Wednesday, December 8, 2010

Some-All Analogies and the Ontological Argument

The easiest way to express the ontological argument is like this (where "God" = a maximally great being, or a being that is omnipotent, omniscient, and morally perfect in every possible world):

1. God is either necessary or impossible. (Definition)

2. God is not impossible. (Premise)

3. Therefore, God is necessary. (From 1 and 2)

Transpositionally, (2) implies that God is possible. Given God's possible existence and S5, it follows that God exists. I argued earlier that one may demonstrate (2) by way of reductio ad absurdum. However, after giving it some further thought, I also think there is promise in arguing by way of analogy.

Take the proposition p1, "some of the existing apples are on earth." Now, according to Boolean logic, the quantifier, "some," does not necessarily imply that there are some existing apples that are not on earth. Nevertheless, given the possibility that p1, it is also reasonable to infer the possibility of p2, "all of the existing apples are X." In other words, the possibility of some implies the possibility, even if not the actuality, of all.

Applied to the ontological argument, we know that there are agents (such as ourselves) who possess some power, some knowledge, and some moral goodness in some possible worlds. If the some-all analogy is correct and taken to its logical conclusion, it follows that God possibly exists. This is all that is needed to show that (2) is true. Of course, (2) in conjunction with (1) implies that God is necessary, or has existence in all possible worlds.

Given that God exists in all possible worlds, and given that the actual world is a member of the set of possible worlds, it follows that God exists in the actual world. Therefore, God exists.

Of course, if one is not persuaded by the some-all analogy, then he/she will not necessarily accept the conclusion that God exists. For the rest of us, though, the knowledge of our limited perfections only confirm our conviction that God exists. As C.S. Lewis quips (and I paraphrase), we only know that a line is crooked if we have some idea of what a straight line looks like.

65 comments:

  1. Walter Van den AckerDecember 8, 2010 at 10:47 AM

    Sorry, Doug, but these ontological arguments are nothing but word-magic. If ever someone succeeds in building a persuasive argument for the existence of God, it will have to include much more than this.
    Just a small modification will, hopefully, make it clear why these kinds of arguments are so weak.
    Applied to the ontological argument, we know that there are entities (such as stones) that possess no knowledge, and no moral goodness in some possible worlds. If the some-all analogy is correct and taken to its logical conclusion, it follows that there is a possible world in which no entities exist that have knowledge or moral goodness.
    Hence, God is impossible.

    What you are doing in your argument, is equivocating epistemic with logical (or actual) possibility. God may be epistemically possible but that does not imply that there is a possible world in which God exists, for the simple reason that it is also at least epistemically possible that there is a world in which no God exists, which would make God impossible.

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  2. What the ontological argument shows, at the very least, is that the existence of God (where "God" is a maximally great being, not just a generic creator of the universe) is not merely a contingent matter. If God were to exist contingently, then He wouldn't be God. So, God is either necessary or impossible. Notice I'm not talking about epistemic possibility only. Regardless of one's epistemic status, a maximally great being either exists in all possible worlds or in no possible world. When you call it "word magic," then, it's hard to decipher if you're talking about what I just described, which is really just logic, not word magic, or else the support I and others offer in defense of the possibility premise.

    "Applied to the ontological argument, we know that there are entities (such as stones) that possess no knowledge, and no moral goodness in some possible worlds. If the some-all analogy is correct and taken to its logical conclusion, it follows that there is a possible world in which no entities exist that have knowledge or moral goodness.
    Hence, God is impossible."

    This isn't a sound parody of the argument. Just one reason is that your counter-argument jumps from a qualifier (some knowledge, etc.) to a quantifier (x-number of entities). What the original some-all analogy does is jump from qualifier to qualifier - the possibility of some power implies the possibility of all power. You could modify your counter-argument to something like this: the possibility of no knowledge, as in the case of a rock, implies the possibility of no knowledge. But, that's not a very interesting argument, nor is it detrimental to the ontological argument.

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  3. Walter Van den AckerDecember 9, 2010 at 10:18 AM

    Doug said

    "What the ontological argument shows, at the very least, is that the existence of God (where "God" is a maximally great being, not just a generic creator of the universe) is not merely a contingent matter. If God were to exist contingently, then He wouldn't be God. So, God is either necessary or impossible."

    No, Doug, the ontological argument does not show that, it asserts it in a definition. If one defines, as Swinburne e.g. does, God as a contingent being, then he would still be God under that definition.
    I am willing to accept that God is either necessary or impossible, but that also means that if there is one possible world without God, God does not exist.

    Doug
    "What the original some-all analogy does is jump from qualifier to qualifier - the possibility of some power implies the possibility of all power."
    Some and all are NOT qualifiers, they are quantifiers , the alternative you propose, as you say, implies the possibility of no knowledge,IOW a possible world with no knowledge, which means there is a possible world where God (who is defined as 'possessing all knowledge') does not exist. Hence God is impossible. So, it is detrimental after all.
    That's why I call this word-magic. You can prove whatever you want to prove. As I said, your argument jumps from epistemic possibility to actual possibility.If some agents have some knowledge it is epistemically possible that there is an agent who possesses all knowledge etc. but that does not mean there is a possible world in which this is the case, and even if it were the case, it does not follow that this is the case in all possible worlds, unless you wish to claim that there are apples in every possible world too. Trying to prove the existence of a necessary being by just looking at one or a few possible worlds is a category error. It just cannot be done, despite the pathetic effort by Plantinga to pull this off, because if there is one possible world without God, God cannot possibly exist.

