A simplified argument from motion

[BlaineTog]

So when God commands genocide or murder, as he commonly did in the Old Testament, it is good to commit such acts? How can that be reconciled with a morally absolutist stance that says those very acts are universally wrong?

Hey, whoa, slow down there. I’m Catholic. What makes you think I know anything about scripture?

In all seriousness, though, yes, it was good to commit such acts, though I’m not really sure about the true significance of those passage and you’d need to ask a theologian. Murder is only wrong because it’s usurping God’s right to choose when to end life. If God himself told you it was ok to kill someone, then it must be their time to die. Again, though, I’m no theologian and I suspect those passage as far more complicated than this, and additionally, I think the number of instances in which you have a God-given right to kill someone is probably next to zero, if not zero, in the modern world, so this is no excuse anymore.

I am open, but it’s kinda like waiting for somebody’s imaginary friend to give me candy.

Ok, good. You know, that imaginary friend has some really awesome candy. I think he might be half Belgian.

It would have removed the potential for sin, not free will – a concept I don’t have much truck with in the first place. Adam and Eve would still have been free agents, able to choose how they lived their lives; but they would not have had to deal with questions of morality.

Once again, removing the potential for sin also removes free will, since you can’t possibly have free choice without something to choose between.

God’s best wasn’t good enough?

Yep. You could have the best defense attorney imaginable and the judge could still sentence you to die. God will do his best to persuade us, but since he respects our free will, he will not rape us by dragging us kicking and screaming into heaven. Hardness of heart and all that.

 

[Mirdath]

In all seriousness, though, yes, it was good to commit such acts, though I’m not really sure about the true significance of those passage and you’d need to ask a theologian. Murder is only wrong because it’s usurping God’s right to choose when to end life. If God himself told you it was ok to kill someone, then it must be their time to die. Again, though, I’m no theologian and I suspect those passage as far more complicated than this, and additionally, I think the number of instances in which you have a God-given right to kill someone is probably next to zero, if not zero, in the modern world, so this is no excuse anymore.

This, I think, is a whole new (or old, for that matter) thread. Suffice to say I disagree, and vehemently.

Once again, removing the potential for sin also removes free will, since you can’t possibly have free choice without something to choose between.

Going back to my Aquinian mistake, the Angelic Doctor does posit that the angels possess free will while simultaneously being unable to sin. Obviously such a thing is not impossible for God, who created the laws of logic and could have created them differently if he chose to.

Yep. You could have the best defense attorney imaginable and the judge could still sentence you to die. God will do his best to persuade us, but since he respects our free will, he will not rape us by dragging us kicking and screaming into heaven. Hardness of heart and all that.

God is not the district DA; he is the judge, the jury, and the executioner, with Satan as prosecutor. He may be a lenient, forgiving judge, but it’s a kangaroo court for all that. You might be compared to Hans Beckert in M, who knew what he did; I am more in the situation of Josef K in The Trial.

 

[punkforchrist]

OK. That is the only point I was trying to make about counting from 1 to 10. So therefore your argument about the book stands refuted. There is only a finite number of moves necessary to get the book from whoever has it now to me.

In the analogy, each person in the set must borrow the book from another. The set is infinite.

An infinite set cannot be formed by a finite number of successive additions. As the limit of the number of successive additions goes to infinity, however, the set approaches the (countably) infinite set.

In other words, if the set is infinite then it is infinite, which is a tautology.

And, you still haven’t provided any proof for the claim that an infinite set (in this case a hypothesized infinite regress of motion) must be formed by successive addition. Sets can be formed by successive addition but that doesn’t mean they must be.

Unless one denies the view of dynamic time, which is the prevalent position, in favor of some kind of static time, then motion is formed by successive addition. In dynamic time there is an actual change being formed.

There is no mover in the “infinite past” because there is no “infinite past”.

That’s fine, but what’s the difference between that and the claim that the past is finite?

There is a difference between having a set with an infinity of members, but with each member a finite distance from zero, and a finite set with each member a finite distance from zero. You do agree that the “set of all finite negative integers” is an infinite set, yes? Your confusion appears to be in demanding that an infinite set have “negative infinity” as a member.

I understand that aleph-null is the set of all contained integers rather than a number itself. However, if all past events have been actualized, then each member of that set must have been actualized. This means that an infinite series of numbers must have been traversed in order to arrive at the present. If this is impossible, then the past is finite.

