The circumference of the topographical position of any country, is infinite. — SethRy

Eventually, zooming in, you reach atom level. So the circumference is not infinite.

You haven't addressed the arguments of those mathematicians who advance modern infinity theory, you've just declared them all to be 'wrong'. — Isaac

I have addressed them - sorry for repeating myself- but If infinity were a number it would be a number X such that it is greater than all other numbers. But X+1>X so infinity is not a number. If you can disprove this argument please tell me how - I've been posting it for months and no-one seems to have a valid counter argument.

If you look at set theory, all it does is axiomatically declare that an infinite set exists - it does not prove anything at all and yet its easy to show infinity does not exist - see above - or see any of the numerous contradictions that are thrown up with infinity.

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Well reasoned counter argument :(

infinity were a number it would be a number X such that it is greater than all other numbers. But X+1>X so infinity is not a number. — Devans99

I wasn't asking for a repeat of your assertion, I was asking you to address the counter arguments of mathematicians. What do your opposition have to say about this, what counter arguments have you read, and where are they wrong?

you can disprove this argument please tell me how - I've been posting it for months and no-one seems to have a valid counter argument. — Devans99

Of course I can't disprove that argument. I don't know the first thing about maths (beyond what I've read in 'popular maths' type books. My interest is in how you are supporting your argument. What do you think is going through the minds of the world's top mathematicians, the absolute geniuses at the top of their game, when they think about infinity and reach a conclusion which even some random internet poster can see is wrong? What exactly do you imagine they are all thinking at that moment? "I hope no one notices that this is all wrong"? "I don't know how I blagged my way to the top of the maths department because the truth is I don't even understand this basic explanation"?

I'm fascinated by how your mind might work through this, how it rejects the possibility that there is a very good argument for the conventional view which you either have not come across or do not understand, in favour of what seems to be the completely untenable position that you are right and every one else is wrong.

I wasn't asking for a repeat of your assertion, I was asking you to address the counter arguments of mathematicians — Isaac

But I know of no objections to my argument. Hence my reason for posting this argument is to gather any such objections. Philosophers tend to be more open minded and have less invested in infinity than mathematicians, hence this audience.

I have a 1st in maths so I do understand the maths.

It is the case that there is a huge flaw in the root of set theory called 'the axiom of infinity'. As I mentioned to you before, there was a big debate at the turn of the century as to whether infinity should be included in maths. Cantor won the debate and its been taught in schools ever since.

So I think there is groupthink going on here. There are only a few people around like me who are actually speaking out on the obvious flaws of infinity. I also think mathematicians are working at too high a level of abstraction - the flaws are obvious in that, for example, infinity is completely incompatible with basic arithmetic - but most mathematicians cannot see the wood for the trees - they are too immersed in higher level abstractions to see the basic problems.

I know of no objections to my argument. — Devans99

there was a big debate at the turn of the century as to whether infinity should be included in maths. Cantor won the debate — Devans99

For a start, these two statements contradict one another. You clearly do know of objections to your argument. Presumably Cantor, and those who follow him, haven't just written "some infinities are bigger than others" on the back of an envelope and that's what's guided mathematics for the last hundred years. I presume there is an argument, and quite a long one I'll bet, as to why Cantor thought some infinities could/should be larger than others. So why don't you lay out his argument, step by step and show where he went wrong.

I have a 1st in maths so I do understand the maths. — Devans99

I have a first in psychology, but that doesn't alone give me authority to dismiss any arguments in that field without analysis.

Lay out the arguments Cantor, and others, have made, and show exactly where they went wrong. That way people here (probably not me) can actually get involved in the debate.

For a start, these two statements contradict one another. You clearly do know of objections to your argument. Presumably Cantor, and those who follow him, haven't just written "some infinities are bigger than others" on the back of an envelope and that's what's guided mathematics for the last hundred years. — Isaac

That is what they have done. The axiom of infinity could fit on the back of an envelope and just baldly states that infinity exists. They have no logical justification for including Actual Infinity in maths.

Lay out the arguments Cantor, and others, have made, and show exactly where they went wrong. That way people here (probably not me) can actually get involved in the debate. — Isaac

For example the bijection procedure gives spurious results (like naturals and rationals being the same size). Or all the paradoxes listed here:

https://en.wikipedia.org/wiki/List_of_paradoxes#Infinity_and_infinitesimals

A paradox is usually the sign that you are working with something contradictory. The common thread through all these paradoxes is infinity - it is the contradictory thing that leads to those paradoxes.

