Yes it does:

- Assume infinite time
- so anything than can possibly happen will eventually happen
- If it happens once it will eventually happen again
- So it will eventually happen an infinite number of times

What’s wrong with the simplist argument?

The Actually Infinite exists. Reductio ad absurdum. No it doesn’t.

Give me a counter example from nature of the Actually Infinite (one you can actually prove exists please) if you can...

But just because you cannot be directly aware of something does not mean that that something does not exist. — Magnus Anderson

You are making things complicated. Zeno’s paradoxes disappear if we assume time is discrete for example (IE then Archiles only has to cover a finite number of steps to catch the tortoise).

Don’t you get it, logical contradictions like Zeno’s, Hilberts Hotel etc... exist because we have an absurdity (Actual Infinity) at the core of our reasoning

Ok here is the proof that Actual Infinity does not exist:

We have the concept of ‘Reductio ad absurdum’ which Wikipedia defines as:

‘In logic, reductio ad absurdum is a form of argument which attempts either to disprove a statement by showing it inevitably leads to a ridiculous, absurd, or impractical conclusion, or to prove one by showing that if it were true, the result would be absurd or impossible.’

Returning to the Actually Infinite, my proof that it does not exist is that THE ARGUMENT STARTS WITH AN ABSURDITY.

For example infinite time implies anything can happen will happen an infinite number of times which is absurd.

However, that DOES NOT mean that it is impossible for an infinite number of things to happen between two points in time. — Magnus Anderson

You are assuming time is continuous.

- Assume we have a system
- Watch it evolve over a finite time period
- Will we observe it pass though an actually infinite number of states?

My gut feeling is no so time is probably discrete.

You say that you believe time is continuous but you don’t give an argument why.

I say time is discrete because otherwise we get logical contradictions.

My target is the use of actual infinity in the physical sciences.

We can’t conceive of logically inconsistent concepts like Actual Infinity in a logically consistent way.

I’d allow for the existence of the inconceivable only if it where possible. No need to allow for impossibilities like Actual Infinity.

No wonder we cannot mentally conceive the Actually Infinite; it does not exist.

see https://en.m.wikipedia.org/wiki/Actual_infinity

I'm saying that the nature of space itself is such that it is infinitely divisible already. — MindForged

But it’s impossible to construct a smallest possible distance (1/infinity) - we can merely construct successfully smaller distances in a process that tends to but never reaches 1/infinity. That’s the definition of potentially infinite. I asked for an example from nature that is actually infinite...

Space is infinitely divisible — MindForged

If it is, it’s a potential infinity rather than an actual Infinity (you do understand the distinction?).

The division of space takes time, first we must cut one inch, then 1/2 an inch, then 1/4... No matter how many cuts we make we never get to actual infinity, just some small number.

Numbers aren't part of the mind — MindForged

So you are a Pythagorean? All is number? But you believe in actual infinity too? So that means you believe the physical world is actually infinite?

Give me an example of the actually infinite from nature.

No, numbers are a figment of our minds so can be actually infinite. Time however is part of the physical universe so it can’t be actually infinite.

For every moment before this very moment, there is another moment. — MindForged

I believe that leads to contradictions. For example, how could we ever reach today if the past stretches to negative infinity (no matter many moments you add to negative infinity you still get negative infinity).

For every moment before time "t" there is another moment. — MindForged

The above refers to future which is potentially infinite which is not the subject of this thread.

Past infinite time is however an Actual Infinity so is disallowed. For example this argument:

- Time is a series of moments
- The moments so far must be an actual number not infinity
- So time has a start

No no no, calculus makes use of multiple legitimate infinities — MindForged

Yes I was discussing this briefly with a mathematician. The foundations of calculus do you indeed make use of actual infinity as defined in set theory. But set theory merely states that the actually infinite exists as an axiom; it does not prove anything. So the foundations of calculus rest on rather shaky ground.

Yes the paradox is due to the use of actual infinity in a logical argument.

Imagine a timeless being existing permanently; he would be finite but permanent in the sense he is outside time. That solves the paradox as far as ‘god’ goes; a timeless, permanent, finite being.

