a better reason why the past cannot be infinite

If the past is beginningless, then the amount of events before now is literally infinite.

So if the past is infinite, then we are still adding to that past as present moments succeed one another. 

In essense, we have created an infinite through successive addition. 

So this would mean that the present moment is point "infinity" in this set

But there is no point "infinity" in infinite set theory.

Ergo, there's a contradiction. 

Yes a contradiction in terms of language and finite perception of something infinite. ;)Teenaged

To say that there is no unit 'infinity' in an infinite set, and yet say that infinites can be formed through successive addition is a flat contradiction. 

Yup, good argument. There was obviously a beginning.Lansdowne5

>_>

I don't even understand what this argument is trying to say.  If you have the set R- = {x : x is in R and x < 0}, you can then very easily create the new set R- U {0}, which has a new element.  There is no contradiction here whatsoever - 0 is not "point infinity"; it's just a new element in an infinite set.

Yup, good argument. There was obviously a beginning.Lansdowne5

An argument is not good just because you agree with the conclusion. :P  I see this all the time, and I've never understood it.

I don't think you can add something up to infinity. Infinity is not a quantity, so I don't think anybody makes the claim that infinities can be formed through successive addition.Frattracide

I don't even understand what this argument is trying to say.  If you have the set R- = {x : x is in R and x < 0}, you can then very easily create the new set R- U {0}, which has a new element.  There is no contradiction here whatsoever - 0 is not "point infinity"; it's just a new element in an infinite set.

No offense, but these discussions on infinity would be much easier if you thoroughly learned set theory beforehand.
GabuEx

furthermore, its not just adding one unit to an infinite, its CREATING an infinite set through successive addition. But surely this cannot be done. 

Yup, good argument. There was obviously a beginning.Lansdowne5

To say that the past is infinite necessarily implies that we have just formed an infinite amount of moments. danwallacefan

furthermore, its not just adding one unit to an infinite, its CREATING an infinite set through successive addition. But surely this cannot be done. 

danwallacefan

Sure it can.  You just need to add a new item an infinite number of times.  I can create the set of natural numbers by adding 1, then 2, then 3, then 4, then... well, you get the idea.  If you do this in a regular, finite interval of time (any regular, finite interval will do), you'll have an infinite-sized set after an infinite time if you keep at it the entire time.  For example, if you add an item to a set each second, and if you consider a span of time equal in number of seconds to the size of the set of natural numbers, then by the time that span of time has elapsed, you'll have a set equal in size to the set of natural numbers, built by adding one item at a time.

Thus, this is only impossible if there cannot be such a thing as an infinite amount of time elapsed in the past - but, considering that your entire argument is trying to show that this cannot be the case, you have effectively shown only that there cannot be an infinite amount of time elapsed if there cannot be an infinite amount of time elapsed.  And, needless to say, that is a tautology, not an argument that proves anything.

[QUOTE="danwallacefan"]

furthermore, its not just adding one unit to an infinite, its CREATING an infinite set through successive addition. But surely this cannot be done. 

GabuEx

Sure it can.  You just need to add a new item an infinite number of times.  I can create the set of natural numbers by adding 1, then 2, then 3, then 4, then... well, you get the idea.  If you do this in a regular, finite interval of time (any regular, finite interval will do), you'll have an infinite-sized set after an infinite time if you keep at it the entire time.  For example, if you add an item to a set each second, and if you consider a span of time equal in number of seconds to the size of the set of natural numbers, then by the time that span of time has elapsed, you'll have a set equal in size to the set of natural numbers, built by adding one item at a time.

Thus, this is only impossible if there cannot be such a thing as an infinite amount of time elapsed in the past - but, considering that your entire argument is trying to show that this cannot be the case, you have effectively shown only that there cannot be an infinite amount of time elapsed if there cannot be an infinite amount of time elapsed.  And, needless to say, that is a tautology, not an argument that proves anything.

Wait, what is this debate even about? What does the past being finite/infinite have anything to do with theism/atheism?bean-with-bacon

I was asking myself the same thing. 

[QUOTE="bean-with-bacon"]Wait, what is this debate even about? What does the past being finite/infinite have anything to do with theism/atheism?_Tobli_

I was asking myself the same thing. 

If the past stretches into the ...past infinitely then thats a good indication that god didnt have to exist or generally be the reason for everything around us, because simply the idea of a begining-less universe kinda refutes the idea of god. (at least the Abrahamic god)

But if there is a begining then surely God can be chronologically be "placed" before its begining leaving room for argumentation in favor of him being the creator.

[QUOTE="_Tobli_"]

[QUOTE="bean-with-bacon"]Wait, what is this debate even about? What does the past being finite/infinite have anything to do with theism/atheism?Teenaged

I was asking myself the same thing. 

