Could everything have existed forever?

[devans99]

If "neither 1 nor 0" isn't a third possible value # but nothing, then, of course, #s aren't part of the infinite series of 1s and 0s.

The set of negative integers as a whole and all its members are mathematically well-defined; and this set is complete in the sense that it contains all negative integers, which constitute an actual infinity of numbers.

Again, the beginninglessness or startlessness of a series doesn't prevent it (and its elements) from being well-defined and well-ordered.

I'm sorry, but you haven't presented any sound argument against the possibility of series with an infinite regress.

It is a matter of opinion whether the negative integers is well defined - finitists say no. How many members are there in the set? Unless you can give a size of a set then the set is not fully defined. And using made up numbers (like Aleph-naught) is not giving the size of a set IMO.

To reiterate my early argument - if there is no first element in a regress (IE the bit is UNDEFINED rather than 0 or 1), then the second element is UNDEFINED and by induction the whole regress is UNDEFINED.

[RJG]

You'll have to prove that a static timeless universe cannot exist.

A static timeless universe is just that. Nothing happens. EVER.

A static timeless universe could never-ever "start" an event. It would therefore stay hopelessly static and timeless (and event-less) for all of eternity.

Since I trust you can experience the event of reading my words here, then this is proof that our universe has never-ever been timeless.

By "starting from scratch" I do not mean creating something from nothing but arranging or rearranging the basic elements in a new way: same ingredients but a different recipe.

Bingo (agreed).

[Consul]

It is a matter of opinion whether the negative integers is well defined - finitists say no. How many members are there in the set? Unless you can give a size of a set then the set is not fully defined. And using made up numbers (like Aleph-naught) is not giving the size of a set IMO.

A set is well-defined iff it is possible to determine whether or not a given thing belongs to that set; and in the case of the set of negative integers, this is certainly possible.

As for the cardinality of the set of negative integers, if you regard Aleph_0 as a pseudonumber, you can alternatively say that it's (literally) numberless, such that there is no such thing as the number of negative integers. But to say that they are or their set is "numerically undefined" doesn't mean that they aren't or their set isn't well-defined in other respects (such as the one above).

The general point is that even if there is no such thing as the number of things in an actual infinity of things, it doesn't follow that there isn't any actual infinity of things.

To reiterate my early argument - if there is no first element in a regress (IE the bit is UNDEFINED rather than 0 or 1), then the second element is UNDEFINED and by induction the whole regress is UNDEFINED.

But that's just a reiteration of your premise—which is false.
Can you tell me e.g. what's "undefined" about the number –256?

[devans99]

A set is well-defined iff it is possible to determine whether or not a given thing belongs to that set; and in the case of the set of negative integers, this is certainly possible.

As for the cardinality of the set of negative integers, if you regard Aleph_0 as a pseudonumber, you can alternatively say that it's (literally) numberless, such that there is no such thing as the number of negative integers. But to say that they are or their set is "numerically undefined" doesn't mean that they aren't or their set isn't well-defined in other respects (such as the one above).

The general point is that even if there is no such thing as the number of things in an actual infinity of things, it doesn't follow that there isn't any actual infinity of things.

For example, I think you must agree that the set {1,2,3} is 'more defined' than {1,2,3,4,...} - we know how many members there are in the first. So the fact that finite set is 'more defined' than the infinite set can be taken as indicating that the infinite set is not fully defined - IE UNDEFINED. I think maths defines sets inconsistently - you can have a fully finite defined set like {1,2,3} but it also allows just the 'selection criteria' for a set to count as a set (by selection criteria, I mean for example 'all negative integers'). In my book, the 'selection criteria' is different from the set itself and the selection criteria does not completely define a set.

The axiom of infinity claims the existence of a set with a non-finite number of members - how in the real world is it possible to have a set with a non-finite number of members? The universe is finite IMO (its expanding so it can't be infinite at the same time) so everything in it must be finite.

But that's just a reiteration of your premise—which is false.
Can you tell me e.g. what's "undefined" about the number –256?

Well, try it with another sort of infinite regress - an immortal alien who has always been counting - he can't be on any finite number (because then he'd be mortal) and he can't be on infinity (because its impossible to count to infinity). So that rules out ALL the numbers - he can only be on UNDEFINED (because he never started count) - infinite regresses are impossible.

