Does infinity exist?

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.

Serendipper, the math is beyond me, but my take is that you are not coming off well in this exchange. You seem to be insulting someone with a deeper knowledge of math than you. Doesn’t mean he or she is right, but your explanations seem less grounded to this layman than yours. Are you sure you are not jumping past your own concerns that you are out of your depth and presenting a ‘I am sure of what I am saying’ front?

If so, just admit it, cut losses and see what you two can learn together.

I’ve noticed the tendency on your part to go ad hom or insulting in relation to me, rather than focusing on the substance of the issues, and it’s actually good to watch it unfold in relation to someone else.

Seriously, why not cut this shit out?

Well, as a curiousity to wtf,

The probability of any finite string existing, according to convergence theory (which sets the bounds) is zero percent. When the infinite converges, the finite strings also converge, so infinitesimally small, that if convergence theory is true, they can’t exist.

And there we have it. How can I explain to you something that you cannot see? If you cannot differentiate between boundless quantity and boundless identity, then there is no possible way for me to show you your error. If you can’t tell the difference between what something is and how many there are, then how can I help you?

I’ve defined it over and over, but it’s like a color that you can’t see.

The category is the set of numbers between 1 and 0 of which there are infinitely many. There are no bounds to the number of numbers within the category of 0 to 1. A category is identity… the identification of what you’re talking about… a definition. If I say cat, I do not mean dog. The category is cat. There may be infinite cats, but there are not infinite categories. And just because there are not infinite categories does not mean there are limits to the number of cats. The number of cats is unbounded, but the category of cat is not; it’s bounded by identity.

I did. Over and over. It’s like explaining red to a blind man.

Math is not the universe and math doesn’t even represent it fully. Whether something applies within math is irrelevant. You could axiomize anything and then state that within that construct that certain truths apply, but it’s irrelevant to the universe. Appeals to math are like appeals to authority or any other logical fallacy.

So your assertion is the unbounded is bounded. That’s ridiculous. Make up your mind… is infinity bounded or is it not?

Not that I can see. You’re dodging and being dogmatic in asserting that the unbounded can be bounded and further demonstrating inability to see your error.

You started it with your cocky tone in saying “I’m afraid I must dash your hope” instead of “How about we define infinity as _____________ instead of boundless.”

You have taken the position that infinity exists and are dogmatically determined to defend that position even if it means asserting absurdities as truth, such as the bounded unbounded. Evidently this is your religion because it’s not rooted in reason because absurdities are not reasonable. You are the dogmatist who I referred to in my OP who I didn’t want to clutter the thread with pages and pages of dogmatic refusals to see reason which renders the thread useless.

Right, unbounded numbers of apples have the bound of being only apples and not oranges. Bounded by identity, but unbounded in quantity.

Cardinality is just a fancy word for quantity within a set. Your pretentiousness is showing. In your example, the “length” is the set and the “cardinality” is the quantity within the set. So the set of all numbers between 1 and 0 is infinite. The set of all numbers between 1 and 2 is infinite. The set of all numbers between x and y is infinite where x and y is anything you want. Once you define x and y, you define a set with infinite cardinality.

You’re ignoring points!

Per the rules:

2.2 Arguments should be made in good faith: no trolling. If a moderator sees a poster presenting an argument and dismissing any counterpoints without engaging them, or suspects someone of presenting arguments purely for the sake of inflaming debate or annoying other posters, a warning may be issued. viewtopic.php?f=1&t=175550

You are “annoying other posters” by refusing to define infinity clearly while dogmatically objecting to my definition. And this definition is the same as mine: “Mathematically, a set is infinite if it may be bijected to a proper subset of itself” because the only way anything can biject with a subset of itself is if it has no bounds (which I said before and you ignored), so you said the same thing and still claim my definition is wrong.

Tell me exactly and clearly what infinity is… in plain english without math jargon that obfuscates the definition.

You are “annoying other posters” by having an inability to see the difference in boundless quantity and boundless identity.

You are “annoying other posters” by asserting the boundless has a bound.

You are not in good faith seeking the truth, but imposing your dogma and it’s “annoying other posters”.

If you don’t know something, I’ll gladly help you until you understand, but when you come across as flattering yourself for being right when you can’t even see what I’m saying, then it’s annoying.

Now I’ve linked to a Yale Phd in Mathematics and former professor at Stanford who asserts infinity doesn’t exist and that should at least give you pause before you come storming on here “dashing my hopes” as if you’re the grand poobah of math… and even if you were, it still wouldn’t be justification to make authoritative statements about the universe.

Oh, so, now there are not unlimited numbers of numbers between 1 and 0. Make up your mind! You’re annoying! Is there a limit to the number of numbers between 1 and 0 or is there not?

This from someone who asserts the unbounded has a bound :laughing:

This from someone who asserts infinity is not unbounded and then provides definition which requires infinity to be unbounded. :laughing:

Axiom - a statement or proposition on which an abstractly defined structure is based. You stated 1,0 is the set and that’s the axiom upon which we work.

I took algebra II and geometry at the same time against the recommendations of the counselors and aced them both, then was sent to a special school for mathematically gifted students, then completed college calculus before I graduated high school and on the state’s dime. Admittedly, that was a long time ago and I’ve not kept up, but I’m not an idiot and these constant referrals to “anyone who has taken _____ should know _____” are annoying.

