## Could everything have existed forever?

Discuss any topics related to metaphysics (the philosophical study of the principles of reality) or epistemology (the philosophical study of knowledge) in this forum.
devans99
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### Re: Could everything have existed forever?

Consul wrote:
July 11th, 2019, 1:51 pm
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.
I am a little confused with your definition of an infinite set - if S** is a finite proper subset of S* then N* < N must hold? The text you've quoted though reads to me as if he is saying that infinite sets do not have a cardinality and are not well defined?
Consul wrote:
July 11th, 2019, 1:51 pm
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.
I think there is a general rule here: 'To be X, you must start X'. So X could be counting, reciting, spinning, oscillating and ultimately existing. The initial state of all these activities determines the subsequent states. If there is no initial state, there are no subsequent states.
Consul wrote:
July 11th, 2019, 1:51 pm

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."
The number on its own is well defined. It is the whole infinite series containing it that I argue is undefined.

Felix
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### Re: Could everything have existed forever?

RJG: 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.
Well, you are fond of making absolutist blanket statements about reality but the truth is that our Universe is a wild child allowed to do the seemingly impossible: generate life from inanimate matter, hold gala black hole events where time can stand still and gravity fields become infinite, etc., etc.
"We do not see things as they are; we see things as we are." - Anaïs Nin

Tamminen
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### Re: Could everything have existed forever?

Thomyum2 wrote:
July 11th, 2019, 1:15 pm
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?
Start of time means start of being. RJG says this does not make sense. But imagine that you are the only being in the world. You begin to exist. You came from nowhere. Suddenly you just are there. You and time. We all are in this situation now.

This is an analogy of course. But I think it proves that the beginning of existence and beginning of time are not self-contradictory ideas. I do not claim that they are necessarily true though. But the empirical fact of the Big Bang supports these ideas. Nevertheless, I would not exclude the possibility of infinite physical past. Both alternatives seem to be impossible, as Kant demonstrated, but one or the other must be the case, because the problem is well defined, I think. So which is it? We know RJG's proof and devans's proof, and both are convincing in their own way. Perhaps we must ask Consul?

Consul
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### Re: Could everything have existed forever?

devans99 wrote:
July 11th, 2019, 2:36 pm
Consul wrote:
July 11th, 2019, 1:51 pm
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.
I am a little confused with your definition of an infinite set - if S** is a finite proper subset of S* then N* < N must hold?
Okay, I see that my formulation is ambiguous. I mean:

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** of S with a finite cardinality N* such that N* > N.
devans99 wrote:
July 11th, 2019, 2:36 pm
The text you've quoted though reads to me as if he is saying that infinite sets do not have a cardinality and are not well defined?
A set's well-definedness doesn't depend on its having some determinate cardinality.

"A set is a well-defined collection of objects. Objects in the set are called elements.
The phrase 'well-defined' separates sets from other collections. If we take the word 'well' to mean good and the word 'defined' to mean description, then a set is a collection that has a 'good description'. In other words, a set is well-defined if we know exactly which objects are or are not in the set. So we must avoid describing sets with relative words that can take on different meanings depending on the situation."

(Freitag, Mark A. Mathematics for Elementary School Teachers: A Process Approach. Belmont, CA: Brooks/Cole, 2014. p. 77)
devans99 wrote:
July 11th, 2019, 2:36 pm
I think there is a general rule here: 'To be X, you must start X'. So X could be counting, reciting, spinning, oscillating and ultimately existing. The initial state of all these activities determines the subsequent states. If there is no initial state, there are no subsequent states.
This is refuted by the fact that the beginningless infinite series of negative integers is well-defined and well-ordered. And, for example, there is a corresponding (possible) beginningless infinite series of years BC; and this series is well-defined and well-ordered too:
… -4, -3, -2, -1
… -4 BC, –3 BC, -2 BC, -1 BC
devans99 wrote:
July 11th, 2019, 2:36 pm
Consul wrote:
July 11th, 2019, 1:51 pm
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."
The number on its own is well defined. It is the whole infinite series containing it that I argue is undefined.
Part of this number's definition is its position in the infinite series of negative integers.

Anyway, your "undefined" is undefined. What's your definition of "well-definedness" in this context?
"We may philosophize well or ill, but we must philosophize." – Wilfrid Sellars

Consul
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### Re: Could everything have existed forever?

