But that's a tiny minority of possible numbers. The vast majority of numbers have infinite decimal places - that infinity of decimal places (=information) would be the same for the particle in a millimetre of space as for a particle in a light year of space which seems absurd to me. — Devans99

Were you aware there is a one-to-one correspondence between any interval on the real line, no matter how small, and the entire infinite real line? It's easy to construct. You could do it quickly with a pencil and paper. :cool:

My contention is that something with the structure of the real line does not and could not exist in reality - maths is not reality - and we have never found anything infinitely divisible in nature. For example, how many actually infinite sets have you encountered in your life?

and we have never found anything infinitely divisible in nature — Devans99

Maybe we haven't tried hard enough? I've seen arguments like this many times, projecting past failures to future attempts.

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

Some people do object - spacetime looks like a creation (see the BB). It's impossible to create anything infinite in size, so therefore spacetime should be finite. — Devans99

Thanks for the link. When I said that people don't find it difficult to conceive space as infinite I mean that it doesn't lead to an infinite regress like if time was infinite.

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

And I look forward to the day. Spacefoam anyone? :nerd:

I find it hard to accept that, whilst I sit here typing, my fingers are passing through an actual infinity of positions. — Devans99

Yes, they're not. 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.

Time is 'stuff' because:

- The physical laws of the universe are time-aware, so time must be something (IE 'stuff')
- Time has a start, so when time started something physical about the universe changed, so time must be 'stuff' — Devans99

Well, time exists, but not everything that exists is a substance. 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 - that is, actually extend intinity - which is manifestly impossible. (not all substances are extended, but time would have to be an extended substance - so it is extended substances, not substances per se, that contain actual infinities).

So, it seems to me that you are fallaciously inferring from the reality of time, the substance of time. But time can be real yet not be a substance - which is what we must conclude if the argument's I've presented go through.

Because scientists are not investigating what time is - they are just measuring stuff - whatever they say will be consistent with what time is.

It 'does' lead to an infinite regress.

It's true that there's at least one additional reason to think that time is not a substance (a reason to do with the intrinsic difference between past, present and future), but when it comes to the problem of actual infinities, the problem is the same. Space and time go the same way.

Time, if it is a substance, would have to extend infinitely because otherwise it would not be possible for an event to become ever more past for infinity. And that's manifestly absurd - no substance can extend infinitely.

But exactly the same is true of space as well. Space has to extend infinitely - how could it have a boundary? Whatever is outside the boundary would also be space.

And any region of space is going to be infinitely divisible.

One can just insist that this is not so - that is, one could, as Devans99 seems to be doing - reason that as no actual infinities can exist (correct), space must be reducible to discrete portions or atoms of space. But the problem with that is that it doesn't recognise that the problem is with space per se - any portion of space is going, by its very nature, to be divisible. I mean, try and imagine a portion of space that isn't divisible - it's impossible.

What we must conclude, on pain of simply refusing to face up to what reason is telling us, is that we are thinking about space and time incorrectly.

It 'does' lead to an infinite regress.

It's true that there's at least one additional reason to think that time is not a substance (a reason to do with the intrinsic difference between past, present and future), but when it comes to the problem of actual infinities, the problem is the same. Space and time go the same way.

Time, if it is a substance, would have to extend infinitely because otherwise it would not be possible for an event to become ever more past for infinity. And that's manifestly absurd - no substance can extend infinitely.

But exactly the same is true of space as well. Space has to extend infinitely - how could it have a boundary? Whatever is outside the boundary would also be space.

And any region of space is going to be infinitely divisible.

One can just insist that this is not so - that is, one could, as Devans99 seems to be doing - reason that as no actual infinities can exist (correct), space must be reducible to discrete portions or atoms of space. But the problem with that is that it doesn't recognise that the problem is with space per se - any portion of space is going, by its very nature, to be divisible. I mean, try and imagine a portion of space that isn't divisible - it's impossible.

What we must conclude, on pain of simply refusing to face up to what reason is telling us, is that we are thinking about space and time incorrectly. — Bartricks

My bad. Sorry. I wasn't clear enough. Infinite space does lead to an infinite regress but that isn't a problem. People don't usually introduce infinite regress as an even a minor issue with infinite space.

However, infinite regress is a problem with infinite time because to get to this point in time we would have had to pass through an infinite past which seems inconceivable, infinity defined as it is.

Hmm, I still don't see a difference: if time is a stuff, then there is an infinite amount of past earlier than now, and an infinite amount of future later than now. If space is a stuff, then there is an infinite amount of it behind me and an infinite amount of it in front of me.

The problem with infinite regresses is the 'infinite' bit. So, that we recognise an infinite regress to be a problem just underlines that actual infinities are problems - for an infinite regress just is an actual infinity.

