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[psyreporter]

I noticed the following article in a news feed:

Philosopher Wes Morriston and I have coauthored a paper on the Kalam cosmological argument, and it has been accepted publication in the journal Philosophical Quarterly. Once it is actually available on their page access will probably be limited, unless you have an institutional subscription. However, for now you can download it (for free) via this link.

Endless and Infinite

Abstract: It is often said that time must have a beginning because otherwise the series of past events would have the paradoxical features of an actual infinite. In the present paper, we show that, even given a dynamic theory of time, the cardinality of an endless series of events, each of which will occur, is the same as that of a beginningless series of events, each of which has occurred. Both are denumerably infinite. So if (as we believe) an endless series of events is possible, then the possibility of a beginningless series of past events should not be rejected merely on the ground that it would be an actual infinite.

Proponents of the Kalam cosmological argument seek to establish that any temporally ordered series of discrete events must have a beginning. One of their principal arguments for this conclusion is that a beginningless series of discrete events would have the paradoxical features of an actual infinite – features that could not be instantiated ‘in the real world’. In particular, they point out that an actually infinite series has a distinctive property, which we shall call the ‘Cantorian Property’. A series has the Cantorian Property when it can be placed in one-to-one correspondence with infinitely many of its proper parts, so that the whole has the ‘same number’ of elements as its parts. For instance, there are just as many natural numbers as there are even numbers, etc. But in the ‘real world’, they say, the whole must always be greater than any of its proper parts. So, in the real world (as opposed to the world of mathematics), an actually infinite series is impossible; nothing real can have the Cantorian Property (See Craig & Sinclair 2011: 110). And this is said to establish the first premise of the following argument:

• An actual infinite cannot exist.
• An infinite temporal regress of events is an actual infinite.
• Therefore, an infinite temporal regress of events cannot exist. (Craig & Sinclair 2011: 103)

Now one might have thought that if these considerations were sufficient to show that a beginningless (and therefore infinite) series of past events is impossible, they would apply with equal force to an endless (and therefore infinite) series of future events.1 After all, one could make a seemingly symmetrical argument as follows:

• An actual infinite cannot exist.
• An infinite temporal progress2 of events is an actual infinite.
• Therefore, an infinite temporal progress of events cannot exist.

If this second argument were equally as sound as the original one, this would be bad news for the proponents of the Kalam. For one thing, it is implausible to claim that the future could not be endless. For example, one can easily imagine a series of future events, each of which is causally sufficient for another. Again, one can imagine an endless series of events, each of which is fore-ordained by an all-powerful God. As far as we can see, these are genuine metaphysical possibilities.

https://useofreason.wordpress.com/2020/ ... -infinite/

The questions:

1) is it possible for true infinity to exist?
2) is it plausible to assume that time must have had a beginning?

[Steve3007]

Regarding the paper: an interesting find.

1) is it possible for true infinity to exist?

I think this is another "it depends what you mean by..." situation that is very common in discussions about things like this.

In this case, it depends what you mean by the verb "to exist". If you mean "to be a part of the world that we propose to be the cause of our sensations" (sometimes arbitrarily referred to as "the material world") then I would say no. It is part of the definition of infinity that it does not exist in that sense. It is an abstract mathematical construct that, by its nature, doesn't correspond to anything physical. It is a limit towards which physical quantities can tend but never reach. But if you used the verb "to exist" to include such abstract mathematical concepts then, yes, it does exist.

2) is it plausible to assume that time must have had a beginning

In order to even begin discussing what such things might mean we have to try to dispense with language that is trapped inside the temporal world, or failing that state our redefinitions of those language elements. In normal, every usage, the word "beginning" refers to the head of a queue of events and the word "event" refers to a point within time. So, when using words in that everyday sense, the expression "the beginning of time" is a category error. It makes no more sense than other category errors, such as "the colour of time". (Although obviously such expressions can still be used metaphorically or poetically.)