No, it means that there is an infinity of points that have been actualized, not there must be an actual point in the infinite past. “Negative infinity” is not a member of the set. For each member of the set by definition has another member which is 1 less than it.

Please see above.

It is not. Again, because there is an infinity of movers does not imply there is an infinite past. Every one of the movers exists at a finite time in the past from today.

This is highly problematic if each member of the set is traversed.

 

[john_doran]

Going back to my Aquinian mistake, the Angelic Doctor does posit that the angels possess free will while simultaneously being unable to sin. Obviously such a thing is not impossible for God, who created the laws of logic and could have created them differently if he chose to.

i’m kind of jumping into the middle of something here, but i feel it incumbent upon myself to point out that free choices are not made only between good and evil, but also between goods; that angels choose freely but do not sin is not a logical paradox - they never sin because there’s nothing about putatively sinful alternatives that seems choiceworthy.

in fact, anyone who makes it to heaven and attains the beatific vision will be in the same situation: nothing sinful will seem choiceworthy, so the only free choices they make will be between alternatives all of which are good.

oh, and god doesn’t create logic…

 

[BlaineTog]

This, I think, is a whole new (or old, for that matter) thread. Suffice to say I disagree, and vehemently.

It is relevant, though. Why is murder wrong if not because it’s usurping God’s right to choose when life should end? Life must end, after all. It’s not like murder causes something to happen which might otherwise have been avoided, except in a purely temporal sense.

Going back to my Aquinian mistake, the Angelic Doctor does posit that the angels possess free will while simultaneously being unable to sin.

I’m not going to pretend to be an expert on Angels, but I do have a few salient points: first, Angels function differently from humans. Their potential is far below ours. Second, angels are outside of time, so the same concepts of sinning and choice functions differently in them (as it does for the souls in heaven). Indeed, since all human thought is in the form of time, it’s impossible for us to truly understand how things could be without time, and they closest we can come to to say “a choice made for eternity,” or something like that. Or at least that’s the closest I can come. Maybe someone could write a novel about it to get us closer, I dunno. Third, Angels do have the ability to sin, in a sense, though since it’s a choice made throughout eternity, angels who have remained angels and not become demons (who are angels who freely chose to leave God’s service) have already made their choice. As I said, it’s difficult to talk about this, just as it’s difficult to imagine a paper cutter existing without space.

Obviously such a thing is not impossible for God, who created the laws of logic and could have created them differently if he chose to.

God did not create logic. Logic is part of God in the same way that omnipotence and justice are. It goes all the way up to the top.

God is not the district DA; he is the judge, the jury, and the executioner, with Satan as prosecutor. He may be a lenient, forgiving judge, but it’s a kangaroo court for all that. You might be compared to Hans Beckert in M, who knew what he did; I am more in the situation of Josef K in The Trial.

You’ve extended my metaphor further that I intended it, as well as misinterpreted it, though I should have been more clear. To change it, if life is a jury trial, the defense attorney is the Holy Spirit, Jesus is the defendant, and the Father is the judge. You are the jury, and no matter how hard the defendant’s attorney argues, you still might come back with a verdict against him.

Sorry, I really wasn’t intending the metaphor to stretch this far. The point was just that incredible skill isn’t always sufficient.

 

[SeekingCatholic]

In the analogy, each person in the set must borrow the book from another. The set is infinite.

We’re agreed on this. But not on the conclusion you attempt to draw from it.

Unless one denies the view of dynamic time, which is the prevalent position, in favor of some kind of static time, then motion is formed by successive addition. In dynamic time there is an actual change being formed.

All that shows is that there is an addition (that an individual motion is formed by a single addition), not that the set must be formed by the collection of those additions. I can take the set of negative integers, and then add the largest member plus one. This doesn’t make the set formed by the addition.

That’s fine, but what’s the difference between that and the claim that the past is finite?

I should have used more specific terms. What I mean by “no infinite past” is there exists no point in the past at an infinite distance from now, even in an infinite regress framework, not that the universe has a beginning.

I understand that aleph-null is the set of all contained integers rather than a number itself. However, if all past events have been actualized, then each member of that set must have been actualized.

True.

