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Leibnizian Cosmological Argument

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David Knott

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Cosmological argument seems unconvincing
« Reply #30 on: June 11, 2009, 10:35:36 am »
I agree, let's move on.

   

   I think you're right about your first premise being quite beyond dispute. Statements of that form are always true. You correctly point out two possible points of dispute before moving on to (3).

   

   Concerning ambiguity, your words are clear and your definition seems rigorous enough. My only anxiety about it, I think, stems from the fact that I simply cannot think of anything that "cannot fail to exist"--this causes the category to feel foreign and difficult to intuit, even though it's well defined. But this is not something that has to be addressed right now. I'll grant that it's unambiguous, unless that anxiety I have later on causes a more serious objection.

   

   Your second potential point of dispute is more of a problem for me (whether necessary things need explanations). You have made the argument previously that contingent things need an explanation because, if an entity "could have been different" (a slightly ambiguous phrase), then we have to ask why the entity is one way and not another. I'm not sure I fully agree with that, but if it's true, couldn't we make the same argument about necessary entities, by asking why an entity is necessary instead of contingent?

   

   Perhaps if you explained more fully the relationship between an entity's ability to be different and its corresponding requirement of explanation, things would get cleared up. If you want to do this, then one thing I'd like to understand more fully is what you mean by "could have been different". Does this mean "being able to be imagined, by human beings, as something that it isn't"? Even though this idea, on the face, seems intuitive enough, I find that I cannot define it rigorously.

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loko5

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« Reply #31 on: June 16, 2009, 04:30:05 pm »

daveknott wrote: Perhaps if you explained more fully the relationship between an entity's ability to be different and its corresponding requirement of explanation, things would get cleared up. If you want to do this, then one thing I'd like to understand more fully is what you mean by "could have been different". Does this mean "being able to be imagined, by human beings, as something that it isn't"? Even though this idea, on the face, seems intuitive enough, I find that I cannot define it rigorously.

OK, let me discuss this in conjunction with my premise 3 (that contingent things require an explanation).  Philosophers often use "possible worlds" to discuss metaphysical possibility.  The idea is that there is a possible world that covers every possible contingency, but only one actual world.  Thus, there are many possible worlds in which I don't exist (since I am contingent), and there are other possible worlds in which things are essentially the same as they are in this world except, for example, I ate something different for breakfast today.  When I say that something "could have been different", I mean that it does not exist in some possible worlds.  Since necessary things are things which could not fail to exist, this means that they exist in all possible worlds.  Note also that I am using the word "thing" in a very broad sense, not just for concrete objects.  Thus events, ideas, physical laws, and propositions count as "things".  Such immaterial things must be either necessary or contingent, that is they must exist in all possible worlds or only in some possible worlds.

Now, my contention is that there must be some principle or principles that distinguish our real world from other possible worlds.  Why do some things exist in this world but not in other possible worlds?  We don't need any such explanation for necessary things, because in the entire space of possible worlds, they exist everywhere.  But for contingent things, there must be a reason or reasons why they exist in the real world.

Before going further let me point out two possible objections to "possible world" thinking.  One possible objection is that the real world is the only possible world, which is another way of saying that everything is necessary and there are no contingencies.  This doesn't seem to be your view, so I will only say that this leads to a fatalism and a denial of common sense that nearly everyone would reject.  A second possibility is "modal realism", the idea that every possible world is an actual world and we just happen to be living in one of them.  Under modal realism, we don't need any explanation for contingent things because all contingencies actually exist.  This view also is held by only a small minority (anyone who believes in Occam's razor obviously should reject this view).

But it doesn't seem to me that you hold either of these views. Rather, you seem to object that contingent things don't necessarily require explanations. You also seem to think that it is possible that all contingent things can be explained in terms of other contingent things, i.e. that there are no necessary things. If that's the case, I can continue on why I think these two views are incorrect. But first, let me see if you have any other objections or questions you would like to bring up.


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David Knott

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Cosmological argument seems unconvincing
« Reply #32 on: June 17, 2009, 11:13:33 am »
Well put. Your explanation of "possible worlds" makes things much more clear, but I have some objections to the other things you said.

   

   
We don't need any such explanation for necessary things, because in the entire space of possible worlds, they exist everywhere.

