Does infinity exist?

Then how do you define infinity?

Unlimited in some ways and limited in others is unlimited in quantity and limited in identity/category. One thing is sure: we cannot have a quantity which is both limited and unlimited, so if there are limits, they are not imposed on the quantity that is said to be infinite, but rather they are imposed on the identity of the uncountable things.

I can’t conceptualize it and you can’t either. In actuality, where in the universe do you suspect that it may be possible to draw an infinite line in one direction, but not in the other?

Then, at this moment, it is not infinite because there exists a place for more road. How can you propose having an infinite road when clearly we could make it longer? A road that is truly infinite would extend around and around the universe many many times until it occupied every planck cube in the universe, completely displacing all matter, and until it eventually connected with itself for lack of having anywhere else to go. To say that isn’t so is to say the road has a boundary which would make it not infinite.

Ok, now I forgot why I needed to know that lol

Yes it does matter because if there is a place for another apple, but no apple is there, then we have found a boundary and therefore the number of apples is not infinite.

Size must have a zero like temperature and speed or else it couldn’t exist. We can’t get infinitely colder, infinitely slower, infinitely smaller and if we could, then temperature, speed, size would have no significance/meaning.

I think so.

I don’t know… maybe.

Infinitely wide is ok because it extends in both directions, but infinitely tall would be a wall that extends around the universe until it connected with the other side of the earth.

Huh? Infinite doesn’t mean maximized or maximal.

Pretend you’re talking to a 5-year old kid who doesn’t know what infinity means. If you say “we have an axiom of infinity”, the kid will look at you stupid. If you say, “we can align the set with a subset of itself”, the kid will look at you stupid. If you say, “the infinite is the unbounded, unlimited, unending” then the kid will say “Ooooh!” You cannot do any of these acrobatics (axioms, bijections) until you make it clear what infinity means.

There is no way I could perform a bijection of a set with a subset without already understanding the set is unending. So I would need to know what infinity means before I could understand the definition.

I accept that planets revolve around the sun not because of authority, but because it’s the most sensible scenario.

The infinite is something that cannot be observed (much like god) and there is no evidence for (much like god), yet I am required to prove that it doesn’t exist? There is also no evidence of a teapot orbiting the earth, so do I have to prove that doesn’t exist too?

What’s the biggest number you can think of? Now make it bigger: square it, factorial, define new symbols to reduce the size and continue on and on until you run out of room on the forum to write that number down. Regardless what you devise, you will find a biggest number, but you won’t be able to do anything with it other than bask in its glory.

The issue isn’t whether the bijection is possible, but whether it defines infinity.

I can integrate an area over a height to yield a volume without using infinity. I can add my grocery bill without infinity. What do you need infinity for?

What’s the limit of 1/x where x → 23+10^10^10^10^10^10^10^10^10^10? Zero right? If it’s not zero, then how far am I off? No machine that could ever exist will be capable of discerning the difference, so from the perspective of practicality, we don’t need infinity.

Induction isn’t the same as deduction and if n exists, you cannot say with certainty that n+1 exists. However, if n+1 exists, you can say with certainty that n exists (deduction).

Yes I understand your point, but we still must have a priori understanding that the turing machine never ends. Once again, infinity must be understood before it can be defined with the turing machine.

Yes it does because there are no boundaries. If there are boundaries, then it’s not infinite.

If you claim there are infinite apples and I find a place with no apples, then you don’t have sufficient apples to go around in order to fill every place and therefore the quantity of apples is limited or else there would be apples in every place that apples could exist.

If there could be an apple here, but there is no apple here, then the only reason to explain that is insufficient apples.

If I would claim there are infinite apples available, then yes that would apply. Also with one apple. But to have infinite apples in an infinite universe would not necessarily guarantee any apples within reach.

Like if time is infinite, which it is since beginnings are part of the concept time, then even if you are born now, some of your actions will still have effects for an infinite duration, unless the universe collapses into a singularity which I think is fantasy.

So your deeds would (do) resound in the infinite future, but not in the also infinite past.

Of course it would be easy to negate infinity if you start out with the assumption of a finite universe.

You can just say “the universe is finite, thus it isn’t infinite, thus nothing in it is infinite”.
But who will think this makes sense? Only people who already agreed with you on faith.

You can’t prove an end to the universe, or to a straight line, so to insist it does have one (i.e isn’t infinite) is like being really ambitious without any means.

So basically, an infinitely large basket isn’t going to be filled even with an infinite amount of apples. Because there still is space for an infinite amount of pears.

The whole thing is boringly easily solved when you see that infinite is a predicate and not a proposition.

So “infinity” of itself just means either everything or nothing. But any meaningful statement with infinity in it still gives infinity as a limited part of the proposition, where quality x or y or z is required to make the proposition.

“Does infinity exist” must mean “is existence infinite?”

And if it is, then all things must somehow reach into infinity too. And they do, by their consequences in time.

AH

fuck I understand.

the whole idea of a variable implies infinity.

So the Arabs who came up with algebra (with the contributions of a guy called Al Jabr) and also with 0 destroyed the Euclidean and Parmenidean idea of numbers as elements of a world, and made them magical appearances defying apparent reality yet working very well with the brain.