This means that an infinite series of numbers must have been traversed in order to arrive at the present.

Again, traversed FROM WHERE? What starting point? If you want to specify a trajectory you must specify a beginning and an end. Now what starting point in the past can you point to where an infinite series of numbers must have been traversed? If you say “the absolute beginning”, there is no absolute beginning in an infinite regress, just like the set of negative integers has no “beginning”. And, “negative infinity” is not part of the set. There is no member of the set which is at an infinite distance from now. Thus, for every beginning you can specify which belongs to the set, only a finite series of numbers needs to be traversed.

If this is impossible, then the past is finite.

“Finite” in the sense that every moment in the past is a finite distance from now, yes; “finite” in the sense that there therefore must be a beginning, no.

This is highly problematic if each member of the set is traversed.

An eternal universe is weird. It has no beginning. Every moment in its history is a finite distance in time from us, each moment in its history really happened, and there are an infinite number of such moments, since for every moment there is a moment preceding it. But all these things follow merely from the definition of an eternal universe.

 

[Mirdath]

i’m kind of jumping into the middle of something here, but i feel it incumbent upon myself to point out that free choices are not made only between good and evil, but also between goods; that angels choose freely but do not sin is not a logical paradox - they never sin because there’s nothing about putatively sinful alternatives that seems choiceworthy.

This is actually quite close to my view of how human choice operates: we choose options from a prioritized list, and some of those options we consider absolutely abhorrent.

oh, and god doesn’t create logic…

Interesting! Not that I disagree with you, but what would you say is the genesis of logic, then?

BlaineTog:

It is relevant, though. Why is murder wrong if not because it’s usurping God’s right to choose when life should end? Life must end, after all. It’s not like murder causes something to happen which might otherwise have been avoided, except in a purely temporal sense.

Statements like that make me very afraid that people like you will suddenly decide God has, in fact, commanded just this. Would you shoot me if you were convinced beyond what to you is reasonable doubt that God meant you to be the instrument by which my life is to be ended?

Murder can be considered wrong for a great many more reasons, all of them a great deal more solid than ‘God says hold off but he might change his mind’.

You’ve extended my metaphor further that I intended it, as well as misinterpreted it, though I should have been more clear. To change it, if life is a jury trial, the defense attorney is the Holy Spirit, Jesus is the defendant, and the Father is the judge. You are the jury, and no matter how hard the defendant’s attorney argues, you still might come back with a verdict against him.

How is Jesus the defendant? Is sending him to hell a matter of question here? We are supposedly the ones on trial.

 

[BlaineTog]

I’m going to take this to PM, because it really is starting to get off-topic.

 

[freesoulhope]

That’s what you need to provide some argumentation for in order to prove. As I pointed out an infinite set is obtained in the limit of number of additions going to infinity.

I enjoyed your replys, and i have become aware of the flaws you pointed out; but i thought i’d have another go.

The problem of infinity

If something is going onto infinity, then how can it be trully infinite? It doesn’t seem to me that your speaking of a trully infinite set of something; rather you speaking about a mathematical principle of something. I wish you could show me how integers relate to the real world of cuase and effect.

I argue that, even though we can imagine the concept of an infinite series of finite cuases, would it not be the case that an infinite set of causes, in truth, would be “static”; as in, we can observe that one thing has come before an other(only from outside the universe), but because there is an **infinite past **and an infinite future, we cannot observe “cuasitive duration”. If there isn’t an infinite future, but only a potential one; then there is a point in time that we can certainly call number one(the present moment), from which we can concieve of counting back into the past. So if the future is potentailly finite, then it is not totally bassless to assume that the past is finite. Unless we percieve time as being wholly separate from matter, i don’t see how we can have a passing of moments(cuasitive duration) with an already existing future—a chain of events stretching to infinity. But theres the thing; it doesn’t seem reasonable to have an infinite progress either. If an actual infinite cannot be reached by addition, then why is it reasonable that one can reach an infinite regress? It doesn’t seem to me that an actual infinity exists; becuase, finite numbers, in a causitive duration, will only reach a finite number of things. The same goes when we speak of a regress; we can’t speak of it of being infinite, because the past, no matter how long it indures, it will always be finite in number!!! Thats my proof that the universe is finite in nature!!! The only explanation you have given me is integers, which strikes me as nothing more then the magic of abstract numbers, rather then real tangible reality. Can you please teach me Integers? Maybe I’m missing something? Maybe I,m running into the same floor.