   

   This seems to be a rephrasing of the premise you set out to prove, namely, that necessary things do not need an explanation. You have merely recast the attribute of "necessary" as "presence in all possible worlds", and stated that the latter conception proves the former. I do not see how. My objection to your previous post was that I could ask why some particular entity is necessary instead of contingent, and hence an explanation seems to be required for necessary things. In this framework, I can ask the same question, perhaps even more clearly than before: why is some particular thing present in all possible worlds? You seem to think this is not a valid question--I disagree. We should be more puzzled at the presence of a clown planet in all possible worlds, than its presence merely in a few of them.

   

   So I think my objection still stands. Necessary things require an explanation because we can ask why they are necessary and not contingent. Alternatively, we can ask why they exist in all possible worlds instead of only some. This question seems to be on exactly the same playing field as the question we ask of contingent things (why is a contingent thing present in one possible world, but not another?). You think one of these questions demands an answer, whereas the other can be ignored. You need to show why.

   

   
But it doesn't seem to me that you hold either of these views. Rather, you seem to object that contingent things don't necessarily require explanations. You also seem to think that it is possible that all contingent things can be explained in terms of other contingent things, i.e. that there are no necessary things.

   

   I think there might be uncaused entities that do not exist in all possible worlds, yes. And it might be that there are no necessary things, although I'm not sure. But we can take those issues up later--we've already talked about them at length, actually. For now I want to settle this issue of whether necessary things require explanations.

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loko5

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« Reply #33 on: June 17, 2009, 12:58:41 pm »

daveknott wrote: So I think my objection still stands. Necessary things require an explanation because we can ask why they are necessary and not contingent. Alternatively, we can ask why they exist in all possible worlds instead of only some. This question seems to be on exactly the same playing field as the question we ask of contingent things (why is a contingent thing present in one possible world, but not another?). You think one of these questions demands an answer, whereas the other can be ignored. You need to show why.

Actually, I think it's a perfectly legitimate question to ask why a necessary thing exists, but it's not "on exactly the same playing filed" as the question of why a contingent thing exists.  To ask why a contingent thing exists is to ask why this world, rather than some other world, is the actual world.  But if something is necessary it exists in all possible worlds, so this provides the explanation as to why it exists in the actual world.  The question you seem to want answered is, why would a particular thing be necessary, i.e. why does it exist in all possible worlds rather than just some possible worlds?  This is a perfectly good question, but I'm not sure I can answer it.  However, if one accepts premise (3), and accepts that contingent things cannot be fully explained by other contingent things, then we are forced to the conclusion that something must be necessary, and that something is the root of all that exists, i.e. the First Cause.  This is what the Leibnizian argument gets at.  It doesn't say anything about what that necessary thing is, or even if there is more than one necessarily existing thing.  So if you want an explanation as to what thing(s) is/are necessary, you will have to look to other arguments to answer this.

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David Knott

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« Reply #34 on: June 17, 2009, 01:40:32 pm »
You don't have to provide an answer to my question concerning why something is or isn't necessary; you only have to recognize that it is valid. Your argument that contingent things require explanations seems to stem from your ability to ask the following question: why is some contingent entity present in one world and not another? But clearly, as I've pointed out, and as you have agreed, I can ask a very similar question about necessary entities: why does some necessary entity exist in all worlds, instead of only some, or none? My ability to ask this legitimate question would seem to imply that even necessary things require explanations, or roughly speaking, causes. Therefore, even if I agreed with you that contingent entities must be caused by necessary ones, and that a necessary entity is at the root of all existence, that foundational cause would itself force upon us the very question you initially sought to answer with your cosmological argument: what is the cause of the universe?

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loko5

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« Reply #35 on: June 17, 2009, 02:05:38 pm »
It looks like you are asking the age-old philosophical question, "Why does something exist rather than nothing?"  I'll readily agree that looking at things from necessity-contingency categories can only, at best, partially answer this question.  That is, we can say that necessary things can't "not exist", because they exist in all possible worlds.  And if the Leibnizian argument holds, then we know there must be at least something that is necessary.  It's just hard to explain why it is necessary.  The best I can offer is that:

(a)  We know that something exists (a la Descartes, I think therefore I am)
(b)  We know intuitively that things could be different than they are (the universe is contingent)
(c)  From the Leibnizian cosmological argument, we know that there must be a grounding explanation for existence, something that exists necessarily

I'm not sure that (a) through (c) provide a very satisfactory explanation for the cause of foundational existence.  It only shows that we must accept this existence to be axiomatic.

