But I just showed that infinity is not a number. It definitely does not play by logical rules (see Hilbert's Hotel and all the other paradoxes of infinity). Nature on the other hand does play by logical rules. No place for magic in nature so no place for infinity either.

Maths describes reality to a high degree... no infinity in maths suggest no infinity in nature.

"I think cause and effect only applying to things in time makes sense.
— Devans99
In that case, your previous objections to the unmoved mover dissolve, since it is outside of time and therefore not subject to cause and effect. — aletheist

We can agree on this point I think: a timeless unmoved mover is a possibility.

But my axiom 'events are caused by events' rules out an unmoved mover in time.

As I recall the church was somewhat split on the issue of whether God was inside or outside of time.

Everything is completely still? That's perhaps stumped me the most in what you just typed. — S

Well I admit that is a problem with the spacetime/eternalist model. Seems to be something different about 'now' compared to 'past' and 'future' else we would not be able to tell the difference between them. So some sort of 'now' cursor spinning around the loop of time? That gives a problem of where did it start and why... plus there should be no motion in the 4d space-time view. Maybe time is not quite like a space dimension but some sort of hybrid dimension that allows a time cursor to flow around? Or maybe 'now' is purely a product of consciousness somehow?

An infinite regress that looks like a circle and in which the points reoccur is still an infinite regress. — S

A circle is not an infinite regress. Draw a circle. There are a finite number of points on the paper as a result. There is nothing infinite about it.

If the last event is before the first event, the Big Crunch before the Big Bang it all adds up nicely.

There is a start of time, so time must be real like Einstein said, it can't be infinite, so time must have an end too. Has to be somewhere for all the matter and energy to go at the end of time - must be back to the start of time.

Then that's an infinite regress. It regresses from an event to a prior event infinitely. — S

No because these are the same points. A circle only has one set of points. Try not to think of time as flowing... think of it as like a spacial dimension. So in a 4d spacetime view our universe forms a torus shape with time being the loop shape. Nothing flows, everything is completely still in the 4d spacetime view of the universe. Just one set of events.

Any point on a circle has a prior point/event.

so anything that is "in our minds only" cannot be real — aletheist

No I mean some things can exist in our mind and not in reality or mathematics. Illogical things like inanimate objects that talk. Or infinity. Or a true continua.

But by definition, if it exists in our minds only, it does not exist anywhere else. We conventionally class the contents of our minds as not part of reality. But you could take the opposite definition I guess.

I think cause and effect only applying to things in time makes sense. Without time there is no before or after. Maybe there is another dimension of time for God only and that is circular too. But these are tricky things to reason about:

- Is timeless possible?
- Does cause and effect apply to timeless beings?
- Why is there something rather than nothing?

These questions might be beyond our reasoning capability as creatures of time.

Continua are real in our minds only. Along with infinity and talking trees. Anything is real in our mind; maths and reality are very different in my view; they are constrained to contain logical concepts only.

But we have larges amounts of evidence supporting the statement 'reality is modelled by maths'. If sound maths cannot represent a continuum, then thats strong evidence against continuums existing.

there are potential instantiations beyond all multitude — aletheist

So those instantiations are not multitudes. So the actual instantiations are not multitudes. So you can't compare the two.

What would qualify as "empirical evidence" that the universe is cyclical, repeating the exact same sequence of events over and over? Why would we expect to find any such evidence at all? — aletheist

Well we have the Big Bang - which is one half of the story. What we really need is more evidence for the Big Crunch - the other half of the cyclical time story.

It seems obvious to me that nothing apart from the Crunch could of caused the Bang - exactly the right amount of matter/energy. So more investigations into the current expansion rate of the universe would be good (there are disagreements depending on who you listen too). More investigation into the topology of spacetime would be nice too.

Then why worry about finding a place for God in the picture? — aletheist

He seems to fit in logically - I'm also a fan of the argument from design. The atom for example is a minor miracle of design in my view. So we need a God to explain the evidence of design away.

My understanding is that conceptualizing a true continuum requires the acceptance of infinitesimals — aletheist

I agree. And infinitesimals are just 1/∞. And actual infinity is not a number:

1. If actual infinity is a number, there must be a number larger than any given number.
2. But that’s contradictory.
3. Can’t be a number AND larger than any number.
4. So actual infinity is not a number
5. Invention of magic numbers runs contrary to the spirit of science.

If actual infinity is not a number, a mathematical continuum does not exist IMO. Likely neither in reality...

In fact, you believe that it has happened infinitely many times in the past, and will happen again infinitely many times in the future — aletheist

Potentially infinitely many times would be nice. Believe is too strong a word. Hope is more appropriate at this stage. Science needs to provide more empirical evidence. Its an old idea and its occupied many minds down the years:

https://en.wikipedia.org/wiki/Ouroboros

Why then does science not take it seriously? I'm not sure. I think they are too atheist to take it seriously.