An infinite universe does not disprove God.

Please note, I personally don’t have a problem with an infinite regress, i believe that every cause in that regress has a “nature of being”; which is the reason for why a thing is a ball rather then a triangle. I argue that this cannot be explained by a mere natural cause. Take for instance, the nature of “cuase and effect”, or the “nature of infinity”; such explanations would have to transverse or transcend the physical world. Why not an infinite chain of pink elephants? It seems self evident that a nature of something is more then the sum of its natural cause( whether the universe is infinite or not); this reminds me of Platos “forms”. In this respect, it seems that it is evident that there can be a cause; or unmoved mover to an infinite universe; but such a cause or mover would have to be outside the boudries of natural causes and effects. For there to be an infinite chain of cause and effect, there has to be an unchanging nature which is above but united with the cause; for to say that the laws of nature, gave itself the laws of nature, seems to be contradictory. We can refuse these things an explanation, but what is interesting, is that when we do look for one, we necessarily transcend the objects nature. A thing can certainly be actualised and explained by a natural cause; but it doesn’t necessarilly follow that the prior cause has endowed the effect with the nature of being an effect— the effect has come from the cause—most certainly—but only becuase there is the “nature of effect”, by which the effect exists. For instance a quark is a quark, because it has a nature of a quark; but the quarks nature cannot be explained by the quark. We have to neccesarily look outside of it.

What do you think? Its my attempt at trying to be inteligent .

 

[SeekingCatholic]

The problem of infinity

If something is going onto infinity, then how can it be trully infinite? It doesn’t seem to me that your speaking of a trully infinite set of something; rather you speaking about a mathematical principle of something. I wish you could show me how integers relate to the real world of cuase and effect.

OK, well I’m just using integers here to represent cause and effect; we can use “0” to represent the current event in a causal chain, the negative integers to represent events which have previously occurred, and the positive integers to represent events in the future which have yet to occur.

Now, I define a set {0}. I define an addition rule “add 1 to the last element in the set and add it to the end of the set”; this is equivalent to a causal chain extending in the future to the present. This is of course a finite set after every addition, despite the fact that there is no stopping rule.

Yet it is guaranteed that for every member of the infinite set of positive integers (plus zero), it will be included in the finite set after a finite number of additions. This is because the particular nature of the set is that it is a countably infinite set. You never get to “infinity” in a finite time, but you do get to each particular member of the infinite set after only a finite number of additions. This being the case, we can define the infinite set as those members which can be reached by a finite number of additions to the initial set. And thus, by definition “truly infinite” (in the sense of an infinite set) is identical with “going on to infinity” since every member will be reached after a finite number of additions.

This is not the case for all infinite sets; for instance, for the infinite set of all real numbers between zero and one. Whatever your addition rule is, there will always be numbers which take an infinite number of additions to reach (e.g. if you do successive bisections it will take an infinite number to reach any irrational number).

I argue that, even though we can imagine the concept of an infinite series of finite cuases, would it not be the case that an infinite set of causes, in truth, would be “static”; as in, we can observe that one thing has come before an other(only from outside the universe), but because there is an **infinite past **and an infinite future, we cannot observe “cuasitive duration”.

I really don’t know what you mean by “causative duration”. The same observation of immediate cause and effect is made in a temporal as well as an eternal universe.

If there isn’t an infinite future, but only a potential one; then there is a point in time that we can certainly call number one(the present moment), from which we can concieve of counting back into the past. So if the future is potentailly finite, then it is not totally bassless to assume that the past is finite.

Of course not.

Unless we percieve time as being wholly separate from matter, i don’t see how we can have a passing of moments(cuasitive duration) with an already existing future—a chain of events stretching to infinity.

It seems you’re broaching the deep question of whether the future “exists” in some sense prior to it happening. I have no particular insight on this question, but I am not convinced, as you seem to be here, that the answer is “no”. Questions of simultaneity and relativity are also going to come into play here. This might be a topic for another thread.

But theres the thing; it doesn’t seem reasonable to have an infinite progress either. If an actual infinite cannot be reached by addition, then why is it reasonable that one can reach an infinite regress? It doesn’t seem to me that an actual infinity exists; becuase, finite numbers, in a causitive duration, will only reach a finite number of things.