Consul wrote:
July 11th, 2019, 3:49 pm
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** of S with a finite cardinality N* such that N* > N.
For example, the infinite plurality of natural numbers is such that for all sets S of them with finite cardinality N there is some set S* of them with finite cardinality N* such that N* > N. (Note that no transfinite numbers are involved here!)
"We may philosophize well or ill, but we must philosophize." – Wilfrid Sellars

RJG
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### Re: Could everything have existed forever?

devans99 wrote: ...so a pseudo type of time of some sort. So that would allow for a start of time, the Big Bang etc…
"A pseudo type of time"?? Do you not see that you are digging a deeper hole? -- Okay, just for grins, lets (falsely) assume and accept that some "pseudo time" started "time", okay, so now tell me (without further kicking-the-can-down-the-road!!), what started this "pseudo time"? Are you now going to tell me that there is another "turtle" under this "turtle"? How far down do these turtles go???

Time cannot be started because "starting" is not possible in a timeless existence. Time cannot precede itself to start itself. X<X is logically impossible, and X<X<X<X is also still logically impossible.

Consul
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### Re: Could everything have existed forever?

Consul wrote:
July 8th, 2019, 4:50 pm
How did God create the universe? According to the theistic creation myth, he did so by means of magical speech-acts. But a speech-act (or thought-act), especially a series of speech-acts, is a temporal process with some nonzero duration. The beginning of saying or thinking "Let there be…!" cannot be simultaneous with its end. And the non-instantaneous divine speech-act of creating cannot be simultaneous with what it creates. You can only say consistently that the temporal end of the productive speech-act is simultaneous with the temporal beginning of its product.

And God said, “Let there be light,”…
"I was earlier dismissive of the pretensions of ‘Let there be light’ to serve as an explanation of the origin of light, even when uttered by God, but it might be maintained that, on the contrary, it is through just such acts that creation ex nihilo could be channelled. It is not inconceivable that God should speak and that something should come into existence as ordained, so we cannot rule creation out as logically impossible. Very well, but to say that creation is logically possible is only to say that, if anything rules it out, it is not logic; there could still be other reasons for its exclusion. What would warrant us in speaking of creation when, on God's speaking, something came into existence? How is it that the divine act is efficacious, when uttering words does not normally have such consequences? It is no good saying that the difference resides in the fact that the utterance is an expression of God's will, and God is all-powerful. That leaves us none the wiser as to how it is that the divine word has this consequence. As it stands, the ‘explanation’ is surely no better than the supposition that something might spring into existence uncaused. But suppose that, whenever a certain person uttered certain words, a leaf, say, appeared, seemingly from nowhere. This would hardly be something we could ignore. True, but note that this is an event in time. An act is performed, and something then comes into existence. We have at least the beginnings of a framework in which we might hope to make sense of such happenings, but in the divine case that is totally lacking. To have as much as a relevant fantasy, we had to place God in time and have him decree that something be so; refuse such conditions, and we are left with nothing even to consider as a possible creative act. Again, we have just noted examples of creating which do not involve creating something out of anything, and there are many cases where an F comes into being though nothing becomes an F, as when we dig a hole, utter a cry or start a fire, but whether thought of as temporally extended, as with digging, or occurring at a point of time, as when a flame is caused to be, the causation has an essential temporal dimension."
(pp. 79-80)

"I can get no grip on the idea of an agent doing something where the doing, the bringing about, is not an episode in time, something involving a changing agent and a change induced through its action. What is there left of the notion of cause once it is stripped of these features?"
(p. 77)

(Rundle, Bede. Why there is Something rather than Nothing. Oxford: Oxford University Press, 2004. p. 77)
"We may philosophize well or ill, but we must philosophize." – Wilfrid Sellars

Consul
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### Re: Could everything have existed forever?

"The universe did not come into existence, nor will it cease to exist. And this is not just a matter of empirical fact: there is nothing we could intelligibly describe as the universe's coming into existence or its ceasing to exist. Beginnings and endings join causation in being concepts which, while having innumerable instances within our world, resist extrapolation to the universe itself.
So, if the universe cannot have come into existence and cannot cease to exist, is it temporally infinite in both directions?

