknowns.

The whole proof seems like shit to me, which I’m certainly ready to shred to bits, but I first need to know how he defines existence. If I use my definition, then the proof quickly falls apart, but I don’t know how he defines it, so I can’t do anything until I get that information… which seems to be conveniently missing in light of the fact that he defined everything else under the sun except the most relevant bit.

Are you warming up for a Dunning-Kruger interview or do you honestly believe that?

I certainly stipulate that I have no idea what that means. If it’s something you made up, can you please define it? And if it’s a standard subject in philosophy, can you supply a link?

Now when you say categories, of course I think of category theory, a modern foundational approach to large parts of mathematics that’s an alternative to traditional set theory. Interestingly John Baez, a mathematical physicists and the original Internet math blogger, has applied n-categories, meaning categories of categories etc., to the study of loop quantum gravity in theoretical physics. So it’s quite an interesting area, and one most amateur math fans haven’t heard of yet.

I do not think this is what you mean, though. So why not just say what you’re talking about? It certainly makes no sense to me in the context of the issue at hand.

I say again: In math, the closed unit interval on the real line is a bounded set that contains its upper and lower bound.

Furthermore, one could respond that yes, [0,1] is bounded as a metric space; but its cardinality is infinite, hence (by your argument) not bounded. However you are wrong even here. The cardinality of [0,1] is that of the reals, namely (2^{\aleph_0}). That cardinality is bounded below by (\aleph_0), and bounded above by (2^{2^{\aleph_0}}). So the unit interval is bounded in metric AND bounded in cardinality. It’s bounded every way you can think of.

I hope that you, or at least fairminded readers, can see that I’m making substantive responses to your points. I’d appreciate substantive replies to mine.

I perfectly well agree. If I have infinitely many apples I may well have only finitely many oranges.

Can you explain what that has to do with the boundedness of both the length and cardinality of the unit interval?

I can’t speak to your upbringing or possible neurochemical imbalances.

I do address @Carleas and the other moderators of this site. If this type of discourse is ok then the site’s not for me.

Moderators please advise.

Unlimited? No. There are exactly as many as there are real numbers. That’s much much smaller than the number of possible subsets of the reals, which is less than the number of subsets of subsets of the reals, and so forth.

This is Cantor’s theorem, which says that the powerset of any set has strictly larger cardinality than the set. So that in fact any transfinite cardinal you can name is bounded by the cardinality of its powerset.

Insults in lieu of substantive responses. Emoticons depicting physical violence. Lash out, little man.

So what do you think about Cantor’s theorem? Do you disagree with it? If so why? I’m openminded. I don’t care what position you hold if you can intelligently defend it. Say something intelligent.

  • I have certainly given no axiomitization of anything. The unit interval is a perfectly clear example to anyone who’s takenn algebra II in high school.

  • You have simply repeated your incorrect claim, that infinity means unbounded. That’s clearly false. Repeating a claim doesn’t constitute an argument in support of that claim. It only reveals you haven’t got one.

  • And the “category of identity?” Whats that mean? Something else you just made up?

Well no. I have noted that a standard mathematical object, familiar to everyone who learned the basics of analytic geometry in high school, is infinite; yet is both bounded in length, and also bounded in cardinality.

It’s funny that someone who simply knows what they’re talking about appears arrogant to you.

Of course. But you don’t define your terms. What’s a category and how does it relate to the unit interval?

If anyone here knows what Serendipper is talking about, please tell me. I’m openminded, if there’s something I’m not getting, just explain it to me.

Perhaps you missed it a few days ago when I wrote:

As you can see I already defined mathematical infinity. This particular definition dates back to Dedekind in the 1880’s. It’s been the standard one ever since.