An actual countably infinite set can be reached by addition, since every member of the set can be reached by addition. We’re not talking about “infinity”, the number, we’re talking about an infinite set. (Cont’d…)

 

[SeekingCatholic]

The same goes when we speak of a regress; we can’t speak of it of being infinite, because the past, no matter how long it indures, it will always be finite in number!!! Thats my proof that the universe is finite in nature!!!

But it doesn’t prove the universe had a beginning. It only proves that every point in the past is a finite distance away from the present.

The only explanation you have given me is integers, which strikes me as nothing more then the magic of abstract numbers, rather then real tangible reality. Can you please teach me Integers? Maybe I’m missing something? Maybe I,m running into the same floor.

I hope I described integers in sufficient detail above.

An infinite universe does not disprove God.

Indeed not, and St. Thomas assumed an eternal universe when formulating the Five Ways.

Please note, I personally don’t have a problem with an infinite regress, i believe that every cause in that regress has a “nature of being”; which is the reason for why a thing is a ball rather then a triangle. I argue that this cannot be explained by a mere natural cause. Take for instance, the nature of “cuase and effect”, or the “nature of infinity”; such explanations would have to transverse or transcend the physical world.

IOW, you are asking why the laws of logic and mathematics are the way they are. I’ll have to defer to the experts in the philosophy of mathematics, for I know next to zero about it, but the laws of logic are simply necessary (they can’t be disproven), since one must use those very laws of logic in order to attempt to disprove them. You can’t ask “why is there a cause and effect?” without already assuming there exist at least hypothetical causes and effects.

Why not an infinite chain of pink elephants? It seems self evident that a nature of something is more then the sum of its natural cause( whether the universe is infinite or not); this reminds me of Platos “forms”.

This is assuming a natural cause is incapable of causing a nature of something. This has to be proved, not merely assumed.

In this respect, it seems that it is evident that there can be a cause; or unmoved mover to an infinite universe; but such a cause or mover would have to be outside the boudries of natural causes and effects.

This is true, but the difficulty lies in proving necessity, not merely possibility.

For there to be an infinite chain of cause and effect, there has to be an unchanging nature which is above but united with the cause; for to say that the laws of nature, gave itself the laws of nature, seems to be contradictory.

This might be a valid argument if by “laws of nature” you meant physical laws and so on. However here by “laws of nature” you mean cause and effect. And the trouble here is, as I pointed out, that when you ask “what caused cause and effect” you are already assuming the existence of cause and effect. And that a law is necessary is a sufficient explanation for its existence. For instance, you don’t need God to explain the law of non-contradiction. It exists as a necessary truth. You can’t attempt to disprove it without already assuming its truth.

…it doesn’t necessarilly follow that the prior cause has endowed the effect with the nature of being an effect— the effect has come from the cause—most certainly—but only becuase there is the “nature of effect”, by which the effect exists.

The “nature of effect” is a necessary truth, as I explained.

For instance a quark is a quark, because it has a nature of a quark; but the quarks nature cannot be explained by the quark. We have to neccesarily look outside of it.

The quarks (or anything’s) nature can be explained by what caused it. Again if you disagree with that you need to provide some proof for it.

 

[punkforchrist]

All that shows is that there is an addition (that an individual motion is formed by a single addition), not that the set must be formed by the collection of those additions. I can take the set of negative integers, and then add the largest member plus one. This doesn’t make the set formed by the addition.

Yes, but the set of negative integers is not formed in the same way as the past. In your example, you are taking a set in which all the members co-exist. The series of historical events, on the other hand, is formed by the succession of new events, at least on a dynamic theory of time.

I should have used more specific terms. What I mean by “no infinite past” is there exists no point in the past at an infinite distance from now, even in an infinite regress framework, not that the universe has a beginning.

I think this is a contradiction. All past events have occurred, which means that each member of aleph-null has occurred. If no member is both infinitely distant from today and actual (i.e. it has occurred), then the past does not have any actual infinite past.

Again, traversed FROM WHERE? What starting point? If you want to specify a trajectory you must specify a beginning and an end. Now what starting point in the past can you point to where an infinite series of numbers must have been traversed?