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David Knott

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« Reply #36 on: June 18, 2009, 10:46:06 am »
If the necessary thing itself requires an explanation, then it cannot be the root cause of existence. This contradicts premise 2, and until it's cleared up, I don't see how the cosmological argument has any force.

   

   Let me put things into perspective a little. The cosmological argument strikes me as an elaborate, sophisticated way of saying that everything needs a cause, except God. The fallacy of such a statement, declared by fiat, is obvious: it merely defines God out of the problem by proclaiming him the one exception to the rule. But the LCA doesn't do this directly; instead, it segregates the universe into two somewhat confusing categories, attempts to derive some properties of those categories, determines that the root cause of existence must belong to one of them, and then lets other arguments show that this root cause is a deity. But the overall effect of the argument is exactly the same--an explanation for existence is demanded, and all candidates except God are excluded by virtue of the category distinction.

   

   At this point, I feel as though I have cast some doubt on whether necessary entities, defined as they have been, are really beyond the requirements of causality and explanation. We don't have to do this, but I propose that we do one of two things: either continue the discussion about how necessary entities get off the hook of causation, or move on to the argument that is made to show that the necessary entity must be God. I do not know what argument is normally made to show that the necessary entity is God, so I'm pretty curious to find out. I understand that such an argument isn't part of the LCA itself, but clearly it's necessary to connect the dots.

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loko5

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« Reply #37 on: June 18, 2009, 11:21:22 am »
Let me try to rephrase your objection using possible worlds terminology.  Why, you seem to be asking, can't the empty set be a possible world, i.e. a possible world where there is absolutely nothing?  If this were true, then there would be no necessary things (since nothing exists in the empty set, then there is nothing that could exist in all possible worlds), so everything would be contingent.  This just gets back to my contention in premise (3), that contingent things require an explanation (that is, we require an explanation of why our world is the real world and not some other possible world) and that the explanation cannot be fully provided in terms of other contingent things.  If this contention is correct, then an empty world is not a possible world; and if an empty world is indeed a possible world, then my premise (3) must be false.  So it all boils down to whether premise (3) can be reasonably shown to be true.  Does this make sense?

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loko5

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« Reply #38 on: June 18, 2009, 01:05:39 pm »

I should also add that the same thing could be said for the objection, "Why does something have to be necessary?".  If there is nothing that is necessary, i.e. everything is contingent, then premise (3) can't be true.  But it's at least plausible that there can be necessary things, so if premise (3) is true, then necessary things do exist.  Again, the argument really hangs on premise (3).  If premise (3) can be shown to be more likely true than not, then the rest of the argument seems to fall into place very neatly.  If you disagree, I would be glad to discuss this more, but I really think the crux of the argument is showing premise (3) to be likely true.


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David Knott

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« Reply #39 on: June 19, 2009, 12:33:50 pm »
What you said regarding the empty set being a possible world was quite brilliant, and I hadn't thought of it at all. But I think you have quite missed my point. I am not trying to argue that necessary things don't exist (which would imply that the empty set is a possible world, as you point out). For now I remain agnostic on that point. Rather, I am trying to argue that, even if there were some necessary entity out there in the world, one that exists in all possible worlds, we could still ask, why does that entity exist in all possible worlds? Why all of them, instead of just some, or none? You agreed that this is a valid question to ask, and indicated that you don't have an answer for it. My argument is this: if we can reasonably ask why a necessary entity exists in all possible worlds, then we have admitted that it requires an explanation. Your cosmological argument, in essence, boils down to two key points: that a necessary entity must have caused all the contingent entities, and that only necessary entities do not need an explanation (or cause). If either one of these points is falsified, the whole edifice comes tumbling down. And I am becoming increasingly confident that the second point, that necessary entities do not require a cause, has no justification. I await your evidence on this.

   

   Now, you seem to have misunderstood me as saying that contingent entities do not (always) require an explanation. This is a position I held in much earlier posts, and one that I still hold, but it was not the point I was immediately trying to make. My other argument, that necessary entities require an explanation, if true, is enough to neuter the cosmological argument. In that sense, I do not have to disprove your third premise to demonstrate my position. But with that qualification made, I will take you up on your third premise.