"Infinite" is irrational, and "assuming" is illogical.

Or all the paradoxes listed here: — Devans99

But none of the paradoxes you've referenced here remain problematic. In fact most of them seem to be resolved by ZF or ZFC theory which, I understand, is the basis of most mathematics. Probably why it's so popular.

Open a thread disputing the resolution of these paradoxes by ZFC and I'm sure you'll get more interest from the many keen mathematiciand here than you'll get by just declaring it to be wrong.

How for example has Galileo's paradox been resolved?

'Galileo's paradox is a demonstration of one of the surprising properties of infinite sets. In his final scientific work, Two New Sciences, Galileo Galilei made apparently contradictory statements about the positive integers. First, some numbers are squares, while others are not; therefore, all the numbers, including both squares and non-squares, must be more numerous than just the squares. And yet, for every square there is exactly one positive number that is its square root, and for every number there is exactly one square; hence, there cannot be more of one than of the other. This is an early use, though not the first, of the idea of one-to-one correspondence in the context of infinite sets.

Galileo concluded that the ideas of less, equal, and greater apply to (what we would now call) finite sets, but not to infinite sets. In the nineteenth century Cantor found a framework in which this restriction is not necessary; it is possible to define comparisons amongst infinite sets in a meaningful way (by which definition the two sets, integers and squares, have "the same size"), and that by this definition some infinite sets are strictly larger than others.'

https://en.wikipedia.org/wiki/Galileo%27s_paradox

It remains the case that bijection claims that the number of non-squares is the same as the number of squares. But in every finite interval (of reasonable size) we examine, the number of non-squares is greater than the number of squares. The paradox still stands. The resolution to the paradox is not Cantor's bijection procedure but Galileo's earlier observation that infinite sets cannot be compared. An infinite set is not fully defined (that is what the ... indicates), meaning it is not defined period and it is not permissible to perform operations on it (like comparing sizes).

How for example has Galileo's paradox been resolved? — Devans99

It says in Wikipedia that...

"Galileo concluded that the ideas of less, equal, and greater apply to (what we would now call) finite sets, but not to infinite sets. In the nineteenth century Cantor found a framework in which this restriction is not necessary; it is possible to define comparisons amongst infinite sets in a meaningful way (by which definition the two sets, integers and squares, have "the same size"), and that by this definition some infinite sets are strictly larger than others."

If all you're going to say is" The resolution to the paradox is not Cantor's bijection procedure ", which is exactly what everyone else seems to think the resolution is, then we're back to square one again with you just making bare assertions.

But bijection claims that these are of the same size:

{ 1, 4, 9, 16, ... }
{ 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, ... }

When the 2nd is clearly larger than the first. So how exactly is that a sound resolution to the paradox?

Well, it seems pretty obvious to me that the second set is not obviously larger. They both have little ellipses, indicating that they go on forever.

But for any finite interval, we find more members in the second set than the first set. So we inductively understand that the second set is 'larger' that the first set.

We certainly can't conclude that they are equal (as set theory does) as they are not fully defined as indicated by the ellipses.

So we inductively understand that the second set is 'larger' that the first set — Devans99

But we evidently don't. We come full circle to the root cause of the problem, you presume that the world must be exactly how it seems to you to be. You inductively understand the second set is 'larger', other people do not because they think differently to you. You cannot simply presume that what is inductively evident to you is deductively necessary.

Your mistake (and Cantor's) is thinking that 'larger' could make sense in terms of infinite sets.

Something infinite has no fixed size so it cannot be compared to anything else. An infinite set has no size (cardinality) is the only valid conclusion and thus they cannot be compared.

What Cantor did (in his madness) was to invent numbers to represent the sizes of infinite sets... they are pure inventions... derived from nothing... there is no math behind them... its all a pure figment of Cantor's imagination.

As I said, we're back to a series of bare assertions without any support.

Something infinite has no fixed size — Devans99

An assertion.

An infinite set has no size (cardinality) is the only valid conclusion — Devans99

An assertion.

This is a waste of my time if we're just going to go back to assertion.

You would claim that the set of natural numbers has a fixed size?

If you cannot count something, how can it have a size?

You would claim that the set of natural numbers has a fixed size? — Devans99

I wouldn't claim anything on the subject. I would defer to my epistemic betters. The point I'm making here is a psychological one. That which is evident to you is not so to others, that which you do not understand may seem incoherent but your incredulity alone is not evidence of it being so.

Fundamentally the infinite is unmeasurable. If it is unmeasurable, it has no size. If it has no size it cannot be compared with anything else.

1. Assume space is infinite
2. It is expanding
3. Implying it is not infinite (if it was size X, it is now size X+1, meaning X was not infinite) — Devans99

What do you think of this:
1. Assume N+ is infinite.
2. If defined recursivly (with Start n_1=1 and n_x=n_(x-1) + 1), N is expanding.
3. Implying N is not infinite (if N was size X, it is now X+1, meaning X was not infinite.

Doesn't this show the flaw of trying to understand infinite as specific value instead of using infinite as concept that is not a specific value.

Afterall in math infinite is not understood as value thats why inf +1 = inf.
Aren't you making it yourself a bit to easy by ignoring this view completley and simply stating inf is a specific value like any value in N. Basically equivicating properties of the category with the properties of it's elements?

I agree that infinity is not a number. I also believe there is a numerical property, the size of the universe, and this takes a number as a value (a concept is not a number).

I don't believe infinity is a logical concept and reality is logical so again the size of the universe is not infinite.

Afterall in math infinite is not understood as value thats why inf +1 = inf. — CaZaNOx

Maths claims that infinity is a number (at least set theory does).

Devans99
1.1k
↪Frank Apisa
Well reasoned counter argument :( — Devans99

Devans...exactly what would happen if everyone here deferred to you in this...and agreed that there is no way the universe can be infinite?

What would result? What would be the logical inferences?

Would that, as you suggest, imply that it was created?

And if it was created...what would you be suggesting about that CREATION?

Creating something infinite is impossible (you would never finish creating it). Creating something finite is possible.

So the universe being finite does not imply creation but does allow creation.

Maybe I didn't make myself clear. Lemme try again:

Devans...exactly what would happen if everyone here deferred to you in this...and agreed that there is no way the universe can be infinite?

What would result? What would be the logical inferences?

Are you entirely familiar with process of matching rational fractions between zero and one with real numbers in the same range usually called diagonalization? Are you entirely familiar with the significance of power sets, and that the power set of X is always larger than the set of X itself? These just two elementary and introductory ideas on the way to thinking correctly about transfinite sets.

I have a 1st in maths so I am aware of set theory. The basic fact that set theory ignores is that the infinite is unmeasurable so cannot have a size/cardinality. Cantor just made up magic numbers for the cardinality of infinite sets - there is no math or logic behind it - it is just a fantasy of a deranged mind (Cantor thought that God was talking to him).

It would add weight to the general arguments against infinity if we could establish the universe has a finite size.

The fact that its impossible to create something infinite (you would never finish) is in itself suggestive the universe is finite (the universe is a creation - there is a start of time).

↪Frank Apisa
It would add weight to the general arguments against infinity if we could establish the universe has a finite size.

The fact that its impossible to create something infinite (you would never finish) is in itself suggestive the universe is finite (the universe is a creation - there is a start of time). — Devans99

In other words you are saying that if you are correct in this argument of yours (and you may well be correct)...then it is possible the universe was created!

Why not just say that?

Of course it is possible the universe was "created."

It is also possible the universe was not "created."

Hell...everyone would be agreeing with you.

Are you sure that is where it will lead?

And if so...are you satisfied with that?

This thread is just about if the universe is infinite in size or not. Whether the universe was created would be a separate thread.

I have a 1st in maths so I am aware of set theory. The basic fact that set theory ignores is that the infinite is unmeasurable so cannot have a size/cardinality. Cantor just made up magic numbers for the cardinality of infinite sets - there is no math or logic behind it - it is just a fantasy of a deranged mind (Cantor thought that God was talking to him). — Devans99

You do not make the distinction that everyone else has learned to make, that between transfinite and infinite. You use "infinite" indiscriminately, and thus without understanding. Further, to apply it indiscriminately in maths is simply to engender error. To use "infinite" outside of maths, away from any region of rigorous definition, is poetic or misleadingly metaphoric at best and in all cases with respect to any sort of concrete understanding simply non-sense.

So you need to do the hard work of understanding what the word "infinite" exactly means. Either that, or offer an equally rigorous definition of your own. But to date, it seems unlikely that either you can or would be willing to do either.

And your claims about set theory identify you as the one with the deranged mind. Or plain ignorant. There's a name for ignorance (which btw we all are) that persists and insists on itself in the face of knowledge, and it is nothing as ennobling or tragic as derangement: it's just plain stupidity.