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Leibnizian Cosmological Argument

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Branden Holmes

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An infinite series of events
« on: July 08, 2012, 11:58:42 pm »
Even if we accept that an infinite series of events is impossible (something I do not see any reason to believe nor disbelieve), I do not see how that has any bearing on the actual world. Cosmological arguments claim as part of their premises that an infinite regress is impossible but I do not see how this has any relevance to the actual world. Let me summarize my basic point:

If the universe is constituted of a finite amount of matter then an actual infinite of any kind specifically pertaining to the universe is impossible.

For an infinite series of past events to be an actual infinite you would need to consider all past events as actual. But this is erroneous because I can fashion a piece of clay into one shape and then another shape. Now is it true that the clay is both shapes or merely the latter shape? It is merely the latter shape, and it is no longer the former shape. But for the theist to claim that an actual infinite is impossible they would need to claim that the clay is actually both shapes even though it is clearly only a single shape, and could only ever be a single shape simultaneously.

The theist needs to claim that all past events, even though no trace of their occurrence exists in many cases (and hence are no longer actual), are actual; that they accumulate. Am I guilty of equivocation? Am I misunderstanding the theists argument?
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John M

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An infinite series of events
« Reply #1 on: July 09, 2012, 08:28:09 am »
Surroundx - actually, I was just reading about this objection in the Blackwell Companion to  Natural Theology. If you have that or can get a copy, read the chapter on the kalam and it goes over how the KCA proponent attempts to defeat that objection.

The attack against the KCA (as described in the book) talks about how, on the A-Theory of time, once an event happens, and goes into the past, it no longer "exists" (since on the A-theory, past events don't exist). So how can you say these events can be grouped into an actual infinite if they don't exist?

I can't remember the full argument but you defeat it something like this:

"Even if they don't exist, you can still count them. If you have a blob of clay, and made a shape X, then changed it into a shape Y, even though that clay blob in the shape X doesn't still exist, you can still count them. And it is argued you can't have created an actually infinite number of shapes. You can create a potential infinite of shapes, but not an actual infinite number of them"

I didn't do any of that justice and probably got it wrong (I should go back and refer to that section of the book), but, suffice it to say this objection has been dealt with in the professional literature and I recommend reading that Blackwell article if you are interested in the KCA proponent's full rebuttal to your objection.

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Branden Holmes

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An infinite series of events
« Reply #2 on: July 09, 2012, 09:06:49 am »
Mazzgolf, thanks for your reply. Unfortunately I do not have a copy of that book, and so I will have to rely upon your rendering of how you defeat my objection, which you admit is imperfect, and hence my reply will be likewise imperfect and probably miss its target somewhat.

I never really got the whole "A-Theory" and "B-Theory" of time thing. Perhaps it's because I don't believe that time exists so they're both neither here nor there. But since I don't understand them perhaps I'm being too hasty in giving them short shrift; perhaps they still apply to somebody like me because of how they characterize the relationship between things past and present. Who knows.

My objection is, I believe, a little stronger and more persuasive than the one you have interpreted me as putting forward. I mean, I certainly do agree with the A-Theorists that past events are no longer actual, and I don't think that simply saying that we can count past events refutes the objection (see below). But I added an extra element, which was the clay, which I think raises an important issue. However, looking back at my OP I can see that I didn't elaborate upon it properly, so let me do so here.

I used the clay example to illustrate that since no physical trace is left of the past event (in this case, the clay being shape x) because the clay is now shape y or z or whatever you want to call it, there is nothing left to count. And so without any person witnessing the transformation of the clay nobody would have known, apart from inference that things change and that the clay was likely x number of shapes before the present one because it probably didn't just come into existence, that the clay was shape x before it was its current shape (y or z or whatever). Sometimes I have trouble expressing myself, but I think I've got my point across now.
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John M

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« Reply #3 on: July 09, 2012, 09:27:30 am »
And so without any person witnessing the transformation of the clay nobody would have known, apart from inference that things change and that the clay was likely x number of shapes before the present one because it probably didn't just come into existence

Ah.. OK. I see where you are going. This sounds like you are questioning the ontological status of events that we don't know for sure actually happened. In other words, it sounds like you are asking "How can I count past events if no observers was there to witness them. Maybe they didn't happen?" This almost sounds like "if a tree falls in a forest and no one is there to hear it, does it make a sound"

This is probably an easier thing to refute. Because you would need some argument to explain why the past didn't happen :-) You have to argue why our inference that "past events happen" is false. I think you will be hardpressed to find anyone to agree with your analogy and say, "well, because no one was alive a billion years ago, events didn't happen."