I'm just wondering, if the theoretical and actual worlds do not have common points of analogy, then nothing in one would relate to the other. — BrianW

I agree. The best language clarification I know is Aristotle‘s: https://en.m.wikipedia.org/wiki/Actual_infinity

Relating this to maths, a potential infinity is most close to the limit concept. Actual infinity occurs in set theory.

We are indeed lacking analogy between maths and reality. I can think of no actual example of real world Actual Infinity. On the maths side we have very little also. Set theory basically uses an axiom equivalent to ‘actual infinity exists’ (check here if you are brave https://en.m.wikipedia.org/wiki/Axiom_of_infinity)

So mapping two non-defined concepts is hard... sort of the point of this thread... Actual Infinity is nonsense...

The usual objection to that is to ask - 'but what number did they start on?' to which the answer is 'they didn't start'. — andrewk

Yes; so an object with no start is a non-existent object; IE infinite time is impossible. Same argument for infinite space.

The only thing I can think of without a start is the counting numbers from negative infinity to zero. But they just exist in our heads they don’t correspond to anything real.

Imagine a spaceship that has an accurate odometer. We set the spaceship in motion and it travels across the universe. The reading on the odometer will always be finite no matter how far the ship goes. — frank

I like that story. Here is something similar for time:

- Imagine an eternal being in eternal time
- You notice he’s counting. You ask how long and he says ‘I’ve been counting always’
- What number is he on?

But whatever mathematical formalism is used, they also make recourse to infinity. — MindForged

That’s not correct, they make recourse to the limit concept which is not the same as actual infinity.

You either think it's true or not — MindForged

I believe and so I thought did everyone that relativity is a close approximation only of the large scale universe. The plank length is very small so reality is approximately continuous hence the theory works so well.

The natural numbers can be put into a one-to-one correspondence with a proper subset of itself. That makes it infinite. — MindForged

But numbers just exist in our mind and our minds have finite capacity so numbers are finite in that sense.

Are you aware that denying the actual infinite involves committing to one or the other of the following two propositions?

1. If we travelled far enough through the universe in a straight line we'd end up back where we started

2. The universe has a boundary. In that case, as Aristotle asked, what happens if we go to the boundary and poke a spear through it? — andrewk

It’s a problem I agree but I can think of a way past 2 above: imagine as you get closer to the edge of the universe time slows down and right at the edge time stops. So it’s impossible to poke a spear through the edge of the universe because there is no space time in which to poke the spear.

Time is nothing more than measure of co-ocurences of events with human–created time measure, which is clock... Unverse works as unconscious machine, that removes necessity to count or regard time as important. — Victoria Nova

The universal speed limit - the speed of light - is defined in terms of time (speed=distance/time) and is absolutely fundamental to the universe. Don’t see how you can claim time is unimportant or transitory...

The unspecified ability to act is not synonymous in any way with omnipotence or infinite extent. We have the unspecified ability to act and we are not god.

“Do you agree that every line (regress) of concurrent causality must terminate in a self-explaining cause?”

- the prime mover? Yes I mainly buy it.

“If you do, then God has an unlimited capacity to perform any possible act.”
I
- you’ve made a big jump there. God creating the universe is not demonstrative of omnipotence.

I can sort of believe in an omnipotent god thanks to the wonder of the simulation hypothesis (https://en.wikipedia.org/wiki/Simulation_hypothesis), but in no way can I believe in an actually infinite god and I see nothing in your argument to prove god is infinite.

Good read thanks...

So you believe God is infinite? The problem with that is you are either infinite or you exist - not both at the same time.

A finite god is much more naturalistic...

“But if one removed all phyiscal mass and energy, both the visible and dark, wouldn't empty space simply be infinite vacuum?”

Dark energy maybe inherent to space so it’s not possible to remove it.

“Would you then believe that if space is finite, expansion of the universe will hit the "edges" of space one day? Or do you believe that the expansion of the physical universe determines the size of the space it's in, which is finite?”

We live in 4D space time. I’m not sure but maybe as you get closer and closer to the edge of the universe, time slows down and then reaches a stop? So you can never pass the boundaries as time does not exist outside.

‘If time reached back infinitely, it would reach the future infinitely as well?’