   

   In the terminology of possible worlds, we can ask, as you have said, why some contingent entity is present in some possible worlds and not others. I submit to you that our ability to ask this question does not demonstrate the existence of an answer. I have given, in previous posts, reasons for why this might be the case. I will briefly restate them:

   

   1) Causality is a slightly ambiguous concept. It is not as rigorously defined as other principles, such as the constancy of the speed of light, or Maxwell's equations, or that the quantum wave function of a particle integrated over all space is equal to one. It is nothing like any of that. It seems to me to be closer to an interpretive framework, highly successful but possibly not universally applicable, or representative of "true reality". It is therefore much to my annoyance that people often refer to a "law of causality", as though it were a mathematically and empirically established prohibition against uncaused entities.

   

   2) Physical law is always somewhat tentative in that it can only be said to accurately describe the range of circumstances in which the law's predictions have been verified. Of course we can reasonably generalize our observations to untested circumstances, but history shows us that we have at times extended our generalizations too far. Newton's laws only hold within circumstances of low velocity--outside of that, they are actually false. Classical mechanics breaks down in subatomic scales. And when we peer into even more extreme circumstances of nature, where things are triply very small, very massive and very fast, even modern physics reaches the edge of its dominion, demonstrating that new principles are needed. If there is one set of principles that always breaks down when we examine the extreme parts of our universe, it's common sense. Nothing flies faster out of the window. Here we are talking about the most extreme event in the history of reality, perhaps the most extreme event imaginable, and William Craig and other apologists happily and confidently apply their commonsense conceptions of causality without the slightest hesitation. I find this confidence slightly misplaced.

   

   3) Causality makes little (if any) sense without a reference to time. I think we are in agreement that time itself came into existence at the big bang, meaning that the big bang is essentially the very first instant of time. To demand a cause of that event is to either a) demand the existence of an acting cause that existed "before time", which is a contradiction, or b) ask for causation that took place without reference to time, which is highly incoherent. Take your pick.

   

   But we have been over these before, and I hesitate to drag them out of the closet, for each one of them could spawn a separate debate. Those are, however, some of my reasons for thinking that causality might not apply to all contingent entities.

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loko5

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« Reply #40 on: June 23, 2009, 05:23:35 pm »

I think we have differing ideas on what constitutes an explanation.  The way I define an explanation is, why something is the way it is in the real world.  This means distinguishing why the real world is different from other possible worlds, i.e. explaining contingencies.  Your question seems to be, why does a necessary thing exist in all possible worlds?  I would say that this does not require an "explanation", since by definition something that exists in all possible worlds cannot fail to exist.  That is, there can be no contingent event that would cause a necessary thing to cease to exist.  Still, as I said, the question of what particular things, if any, are necessary things, and how we can deduce that they are necessary, is a good question.  The LCA stipulates that something must be necessary, but doesn't specify what that something is.  I think there are ways to infer what the necessary thing(s) must be like, but I would rather hold off discussion of that until we have finished going through the LCA.

There is more that needs to be said about explanations.  I would refer you here to Godel's Incompleteness Theorem, which states that in any system of logic there will always be true statements that cannot be proven to be true within that system.  Note that we can describe the things existing in our world as a set of true propositions, such as the propositions "A exists", "B exists", "C exists", etc.  Godel's theorem, applied to this situation, says that there are statements of this sort that are true but cannot be proven true within the system.  This is easy to see in terms of causality.  I have not said much to this point about what constitutes a cause, but I don't think an exact definition of "cause" is needed for the LCA to work (which is the main reason I prefer the LCA to the Kalam argument).  All that is needed is a minimum criterion for something to be a cause.  That minimum criterion is a "necessary condition" (not to be confused with a "necessary thing" as it is defined in the LCA).  X is a necessary condition for Y iff X must be existing in order for Y to come into existence.  This surely must be true, because it makes no sense to speak of something being caused by a non-existent entity.