This is part of what I’m claiming is an absurdity. If we have no beginning point, then the present could never arrive. In fact, no point could ever arrive, since before it could an infinite number of events would have to proceed it. It’s like trying to jump out of a bottomless pit.

“Finite” in the sense that every moment in the past is a finite distance from now, yes; “finite” in the sense that there therefore must be a beginning, no.

I don’t see any distinction. If all past events have historically occurred, then all members of the set of past events have occurred. If the past is infinite, then each member of the set would have to have a historical actualization.

An eternal universe is weird. It has no beginning. Every moment in its history is a finite distance in time from us, each moment in its history really happened, and there are an infinite number of such moments, since for every moment there is a moment preceding it. But all these things follow merely from the definition of an eternal universe.

I agree that this follows from the definition of an infinite universe, but that doesn’t make an infinite universe physically possible.

 

[john_doran]

I should have used more specific terms. What I mean by “no infinite past” is there exists no point in the past at an infinite distance from now, even in an infinite regress framework, not that the universe has a beginning.

this doesn’t make any sense…

if the past contains an actual infinite number of past moments, then there must necessarily be at least one moment that exists at an infinite remove from the present moment, or else the past is not actually infinite.

SeekingCatholic:

An eternal universe is weird. It has no beginning. Every moment in its history is a finite distance in time from us, each moment in its history really happened, and there are an infinite number of such moments, since for every moment there is a moment preceding it. But all these things follow merely from the definition of an eternal universe.

sure, and a square circle is “weird”: every point on its side both is and is not equidistant from the point at its centre; it both does and does not have four internal angles each of which is ninety degrees. but all these things follow merely from the definition of a “square circle”…

given that http://mathworld.wolfram.com/images/equations/Aleph-0/inline3.gif has no immediately preceding member, how do you propose to complete an actually infinite set of moments of time by successive addition? that is, how do you propose to ***get to *****http://mathworld.wolfram.com/images/equations/Aleph-0/inline3.gif **by the addition of moments of time to the set of all temporal moments?

 

[SeekingCatholic]

PFC, again you keep repeating the same arguments which I have refuted time and again.

Yes, but the set of negative integers is not formed in the same way as the past. In your example, you are taking a set in which all the members co-exist. The series of historical events, on the other hand, is formed by the succession of new events, at least on a dynamic theory of time.

No, each individual historical event is so formed. Saying “the series is formed by the succession” doesn’t make sense. The series is the succession, by definition. There is no good reason why I cannot conceive of an universe with an infinite past as the set of negative integers, the present as 0, and the future as positive integers, and adding to the end of the array. Of course the element to be added depends on the one that was previously added, just like in “dynamical time” the present historical event is going to depend the immediately preceding one, and that on the one before that. It doesn’t prove the past cannot have an infinite number of elements, just like the set of negative integers.

I think this is a contradiction. All past events have occurred, which means that each member of aleph-null has occurred. If no member is both infinitely distant from today and actual (i.e. it has occurred), then the past does not have any actual infinite past.

But the past can still have an infinite number of elements. “Infinite past” can have two meanings: a) that there is a point in the past an infinite distance from the present; or b) that there exists an infinity of events in the past, each a finite distance from the present.

This is part of what I’m claiming is an absurdity. If we have no beginning point, then the present could never arrive. In fact, no point could ever arrive, since before it could an infinite number of events would have to proceed it. It’s like trying to jump out of a bottomless pit.

Again you have the measuring problem, just restated in different terminology here. You’re trying to measure something which, by definition, can’t be measured in an eternal universe. You’re assuming a starting point which doesn’t exist. The idea of something “before” an eternal universe, which you can then use as a starting point to measure the (infinite) number of events necessary to get to the present, is a fallacy, since an eternal universe has no beginning. Arguing about something “before” an eternal universe is therefore a contradiction in terms. But to measure you need to specify a beginning and an end, by definition. Once you do, the measure will be finite.

You see reality like this:
Beginning → Present → End. This is simply not the version of reality which exists in an eternal universe. There is no beginning and no end. You can’t argue from the version of reality which exists in a temporal universe to argue against an eternal universe simply on the basis that it is not the version which exists in a temporal universe.

I don’t see any distinction. If all past events have historically occurred, then all members of the set of past events have occurred. If the past is infinite, then each member of the set would have to have a historical actualization.