I see no reason why this should be problematic for the One who created the soul and the body — aletheist

I think we will have to agree to disagree. I am a materialist. I see no evidence of the non-material whatsoever. I admit that is just induction so I could be wrong. I hope I'm wrong too.

If the universe is an eternally repeating cycle, perhaps with some random variations — aletheist

No random variation in my view. No stochastic processes. Its all cause and effect. So I view it like Laplace:

"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes."

— Pierre Simon Laplace, A Philosophical Essay on Probabilities

https://en.wikipedia.org/wiki/Laplace%27s_demon

Old fashioned I admit. As far as quantum mechanics goes, there are interpretations that are deterministic, eg:

https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#De_Broglie–Bohm_theory

Why do you think that heaven and hell are not achievable? — aletheist

How exactly do you implement transmigration of the soul? Even in a simulated world; the complexity of mapping the nervous system in this 'reality' to a new nervous system in the reality of heaven or hell seems beyond the capability of all possible Gods.

instead affirming agent causation as part of our everyday experience — aletheist

I think we are just computers. We have inputs and outputs. All of our outputs are eventually but fully determined by our inputs. It's just our incredible complexity that gives the illusion of free will.

If the universe is cyclical and governed entirely by causal determination, then the exact same series of events transpires over and over again. Even if you allow for some random fluctuations with each iteration, this is not a rational explanation of anything; it ultimately treats everything that exists and every event that occurs as a meaningless brute fact. — aletheist

I think there might be follow on arguments that re-enforce the view that there is a God. An eternal circle is the Occam's Razor design for eternal life. If I were God, it's the one I'd go for. It's actually achievable (unlike Heaven and Hell). So if time is circular, it suggests God did it somehow (a timeless being therefore beyond cause and effect, creates another timeless entity, the universe). But above I've diverted from the 'events are caused by events' axiom. So please regard it as speculative.

So I acknowledge in advance that two of my favourite ideas (Circular time and God) are hard to square together...

as someone mentioned above the rejection of causation — SapereAude

I think once we let go of causation, we enter the world of magic, inhabited by other ghostly concepts like infinity and eternity. I very much believe in materialism.

Cause and effect I think is a sound axiom from the standpoint of everyday experience. Yes that is induction but its 100% accurate so far that I have observed no event that was not caused by another event.

This I would argue extends into the world of science where cause and effect is a widely used axiom. I believe it holds (and I'm sure someone will argue the opposite) even in the quantum world.

There are a finite number of total events on a circle of time: say a circle with 4 events A,B,C,D. Event A you could say 'occurs again', but it's the same event A as before. In the 4D spacetime view, events don't really occur, they just exist perpetually in spacetime at a particular co-ordinate.

Actually I think there is a cleaner way to demonstrate an infinite regress is impossible:

1. The number of events in an infinite regress is > any number
2. Thats a contradiction (can’t be both a number and > any number)
3. Making up magic numbers is not allowed (can break any theory if magic is admissible)

Also, I think I'd like to change my original axiom at this point to 'events are caused by events'.

The revised axiom rules out an uncaused cause. The argument above rules out an infinite regress. That leaves circular time.

You're just making up your own rules, it seems. I don't see any reason to accept your made up rules. — S

Put it this way, would you exist if you were not born? Time is a series: A->B->C. For the whole series to be real, it has to have a first member. So an infinite regression cannot be real; it has no first member ( ...->B->C ) so none of the series is defined. Another analogy is pool: The player hits the cue ball, the cue ball hits the black and the black goes into the pocket. With an infinite regress, the black goes in the pocket without the player hitting the cue ball.

How is it not? The burden is on you to demonstrate a contradiction. — S

What is the cardinality of an infinite set? It must be some number X bigger than all possible finite quantities. But that's impossible, because there is no largest number (X+1>X). So an infinite set cannot exist. So an infinite regression (in the past) is impossible.

Sorry that last argument I tried was not right.

An event is defined by all events that caused it (so if A->B and B->C then A,B->C). So with an infinite regress, no events are fully defined (its always ...,A,B->C which is not a complete definition). Events must be fully defined to be part of reality.

The past actually happened so all of those past events must form a concrete set of events. But if there is an infinite regress of events then the set must be actually infinite in size. An infinite concrete set... how is that possible?

"If all of the of events occurred a finite time ago, there must a point in time before which no events occurred.
— Devans99

Why must there be? You never set out your reasoning fully, which leaves me guessing. — S

If each event occurred a finite time ago, before each event, there must be an actually infinite number of other events. So there must be an event that occurred at t = -∞ (else it would not be an infinite regress). But that event cannot have a predecessor as there is nothing before -∞. So infinite regress requires actual infinity and that concept does not work with cause and effect.