Now, consider a possible world that consists only of three things, A, B and C.  [You may object that there is no possible world that consists of only three things, and I would be inclined to agree.  But this is for illustrative purposes only.  The same argument would hold for any number n of things existing in a possible world, even if n were infinite (although I think that there are no possible worlds with an actual infinite number of things, for reasons that are unrelated to the LCA).]  Suppose in this possible world we want to say the A is the cause of B, B is the cause of C, and C is the cause of A.  This would require that A, B and C always coexist together, because a minimum criterion for causation is the "necessary condition" that the cause must exist when the effect begins to exist.  So far, so good.  Now, there are several true propositions we can write about this world.  We can say:

(i)  "A exists"

(ii)  "B exists"

(iii)  "C exists"

We have a reason for each of these propositions to be true.  (i) is made true by C being the cause of A, (ii) is made true by A being the cause of B, and (iii) is made true by B being the cause of C.  We can also state the propositions:

(iv)  "Both A and B exist"

(v)  "Both B and C exist"

(vi)  "Both A and C exist"

(iv) is made true because of C's existence, (v) is made true because of A's existence, and (vi) is made true because of B's existence.  But we can also say,

(vii)  "A, B and C all exist"

But what makes this proposition true?  If there is a cause for it being true, then by the minimum criterion for a cause, this cause must be coexistent with the effect; but all three things must always have coexisted together via our original assumption.  There is nothing else in this possible world that exists, so there is nothing that could serve as a cause.  But if A, B and C all exist independently, then certainly they exist together.  Another way of looking at it is, if this possible world were the real world, why would it consist of just A, B, and C and not, for example, D
   , E and F, where D is the cause of E, E is the cause of F, and F is the cause of D?  We can't answer this question within this system of logic.

Note, though, that in this hypothetical world it doesn't have to be proposition (vii) which is unprovable.  Let's suppose instead that A is the cause of B and A is the cause of C, and that A exists without cause.  In this case, A must exist logically prior to B and C.  Let's look at the above propositions again.  (i) is true without cause.  (ii) and (iii) are both true because A exists, as is (v).  (iv), (vi) and (vii) are all true because of A's existence, since A's existence is logically prior to B's and C's existence (both B and C began to exist when A was already present).

This is where Occam's razor comes in.  Is it more plausible for one thing to exist uncaused or for three things to exist together uncaused?  And what of our real world, which consists of an unimaginably large number of things?  Does it make more sense for one thing to be uncaused, or for this huge number of existing things to exist together uncaused?


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David Knott

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« Reply #41 on: June 24, 2009, 01:46:36 am »
Though there is much to be said in response to this last post, I will try to be brief.

   

   
The way I define an explanation is, why something is the way it is in the real world. This means distinguishing why the real world is different from other possible worlds, i.e. explaining contingencies.

   

   My objection was that one could reasonably ask why some entity possesses the attribute of being necessary. Our ability to ask that question would seem to indicate that the necessary entity, whatever it is, owes one of its characteristics (necessity) to an antecedent event. Now, I am convinced that such an explanation should be forthcoming. If it were found that, for instance, beavers existed in every possible world, would this not be an extremely curious discovery, demanding an explanation? From this stems my complaint: I say that, indeed, an explanation is demanded, and that your necessary entities do not get off the hook of causality.

   

   And here is your response to that objection. You define explanation so that it only can encompass contingent entities. But the fallacy in doing that is obvious. You have merely changed the definition of explanation, in the most ad hoc way, so that it won't be applied to the necessary entity. It's as though you defined explanation as "that which gives an account for any set of circumstances or facts, except God". I do not find this a satisfying response at all. I want to reiterate that I am not, contrary to what you keep thinking, throwing you the softball question of how we can know whether an entity is necessary or not. I am saying that, given that an entity is in every possible world, we can ask why it is in every possible world. What caused that circumstance to occur? Asserting that such a question has no answer, without substantial justification, would be analogous to me asserting, by fiat, that an explanation for the universe is a concept that has no coherency.

   

   
There is more that needs to be said about explanations. I would refer you here to Godel's Incompleteness Theorem, which states that in any system of logic there will always be true statements that cannot be proven to be true within that system.

   

   I am no logician, but this strikes me as sheer equivocation. The incompleteness theorem applies to systems of arithmetic like Principia Mathematica that are sufficiently flexible as to be able to make indirectly self referential statements. A set of mere statements about the world wouldn't constitute such a system by any stretch of the imagination. To make this argument, your first responsibility would be to show that the universe, a physical thing, is actually a theory of arithmetic--an extremely ambitious goal not likely to be accomplished by even an outstanding philosopher. The only thing you say in regard to this severe difficulty is this almost parenthetical statement:

   

   
Note that we can describe the things existing in our world as a set of true propositions, such as the propositions "A exists", "B exists", "C exists", etc.