Perhaps you need to refine your objection a bit. I don't know if I understand you right.

I, personally, feel justified in believing the past occurred - even though I wasn't there for but a tiny, miniscule fraction of past events. And the question becomes, if past events really did occur, why couldn't I theoretically count them? The way I think of it is: as a thought experiment, say there exists some theoretical world clock that has always existed as long as time has existed that ticks away second by second. Theoretically, I could count the number of seconds that have ticked in the past. Would I count an actually infinite number of seconds? The clock-tick is a metaphysical representation of past events of equal duration.

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Branden Holmes

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An infinite series of events
« Reply #4 on: July 09, 2012, 09:37:00 am »
No, I'm not questioning the ontological status of events. Quoting that single sentence out of my whole post I can see how the context of that sentence got lost in my argument. I'm sort of splitting the two positions down the middle. I'm not questioning the reality of past events. Rather I'm simply saying that you cannot count them because there is no physical trace of them left and so they are not actual as they would need to be on the theists account, although they certainly are real and did happen. Has that clarified things?
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lehmar

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An infinite series of events
« Reply #5 on: August 01, 2012, 10:06:14 pm »
I would agree with what mazzgolf has said - even if past events no longer exist, we can still count them.

You seem to think that we can't count them because "there is no physical trace of them left". But how does that show that we can't count them? There is no physical trace of my dead pets anymore, but surely I can count how many pets I've had.

Your argument works only on the assumption that the only things we can count are those that leave physical traces. Why think this? Furthermore, this assumption is false. Again, we can look at the example of my dead pets. I know I had 3 of them, even though there are no physical traces of them left.

Furthermore, if your argument is right, that means we can't count any past duration. If your argument is right, then I can't know that I have been alive for X number of years, or that I was asleep X hours ago, and so on. But surely I can know this!

I was about to give a thought experiment similar to mazzgolf's, but was beat to it, haha, so I'll just suggest that you reflect on that thought experiment.

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Branden Holmes

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An infinite series of events
« Reply #6 on: August 02, 2012, 04:53:55 am »
lehmar wrote: I would agree with what mazzgolf has said - even if past events no longer exist, we can still count them.

You seem to think that we can't count them because "there is no physical trace of them left". But how does that show that we can't count them? There is no physical trace of my dead pets anymore, but surely I can count how many pets I've had.

Your argument works only on the assumption that the only things we can count are those that leave physical traces. Why think this? Furthermore, this assumption is false. Again, we can look at the example of my dead pets. I know I had 3 of them, even though there are no physical traces of them left.

Furthermore, if your argument is right, that means we can't count any past duration. If your argument is right, then I can't know that I have been alive for X number of years, or that I was asleep X hours ago, and so on. But surely I can know this!

I was about to give a thought experiment similar to mazzgolf's, but was beat to it, haha, so I'll just suggest that you reflect on that thought experiment.
Subjectively you can still count them, but not objectively. You cannot objectively count your pets because they no longer exist. But you can still count them in a sense because you have memories of your past pets. But your memories of your past pets, and your actual past pets, are not the same thing. And so although your past pets actually existed, they no longer exist.   I don't know how to express my argument any better than that.

For there to be an actual infinite there needs to be an actually infinite group of things that exist at this moment. Past events/actions/people/pets etc. are no longer 'actual' but rather past. And so I believe that there can have been an infinite number of past (i.e. not actual) events/objects. I hope this makes sense. Seems I have problems explaining my arguments.
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lehmar

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« Reply #7 on: August 02, 2012, 07:30:31 am »
Surroundx wrote:
Subjectively you can still count them, but not objectively. You cannot objectively count your pets because they no longer exist. But you can still count them in a sense because you have memories of your past pets. But your memories of your past pets, and your actual past pets, are not the same thing. And so although your past pets actually existed, they no longer exist.   I don't know how to express my argument any better than that.