I’m not disagreeing here.

I agree that this follows from the definition of an infinite universe, but that doesn’t make an infinite universe physically possible.

No, but you need to do a little better than arguing, circularly, that an infinite universe must be impossible because it is infinite.

 

[SeekingCatholic]

this doesn’t make any sense…

if the past contains an actual infinite number of past moments, then there must necessarily be at least one moment that exists at an infinite remove from the present moment, or else the past is not actually infinite.

An infinite set does not have to contain the member “negative infinity”. All members of the set of past moments exist at a finite remove from the present moment, if I define the set as “the set of all finite negative integers”.

sure, and a square circle is “weird”: every point on its side both is and is not equidistant from the point at its centre; it both does and does not have four internal angles each of which is ninety degrees. but all these things follow merely from the definition of a “square circle”…

An eternal universe involves no contradiction in terms.

given that http://mathworld.wolfram.com/images/equations/Aleph-0/inline3.gif has no immediately preceding member, how do you propose to complete an actually infinite set of moments of time by successive addition? that is, how do you propose to ***get to ***http://mathworld.wolfram.com/images/equations/Aleph-0/inline3.gif by the addition of moments of time to the set of all temporal moments?

I don’t. All I am saying is that each member of the “set of all temporal moments” will be reached, eventually, by the sequential addition of moments of time to the set of all currently existing temporal moments. BTW this argument seems only to apply to a future infinite universe, not a past infinite universe.

 

[SeekingCatholic]

Let’s look at an eternal universe this way (this argument works for past-eternal universe and future-eternal). Let’s assign a finite (small) probability p that this temporal moment will be the last; unless an eternal universe is demanded a priori, p will be greater than zero. After a series of temporal moments N, the probability that the universe will still be in existence by then will be P(U) = (1-p)^N. Now in the limit of N going to infinity, P(U) will go to zero. However, for any finite N, P(U) will be nonzero. We can make P(U) as arbitrarily small as we like by extending out the temporal chain (making N larger). We can also make the same argument going backwards in time (e.g. the probability that a given temporal moment is the first). What all this shows is that an eternal universe (in fact, even a very long universe) should be excluded under inference to the best explanation, and that “best” explanation can be as “best” as we like.

This IMHO is a much more convincing argument than arguing about philosophical impossibilities of an infinite regress. To refute it an atheist would have to disprove even the possibility of a First Cause which could start or end the universe at any moment. Thoughts?

 

[john_doran]

An infinite set does not have to contain the member “negative infinity”.

true, but so what? an infinite set, in order to be infinite, has to have the cardinality of http://mathworld.wolfram.com/images/equations/Aleph-0/inline3.gif; whether or not there is an infinitieth number that is “in” the set is irrelevant.

SeekingCatholic:

All members of the set of past moments exist at a finite remove from the present moment, if I define the set as “the set of all finite negative integers”.

how can this possibly be true? how can a set, each member of which is a finite remove from one terminal member, have an infinite cardinality?

SeekingCatholic:

An eternal universe involves no contradiction in terms.

well, that’s what we’re trying to determine, isn’t it?

tell me this: does the proposition “my favorite shape has 3 internal angles that sum to 180 degrees” involve a contradiction? does goldbach’s conjecture contain a contradiction? do you think that frege realized that his work of formal logic, the begriffsschrift, contained the contradiction finally pointed out by russell?

a proposition or theory doesn’t always wear its contradictoriness on its sleeve…

i think that the idea of an eternal universe does contain a contradiction, and i believe i have shown how.

SeekingCatholic:

I don’t. All I am saying is that each member of the “set of all temporal moments” will be reached, eventually, by the sequential addition of moments of time to the set of all currently existing temporal moments.

how is that possible? for any temporal point, p, arbitrarily distant from the present moment, there will be an infinite number of temporal moments prior to p. that is to say, if the set of prior moments is actually infinite, then it was actually infinite at ***every prior temporal moment ***- 5 years ago, a million years ago, a trillion years ago - however far back you go, there was always an actually infinite amount of time that had already elapsed. and if that’s true, then how have we “reached” here?