If the past stretches into the ...past infinitely then thats a good indication that god didnt have to exist or generally be the reason for everything around us, because simply the idea of a begining-less universe kinda refutes the idea of god. (at least the Abrahamic god)

But if there is a begining then surely God can be chronologically be "placed" before its begining leaving room for argumentation in favor of him being the creator.

Well sure but how is it a relevant argument? I don't think there are any probable hypothesis's that treat the universe as having no beginning, so it's kind of a pointless debate isn't it?

If the past stretches into the ...past infinitely then thats a good indication that god didnt have to exist or generally be the reason for everything around us, because simply the idea of a begining-less universe kinda refutes the idea of god. (at least the Abrahamic god)Teenaged

[QUOTE="Teenaged"]If the past stretches into the ...past infinitely then thats a good indication that god didnt have to exist or generally be the reason for everything around us, because simply the idea of a begining-less universe kinda refutes the idea of god. (at least the Abrahamic god)ChiliDragon

And it makes sense to me too, because if god didnt create everything then he is not that omnipotent, because if he just created heaven and earth (meaning Earth as a planet) then who created the rest planets and the rest of the universe?

Good try but no cigar this time unfortunately. It's all peachy until you say that the present moment is point infinity, as if to imply that ten seconds ago we were not at infinity. Like I said in my other thread if there is no beginning then successive addition will lead to infinity and regardless of whether or not moments in time are being added it still stays at infinity.

So yeah, no contradiction.

[QUOTE="ChiliDragon"][QUOTE="Teenaged"]If the past stretches into the ...past infinitely then thats a good indication that god didnt have to exist or generally be the reason for everything around us, because simply the idea of a begining-less universe kinda refutes the idea of god. (at least the Abrahamic god)Teenaged

And it makes sense to me too, because if god didnt create everything then he is not that omnipotent, because if he just created heaven and earth (meaning Earth as a planet) then who created the rest planets and the rest of the universe?

Sure you can actually create an infinite through adding to a set over an infinite period of time, but the problem is that the amount of time is a set. So in attempting to prove that infinites can be created through successive addition, you're begging the question. Second, to say that we HAVE created an infinite set through successive addition, you almost treat infinite as an integer, which is absurd as you so eloquently demonstrated much earlier. danwallacefan

If you want to just talk about creating an infinite set through successive addition, then here:

S_1 = {1}

S_2 = S_1 U {2} = {1, 2}

...

S_n = S_(n-1) U {n} = {1, 2, ..., n}

lim (n -> inf) S_n = {1, 2, ...} = N

There, I just created the set of natural numbers, one number at a time.  No contradictions here.

As for the issue of time, all I have said is that it takes an amount of time larger than any finite number to do so if it takes a non-zero amount of time per addition.  That's not begging the question; I have never said the amount of time is a set - I said that it is equal to the size of an infinite set.  This is just a way to express an infinite amount of time without making the error that you mention of treating "infinity" as if it were a set quantity rather than just a concept manifest in many different forms and orders.

No matter how hard I try, I just cannot make myself believe that when eventually I stand in front of God on the day of final judgment (please interpret that particular concept as literally or metaphorically as you prefer), the question he will ask me is, "Did you believe in a literal interpretation of the first chapter of Genesis, in every philosophical argument for my existence, and in the infallibility of the Holy Church?"ChiliDragon

Nonsense!  Don't you remember all those verses which I will conveniently not quote where Jesus was asked what one must do in order to attain eternal life, and to which he responded "believe that Genesis is a completely literal historical account"?

...oh, wait.

To be honest, on a note completely unrelated to the topic of this thread, I've never much understood that whole scenario at large where God will supposedly sit and ask you why you should be let into heaven.  It's not in the Bible, at least not that I'm aware of.  I've always just figured I'd answer, "I dunno, you tell me; you're the one who knows everything". :P  Frankly, I've always felt that if someone has a completely pat and rehearsed answer to that question that they truly believe will satisfactorily answer it on every level, then they aren't doing it right.  I'm under no delusions that anything I either believe or do ought to be good enough.

Nonsense! Don't you remember all those verses which I will conveniently not quote where Jesus was asked what one must do in order to attain eternal life, and to which he responded "believe that Genesis is a completely literal historical account"?GabuEx

I'm under no delusions that anything I either believe or do ought to be good enough.GabuEx

[QUOTE="Teenaged"]

[QUOTE="ChiliDragon"][QUOTE="Teenaged"]If the past stretches into the ...past infinitely then thats a good indication that god didnt have to exist or generally be the reason for everything around us, because simply the idea of a begining-less universe kinda refutes the idea of god. (at least the Abrahamic god)ChiliDragon

And it makes sense to me too, because if god didnt create everything then he is not that omnipotent, because if he just created heaven and earth (meaning Earth as a planet) then who created the rest planets and the rest of the universe?