-256 is fully defined.

[Tamminen]

Well, try it with another sort of infinite regress - an immortal alien who has always been counting - he can't be on any finite number (because then he'd be mortal) and he can't be on infinity (because its impossible to count to infinity). So that rules out ALL the numbers - he can only be on UNDEFINED (because he never started count) - infinite regresses are impossible.

You are describing the logic of subjective time. Subjective past cannot be infinite. You cannot end up at your present experience if there was not the first experience that started the succession of your experiences. Subjective endless future on the other hand is logically possible because it does not presuppose actual infinity, only an experience after each experience and no last experience.

But physical time is not as simple as this. It has no present, past or future, only events earlier than other events or later than other events, or simultaneous events defined by some appropriate methods. Physical time is measured with clocks. Clocks are more or less regular physical events that can be used to measure simultaneous other events. It is not clear to me if there must necessarily be the absolutely first physical event or if some kind of actual infinity of physical time is possible. Perhaps this is a question of the geometry of spacetime. Scientific cosmology may give us the correct answer some day.

We are temporal beings, measuring physical time with our clocks. Time is originally subjective, but the relationship between subjective time and physical time needs some phenomenological and logical analysis.

[devans99]

But physical time is not as simple as this. It has no present, past or future, only events earlier than other events or later than other events, or simultaneous events defined by some appropriate methods. Physical time is measured with clocks. Clocks are more or less regular physical events that can be used to measure simultaneous other events. It is not clear to me if there must necessarily be the absolutely first physical event or if some kind of actual infinity of physical time is possible. Perhaps this is a question of the geometry of spacetime. Scientific cosmology may give us the correct answer some day.

We are temporal beings, measuring physical time with our clocks. Time is originally subjective, but the relationship between subjective time and physical time needs some phenomenological and logical analysis.

So would you class yourself an eternalist? Myself I am undecided on the true nature of time.

I think we can say that physical time seems to require a start by considering the objects within it. For example, a clock needs an initial state (say 12:00) for there to be any subsequent states (13:00 etc...). In the same way the universe needs an initial state (s0) for there to be any subsequent states (s1 etc...). What can give the universe an initial state?

- The universe cannot have existed 'forever' because there is no start (initial state) to 'forever'
- The contents of the universe cannot have acquired its initial state by appearing ex nilhilo in the middle of eternal time (violates conservation of energy)
- That leaves the start of time as the only possible point at which the universe could have an initial state (acquired its 'realness')

I think that the Big Bang theory is supportive of this viewpoint.

[Tamminen]

So would you class yourself an eternalist? Myself I am undecided on the true nature of time.

So am I.

That leaves the start of time as the only possible point at which the universe could have an initial state (acquired its 'realness')

I think that the Big Bang theory is supportive of this viewpoint.

So do I.

[devans99]

So would you class yourself an eternalist? Myself I am undecided on the true nature of time.

So am I.

That leaves the start of time as the only possible point at which the universe could have an initial state (acquired its 'realness')

I think that the Big Bang theory is supportive of this viewpoint.

So do I.

It does seem though that if there was a start of time, then at least strict presentism is ruled out: if only now exists and we take that away (due to the start of time), that leaves precisely nothing. So in this scenario, presentism would be like creation ex nilhilo in the strictest sense.

[Thomyum2]

It does seem though that if there was a start of time, then at least strict presentism is ruled out: if only now exists and we take that away (due to the start of time), that leaves precisely nothing. So in this scenario, presentism would be like creation ex nilhilo in the strictest sense.

Not necessarily - I don't think that follows. I think one might accept presentism under the premise that the past and future exist only in the mind - past being that which is remembered; future being that which is imagined - but neither of which exist in any real sense. But I think then that one might also have to accept presentism in conjunction with a strict idealism - that both matter and time exist in the mind. Since we experience an interaction between both time and matter, it's hard to take one out and leave the other.

[Tamminen]

It does seem though that if there was a start of time, then at least strict presentism is ruled out: if only now exists and we take that away (due to the start of time), that leaves precisely nothing. So in this scenario, presentism would be like creation ex nilhilo in the strictest sense.