   

   I'm unconvinced this demonstrates that a theory of logic actually applies to a physical entity. Worse is that your argument bafflingly confuses provability within a logical system with causation in the universe. At best it is a gross analogy, but I think you intended me to take it as much more than that.

   

   
This is where Occam's razor comes in. Is it more plausible for one thing to exist uncaused or for three things to exist together uncaused? And what of our real world, which consists of an unimaginably large number of things? Does it make more sense for one thing to be uncaused, or for this huge number of existing things to exist together uncaused?

   

   You pose this last question as though I ever espoused the idea that every true proposition about the universe simultaneously causes every other true proposition. That is an idea I had never even imagined, let alone advocated. A cause being simultaneous with its effect seems incoherent to me. And the idea that there is an uncaused entity (or entities) is something I have, as you'll recall, supported throughout our entire discussion, and I have no idea why you're posing it to me now as though I had rejected it.

   

   I feel that you've evaded my question of why the necessary entity (whatever it is) exists in all possible worlds instead of just one, and ignored wholesale the objections I gave for thinking that causality is a universal requirement to which even creation must bow. But my real problem here is that your argument is being made from a proverbial armchair. You employ slippery notions, subtly interchanging causality with provability, switching the universe at large with formal logical systems, treating statements as though they were equivalent to physical objects, arbitrarily bending the definition of explanation but presumably maintaining its universal applicability, and so on. Your argument exists in pure reason alone. It does not consist of a robust convergence of empirical evidence. You seek to create an argument so air tight, so rigidly correct, that an honest person is forced to accept its conclusions, or lightning will strike them. And this is where the argument loses all of its force. Such an argument from pure reason will only carry weight if it is truly air tight. But the cosmological argument you have been giving me is, so far as I can tell, riddled with difficult issues of ambiguity and uncertainty. If one piece is falsified, the whole thing crumbles. That's why you are eager to walk me through the argument, step by step. And that is perhaps the primary source of my incredulity.

   

   The argument that might be made for a spherical earth does not rest upon any rigid definitions of "sphere", or complex logical derivations from first principles. It would be, rather, a robust presentation of thousands of independent observations, none of which would individually be crucial to the argument. It could turn out, for instance, that Columbus and Magellan are fictional characters that were concocted in an epic, centuries old hoax. But the argument would hardly lose any of its force. The cosmological argument is not like this at all. Everything has to be perfect, and that's why it's utterly unconvincing. We have spent pages discussing the nuances of this subject, and I think we could fill several books debating even the meaning of causality. The compact, step by step, if-x-then-y mathematical structure of the argument is a silly pretense. There is nothing in the LCA, so far as I can tell, that puts it on par with mathematics in terms of definitional clarity or in terms of using previously established premises. But such clarity and certainty are absolutely necessary for it to have any effect at all. Needless to say I think it falls short of this ambition.

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loko5

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« Reply #42 on: June 30, 2009, 11:28:37 am »

Dave,

I have to admit to being totally confused by your last post.  First off, I'm confused on what you want an explanation for.  As best as I can tell, you are asking, for a particular thing A, why is A would be necessary rather than contingent, or (using possible worlds terminology), why A would exist in all possible worlds rather than just some possible worlds.  The problem is, I'm not sure what would count as a satisfactory answer for you.  Think of it this way.  The only things that actually exist are things in the actual world.  All other possible worlds are merely metaphysical constructs, not real things.  They are ways that the real world could be, or could have been, if contingencies had been different.  Now, let's call the real world w0.  The only things that could explain the things in the real world are the things that exist in the real world.  We can't "borrow" an explanation from some other possible world w1, unless the explanans also exists in w0.  Otherwise, we are trying to use something that doesn't exist as an explanation for something that does exist.  To ask why A exists in all possible worlds is to ask, for all possible worlds wN, what explanation exists in wN that explains why A is there.  If there is a single explanation, that explanation must exist in all possible worlds.  So we can only explain why A exists in all possible worlds if the explanation itself exists in all possible worlds.  I suspect you will not find this very satisfying, but if you object then please show where my logic is wrong.