So the argument in full again:

An infinite regress of events is not possible (if cause and effect apply):

1. Assume an infinite regress of time ordered events
2. So some events must have taken place infinity long ago *
3. These events must have been caused by prior events
4. But thats impossible by the definition of infinity (nothing before time = -∞)
5. Contradiction; an infinite regress of events is impossible

* If all events occurred finitely long ago then then before each such event is an actual infinity of past events (if it was a finite number of prior events, would not be an infinite regress). So there must be some events occurred at time/event number -∞. There is nothing prior to this to cause such events; so thats impossible by axiom of cause and effect.

You can do all kinds of things with infinity mathematically, but what you cannot do is treat it as if it were just another quantity. Infinity is a different kind of thing from any discrete number, no matter how large (or small). — aletheist

How about cannot treat infinity as a quantity because it is not a quantity?

What does it mean for an event to have taken place infinitely long ago? — S

I don't know. Nonsense as far as I can tell but thats because infinity is nonsense. I'm trying to present an argument based on the rules of infinity and then to arrive at a contradiction. Problem is infinity is so shot through of contradictions that it's hard work to avoid them on the way...

And no, there's nothing about an infinite regress which necessitates that each event in the chain cannot have occurred a finite length of time ago. — S

If all of the of events occurred a finite time ago, there must a point in time before which no events occurred. That implies a first event; IE not an infinite regress.

"4. But thats impossible by the definition of infinity (nothing before time = -∞)
— Devans99

What? You need to explain that properly. — S

Its a problem with infinity; events are time ordered but that ordering breaks down at -∞; all events at an infinite distance in time from us are co-incidental which is mad...

Interesting. So consider length, the human concept of length. It has no length, being a non-physical thing. But it exists. And remember that axioms are guesses, that we call axioms partly to make them sound more credible and scientific, but mainly because we cannot prove them, so we assert them instead, without a shred of evidence or justification. If we could prove them, we would. When we can't we pretend: axioms. — Pattern-chaser

I would argue that length is a concept and concepts can exist in our minds only. Maybe I should have said: 'things need a non-zero length to exist in reality'. Anything can exist in our minds. Talking trees and Santa. Reality is material and you cannot have a material thing with length=0.

An axiom should be more than a guess IMO. The original definition of axiom was 'self evident truth'.

..always remembering that it is mathematically invalid to divide both sides of the equation by infinity. You did remember that, right? :chin: — Pattern-chaser

Sorry I have given up on the maths of infinity. What is the point of having a quantity (infinity) that you can do nothing with mathematically; you cannot add/subtract/multiply/divide without hitting a contradiction... sort of my point... every way we turn, infinity leads to contradictions. It's too illogical to be a real world concept.

If your first statement were true, then your second statement would also be true. But your first statement is false, so your second statement is also false. — aletheist

Why is my first statement false?

∞ = ∞ * 100
So an infinite interval is composed of infinity many finite intervals (of 100 length in this case).

Interesting. And do you know any rational explanation on how could anything be "eternal outside time"? — Patrick Aoun

1. Can't get something from (the philosopher's) nothing
2. So something must have permanent existence
3. Time is finite *
4. So something must have permanent existence outside of time.

* Proof via contradiction time is finite:

1. Assume time is infinite
2. So some events must have taken place infinity long ago
3. These events must have been caused by prior events
4. But thats impossible by the definition of infinity (nothing before time = -∞)
5. Contradiction; time must be finite.

Not sure it's worthwhile mentioning the obvious, but that's what a bijection does — jorndoe

Bijection gives non-sensical answers: it says there are the same amount of even integers as there are integers. But any finite interval; there are twice as many integers as even integers. And the infinite interval is composed of infinitely many finite intervals. Thats a contradiction that proves bijection is plain wrong.

How about this one:

1. Assume an infinite regress of time ordered events
2. So some events must have taken place infinity long ago *
3. These events must have been caused by prior events
4. But thats impossible by the definition of infinity (nothing before time = -∞)
5. Contradiction; so an infinite regress of events is impossible

*If all events occurred finitely long ago, then it is not an infinite regress

How would you define "eternally" in this context? In other words, what is your definition of "eternal" or "eternity"? — Patrick Aoun

The dictionary gives two definitions of eternal:

- eternal inside time. This is presentism. Requires actual infinity to exist.
- eternal outside time. This is eternalism. Does not require infinity.

So I believe the 1st is impossible whereas the 2nd is possible.

Please think this through. An infinite chain of cause and effect cannot be broken, otherwise it wouldn't be an infinite chain of cause and effect — S

I am not suggesting breaking the chain. It is just a fundamental characteristic of a chain that it has a start. All chains have starts. I suggesting imagining a chain without a start... clearly such a chain cannot exist.