SeekingCatholic:

BTW this argument seems only to apply to a future infinite universe, not a past infinite universe.

not so. here’s your set of negative integers:

http://mathworld.wolfram.com/images/equations/Aleph-0/inline3.gif{...-6,-5,-4,-3,-2,-1,0}

if i were to traverse that set, one member at a time (in the manner that time elpases), and reach 0, then i would have to traverse http://mathworld.wolfram.com/images/equations/Aleph-0/inline3.gif; but how can i do*** that*** if there is no member of the set that comes*** after http://mathworld.wolfram.com/images/equations/Aleph-0/inline3.gif**?*

 

[john_doran]

Let’s assign a finite (small) probability p that this temporal moment will be the last; unless an eternal universe is demanded a priori, p will be greater than zero. After a series of temporal moments N, the probability that the universe will still be in existence by then will be P(U) = (1-p)^N.

why should anyone believe that?

 

[SeekingCatholic]

true, but so what? an infinite set, in order to be infinite, has to have the cardinality of http://mathworld.wolfram.com/images/equations/Aleph-0/inline3.gif; whether or not there is an infinitieth number that is “in” the set is irrelevant.

OK, so we’re agreed on this point.

how can this possibly be true? how can a set, each member of which is a finite remove from one terminal member, have an infinite cardinality?

Why can’t it? What is the cardinality of the set of all finite negative integers? Or for that matter (not that it’s relevant here, but anyway), what is the cardinality of the set of all real numbers between 0 and 1?

a proposition or theory doesn’t always wear its contradictoriness on its sleeve…

True, but contradictoriness must be shown.

i think that the idea of an eternal universe does contain a contradiction, and i believe i have shown how.

Where’s the contradiction, then?

how is that possible? for any temporal point, p, arbitrarily distant from the present moment, there will be an infinite number of temporal moments prior to p. that is to say, if the set of prior moments is actually infinite, then it was actually infinite at ***every prior temporal moment ***- 5 years ago, a million years ago, a trillion years ago - however far back you go, there was always an actually infinite amount of time that had already elapsed.

True.

and if that’s true, then how have we “reached” here?

Reached here from where? From “the beginning”? There is no beginning.

not so. here’s your set of negative integers:

http://mathworld.wolfram.com/images/equations/Aleph-0/inline3.gif{...-6,-5,-4,-3,-2,-1,0}

if i were to traverse that set, one member at a time (in the manner that time elpases), and reach 0, then i would have to traverse http://mathworld.wolfram.com/images/equations/Aleph-0/inline3.gif;

Again, define your starting point. There is no “beginning” of the set.

 

[punkforchrist]

PFC, again you keep repeating the same arguments which I have refuted time and again.

I realize you believe your refutations are sound, but all I can say is that I think they fail to undermine the strength of the argument.

No, each individual historical event is so formed. Saying “the series is formed by the succession” doesn’t make sense.

I don’t see any distinction here. If set A contains the integers {-3, -2, -1, 0}, then the series itself is not formed until each element of the set is formed by succession.

The series is the succession, by definition. There is no good reason why I cannot conceive of an universe with an infinite past as the set of negative integers, the present as 0, and the future as positive integers, and adding to the end of the array. Of course the element to be added depends on the one that was previously added, just like in “dynamical time” the present historical event is going to depend the immediately preceding one, and that on the one before that. It doesn’t prove the past cannot have an infinite number of elements, just like the set of negative integers.

Unless there is an infinity in which all the members of aleph-null co-exist simultaneously, then each member of the set of aleph-null must be so formed by succession. The difficulty that you are overlooking is that in an infinitely old universe, in order for any event to arrive, an infinity of events must precede it. Hence, there will always and indefinately be another member that will have to occur before any time t can arrive.

But the past can still have an infinite number of elements. “Infinite past” can have two meanings: a) that there is a point in the past an infinite distance from the present; or b) that there exists an infinity of events in the past, each a finite distance from the present.

Option (b) does not account for how past events are collected. Each member of the set of past events has necessarily occurred in order for them to be part of the historicial past.

Arguing about something “before” an eternal universe is therefore a contradiction in terms. But to measure you need to specify a beginning and an end, by definition. Once you do, the measure will be finite.

I never argued that there was something before an eternal universe. I’m simply saying that each member of an infinite set must have been actualized in order for the set itself to correspond to the historical past. If the set aleph-null is not actual, then the past cannot be infinite.