Where? Nothing isn't evidence. — Bartricks

Indeed.

Hmm, I still don't see a difference: if time is a stuff, then there is an infinite amount of past earlier than now, and an infinite amount of future later than now. If space is a stuff, then there is an infinite amount of it behind me and an infinite amount of it in front of me.

The problem with infinite regresses is the 'infinite' bit. So, that we recognise an infinite regress to be a problem just underlines that actual infinities are problems - for an infinite regress just is an actual infinity. — Bartricks

No. An infinite regress, as I understand it, refers to the specific problem of an infinite task being impossible to complete. Infinity is the condition of being boundless.

You need to show me how space/time being infinite leads to an infinite task that can't be completed and that would be a problem.

No, why is an infinite regress a problem? It is a problem because you can't have an actual infinity of anything.

For example, consider the first cause argument. Anything that has come into being needs a cause of its being. Positing another being that has come into being as the cause of those beings that have come into being starts one on an infinite regress. Why is that a problem? Why can't it be 'turtles all the way down'? Because you can't have an actual infinity of anything, be that causes, objects, actions.

Yep. And?

No, why is an infinite regress a problem? It is a problem because you can't have an actual infinity of anything.

For example, consider the first cause argument. Anything that has come into being needs a cause of its being. Positing another being that has come into being as the cause of those beings that have come into being starts one on an infinite regress. Why is that a problem? Why can't it be 'turtles all the way down'? Because you can't have an actual infinity of anything, be that causes, objects, actions. — Bartricks

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

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.

I can't even comprehend the terms that are being used.
Like here.

It is not, I think, a kind of stuff or dimension. This is for numerous reasons. Conceived of as a stuff (or dimension, if dimensions are not stuff)

Yeah. The confusion of stuff and dimension. Like saying that time is neither democracy nor cheese.

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.

It isn't really a paradox anymore. Consider a line segment of length 1. It can be cut into length 1/2,1/4,1/8,1/16 and so on if we add up all the lengths, we get a line segment of length 1. A line segment is made up of countably infinite number of points. That's the way the real numbers work. That's also the reason why we don't have a smallest number "a" that is greater than say another number "b" .

That had me laughing out loud. :lol:

Well, it's right, isn't it? Time is not democracy. That is self evident.

Now, if time were a cheese, it would necessarily be one sort of cheese, or it would be another. But it is not a cheddar. Nor is it a soft cheese. So, what sort of cheese is it? Feta? Too much salt.

Well l will see what l can say. Let's try this.

1. If cheese is a dimension, then it will be infinitely divisible
2. Nothing existent( cheese) can be infinitely divisible.
3. Therefore, if cheese is a dimension it does not exist
4. Cheese exists :yum:
5. Therefore, cheese is not a dimension

Spot on.

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

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. — TheMadFool

Er, no. It is the impossibility of an actual infinity that makes an infinite task impossible!!

Numbers aren't things. There aren't an actual infinity of numbers, rather they constitute a potential infinity.

1. If cheese is a dimension, then it will be infinitely divisible
2. Nothing existent( cheese) can be infinitely divisible.
3. Therefore, if cheese is a dimension it does not exist
4. Cheese exists :yum:
5. Therefore, cheese is not a dimension — Wittgenstein

Yes, that argument is valid and sound. Like mine.

I mean, I assume you accept that cheese is not a dimension? And I assume you acknowledge that the argument is valid? Yes?

Right. Now substitute the word 'cheese' for 'time'. Do any of the premises suddenly become false? No. Does the argument somehow become invalid? No.

So, what. Exactly. Is. Your. Problem?

I can't even comprehend the terms that are being used.
Like here.

It is not, I think, a kind of stuff or dimension. This is for numerous reasons. Conceived of as a stuff (or dimension, if dimensions are not stuff) — Wittgenstein

What, exactly, are you having trouble with?

Er, no. It is the impossibility of an actual infinity that makes an infinite task impossible!!

Numbers aren't things. There aren't an actual infinity of numbers, rather they constitute a potential infinity. — Bartricks

Yes, but there has to be a practical implication, an infinite task, that creates the difficulty.

In fact all paradoxes of infinity boils down to showing the practical impossibility of infinity.

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.

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.

Yes, but there has to be a practical implication, an infinite task, that creates the difficulty. — TheMadFool

No, even if there are no agents, you cannot have an infinite amount of anything. You don't make 'infinity' a problem just by adding 'task' to it.

Again, the reason infinite tasks are impossible is not because tasks are impossible, but because infinities are.

Er, no. It is the impossibility of an actual infinity that makes an infinite task impossible!! — Bartricks

And yet we differentiate.

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

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).

I have no idea what you're on about. Ever. It's just nonsense.