I am not sure if I understand what you mean, but my view is that time is essentially subjective: it is the present experience becoming a past experience and a new experience appearing from the future. So original time has the structural components of present, past and future as its essential elements. Also the subjective past exists, only in the mode of 'was'. And because we live in the material world, also the world must have a temporal dimension. But it gets its time from us who exist in the world. There is no objective time, time "in itself". The world without us would be timeless if it could exist in the first place.

As I said, we must do some thinking to make it clear what the relationship is between subjective time and the time we meet when we exist in the material world, but the standard model of cosmology suggests that physical time had a beginning.

The question of what "created" time and the world does not depend on whether time is finite or infinite. I assume you think some transcendent power created all this, whereas I think the subject's existence is causa sui and also the cause and reason of the existence of the world.

[RJG]

That leaves the start of time as the only possible point at which the universe could have an initial state (acquired its 'realness')

If someone were to say "it-takes-time-to-create-time", ...we would all laugh at such nonsense, as this is an obvious logical self-contradiction (form X<X).

So I hope you don't mind if I laugh at the nonsense of this phrase - "start of time". "Start" is a temporal word implying time. If time does not yet exist, then "starts" don't exist. There can be NO "starts" in a timeless state! ...the phrase "start of time", is therefore a self-contradicting, logically impossible, oxymoron.

In short: Time cannot be "started", because "starting" requires 'time'. ...S>T and T>S are mutually exclusive!

[Thomyum2]

If someone were to say "it-takes-time-to-create-time", ...we would all laugh at such nonsense, as this is an obvious logical self-contradiction (form X<X).

So I hope you don't mind if I laugh at the nonsense of this phrase - "start of time". "Start" is a temporal word implying time. If time does not yet exist, then "starts" don't exist. There can be NO "starts" in a timeless state! ...the phrase "start of time", is therefore a self-contradicting, logically impossible, oxymoron.

In short: Time cannot be "started", because "starting" requires 'time'. ...S>T and T>S are mutually exclusive!

Yes, unless time is multi-dimensional the way space is. We experience time in one dimension only, like a line. But if we could step off the line and observe it from outside, then it might make more sense, seeing the time we experience from a part of time outside of that. Sort of like the the sphere that visited Flatland?

[devans99]

If someone were to say "it-takes-time-to-create-time", ...we would all laugh at such nonsense, as this is an obvious logical self-contradiction (form X<X).

So I hope you don't mind if I laugh at the nonsense of this phrase - "start of time". "Start" is a temporal word implying time. If time does not yet exist, then "starts" don't exist. There can be NO "starts" in a timeless state! ...the phrase "start of time", is therefore a self-contradicting, logically impossible, oxymoron.

In short: Time cannot be "started", because "starting" requires 'time'. ...S>T and T>S are mutually exclusive!

I think if you view the universe as a larger container that contains spacetime as a subset then a start of our spacetime makes sense - 'start' is a word that makes sense in a spacial as well as temporal sense. So we can talk about the start of spacetime - the Big Bang probably.

If we reformulate Leibniz's PSR so that it makes more sense to:
- Everything in time has a reason
- Nothing can be a reason for itself

You can see that there is an impossible infinite regress of reasons if everything is assumed to be within time. Causality forms a pyramid with current events being the base of the pyramid. We need a brute fact to exist to form the top of the pyramid. But brute facts cannot exist in time - everything in time has a reason. So that requires something without time (which can be uncaused and have permanent existence). Else there would be nothing at all in the universe.

That something has to be causally efficacious which is a challenge to my viewpoint I admit. Maybe the wider universe, beyond spacetime, its a bit like the growing block theory of time - it could support uncaused brute facts - things that have permanent existence, but the environment would extend somehow when a change is made - so a pseudo type of time of some sort. So that would allow for a start of time, the Big Bang etc...

[Consul]

The general point is that even if there is no such thing as the number of things in an actual infinity of things, it doesn't follow that there isn't any actual infinity of things.

For example, I think you must agree that the set {1,2,3} is 'more defined' than {1,2,3,4,...} - we know how many members there are in the first. So the fact that finite set is 'more defined' than the infinite set can be taken as indicating that the infinite set is not fully defined - IE UNDEFINED. I think maths defines sets inconsistently - you can have a fully finite defined set like {1,2,3} but it also allows just the 'selection criteria' for a set to count as a set (by selection criteria, I mean for example 'all negative integers'). In my book, the 'selection criteria' is different from the set itself and the selection criteria does not completely define a set.