Time does not reach back infinity far that would be an actual infinity. Is time future infinite, that is only a potential infinity in a 3D + Time world but it is an actual infinity if you buy Einstein. I buy Einstein so time has an end too for me.

Three instances where infinity clouds the issue:

- The big rip
- Black holes and the singularity
- The debate over continuous/discrete

I’m not suggesting dropping infinity from maths. It’s fine with the limit concept and set concept. I’m suggesting dropping actual infinity in physics and metaphysics when used as the value for real world quantities.

Relativity is an approximation of reality not reality - We don’t know for sure if space is continuous. Anyway continuous space is a Potential Infinity whereas I’m talking about Actual Infinity.

There is an argument that the natural numbers are only potentially infinite - we have used finitely many of them so far and that will remain the case.

I’m hardly the only person to have a problem with actual infinity. The great German mathematician Hilbert posed his Infinite Hotel paradox. Just one of many paradoxes that stem from actual infinity.

I know it’s possible to construct consistent mathematical systems around infinity; that is not what I’m objecting to. I’m objecting to the use of actual infinity in physical sciences.

I don’t have your knowledge of quantum mechanics admittedly but I’m sticking with my claim - infinite space and time is nonsense:

- Empty space has vacuum or dark energy associated with it. Total energy content of universe has to be finite. Space is finite.
- If time reaches back infinitely then it’s impossible to reach today. Time is finite.

Good for modelling and approximations I agree. It’s the use of actual infinity to stand real world quantities that disturbs me. Statements like space or time maybe actually infinite... nonsense.

Certainly has lots of uses in maths but it’s interesting to note that Actual Infinity is not constructable geometrically or otherwise mathematically (in the limit is not the same as actual infinity). So even in maths, actual infinity is unrealisable.

Yes, to clarify I mean actual infinity in the context of the physical sciences. I.e. when it is applied to real world entities.

What created time? It must of been created either by random or on purpose:

- A random process (eg quantum fluctuations) somehow create time. Seems an unsatisfactory explanation. For example, an infinite number of fluctuations is impossible and a finite number begs the question what started the fluctuations?
- Which leads to the other option, time was created on purpose by some sort of timeless being or beings. I prefer this option: creation of time seems to need intelligence and there are other signs of design in the universe that also suggests an intelligent creator(s).

Time is real in a material sense I believe:

- It was created in the material world (base reality is material I’m sure) so it must exist as a physical thing
- Base reality is timeless so all information encoded in time would be permanently represented in base reality

The idea is that base reality is permanent but not infinite. The idea is nothing is infinite in a physical system and base reality is a physical system.

Not sure exactly what time is; the reasoning above highlights some attributes of time (finate, permanent, real) but does not pin down the exact nature. I think general relativity’s treatment of time as a dimension is probably close to the truth.

In the domain of physics my view is actual infinities must be avoided. The actually infinite is impossible to achieve even with time - no matter how long you add one you never reach infinity because it’s not a number and it has no place in physics except as an approximation for the very large or small. Infinity also introduces logical contradictions and bizarre scenarios (anything that can happen will happen... an infinite number of times).

By base reality I mean the presence of dimensions (as opposed to nothing which would by a zero dimensional ‘reality’). We are contained in base reality but we are tied to time so I’d guess we don’t experience it like the residents of base reality do.

I’m accepting time is infinite (for the sake of this argument)

Infinite space does not matter because then the Boltzmann brains are almost infinitely far away from us so they cannot effect us.

We needed infinite time to produce local Boltzmann brains which is impossible as shown above.

Anything that can happen will happen is wrong - at least when you take into account the event horiqzon.

Yes but then there has been an infinite amount of time for the probability space to shrink:

- Things that are impossible can’t become possible
- Things that are possible can become impossible
- So the probability space shrinks with time
- So infinite time does not make everything possible

Oh dear I have the math wrong. Sorry to waste your time...

An assumption is required to complete the calculation. We have taken into account everything we know about dogs and we still have 30% of dogs for which no evidence is available so we have to guess what proportion are mean. What is the best possible guess?

- We could assume 100% of then are mean
- We could assume 0% are mean
- We could assume 50% are mean

The 3rd answer is best because the normal distribution is the most common distribution. Distributions where 100% or 0% is the best choice are much rarer.