But this defiance can be because whats defied is what wasn’t proven yet. Maybe they were like hold on, its taken pretty long now that we sought for the end-all, and we didn’t find it so lets just suppose it goes on forever. Then at least we can be free of this supposed end-all and appreciate what we really see.

In my understanding, both 0 and infinite are predicates, and for X=existence they give respectively false and true because otherwise the concepts are contradicted.

If the axiom is “something exists” then for 0 to be true there needs to be a thing that is withdrawn from another.
For infinity to be true there needs only be one thing, it just needs to be infinite. So 0 is a higher order operator than infinity.

Still, infinity is a higher order principle to 1.

2 and uncountability are the same by implication because to get from 1 to 2 you need an assumption, which is that things are separate and not unified, and if you do that there is certainly no way of demonstrating any limits to the number of things that can be listed. And infinity is a higher order function of uncountability.

Only after all this is fixed we get to 0.
Or while its not being fixed but then 0 is seen as the basic depth of the thing where it is actually the summit.

Infinity is the root of all hypothetical numbers, including 0. 1 is the only non hypothetical number because it is the only number which can contain all others.

???. Doesn’t parse at my end.

Infinity can’t be true or false. It’s not a thing that can be true or false. A set being infinite might be true or false. Precision is critical.

Doesn’t make sense to me.

Order of what? Haven’t seen order defined.

Nonsense.

More nonsense. I have one apple, I have two apples. I have no idea what you are talking about. Have you a reference so I can have some clue as to what domain of discourse you’re working in?

Doesn’t parse. Says nothing. Word salad.

After all what is fixed? What’s broken?

You often make sense. This post of yours does not make any sense.

What is a hypothetical number? What other kinds of numbers do you have in mind that aren’t hypothetical? The root? Like the root of a polynomial, or a square or cube root? You’re just throwing out random words. This is unlike your usual posts, which are generally connected with reality and sense.

Bullpucky.

Isn’t the collection of even numbers infinite? They’re clearly only a part of something larger. They’re not everything. They don’t include the odd numbers, for example.

I see you wrote several posts, not just one. But you seem to have decided to wake up this morning and post strings of word salad, devoid of meaning or sense. I don’t mean for that to be an attack. Only an observation. I’ve come to expect sensible posts from you. If you only posted nonsense I wouldn’t bother to mention it.

You might enjoy Hilbert’s hotel. Or then again, maybe this will only confuse the issue.

en.wikipedia.org/wiki/Hilbert%2 … rand_Hotel

No. Consider a variable x that ranges over the set {1, 2, 3}. Consider basic finite probability theory. The roll of a single six-sided die. You use variables to stand for things like “I roll a 3,” or “I roll and even number.” There is no implication of infinity.

No. What can you possibly mean by that?

Word salad. Makes no sense. I’m disturbed by the fact that I formerly thought you were making some level of sense in your posts, and now I wonder if I missed this strain of illogic. Can you put your morning flood of posts into context? It all seems … well, not good.

lol, yeah this is why you’re not a philosopher.
I managed to keep it extremely simple for you, go along in your little baby steps, doing a bit of theatrics, that was when you thought I was making sense.

I should take offence at your radical laziness but I know mathematicians hold this for some sort of virtue.
Ive been ahead of you constantly, drawn your proud definitions and drawings out of you by pretending I didn’t understand so well, telling you the difficulties along the way. This is all because I don’t think inside of language but just use language where it is constructive.

Now Ill leave you to your graceful temper. :wink:

No. The idiotic thing in your approach is the assumption that these issues have been satisfactorily figured out, even though in your discourse your examples all point to the opposite.

The only thing that was ever to learn here is Russells type theory which validates him as a philosopher, and elevates him above the ballroom of mathematicians.

I think set theory stands refuted at this juncture.

If philosophy is to be concerned in any case.
Which I think should gradually become an issue for mathematics.

When a philosopher takes a couple of steps running the mathematicians all stop walking, instead of trying to catch up. It is unfortunate.
in baby steps:

Infinity is something that is a condition.
That means it applies only to things that have already been defined.

Do you get this?

This is where you will have to put on your thinking cap.

I disagree here. Eternity can be taken to be implicit in the concept of time, given that this concept includes all beginnings and ends.
“Time began” is a problematic idea.
Eternity is an infinity of moments, the idea of an unfolding dimension made subjective, tied to a reference frame.

Absent reference frames there is not eternity but chaos.

Ah! This is where I really disagree.

First of all, “The” infinite is not the same as Infinity.

Infinity is a predicate to a given, it is not a starting point. If you presume it and ask if it exists, thats the wrong order.

You must observe things and then ask if they are infinite to ground it in reason.

The conclusion all along was very old, that if you’re committed to abstracting empirical data all the way, unlike the Greeks were, the ideas of infinity and 0 become available.

Sets are just ultra lazy abstractions without any class or style.
Russell at least had class and style, which is why he pricked through set theory in one gesture, and liked Wittgenstein, who is a fledgeling philosopher in how he overcame his Tractatus.

Serendipper for the win because he exposed the grammatical naiveté which causes all the various perspectives unawareness of being various.

:open_mouth:

:laughing: