That's reassuring.

Limits, in mathematics, are calculations - tasks - that are infinite; they involve infinite steps.

You asserted that any task with infinite steps is impossible:

It is the impossibility of an actual infinity that makes an infinite task impossible — Bartricks

Limits show that your claim, again, is wrong.

A line segment is made up of countably infinite number of points. That's the way the real numbers work. — Wittgenstein

Actually they don't. You are very wrong. But that's OK, carry on. :scream:

Question begging. Look it up. It's what you're doing.

Tasks involving infinite steps are, indeed, impossible. That doesn't mean tasks are impossible. It means tasks involving infinite steps are.

True, that.

I meant the real number line but the set of real numbers is uncountably infinite so l think l did mess up there. You can clear things up . :smile:
I hope it is correct now.

And limits involve infinite steps... 1 + 1/2 + 1/3 + 1/4...

So, it's impossible. Says you.

Jesus, you won't get far if you admit mistakes. You are supposed to dig in and insist that everyone else is wrong.

That's obviously question begging. You can't have actual infinities, so time is 'not' a dimension.

The same applies to space. You don't solve one problem by showing how it arises for other things.

Because we can't have actual infinities of anything, we need to rethink time and space - we 'must' be thinking about them in the wrong way. I am focussing here on time. Bringing space in - given that it raises many of the same problems - is unhelpful.

Time - time - is not a stuff, not a dimension. Why? Because thinking of it that way means it would instantiate actual infinities. That's sufficient to establish that it is not a stuff, not a dimension. But additionally, there would be no intrinsic difference between future, past and present (yet clearly these are radically different). — Bartricks

Ok. Let's study this problem together.

Your claim: Time can't be infinite because of infinite regress.

Your reason: If time is infinite than we have an infinite past which raises the question "how did we reach this point in time?" Infinite regress.

Is this your argument?

(This will be funny...)

(This will be funny...) — Banno

:smile:

Your claim: Time can't be infinite because of infinite regress. — TheMadFool

No, that's not my claim. Look, I laid the arguments out.

Why is an 'infinite regress' a problem? Because.....you can't have actual infinities.

So, the claim is that you can't have actual infinities.

That's why infinite tasks are impossible. They're impossible because they would involve an actual infinity of something, namely tasks. Thus, as there can't be actual infinities, infinite tasks are impossible.

You seem hell bent on focussing on the wrong thing. So, it is not the 'taskiness' of infinite tasks that makes them impossible, but their infinite nature. And it is not the 'regress' of an 'infinite regress' that is the problem, but the 'infinite' bit. Why? Because - wait for it - you can't have actual infinities of anything.

Your reason: If time is infinite than we have an infinite past which raises the question "how did we reach this point in time?" Infinite regress. — TheMadFool

Again, that's not anything I've said.

An event - P - that is in the past is going to get more and more and more past, yes? Potentially infinitely, yes?

That, in itself, is not a problem. Potential infinities aren't actual infinities. So the fact that past events become ever more infinite - and will go on doing so forever - isn't, in itself, the problem.

Here's the problem. If time is a dimension, then in order to be able to accommodate the above, it would need to extend for an actual infinity. And nothing can be like that. So it isn't a stuff.

So, again, events in the past are becoming more and more and more past, potentially for infinity. But for that to be possible, 'actual' past - the time gloop these events are floating about in - would need to extend infinitely. And that's impossible.

Learn to distinguish between actual and potential infinities.

Take rage. Some people are enraging. And the more you interact with some people, the angrier they make you. Is there any upper limit to how much anger one can feel? No. Anger can just go on getting more and more intense. There is no limit - it represents, then, a potential infinity.

Counting is like this. You can keep counting - 1,2,3 - on and on and on, potentially forever. There is no biggest number. Tell you what, try it - go and sit in the corner and start counting and tell me when you get to the biggest number possible, then report back.

For a living, I assume? — Bartricks

Nuh. That 'd be too hard. Cooks have to work long hours at odd times. Not for me.

you can't have actual infinities. — Bartricks

Because of...

Infinite tasks or the correct terminology being supertasks.

As you already know, super tasks, to be effective paradoxes and thus become problematic, are usually introduced with or within (a) limit(s) and are about infinitesimals which eventually spiral into infinity. For instance Zeno's paradoxes are about how a line is divisible into infinitesimals which lead to an infinity of points that must be traversed or considered.

The only way time as infinite is paradoxical is because of the supertask involved in reaching the present from an infinite past.

I meant the real number line but the set of real numbers is uncountably infinite so l think l did mess up there. You can clear things up . :smile:
I hope it is correct now. — Wittgenstein

Any open line segment is in one-to-one correspondence with the entire real line, thus the points on it are uncountable.

Again, you change the topic.

Reiterating, you said:

It is the impossibility of an actual infinity that makes an infinite task impossible!! — Bartricks

SO, here is an infinite task: (1+½+⅓+...). The harmonic series. It diverges to infinity.

An infinite task, done.

More fun might be a convergent series - say 1-½+⅓-¼+... which adds to ln 2.

An infinity of tasks, done.

How are you not in error here?

Do you really think Bart is talking about supertasks? I still think he is talking about simple sequences.

We will never, ever, be able to empirically prove spacetime is continuous, but we might be able to empirically prove it is discrete. — Devans99

cool. I agree a circle for instance doesn't exist in nature. Its a philosophical concept. There are things that are very close to being circles but nothing actually fits the definition described in a geometry text book.

That's my principle of engagement unless l get called out on my BS and the BS smells really bad and is clear as the day. Sometimes I just say
Go ahead punk ,make my day
Then blow off all the steam and bury everything into the ground.

We can actually, with help of computer software then print it out. Dud dahh !!

Do you really think Bart is talking about supertasks? I still think he is talking about simple sequences. — Banno

His claim is that an actual infinity is impossible. One way to make sense of that would be the problem of completing supertasks. That's all.

Absolute time would prove there has to be a God I think. I believe in absolute space but see no necessity to believe in absolute time

See David Braine's book

SO, here is an infinite task: (1+½+⅓+...). The harmonic series. It diverges to infinity.

An infinite task, done. — Banno

"..." doesn't constitute doing it. And saying "done" doesn't necessarily mean that it is done. Clearly, "..." symbolizes what is not done, not what has been done. The meaning of the ellipsis symbol is "unfinished". So your claim of"'done" is false.

Your fingers aren't what you think they are - if they were what you think they are, that is, objects extended in space, then they would have to pass through an actual infinity of postions in order to move. So they're not objects extended in space. — Bartricks

Please explain what my fingers are if they are not 'objects extended in space'...

Time is not stuff - not a substance - for the reasons outlined, namely that if it were a stuff there would be no intrinsic difference between future, present and past and because if it was a stuff it would have to extend infinitely — Bartricks

That's not true, under the moving spotlight theory of time, 'now' is a cursor that moves down a line (or around a circle maybe), so time can be a substance and we can still differentiate between past, present and future.

I mean, try and imagine a portion of space that isn't divisible - it's impossible. — Bartricks

To divide something, you have to insert a piece of matter in-between the two parts. If space is made up of some sort of discrete mesh/grid, then it would be impossible to divide a mesh/grid node into two - the particle of matter exactly occupies one node of the mesh/grid at any time.

How many natural numbers are there? Infinite yes? Is that a problem? No. Why? Because it doesn't lead to an infinite task. — TheMadFool

There are an unlimited number of natural numbers - they go on forever in our minds - which is different from infinity - no matter how many times you add 1, you never get to a number called infinity. Only in our minds is it possible for something to 'go on forever' - if this occurred in reality, it would be akin to magic.

How many points are there on a line? Infinite yes? Is that a problem? Yes. Why? As Zeno showed Achilles can't catch up with tortoise. An infinite task.

A point has length 0, say the line segment is length 1, then the number of points on it is 1/0=UNDEFINED. It is not infinite or unbounded, it is just UNDEFINED. It's not surprising considering a point is defined to have length 0 - so cannot exist - something with all dimensions set to zero clearly does not exist - so the question can be rephrased as 'how many non-existent things can you fit on a line segment' - an answer of UNDEFINED is exactly what you'd expect.

This tells us that any ‘point-like’ particle that exists in reality must in fact have a non-zero extension in space. So any real life line segment made up of real life points must have a finite number of points on it.

I see no such problems in infinite space. What other alternative do we have if space is not infinite? Finite space, right? And the next question would be what lies beyond space? In fact infinite regress seems to be in favor of space being infinite rather than finite. — TheMadFool

The BB suggests that space maybe finite - space has been expanding at a finite rate for a finite time since the BB - so that suggests finite space (finite spacetime too). What lies beyond is pure nothing - there is no space and no time beyond the boundaries so nothing can exist.

Given that time is just a spatial dimension we have limited access to, there should be no problem in imagining time too to be infinite. — TheMadFool

But nothing can exist forever in time, so it must have a start. See for example the argument I gave in this OP:

https://thephilosophyforum.com/discussion/6218/the-universe-cannot-have-existed-forever/p1

Time - time - is not a stuff, not a dimension. Why? Because thinking of it that way means it would instantiate actual infinities. That's sufficient to establish that it is not a stuff, not a dimension. — Bartricks

If time was finite in extent and discrete, then it would be a dimension without any actual infinities. Same applies for space.

Limits, in mathematics, are calculations - tasks - that are infinite; they involve infinite steps. — Banno

Limits involve imagining an infinite number of steps which is distinct from actually performing infinite steps - actual infinity is unconstructable. See for example Thompson's Lamp paradox for the sort of nonsense results we get when performing the limit procedure out to actual infinity.

Imagine the dates of the years before Christ, they go:

{ ..., 5BC, 4BC, 3BC, 2BC, 1BC, 0AD }

If time is infinite, how long does this sequence extend out to the left? Well it must extend out to encompass every number. But that's plainly an impossibility - at each point in the past (10BC, 100BC, a million BC, a trillion BC) you are 0% of the way to iteration of all the numbers (because any finite number divided by infinity is zero) - so no progress can ever made towards counting 'all the numbers'.

A believe in infinite past time is therefore akin to a belief it is possible to count 'all the numbers'.

Factoid: The harmonic series (1 + 1/2 + 1/3 + ...) diverges to infinity so slowly that the sum of the first six million terms is less that 21.

Another Factoid: For those of you interested in the real line, did you know that if you have a cube, one foot on a side, say, there are exactly the same number of points within and on the cube as there are along one edge?

And if the Axiom of Infinity disturbs you, you would be frantic if you realized the consequences of the Axiom of Choice: " Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin, even if the collection is infinite"

Doesn't that sound harmless? :nerd:

Oh, God, More Thomists. :wink:

I am suspicious that arguments which have the outward form "time is thus-and-so, hence there must be a god" are actually of the form "There must be a god, hence time is thus-and-so".

I believe in absolute space — Gregory

Why? A new thread?

Factoid: The harmonic series (1 + 1/2 + 1/3 + ...) diverges to infinity so slowly that the sum of the first six million terms is less that 21. — John Gill

Interesting.

Another Factoid: For those of you interested in the real line, did you know that if you have a cube, one foot on a side, say, there are exactly the same number of points within and on the cube as there are along one edge? — John Gill

That doesn't surprise me.

And if the Axiom of Infinity disturbs you, you would be frantic if you realized the consequences of the Axiom of Choice: " Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin, even if the collection is infinite" — John Gill

Looks good. the fuss has settled down.

For those of you interested in the real line, did you know that if you have a cube, one foot on a side, say, there are exactly the same number of points within and on the cube as there are along one edge? — John Gill

Well that would be a paradox, unless we return to the mathematical definition of a point as something with zero extents - it is logically impossible for such a think to have any existence. In each case (line, area, volume of the cube), I would contend that number of points is UNDEFINED. So it does not tell us much about reality except that mathematics (in this instance) does not reflect it.

With the definition of a point as something with non-zero extents, it all makes more sense: there would be less points on the line than the area, and less points in the area than in the volume.

And if the Axiom of Infinity disturbs you, you would be frantic if you realized the consequences of the Axiom of Choice: " Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin, even if the collection is infinite" — John Gill

This is somewhat above my pay grade :grin:. I stopped reading up on maths after encountering the the axiom of infinity. It does, however, strike me that if there is an infinite number of bins, then the selection process never ends - it is not possible to complete the selection process - because the selection process requires infinite time - so therefore to my layman's mind, the axiom seems false.