Now the alternative, of course, is to say that some things exist without explanation (brute facts).  The point of my theoretical possible world consisting of A, B, and C was to show that the existence of things can be expressed in propositional form, and that some of these propositions must be true without explanation.  Interestingly, you did not address this argument at all, but instead complained that Godel's theorem does not apply (which I don't believe to be true but is irrelevant anyway:  if my argument is correct, then some things are true without explanation).  Worse, you state

I'm unconvinced this demonstrates that a theory of logic actually applies to a physical entity. Worse is that your argument bafflingly confuses provability within a logical system with causation in the universe. At best it is a gross analogy, but I think you intended me to take it as much more than that.

I honestly don't understand this.  Expressing the existence of things as a system of true propositions is a standard technique of analytic philosophy.  Why do you find it baffling?  Or a gross analogy?

Finally, you also state,

You pose this last question as though I ever espoused the idea that every true proposition about the universe simultaneously causes every other true proposition. That is an idea I had never even imagined, let alone advocated. A cause being simultaneous with its effect seems incoherent to me. And the idea that there is an uncaused entity (or entities) is something I have, as you'll recall, supported throughout our entire discussion, and I have no idea why you're posing it to me now as though I had rejected it.

But you were the one who suggested an infinite regress of causes to be a viable idea in an earlier post.  So which is it?  Are you saying it is possible to explain all contingencies in terms of other contingent things?  Or are you saying that some things have no explanation?  I really don't know where to go next in this discussion unless I know what point you are trying to argue.


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David Knott

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Cosmological argument seems unconvincing
« Reply #43 on: July 05, 2009, 05:50:07 pm »
And I don't see where the difficulty is in seeing my point. You have consistently argued the premise that necessary entities (entities that exist in all possible worlds) don't require an explanation. You do this, obviously, so that you don't have to answer the question "who created God?". You can just say, "well, he's the necessary entity, and necessary entities don't need explanations, so there." My response to this has simply been to ask why necessary entities don't require explanations, and your answer has more or less been that you don't even understand the question. Your first paragraph makes a compelling case for the idea that only necessary things can cause necessary things. You might be right about that. But I fail to see how it excuses necessary things from the demands of explanation.

   

   
As best as I can tell, you are asking, for a particular thing A, why is A would be necessary rather than contingent, or (using possible worlds terminology), why A would exist in all possible worlds rather than just some possible worlds. The problem is, I'm not sure what would count as a satisfactory answer for you.

   

   Bingo. That is exactly what I'm saying. Given some particular necessary thing A, we can ask, why is A necessary instead of contingent. You recognized in a previous post that this is a legitimate question. The fact that it's a legitimate question suggests that there is some antecedent entity or characteristic that is responsible for A's being necessary. In other words, entity A, even though it is necessary, requires an explanation. If it turns out that some particular conception of foundational logic is true in all possible worlds, then we can ask WHY it is true in all possible worlds. If beavers exist in all possible worlds, then we can ask WHY they exist in all possible worlds. These are legitimate questions that need answering. Your whole argument rests on the idea that necessary entities don't need any sort of explanation. The presence of these questions totally refutes that idea. I do not know how to make it any clearer to you.

   

   
The point of my theoretical possible world consisting of A, B, and C was to show that the existence of things can be expressed in propositional form, and that some of these propositions must be true without explanation. Interestingly, you did not address this argument at all ...

   

   This is totally tangential, and nothing will come of it, which is why I didn't laboriously drag the whole thing out in the previous post, but since you insist on its discussion, fine. This is how you define your system:

   

   
Suppose in this possible world we want to say the A is the cause of B, B is the cause of C, and C is the cause of A.

   

   You then later assert that the unprovable statement about your system is this:

   

   
(vii) "A, B and C all exist"

   

   Here's where you're wrong. Your initial definition for the system consists of implicitly compound statements. When you say, for instance, that A is the cause of B, you are saying BOTH that A exists AND that it is the cause of B. The same trick is pulled with the other two definitional statements of the system. Essentially, then, you're defining the system this way:

   

   A exists, and it is the cause of B.

   B exists, and it is the cause of C.

   C exists, and it is the cause of A.