What nonsense. The missing premise from the above argument would be that all beings must be born, but no one is under any obligation to accept that premise. Obviously many believers would outright reject that premise. It would be kind of silly to argue that God must have been born. — S

You are wrong again. All my argument asserts is that beings must have a temporal start of some form (I called it birth just to make it familiar). Can you imagine a being without a temporal start? That is just impossible. Such a being would have an unexplainable gap in its personal history - its origin and an origin is essential to being.


I may have to offline this discussion as it appears we are going around in circles. Happy XMAS though.

Please advance a rational argument to prove what you assert. — Patrick Aoun

With eternalism, past present and future all exist eternally with no need for creation or destruction, so space-time can exist eternally even though time has a start.

In addition, you can posit that the start of time was preceded by the end of time (Big Bang preceded by Big Crunch).

Mathematical infinity is not actual infinity. Which part of this do you still not understand? — aletheist

Mathematical infinity in set theory is actual infinity.
Mathematical infinity in calculus is potential infinity.

?

Please pay attention. Arguments for a First Mover consistently affirm that every effect has a cause. What they deny is that everything is an effect; specifically, the First Mover is not an effect and requires no cause. — aletheist

I agree: the existing prime mover arguments apply cause and effect in an inconsistent manner; cause and effect are applied for everything accept God.

My argument applies cause and effect consistently throughout.

One more time: Mathematical infinity is not an actual infinity, but it is a real infinity. If we paired up every number with its square, when would we run out of one or the other? Never. How is this a contradiction? — aletheist

There are less squares than numbers in the following intervals:
0-10
0-1000
0-1000000
So via extrapolation, there must be less squares than numbers in ALL intervals.

The fact that actual infinity contradicts the above means we can induce that actual infinity does not exist.

That does not follow at all. Again, your fundamental assumption is that everything is an effect--i.e., everything has a beginning--which is precisely what arguments for a First Mover deny. — aletheist

So how could he exist if he was not born? An unborn being would not exist.

Arguments for First Mover are inconsistent: They say effects do not have a cause (God) - in which case it is wrong to claim that you can trace a chain of cause effect back to God (because some effects do not have causes).

My argument at least applies its axioms consistently.

1. It makes no sense to talk about removing a cause. That's not actually possible. — S

But we need to consider a chain without a first cause, so removing a cause is a way to do this. All real chains of cause and effect have a starting cause. It is only an infinite chain of cause and effect that does not have a starting cause. Because there is no first cause, none of the other members in the chain can exist:

A->B->C->D->E.

If A does not exist, then B, C, D, E do not exist. That is the situation for an infinite regress - the first member does not exist so none of the members exist.

2. There cannot be an infinite chain of cause and effect with a gap in it, so as soon as begin to suggest a gap in the chain, you're no longer talking about an infinite chain. And as soon as you begin to talk about something other than an infinite chain, you're committing a fallacy of irrelevance. — S

I'm not talking about a gap. I'm talking about the absence of the first member.


Maybe an example with less moving parts: Imagine an eternal being; he would have no birth so could never exist. Being is possible we therefore conclude Eternal is not.

IE eternal has no start - no moment of birth - so the rest of the life cannot exist. Very similar to my example of removing A from the start of a sequence.

A sequence of cause and effect:

A->B->C
(A causes B causes C)

If I remove A, then B and C does not happen. Can't you see an infinite sequence has no start so none of it can exist.

It’s impossible to count to infinity so the being cannot be on that (no matter how many times you add one, you never reach infinity). If the being is on a finite number, then he is not eternal; he started counting a finite time ago.

So it's because eternity has no start - it's impossible to start counting, start being, start existing.

If you look at the paradox again - it assumes 3 things and reaches a contradiction - eternity, being and counting. Being and counting are possible so it must be eternity that is not possible.

You may be right. — Banno

He is right. We talk about the magic of infinity and thats just it; its magic not maths. Galileo's paradox I've already mentioned but its pretty central to why infinity is contradictory:

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

So there are clearly more numbers than squares in all intervals. Except an infinite interval when there are the same amount. So we have assumed actual infinity exists and derived a contradiction - Galileo's paradox is proof by contradiction that actual infinity does not exist.

No, there would be no missing cause. We've essentially already been over this and you conceded. There can be no missing cause in an infinite chain of cause and effect. That's simply not possible, else it wouldn't be an infinite chain of cause and effect. — S

No I have not conceded. The sequence as a whole has no start so none of it can exist. Maybe this paradox will help you see the problem with infinity/eternity:

- Say you meet an Eternal being
- You notice he is counting
- You ask and he says ‘I’ve always been counting’
- What number is he on?

However, if we assume that time itself has a beginning, the question of what was before the beginning of time becomes irrational, hence invalid — Patrick Aoun

A start of time rules out presentist models of time; it does not rule out eternalist models.