[W]hile the notion of beginning to exist is suspect in application to the universe as a whole, we have an allowable approximation to this notion in terms of the universe's having been in existence for only a finite time. This is not: there was a time at which the universe did not exist; the universe will have existed at all times. Nor will there be a future time when it does not exist. But, for all that, there could be a finite limit to its duration to date as well as to its future history.

Similar caveats apply when speaking of an initial event, as the Big Bang may be thought to provide. Consider the kinds of physical process required to make sense of temporal notions, and in particular that of an instant. An instant, a point of time, can be annexed to the end-point of a change, as with starting or ceasing to move. However, if there is no preceding state of rest, there is no starting to move, so no possibility of marking a point of time by reference to such a happening. With respect to an initial physical happening, we cannot invoke the model of an event to which an instant of time might be assigned which is in any sense a temporal boundary, a point of division between the start of the event and an eventless period which preceded. We must always remain temporally within the universe, never somehow break the barrier and find ourselves on the other side, but if there were an initial instant there would be another side—just as, for a body to have a surface requires there to be a contiguous space. None of this is to deny anything involved in a Big Bang cosmology. It is just that any talk about the universe as coming into existence is to be replaced by talk of its finite duration—a matter of a more apposite redescription. Big Bang or no Big Bang, there has never been a time when there was nothing, and our conception of the Big Bang has to be accommodated to that consideration.

The notion of a finite duration has been offered as an approximation to that of a beginning of existence for the universe, but someone who wished to speak of the universe as having begun to exist might reasonably protest that they had not meant anything more than what is captured by the former: to say that the universe came into existence so many years ago is simply to say that it is so many years old. There need be no implication that some event took place at a first moment of time. What is important is that we should avoid conceptions of a temporal boundary that carry over conditions applicable only to happenings within the universe; likewise with the notion of the universe as ceasing to exist. It is not as if, were this to happen, there would then be nothing there. States, more generally, may be handled in this way. If a body has at no time been stationary, then it will have been in motion at every moment of its existence, in which case we cannot say that it began to move, but we could still, it would seem, speak of it as having been in motion for only a finite time. What is important is that a beginning, whether of change or of existence, rather than a merely finite duration, appears to be needed if we are to have an event, a happening in time, which raises a question of causation."

(Rundle, Bede. Why there is Something rather than Nothing. Oxford: Oxford University Press, 2004. pp. 122-4)
"We may philosophize well or ill, but we must philosophize." – Wilfrid Sellars

Tamminen
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### Re: Could everything have existed forever?

So, as RJG says, there has always been something, but that "always", the time towards the past, may be finite, as the Big Bang suggests. And we cannot go outside of the universe and say anything like "start of the universe". Looks reasonable, but I am not sure if we can avoid all logical contradictions here. Can you? What does it mean that time is finite? Will we meet a time barrier if we make a time travel to the past? Or is it just a question of the geometry of spacetime? And what does that mean, concretely? No wonder that even as clever a man as Kant could not make a coherent picture of this.

Consul
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### Re: Could everything have existed forever?

Tamminen wrote:
July 12th, 2019, 3:02 am
So, as RJG says, there has always been something, but that "always", the time towards the past, may be finite, as the Big Bang suggests.
Right, because if "there has always been something" means "there is no time in the past when there is nothing", this is true even if the temporal dimension of spacetime is past-finite.
"We may philosophize well or ill, but we must philosophize." – Wilfrid Sellars

devans99
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### Re: Could everything have existed forever?

RJG wrote:
July 11th, 2019, 6:39 pm
devans99 wrote: ...so a pseudo type of time of some sort. So that would allow for a start of time, the Big Bang etc…
"A pseudo type of time"?? Do you not see that you are digging a deeper hole? -- Okay, just for grins, lets (falsely) assume and accept that some "pseudo time" started "time", okay, so now tell me (without further kicking-the-can-down-the-road!!), what started this "pseudo time"? Are you now going to tell me that there is another "turtle" under this "turtle"? How far down do these turtles go???

Time cannot be started because "starting" is not possible in a timeless existence. Time cannot precede itself to start itself. X<X is logically impossible, and X<X<X<X is also still logically impossible.
Something has to have permanent existence (which is not possible inside of our time) and also be causally efficacious at the same time. If its environment is like growing block universe, maybe 'pseudo-time' started with the first movement of the pre-existing brute fact (God I assume)?

devans99
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### Re: Could everything have existed forever?