What do you mean by "subjectively" and "objectively"? Surely it is an objective fact that I had, say, 3 pets. By "objective", I mean independent of what people believe. You seem to mean something else by "objective".

Yes, memories are different from actuals pets. (For one thing, some pets can't fit in my skull, haha.) But you seem to miss the point. The point is that my memories are of those pets, so that, if my memory is reliable, I can have knowledge of the past about those pets. Would you say that memory doesn't give us any knowledge at all of the past?

(Besides, the reference to memory can be removed. What if I get a severe case of amnesia, so I forget all about my pets. Does it follow that there is no fact of the matter that I had 3 of them? Clearly not, that would be a jump in logic.)

Surroundx wrote:  
For there to be an actual infinite there needs to be an actually infinite group of things that exist at this moment. Past events/actions/people/pets etc. are no longer 'actual' but rather past. And so I believe that there can have been an infinite number of past (i.e. not actual) events/objects. I hope this makes sense. Seems I have problems explaining my arguments.

Perhaps you are confusing the term "actual" in the term "actual infinite". The "actual" in "actual infinite" doesn't mean that the infinite number of objects exists right now. It is used in contrast with a "potential infinite" - an actual infinite involves an infinite number of objects, while a potential infinite involves a finite number continuously approaching infinity as its limit. "Actual" here doesn't mean "actually existing in the present moment". So in fact, when you say that "And so I believe that there can have been an infinite number of past (i.e. not actual) events/objects" that's what is meant by saying there was an actually infinite number of past events. In saying this, it is not saying that those events exist now. It is saying what you are saying - that there has been  "an infinite number of past... events/objects".

You assume that we can only count things which exist in the present moment. So far, you haven't really supported this assumption. You have said that we can only count what has left physical traces, but if you require that these physical traces exist in the present, then you are in effect only restating your assumption.

Besides, I think your appeal to physical traces actually works against your conclusion, for if physical traces give us good reason to believe that I had 3 pets, then it follows that we can indeed count objects in the past. If you say that I am only counting my pets in my memory, that doesn't show that we can't count the past, since, if my memory is reliable, then we have good reason to think I had 3 pets in the past.

There is also good reason to think the assumption is false. Prima facie, it is clear that we can count objects in the past. People count things in the past all the time - are you willing to say that they are all mistaken in doing this? Furthermore, we can count objects which can never exist at all - we can say that there are zero married bachelors in the universe.

Thus, we have seen no good reason to think that we can't count objects in the past, and we have good reason that we can count objects in the past.

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Branden Holmes

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An infinite series of events
« Reply #8 on: August 02, 2012, 08:13:12 am »
lehmar wrote: What do you mean by "subjectively" and "objectively"? Surely it is an objective fact that I had, say, 3 pets. By "objective", I mean independent of what people believe. You seem to mean something else by "objective".
I didn't know how else to distinguish between the two; physically counting your pets and counting them through other means such as your memories of each one. Do you have any suggestions of more appropriate terminology?

lehmar wrote: Yes, memories are different from actuals pets. (For one thing, some pets can't fit in my skull, haha.) But you seem to miss the point. The point is that my memories are of those pets, so that, if my memory is reliable, I can have knowledge of the past about those pets. Would you say that memory doesn't give us any knowledge at all of the past?
Of course memory gives us knowledge of the past. We can know that things existed in the past which no longer exist and hence cannot be verified by going out and touching/interacting with it.

lehmar wrote: Besides, the reference to memory can be removed. What if I get a severe case of amnesia, so I forget all about my pets. Does it follow that there is no fact of the matter that I had 3 of them? Clearly not, that would be a jump in logic.
If it is a fact that you had three pets then your amnesia will not affect that reality.