I think an alternative question, such as "is there an infinite amount of time?" (and an analogous question for space) arguably avoids that particular category error. That is a question that has been discussed at a length which sometimes appears itself to tend to infinity in various other topics on this site. I don't think those discussions will ever come to a resolution because, among the many disagreements, there are disagreements as to what constitutes a logical argument. If even that basic conversational foundation has not been laid, people will be doomed to forever talk at crossed purposes with each other.

[Terrapin Station]

What's intuitively implausible about time extending infinitely into the past isn't simply that it posits an actual infinity. It's rather that "we'd never get to point Tn," because there's an infinity of previous times that need to arrive first.

Of course, a beginning of time seems just as intuitively implausible to us, because it would have to happen acausally.

So there's no way around the fact that our options are intuitively implausible.

At any rate, is it possible for something to be an actually infinity? Sure.

Re the second question, I wouldn't say that time must have a beginning, but it's possible that it does.

[Present awareness]

I noticed the following article in a news feed:

Philosopher Wes Morriston and I have coauthored a paper on the Kalam cosmological argument, and it has been accepted publication in the journal Philosophical Quarterly. Once it is actually available on their page access will probably be limited, unless you have an institutional subscription. However, for now you can download it (for free) via this link.

Endless and Infinite

Abstract: It is often said that time must have a beginning because otherwise the series of past events would have the paradoxical features of an actual infinite. In the present paper, we show that, even given a dynamic theory of time, the cardinality of an endless series of events, each of which will occur, is the same as that of a beginningless series of events, each of which has occurred. Both are denumerably infinite. So if (as we believe) an endless series of events is possible, then the possibility of a beginningless series of past events should not be rejected merely on the ground that it would be an actual infinite.

Proponents of the Kalam cosmological argument seek to establish that any temporally ordered series of discrete events must have a beginning. One of their principal arguments for this conclusion is that a beginningless series of discrete events would have the paradoxical features of an actual infinite – features that could not be instantiated ‘in the real world’. In particular, they point out that an actually infinite series has a distinctive property, which we shall call the ‘Cantorian Property’. A series has the Cantorian Property when it can be placed in one-to-one correspondence with infinitely many of its proper parts, so that the whole has the ‘same number’ of elements as its parts. For instance, there are just as many natural numbers as there are even numbers, etc. But in the ‘real world’, they say, the whole must always be greater than any of its proper parts. So, in the real world (as opposed to the world of mathematics), an actually infinite series is impossible; nothing real can have the Cantorian Property (See Craig & Sinclair 2011: 110). And this is said to establish the first premise of the following argument:

• An actual infinite cannot exist.
• An infinite temporal regress of events is an actual infinite.
• Therefore, an infinite temporal regress of events cannot exist. (Craig & Sinclair 2011: 103)

Now one might have thought that if these considerations were sufficient to show that a beginningless (and therefore infinite) series of past events is impossible, they would apply with equal force to an endless (and therefore infinite) series of future events.1 After all, one could make a seemingly symmetrical argument as follows:

• An actual infinite cannot exist.
• An infinite temporal progress2 of events is an actual infinite.
• Therefore, an infinite temporal progress of events cannot exist.

If this second argument were equally as sound as the original one, this would be bad news for the proponents of the Kalam. For one thing, it is implausible to claim that the future could not be endless. For example, one can easily imagine a series of future events, each of which is causally sufficient for another. Again, one can imagine an endless series of events, each of which is fore-ordained by an all-powerful God. As far as we can see, these are genuine metaphysical possibilities.

https://useofreason.wordpress.com/2020/ ... -infinite/

The questions:

1) is it possible for true infinity to exist?
2) is it plausible to assume that time must have had a beginning?

1) Yes, it is possible for infinity to exist!
2) Time is just a measurement and one may measure as far back or forward in time as one likes. All measurements in time begin from the zero point of “now”. The reason that “now” is the zero point is because “now” is already here and it takes no time to get to “now”.