We know how many items there are in an infinite set: infinitely many. Of course, this answer is indeterminate insofar as infinite is not a number; and the question "What's the number of members of an infinite set?" cannot be answered in terms of any finite number. Can it be answered in terms of some transfinite number? Yes, but if the transfinite cardinal numbers (Aleph-numbers) are just pseudonumbers, then the only possible answer is the following one:

"Although there are actual instances of infinitude, there are no infinite numbers. When, for example, there are infinitely many A’s, the A’s do not instantiate some specially large number; rather, the A’s are literally numberless, or beyond number."
(p. 143)

"[A]lthough infinitude is surely a quantitative property, it is not a determinate quantity. To call something infinite is to say something about its number or size, but it is not to assign a specific value to its number or size. Rather, an ascription of infinitude is essentially negative: it says, roughly, that any assigned number or size is insufficient."
(p. 147)

"The thesis that infinity is not a number naturally invites the speculation that an infinite thing cannot even be said to be greater than a finite thing, because ‘greater’ is a relation that only makes sense when applied to numbers.
The above discussion, however, hints at the reply to this concern. If infinitude simply had nothing to do with number – if an ascription of infinitude said nothing about size or numerousness – then indeed an infinite thing would not thereby be larger than a finite thing. But that is not the view suggested here. The view is that infinity is not a specific numerical value (nor is Aleph_0 or any of the other alleged infinite numbers). An infinite thing may definitely exceed the finite, while bearing no determinate quantitative relation to another infinite.
More precisely, the infinite may exceed the finite by having finite parts that are greater than any chosen finite object."
(pp. 147-8)

(Huemer, Michael. Approaching Infinity. New York: Palgrave Macmillan, 2016.)

So, an infinite set can be defined as a set S which is such that for all subsets S* with a finite cardinality N there is some subset S** with a finite cardinality N* such that N* > N.

But that's just a reiteration of your premise—which is false.

Well, try it with another sort of infinite regress - an immortal alien who has always been counting - he can't be on any finite number (because then he'd be mortal) and he can't be on infinity (because its impossible to count to infinity). So that rules out ALL the numbers - he can only be on UNDEFINED (because he never started count) - infinite regresses are impossible.

I think this argument is unsound, because counting is arguably an activity requiring a beginning or start, such that it's not possible for an immortal alien to have always been counting, in the sense that there is no time in the past when he isn't counting.
What doesn't require a beginning or start is reciting some number or other (e.g. per day)—without any particular numerical order as in the case of counting. So your immortal alien could always have been reciting some number or other (per day) without this being a case of counting.

Can you tell me e.g. what's "undefined" about the number –256?

-256 is fully defined.

This is in contradiction with what you wrote in a previous post, since -256 is part of an infinite series lacking a first element:

"To reiterate my early argument - if there is no first element in a regress (IE the bit is UNDEFINED rather than 0 or 1), then the second element is UNDEFINED and by induction the whole regress is UNDEFINED."

[devans99]

I am not sure if I understand what you mean, but my view is that time is essentially subjective: it is the present experience becoming a past experience and a new experience appearing from the future. So original time has the structural components of present, past and future as its essential elements. Also the subjective past exists, only in the mode of 'was'. And because we live in the material world, also the world must have a temporal dimension. But it gets its time from us who exist in the world. There is no objective time, time "in itself". The world without us would be timeless if it could exist in the first place.

As I said, we must do some thinking to make it clear what the relationship is between subjective time and the time we meet when we exist in the material world, but the standard model of cosmology suggests that physical time had a beginning.

The question of what "created" time and the world does not depend on whether time is finite or infinite. I assume you think some transcendent power created all this, whereas I think the subject's existence is causa sui and also the cause and reason of the existence of the world.

Time is observer dependant in SR/GR (or at least effected by velocity and mass) so you may have a point. I think physical time is just that - a physical thing - a container of sorts. It is created and I don't believe a created thing can be actually infinite (you would never finish creating an infinite thing). Seems to be that it is likely that something(s) from outside spacetime caused the creation of spacetime. You hold quite a different view to me.