lehmar wrote: Perhaps you are confusing the term "actual" in the term "actual infinite". The "actual" in "actual infinite" doesn't mean that the infinite number of objects exists right now. It is used in contrast with a "potential infinite" - an actual infinite involves an infinite number of objects, while a potential infinite involves a finite number continuously approaching infinity as its limit. "Actual" here doesn't mean "actually existing in the present moment".
No, I do know the distinction. I'm not confusing them even though it appears that I am. To me infinites do have to be constituted of actually existent entities, because the atoms which made up past entities have been recombined and now make up other entities. Thus they cannot be counted towards an actually infinite number of things (i.e. an actual infinite) because although it is objectively true that past beings existed, they no longer exist because their atoms make up other things. And so although they existed they themselves no longer exist, except as memories. And since entities are physical, them being destroyed means that they no longer exist and it is as if they never existed. Since we only know of their existence from memories, and although it is objectively true that they existed, this information is not stored anywhere. It's just an objective fact that they existed, whether or not anybody is aware of it.

I can clearly see why you think I'm confusing the two senses in which 'actual' is being used. I need to find the words to express my argument properly. The distinction is between the physical entity and our memories of them and the objective fact that they existed.

lehmar wrote: You assume that we can only count things which exist in the present moment. So far, you haven't really supported this assumption. You have said that we can only count what has left physical traces, but if you require that these physical traces exist in the present, then you are in effect only restating your assumption.
No, I agree that we can count things which do not exist in the present moment; either things past or not yet arrived. It's just that the distinction is that in the present the entities actually being counted physically exist now. Whereas those being counted from memories, or otherwise being counted with the aid of something else, no longer exist. There's a fundamental point to be made here, but I can't seem to find the right string of words to express it.
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lehmar

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« Reply #9 on: August 02, 2012, 09:47:23 am »
Perhaps going back to the original post will help.

Surroundx wrote: Even if we accept that an infinite series of events is impossible (something I do not see any reason to believe nor disbelieve), I do not see how that has any bearing on the actual world. Cosmological arguments claim as part of their premises that an infinite regress is impossible but I do not see how this has any relevance to the actual world.


It is relevant because if actual infinites are impossible, then it follows that in the actual world, there are (and can be no) actual infinites. It's just like saying married bachelors are impossible - it follows from this that there are and can be no married bachelors in the actual world.

Surroundx wrote:

For an infinite series of past events to be an actual infinite you would need to consider all past events as actual. But this is erroneous because I can fashion a piece of clay into one shape and then another shape. Now is it true that the clay is both shapes or merely the latter shape? It is merely the latter shape, and it is no longer the former shape. But for the theist to claim that an actual infinite is impossible they would need to claim that the clay is actually both shapes even though it is clearly only a single shape, and could only ever be a single shape simultaneously.

The theist needs to claim that all past events, even though no trace of their occurrence exists in many cases (and hence are no longer actual), are actual; that they accumulate. Am I guilty of equivocation? Am I misunderstanding the theists argument?

First of all, the theist doesn't need to claim that past events are actual (in the sense of being present now) in order to count how many past events there were. (Analogously, I don't need to claim that my pets exist now in order to count how many pets I had.) You conceded this in your previous post when you said:

Surroundx wrote:  

 I agree that we can count things which do not exist in the present moment; either things past or not yet arrived.




I'm not sure how your clay analogy is relevant. Obviously there is only piece of clay in the example, and it can only be molded into one form at a time. But how does that defeat the claim that actual infinites are impossible? I don't see the relevance.

You seem to be making much out of the distinction between past and present events. Assuming an A-Theory of Time, there is a distinction, and the theist need not deny this. But given this distinction, how does this distinction defeat the claim that actual infinites are impossible?

An analogy might help: I believe married bachelors are impossible. Given this, it doesn't matter whether we look for these married bachelors in the past or the present - we know we won't find them. The distinction between past and present events doesn't even come into the picture.

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lehmar

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« Reply #10 on: August 02, 2012, 09:50:28 am »
In fact, given your basic point:

Surroundx wrote:

If the universe is constituted of a finite amount of matter then an actual infinite of any kind specifically pertaining to the universe is impossible.


you seem to be on the side of those who claim that actual infinites are impossible. So right now I'm a bit confused. How are you points relevant to the cosmological argument again? Please do clarify.