One may not talk about time without also talking about space, for time is the measured distance that something travels through space. The second hand on a clock travels through the space on the circle of the clock, which is measured in seconds, minutes and hours. Space itself is infinite by definition because space is defined as that which is not there, so how could something which is not there have an ending?

[Atla]

Abstract: It is often said that time must have a beginning because otherwise the series of past events would have the paradoxical features of an actual infinite.

Assuming that reality is logical (which might not be the case): the above is a false dicohotomy based on illogical linear thinking, a mistake almost everyone makes.
Actual infinites are possible. However we can rule out both time with a beginning, and an endless series of past events as illogical.

[Steve3007]

Assuming that reality is logical (which might not be the case)...

In what sense could the proposition "reality is not logical" ever be meaningful?

[Terrapin Station]

Space itself is infinite by definition because space is defined as that which is not there, so how could something which is not there have an ending?

Something that's not there can't even have a beginning ontically, because it's not there.

[Terrapin Station]

Assuming that reality is logical (which might not be the case)...

In what sense could the proposition "reality is not logical" ever be meaningful?

In the sense that logic is merely a way that we think about relations--just like mathematics is, only mathematics and logic are slightly different types of thought about relations. (Mathematics being focused on quantitative relationships, logic being focused on implicational relationships.)

"Reality is not x" is a way of saying that x doesn't occur in the world outside of how we think about it.

[Atla]

Assuming that reality is logical (which might not be the case)...

In what sense could the proposition "reality is not logical" ever be meaningful?

Why would it have to be meaningful?

[chewybrian]

Assuming that reality is logical (which might not be the case)...

In what sense could the proposition "reality is not logical" ever be meaningful?

You might as easily ask what is logical about reality. Doesn't logic imply fairness? Wouldn't a logical reality reward effort and punish laziness, and give all of us the same skill set to work with? What is logical about the way the universe randomly doles out good fortune or misfortune, life and death? Logic makes sense; the reality does not.

There is also a limit where logic and science break down, as in discussions of infinity. The universe is clearly absurd, at least from our current level of understanding. It does not provide us with any guidance as to what we should be doing, what might make us happy. It presents us with irreconcilable contradictions or dilemmas, like a choice between free will and cause and effect. Reality is what it is. Logic is a device we have constructed to try to understand reality. It does a good job sometimes, and sometimes it breaks down, or we lack the knowledge to use the next level up of logic. Perhaps, if we had perfect knowledge, the universe would be seen to be perfectly aligned with our logic. But, when we lack the knowledge, and there appear to be contradictions, we must concede the possibility that our logic might never explain it all.

[Terrapin Station]

You might as easily ask what is logical about reality. Doesn't logic imply fairness?

?? No.

Logic is simply about implicational relations. You can think of it as one huge or overarching conditional--If P, then Q.

Logic never tells us what's actually the case. And it certainly doesn't tell us any normatives, like fairness.

It only tells us that if P is the case, then Q follows.

[Present awareness]

Space itself is infinite by definition because space is defined as that which is not there, so how could something which is not there have an ending?

Something that's not there can't even have a beginning ontically, because it's not there.

Exactly, no beginning or ending = infinite

[Wossname]

Steve3007 said

I think this is another "it depends what you mean by..." situation that is very common in discussions about things like this.

In this case, it depends what you mean by the verb "to exist". If you mean "to be a part of the world that we propose to be the cause of our sensations" (sometimes arbitrarily referred to as "the material world") then I would say no. It is part of the definition of infinity that it does not exist in that sense. It is an abstract mathematical construct that, by its nature, doesn't correspond to anything physical. It is a limit towards which physical quantities can tend but never reach. But if you used the verb "to exist" to include such abstract mathematical concepts then, yes, it does exist.

I am attracted to this argument. This may reflect the prejudice of a finite brain designed to survive in an environment of finite challenges, and which cannot get beyond its limited thinking to grasp the notion of a truly infinite universe in which all metaphysically possible events can happen/have happened/will happen.