   

   Phrased this way, it's obvious that the statement "A, B, and C all exist" is easily proved from the axioms you gave. To make it more obvious, suppose that I'm wrong, and the existence of A was NOT implied in the statement "A is the cause of B". Then your system can be rephrased as:

   

   A is the cause of B, but A may or may not exist.

   B is the cause of C, but B may or may not exist.

   C is the cause of A, but C may or may not exist.

   

   If we take this interpretation, then the statement "neither A, B, nor C exist" would seem to be equally true under your system as the supposedly unprovable statement you gave, which of course, would be a contradiction. The existence of true but unprovable theorems is not guaranteed for all sets of axioms. For an ACTUAL Godel sentence to exist, you have to have a system that is capable of sufficiently rigorous number theoretic computation, a scheme that converts logical statements into numbers, and a way of compressing a particular number to allow the Godel sentence to reference itself. At least that's my kindergarten understanding of it. I could be wrong. But, like I said, your promiscuous employment of the theorem in this situation smells like equivocation.

   

   
Expressing the existence of things as a system of true propositions is a standard technique of analytic philosophy. Why do you find it baffling? Or a gross analogy?

   

   Because you've taken a theorem about the provability of statements in systems of arithmetic, and argued that it shows that things in the universe can exist without cause. Provability and causation are not the same thing. Systems of arithmetic and universes are not the same thing. That's why I accused you of equivocating, and that's why I said your argument was at best analogical.

   

   
But you were the one who suggested an infinite regress of causes to be a viable idea in an earlier post. So which is it? Are you saying it is possible to explain all contingencies in terms of other contingent things? Or are you saying that some things have no explanation? I really don't know where to go next in this discussion unless I know what point you are trying to argue.

   

   I thought you might make this objection and almost added a paranthetical clarification, but decided not to in order to maintain continuity and rhythm. An infinite regress is my least favorite candidate for explaining reality, but it's one that I do not think we can completely rule out. I made this clear more than once. But the idea that you proposed was NOT an infinite linear chain of causal relationships (A was caused by B, B was caused by C, C was caused by D, ...), which is what I defended in previous posts. You proposed simultaneous causation (A was caused by B, B was caused by C, but C was caused by A), which is something that I find highly incoherent. The two concepts are distinct.

   

   Now, all this talk of simultaneous causation, Godel, the representation of reality as a system of propositions, and so on, has felt really tangential and I don't care much about any of it. I'm interested, much more than anything else, in whether necessary entities require an explanation or not--that is, whether they require a CAUSE or not. So if you want to limit your remarks to that topic, I'd be just fine with that.

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loko5

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Cosmological argument seems unconvincing
« Reply #44 on: July 16, 2009, 04:12:13 pm »

Dave,

Sorry for the delay.  I was out on vacation and have been trying to get caught up on things.

Since you feel that our discussion has been tangential, let me get it back on track by going back to the Leibnizian argument again:

(1)  Everything that exists is either necessary or contingent.
(2)  Necessary things require no explanation for their existence, because they could not fail to exist.
(3)  Contingent things require an explanation.
(4)  The universe is contingent.
(5)  Therefore, the universe must be explainable in terms of something that is necessary.
(6')  Therefore naturalism is false, i.e. there must be some necessarily existing First Cause external to the universe that explains why the universe exists.

Since you seem to find possible worlds semantics helpful, let me recast the argument using possible worlds terminology:

(1p)  Everything that exists is either necessary or contingent, where necessary things are defined as those things that exist in all possible worlds, and contingent things do not exist in at least some possible worlds.
(2p)  Contingent things require an explanation for why they exist in the actual world; that is, there must be an explanation as to why this is the actual world rather than some other possible world being the actual world.
(3p)  Necessary things require no explanation for why they exist in the actual world, since they exist in all possible worlds.
(4p)  The universe is contingent; that is, there are possible worlds where the universe doesn’t exist or is entirely different than it is in this world.
(5p)  Therefore, the universe must be explainable in terms of something that is necessary.
(6p)  Therefore naturalism is false, i.e. there must be some necessarily existing First Cause external to the universe that explains why the universe exists.

Now, seen in this light, it should be obvious that your insistence for an explanation for why necessary things are necessary is a red herring.  It may be an interesting question, but it is irrelevant to the argument.

It seems to me that 1p and 3p are unobjectionable, and I don’t think you are in disagreement with 4p.  So, let me ask you then just where you find the argument unconvincing.