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Branden Holmes

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« Reply #11 on: August 02, 2012, 10:14:47 am »
lehmar wrote: You seem to be on the side of those who claim that actual infinites are impossible.
I'm undecided personally. But that means that I need to consider that either possibility could be true (I would of course need to consider this anyway even if I did have a firm position on the issue; unless of course I had a proof or disproof of one or the other). If actual infinites are coherent then there is no problem in there being any actual infinites. It would be circumstantial evidence for atheism and/or theism (i.e. consistent with both worldviews). It would be inconsequential so to speak, at least in this context.

But the opposite, that actual infinites are impossible, is anything but inconsequential. Thus whether actual infinites are impossible is of the utmost importance in the current debate, because the Cosmological argument seeks to show that without god there must be an actual infinite, which is impossible. And since it is impossible, therefore god must exist in order to explain how there is no actual infinite.
lehmar wrote: So right now I'm a bit confused. How are your points relevant to the cosmological argument again? Please do clarify.
If an actual infinite is impossible then the actual world cannot contain any actual infinites. There would therefore be two options: either god is the first cause so to speak. Or, we need to make a distinction between infinites and actual infinites; infinites being able to exist, but the latter clearly not. The question then is, which is it? The theist is the one who makes the case that without god as an explanatory hypothesis we are left with an infinite regress which needs resolving, and therefore we invoke god to dissolve the problem. I can only object to this argument since I am not the one making it. I am defending my worldview against the Cosmological argument, or at least any version of it which pertains to the content of my posts.

As I do not believe in the existence of god, I need to show either that actual infinites are indeed possible (something I have no definite opinion on, and so cannot make a confident argument for). Or I need to show that infinite is possible so long as it is not an actual infinite. I do not see any third option. So to answer your question directly, I am attempting to show that even if actual infinites are impossible there is no problem with affirming naturalism. I'm trying to argue that there can have been an infinite series of past events and that this does not count as an actual infinite because of the relationship between entities past and present (entities past, although they can be counted, do not contribute to any actual infinite, for reasons I have not yet been able to put my finger on; it's not the fact that they no longer exist per se, but definitely something related to that).

Does this clarify things for you?

P.s. I'm going to bed now, so I shall reply again in 18-20 hours. I'll also try and reply to your other posts in my thread on the Ontological argument as well. My apologies about taking so long to get back to you on that.
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lehmar

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« Reply #12 on: August 02, 2012, 10:29:10 am »
Surroundx wrote:
If an actual infinite is impossible then the actual world cannot contain any actual infinites. There would therefore be two options: either god is the first cause so to speak. Or, we need to make a distinction between infinites and actual infinites; infinites being able to exist, but the latter clearly not. The question then is, which is it? The theist is the one who makes the case that without god as an explanatory hypothesis we are left with an infinite regress which needs resolving, and therefore we invoke god to dissolve the problem. I can only object to this argument since I am not the one making it. I am defending my worldview against the Cosmological argument, or at least any version of it which pertains to the content of my posts.

As I do not believe in the existence of god, I need to show either that actual infinites are indeed possible (something I have no definite opinion on, and so cannot make a confident argument for). Or I need to show that infinite is possible so long as it is not an actual infinite. I do not see any third option. So to answer your question directly, I am attempting to show that even if actual infinites are impossible there is no problem with affirming naturalism because we do not need to postulate god to explain how there is no actual infinite which there should be if god does not exist and past events stretch back into the eternal past.

If actual infinites are impossible, I don't see how you can avoid positing God (or something like God at least). Trying to make a distinction between infinites and actual infinites won't help, because even if the former does apply to the universe (what does it mean anyway?), it doesn't affect the cosmological argument since it is latter which is relevant to the argument. So the issue turns on whether actual infinites are impossible or not.

But let's get back to your original post. I'm still not sure how your comments there defeat the cosmological argument. Or maybe we can see that they don't?