Then you better inform all the dictionaries on earth that they are incorrectly defining infinity lest the world get confused. I’m not appealing to the dictionary, but simply saying you could be famous for correcting them. Let me know what they say.

Wikipedia says: Infinity is a concept describing something without any bound

Oxford says: Limitless or endless in space, extent, or size

Dictionary.com says: Unbounded or unlimited; boundless; endless

Webster says: extending indefinitely : ENDLESS

Wtf says: the bounded unbounded

I say: wtf?

Yeah, kinda like the category of categories you made up.

Baloney! You said:

[i]I ask you to consider as a mathematical example the closed unit interval [0,1], which is defined as the set of all real numbers between 0 and 1, inclusive.

We know that this set contains infinitely many real numbers; in fact, an uncountable infinity of them. Yet this set is bounded.[/i]

So you’re asserting bounded unbounded; the limited unlimited, the finite infinite. You said it.

No one knows what you’re talking about, including you.

Now you’re lying.

A category is identity… what something is and a set to which it belongs. A unit interval is a category.

Openminded you are not. Dictionaries are wrong, accomplished mathematicians are wrong, my logic is wrong, but absurdities are right because you said so. I see why you named yourself wtf :laughing:

That’s an obfuscating way of stating unbounded.

So you’re saying you have no idea, but your idea is __________.

If “the math is beyond” you, then how can you tell? In order to judge an authority you have to be one.

How about Yale educated and former Stanford professor of mathematics, NJ Wildberger? Is he over his head too? Heck, his whole thesis is “being grounded in reality” (limited by the size of the universe) rather than off in fantasy land like his many of his colleagues. How can I be less grounded when the premise of my argument is to be grounded (finite) rather than hinged in obscurity (infinite)?

Well I’m sure the bounded unbounded can’t exist because it’s a direct contradiction. Either infinity is bounded or it is not.

We can’t say there are infinite apples and then claim there is a bound to the number of apples because there are not infinite oranges. Either the number of apples is without limit or it’s not. We can’t have limited unlimited. If you are not siding with me, then that is what you are asserting.

The way to show me I am wrong is to show me; not gang-up.

I have no problem admitting I am wrong, but first you must show me a how something can be bounded and unbounded in quantity.

That is an ad hom. The subject is infinity and the definition of and the existence of; not whether or not I ad hom.

This is why I said in the OP “Questions are encouraged, but dogma is not.” If someone asserts and clings to absurdities, which are inherently unreasonable and therefore dogmatic, then they shouldn’t be surprised if ad homs follow because the subject then transitions from discussing the differences between categories and quantities to someone’s inability to see the difference.

Why indeed.

Show me a quantity that is both unbounded and bounded and the shit will be cut out. Or admit that it’s not possible and the shit will be cut out. Continue this dogmatism and the shit goes on.

What else can I say? I can’t concede the bounded boundless exists until someone can show me how.

Until then, the definition put forth by every dictionary on earth stands, which is infinity is unbounded, limitless, endless.

If you disagree, then simply submit a CLEAR definition in PLAIN ENGLISH without obfuscating words reliant upon axioms of boundlessness.

Convey to me exactly what you think infinity is.

It’s easy! Simply say “infinite = _______________”

Otherwise concede that you accept my definition. If one can do neither, then one’s purpose here is to annoy, right?

If one can’t accept my definition and one can’t replace my definition and yet one keeps using the word while ignoring repeated pleadings to define the word they’re using, then their only purpose is to be annoying. What else could it be? :confusion-shrug:

You’re not fooling anyone but yourself. If that.

To be clear, what you are doing is pretend to be mentally challenged when that suits you so that you can ignore the logic that you are challenged with. It’s not very impressive except in how much time and effort of yourself and others you are wasting with it.

You’ve been refuted about sixty times in this thread alone, but like I ambiguous, this only seems to embolden you. Lol.

Thanks! Of course I’m not fooling anyone since I’m speaking sense. Those fooling folks are speaking nonsense that’s imperceptible to the ones being fooled.

Well at least I can type with decent grammar when insulting people :laughing:

What happened to “feigning ignorance” that you used to accuse everyone of? Did you wear it out?

All you have to do is show me how I’m wrong and that will take the wind from my sails, if that’s what you’re after. Otherwise, claiming I’ve been refuted when I clearly haven’t only flatters me that you’re groping for any insult you can find in lieu of counterpoint debate because what’s important is that I’m wrong, right?

Infinity must be defended at all costs :bow-blue: Infinity

Karpel, did you forget you said this?

I think shaming is good. I wish the community would shame not content but inability to carry out coherent dialogue with integrity. I mean, it does happen. A number of people have reacted to Prismatic who is a classice example of someone so sure they are right, they cannot acknowledge the slightest mistake and commit many of the sins I mentioned above. AT least three people have bluntly commented on his shortcomings here, after trying through many, many posts to have a rational dialogue with him. I think that kind of shaming is good. In fact I would like to see more shaming and less banning. Not that it has worked in Prismatic’s case, nor am I optimistic with some of the people mentioned earlier in this thread. viewtopic.php?f=7&t=193363&p=2693911&hilit=shaming#p2693911

Now you’re admonishing me for shaming him for “inability to carry out coherent dialogue with integrity”.

You’ve also given me plenty of grief over Alan Watts’ attacks on displays of emotions, so when I display emotions, you give me more flack. I just can’t win with you man. I think you just have it out for me and I don’t know why. I’ve always liked you.