Its just that seeing even the evangelists believing that God created the whole universe (right?) I supposed this is the case for any Christian.

But yeah even when I was a Christian I couldnt care less about those (to me) details, in terms of how much they matter about what I am as a person.

To be honest, on a note completely unrelated to the topic of this thread, I've never much understood that whole scenario at large where God will supposedly sit and ask you why you should be let into heaven.  It's not in the Bible, at least not that I'm aware of.  I've always just figured I'd answer, "I dunno, you tell me; you're the one who knows everything". :P  Frankly, I've always felt that if someone has a completely pat and rehearsed answer to that question that they truly believe will satisfactorily answer it on every level, then they aren't doing it right.  I'm under no delusions that anything I either believe or do ought to be good enough.

GabuEx

I think the geniuses that come up with this trend (or even those who want to pose this scenario to a person they are talking to) are just trying to express their disbelief that the person they are talking to will go to heaven.

Its like implicitely saying: "you sir most deffinetely wont go to heaven"

No reason, its just that people like to have the exclusives.... some of them at least.

As far as I know, this is where that whole crucifixion story comes in... ;)ChiliDragon

Well, that's not really what I meant.  Whether one believes hell to be eternal torment or just a temporary place, the Bible seems pretty darn clear that even with the death and resurrection of Christ, not everyone is going directly to the same place when they die.  That's what I was referring to - I'm not so arrogant as to presume that I know with 100% certainty what's going to happen when I die.

Can I answer?

I think the geniuses that come up with this trend (or even those who want to pose this scenario to a person they are talking to) are just trying to express their disbelief that the person they are talking to will go to heaven.

Its like implicitely saying: "you sir most deffinetely wont go to heaven"

No reason, its just that people like to have the exclusives.... some of them at least.

Teenaged

I didn't really want to express my unprovable suspicions about certain people, but yes, I think that about covers it. :P

Personally, I've always thought it interesting in Matthew 25:31-46 that those who find themselves in favor with God appear to be surprised at that fact, and likewise for those who find themselves out of God's favor.  I've felt for quite some time that this holds a fair bit of significance with respect to those who are absolutely convinced that they're righteous and are now part of what they tend to seem to fancy as an exclusive club.

[QUOTE="ChiliDragon"]As far as I know, this is where that whole crucifixion story comes in... ;)GabuEx

Its just that seeing even the evangelists believing that God created the whole universe (right?) I supposed this is the case for any Christian.Teenaged

Okay I think I gave a kind of half-assed reply before (I was at uni at the time) so let me try to respond again in a little more depth.

If the past is beginningless, then the amount of events before now is literally infinite.danwallacefan

Yes that's correct. We normally say that if something begins and then does not end then it is infinite (or endless as per the definition of infinity). This case is exactly the same except that now it is backwards and we have somehing that ended but never began.

So if the past is infinite, then we are still adding to that past as present moments succeed one another.danwallacefan

Yes, but not without a qualification. You say that every present moment is "adding" onto the past but we must remember that since the past is infinite in this scenario an addition of further time will not increase its overall age like it would if it was finite. This means that ten seconds ago the past was still infinite or that ten billion years ago the past was still infinite etc etc

In essense, we have created an infinite through successive addition.danwallacefan

Yes that's correct again (assuming that I have not mistaken your meaning). There would be a succession of events that stretch towards the present point in time it's just that there was never one first event that began the succession.

So this would mean that the present moment is point "infinity" in this setdanwallacefan

No that's wrong this time unfortunately. We can say that there are an infinite amount of past events that preceded the present moment or that the past is infinite but that in no way leads us to conclude that there is some "point" at which we mark infinity on our timeline.

When you talk about points in time or points along any kind of range you need a reference with which to frame it. For example if I said that I would meet you at the half-way point of a football field I would of course be talking about "half-way" in reference to the field or perhaps in reference to the two goal posts. If there was no field or no goal posts would I be able to say that a half-way point exists at all? Absolutely not for what would it be half-way between.

The same kind of thing occurs with infinity. There is no "point infinity" because there is no beginning, no frame of reference to relate it to.

So in short, no the present moment is not point infinity.

But there is no point "infinity" in infinite set theory.danwallacefan

I agree, for the reason I just outlined above.

Ergo, there's a contradiction.danwallacefan

Your reasoning has a faulty premise so this conclusion is not valid.

My question is, could any given point in time be described as "infinity+1" the next one "infinity+2" then "infinity+3", and so on and so forth infinitely? Or is that not possible, and I'm not in fact understanding this at all? ChiliDragon

My question is, could any given point in time be described as "infinity+1" the next one "infinity+2" then "infinity+3", and so on and so forth infinitely? Or is that not possible, and I'm not in fact understanding this at all? ChiliDragon

Well like we said there is no such thing as a point infinity so saying that there is such a thing as a point in time that is described as "infinity+1" is equally problematic. It would imply that the moment before it was point infinity.