Consul wrote:
July 11th, 2019, 3:49 pm
Okay, I see that my formulation is ambiguous. I mean:

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** of S with a finite cardinality N* such that N* > N.
Still not with you. All subsets S* with finite cardinality cannot have a single cardinality value of N - there must be an N1, N2, N3, etc?
Consul wrote:
July 11th, 2019, 3:49 pm

A set's well-definedness doesn't depend on its having some determinate cardinality.

"A set is a well-defined collection of objects. Objects in the set are called elements.
The phrase 'well-defined' separates sets from other collections. If we take the word 'well' to mean good and the word 'defined' to mean description, then a set is a collection that has a 'good description'. In other words, a set is well-defined if we know exactly which objects are or are not in the set. So we must avoid describing sets with relative words that can take on different meanings depending on the situation."
This definition is very vague. He starts with 'A set is a well-defined collection of objects' - which I agree with - it is a finite list of objects. Then he goes onto say a collection that has a 'good description' - that is hardly the foundation of a rigorous theory of sets.
Consul wrote:
July 11th, 2019, 3:49 pm
This is refuted by the fact that the beginningless infinite series of negative integers is well-defined and well-ordered. And, for example, there is a corresponding (possible) beginningless infinite series of years BC; and this series is well-defined and well-ordered too:
… -4, -3, -2, -1
… -4 BC, –3 BC, -2 BC, -1 BC
The collection of negative integers exists purely in our minds - it is not physical like a particle or the universe. Illogical/undefined things can exist in our minds (like square circles), illogical/undefined things cannot exist in reality. Take the example of an eternal, 24 hour clock. Then if we represent time as t in hours, then the clock always reads t % 24. So if t = 49, then 49 % 24 = 1:00am. If t is UNDEFINED (because time never started), then the clock always reads UNDEFINED % 24 = UNDEFINED. So this an example of a general rule - the initial state determines all the subsequent states - an initial state (a start of time) is required for there to be any subsequent states. This rule applies to everything in the universe (except the contents of our minds which are allowed to flaunt logic).
Consul wrote:
July 11th, 2019, 3:49 pm
Part of this number's definition is its position in the infinite series of negative integers.

Anyway, your "undefined" is undefined. What's your definition of "well-definedness" in this context?
Well, I think that -256 is well-defined in the sense I can define it by counting backwards:
{ 0, -1, -2, ..., -256 }

But I cannot define -256 by counting forwards:
{..., -255, -256 }

The first sequence is realisable in reality - it has a concrete starting point which gives concreteness to all subsequent members. The second sequence starts with '...' - IE it has no concrete starting point so nothing in it is well defined.

RJG
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### Re: Could everything have existed forever?

devans99 wrote:Something has to have permanent existence…
YES! -- and the only solution that passes the muster of sound logic is --- Matter-Time-Space is "permanent"; has always existed (never not existed).

Causations (events) are the interactions of matter WITHIN time and space, which EXCLUDES them (matter-time-space) from having a causative start.

It is the 'action' of the stuff 'inside' the container that is subject to causative starts and ends, not the container itself (or the stuff itself). The "permanent" container and stuff are prerequisites to the existence of 'action' (events), ...not the other way around!

devans99
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### Re: Could everything have existed forever?

RJG wrote:
July 12th, 2019, 7:43 am
YES! -- and the only solution that passes the muster of sound logic is --- Matter-Time-Space is "permanent"; has always existed (never not existed).

Causations (events) are the interactions of matter WITHIN time and space, which EXCLUDES them (matter-time-space) from having a causative start.

It is the 'action' of the stuff 'inside' the container that is subject to causative starts and ends, not the container itself (or the stuff itself). The "permanent" container and stuff are prerequisites to the existence of 'action' (events), ...not the other way around!
If we view things in terms of causality, which of the following statements would you disagree with and why?

1. Everything effect in time must has a cause
2. No effect can be the cause of itself
3. So at least one cause must be outside of time

devans99
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### Re: Could everything have existed forever?

Sorry, typo, obviously I meant:

If we view things in terms of causality, which of the following statements would you disagree with and why?

1. Every effect in time must has a cause
2. No effect can be the cause of itself
3. So at least one cause must be outside of time