My prejudice arises because of Bluebell. Bluebell is a red dragon who likes to eat baked beans and drink beer. She often wears a tutu, and on every second Tuesday she likes to stand in a tub of warm custard and sing “God save the queen” in a Chinese accent to her pet halibut which Bluebell calls fluffy but which actually answers to the name whywon’tyoufortheloveofallthat’sholyshutupGeorge II. It is hard to tell if whywon’tyoufortheloveofallthat’sholyshutupGeorge II is impressed by Bluebell’s performances. He is outwardly sanguine. But Bluebell does have quite a nice soprano, and she is generally well liked apart from her occasional bouts of disturbingly violent flatulence (beans and beer being a somewhat unfortunate mix). Bluebell is politically left wing and viewed with suspicion by her next door neighbour, a blue dragon called Adolf, but then he has a grating tenor and couldn’t hold a note if it was glued to his hand.

I don’t actually believe Bluebell exists. That would be silly. But I fear that somewhere there is a fervent eyed mathematician who is willing to tell me that, in an infinite universe, Bluebell does exist. She must exist. Worse still, in an infinite universe there are an infinite number of Bluebells. Even worse still, I must accept that in an infinite universe there are an infinite number of mathematicians regaling me with terrible claims about my poor Bluebell which can be of infinite variety and many of which are unrepeatable in polite company. That’s mathematicians for you.

I suppose I ought to be entranced by the thought of an infinite number of Bluebell’s. But I am not. I am grumpy. I should tell any mathematician making such claims to my disbelieving face to shove their abacus and fanciful, ridiculous and sometimes obscene claims about Bluebell up their backside (fanciful or not). I might do this at considerable volume. And then I would probably sulk.

But I can’t help but think this would show the tiniest smidgeon of a lack of grace on my part. I am not attracted to this vision of a universe in which there are infinite numbers of me sulking gracelessly.

And just maybe…….

[Steve3007]

In what sense could the proposition "reality is not logical" ever be meaningful?

In the sense that logic is merely a way that we think about relations--just like mathematics is, only mathematics and logic are slightly different types of thought about relations. (Mathematics being focused on quantitative relationships, logic being focused on implicational relationships.)

"Reality is not x" is a way of saying that x doesn't occur in the world outside of how we think about it.

Ok, fair enough. So it could be simply a way of drawing attention to a potential category error, with the two categories being reality and the abstract concepts of logic and mathematics. A bit like pointing out that logic is not a species of fish. It's not. I can't argue with that.

I wonder if that was Atla's intended meaning.

Why would it have to be meaningful?

It wouldn't have to be. I was just curious as to whether you thought there was any sense in which it is.

[Atla]

It wouldn't have to be. I was just curious as to whether you thought there was any sense in which it is.

Well, all that humans are capable of doing is come up with metaphysicses that account for all known facts, and also make sense. And then maybe argue about which one of these metaphysicses is the simplest and therefore most likely one.

So far reality seems to make sense, everything seems to be ordered, logical, so we can make laws about it. It's even possible to explain QM in a logical way, it's just extremely difficult. But we don't observe things happening that are patently illogical or a-logical, that just can't make sense to us in any way.

So in metaphysics we could just discard the illogical idea of change in general. All change is impossible therefore illusory, so both linear time with a beginning and linear time without a beginning is just our everyday projection of linear thinking onto reality, which logically should obviously be circular in nature. (People are bad at logic.)

But it's also possible that, say on a larger scale, reality does in fact behave in ways that patently make no sense to us, and can never make sense to us. We just haven't observed such behaviour yet. Maybe reality is patently illogical or a-logical, and in a way that would be the end of the road for philosophy there.

(I'm a nondualist, by reality I simply mean the universe/multiverse/all that exists, or the nature of the universe/multiverse/all that exists.)