That's not to say that you couldn't describe a point in time if the past was infinite though, you just need to give it the appropriate frame of reference to make it comprehensible.

[QUOTE="ChiliDragon"] My question is, could any given point in time be described as "infinity+1" the next one "infinity+2" then "infinity+3", and so on and so forth infinitely? Or is that not possible, and I'm not in fact understanding this at all? domatron23

Well like we said there is no such thing as a point infinity so saying that there is such a thing as a point in time that is described as "infinity+1" is equally problematic. It would imply that the moment before it was point infinity.

That's not to say that you couldn't describe a point in time if the past was infinite though, you just need to give it the appropriate frame of reference to make it comprehensible.

[QUOTE="domatron23"]

[QUOTE="ChiliDragon"] My question is, could any given point in time be described as "infinity+1" the next one "infinity+2" then "infinity+3", and so on and so forth infinitely? Or is that not possible, and I'm not in fact understanding this at all? ChiliDragon

Well like we said there is no such thing as a point infinity so saying that there is such a thing as a point in time that is described as "infinity+1" is equally problematic. It would imply that the moment before it was point infinity.

That's not to say that you couldn't describe a point in time if the past was infinite though, you just need to give it the appropriate frame of reference to make it comprehensible.

Yes, I think you're more or less got it.

The biggest problem with your initial post, however, was that you were treating infinity as a number, which is one of the most widely-held misconceptions in existence about the concept.  The idea that many people have is that you have the set of natural numbers - 1, 2, 3, et cetera - and that at the "end" of that sequence is the number "infinity".  But that doesn't make any sense.  The set has no end; if it did, it wouldn't be infinite.  The bottom line is this: infinity isn't a number; it's a description.  Saying "infinity + 1" is really like saying "largeness + 1".

The idea that many people have is that you have the set of natural numbers - 1, 2, 3, et cetera - and that at the "end" of that sequence is the number "infinity". But that doesn't make any sense. The set has no end; if it did, it wouldn't be infinite. The bottom line is this: infinity isn't a number; it's a description. Saying "infinity + 1" is really like saying "largeness + 1". GabuEx

Infinity is not a number, it's a quantity or description.ChiliDragon

Well, I'm not sure I would call it a quantity, either.  That would imply that there is one single, set size that is denoted as "infinity", which is not actually the case.  As I've said before, there are different levels of infinity - the set of real numbers can be shown to be larger than the set of natural numbers, despite the fact that both sets are infinite.  "Infinity" really is, in my view, solely a description: it is the state where the size of something is not quantifiable through the use of finite numbers.  Infinity is just the lack of finiteness, nothing more.

[QUOTE="ChiliDragon"]Infinity is not a number, it's a quantity or description.GabuEx

Well, I'm not sure I would call it a quantity, either.  That would imply that there is one single, set size that is denoted as "infinity", which is not actually the case.  As I've said before, there are different levels of infinity - the set of real numbers can be shown to be larger than the set of natural numbers, despite the fact that both sets are infinite.  "Infinity" really is, in my view, solely a description: it is the state where the size of something is not quantifiable through the use of finite numbers.  Infinity is just the lack of finiteness, nothing more.

Just like darkness is just a lack of light. Surely there can be intangible quantities of things/items/nouns of all kinds. "Abstract" is also a description and quantity, so in a way, though "infinity" is a description, it's also what it describes, the quantity of "not finite", or "infinite". Makes sense?ChiliDragon

I'm not sure I understand your use of the word "quantity" - do you mean "quality"? The former is always used to refer to an amount of something.

[QUOTE="ChiliDragon"]Just like darkness is just a lack of light. Surely there can be intangible quantities of things/items/nouns of all kinds. "Abstract" is also a description and quantity, so in a way, though "infinity" is a description, it's also what it describes, the quantity of "not finite", or "infinite". Makes sense?GabuEx

I'm not sure I understand your use of the word "quantity" - do you mean "quality"? The former is always used to refer to an amount of something.

[QUOTE="GabuEx"]

[QUOTE="ChiliDragon"]Just like darkness is just a lack of light. Surely there can be intangible quantities of things/items/nouns of all kinds. "Abstract" is also a description and quantity, so in a way, though "infinity" is a description, it's also what it describes, the quantity of "not finite", or "infinite". Makes sense?ChiliDragon

I'm not sure I understand your use of the word "quantity" - do you mean "quality"? The former is always used to refer to an amount of something.

Hah those terms are definitely not synonymous. Never mind though we get your meaning.

Hah those terms are definitely not synonymous. Never mind though we get your meaning.

domatron23