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  4. Walter: "No, Doug, the ontological argument does not show that, it asserts it in a definition. If one defines, as Swinburne e.g. does, God as a contingent being, then he would still be God under that definition."

    Swinburne's God isn't maximally great. Would such a being still be worthy of being called "God"? Sure, but He's not the maximally great being of the ontological argument.

    Walter: "I am willing to accept that God is either necessary or impossible, but that also means that if there is one possible world without God, God does not exist."

    This is basically what I said about how the ontological argument shows that a maximally great being's existence is not merely a contingent matter. Yes, if there is a possible world in which such a being does not exist, then that being is impossible. On the other hand, if there is one possible world in which a maximally great being does exist, then a maximally great being actually exists.

    Walter: "Some and all are NOT qualifiers, they are quantifiers , the alternative you propose, as you say, implies the possibility of no knowledge,IOW a possible world with no knowledge, which means there is a possible world where God (who is defined as 'possessing all knowledge') does not exist. Hence God is impossible. So, it is detrimental after all."

    First, some and all can most certainly be qualifiers. If we propose a fictional entity who possesses great, but not all knowledge, the quantifier that corresponds to it is still 0. This is because there is no instantiation of this entity.

    Walter: "That's why I call this word-magic. You can prove whatever you want to prove. As I said, your argument jumps from epistemic possibility to actual possibility."

    You might want to try interacting with what I said about the distinction between epistemic possibility and actual possibility. Reasserting that I'm committing this error while simultaneously ignoring what I wrote about it is unproductive.

    Walter: "Trying to prove the existence of a necessary being by just looking at one or a few possible worlds is a category error."

    A category error is when one treats an abstract object like a concrete object, or vice-versa. The ontological argument commits no such logical fallacy.

    Walter: "It just cannot be done, despite the pathetic effort by Plantinga to pull this off, because if there is one possible world without God, God cannot possibly exist."

    I'm going to ask you not to use terms like, "pathetic," to describe anyone's views. This applies to both theist and atheist.

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  5. Walter Van den AckerDecember 9, 2010 at 11:09 PM

    Just one thing, Doug

    Doug said:
    "This is basically what I said about how the ontological argument shows that a maximally great being's existence is not merely a contingent matter. Yes, if there is a possible world in which such a being does not exist, then that being is impossible. On the other hand, if there is one possible world in which a maximally great being does exist, then a maximally great being actually exists."

    I am willing to accept the necessity of God for the sake of the argument and there may be arguments for it, but the argument you propose,
    "1. God is either necessary or impossible. (Definition)

    2. God is not impossible. (Premise)

    3. Therefore, God is necessary. (From 1 and 2)", just treats it as an assertion.
    More importantly, epistemic possibility of a necessary being does not suffice to prove its existence, because EP would imply there are some possible worlds with and some possible worlds without it. And that's where tha some-all anology leads us: to the epistemic possibility that a being with all powers exists in all possible worlds, which of course implies that there is also the possibility that this being does not exist in any world.
    So, to draw your conclusion, you have to jump from epistemic to actual possibility, which is not justified by your argument.
    And I do apologize for the therm "pathetic", but I feel that arguments like Plantinga's ontological argument make debates impossible by focussing on semantic games instead of on important issues. After all, Platin a admits that his argument does not work to prove God.

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  6. No need to apologize. I realize you're not attacking Plantinga as a person. I just wanted to set a precedent that would prevent anyone from going down that path, whether it's with respect to a theist, like Plantinga, or an atheist, such as Dennett.

    The argument I propose isn't just an assertion. (2) needs to be supported, and I think there are good arguments in favor of it.

    I agree with you that epistemic possibility does not suffice to show actual existence, or even actual possibility. As you allude to, Plantinga does not regard his ontological argument as a proof. He begins with an epistemic premise and ends with an epistemic conclusion, e.g. it is rational to believe in God based on the argument.

    However, I disagree that the epistemic possibility of X implies the possible non-existence of X. The possible non-existence of X would just be an open question. After all, possibilities are of two types: necessities and contingencies. I emphasize the former.

    By the way, you probably notice that I don't often debate the ontological argument. One reason is because I find it less persuasive than other arguments. As far as I'm concerned, if I believe that the cosmological argument is equally correct (take "equally" however you want), but that it is also more persuasive - and also likely more demonstrable - then I'm going to focus instead on the cosmological argument.

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  7. Walter Van den AckerDecember 10, 2010 at 4:23 AM

    I’ ve just semi-formalized your argument, to show where I think the flaw is.

    (1)there are agents who have some power, some knowledge and some moral goodness
    (2) it is possible that an agent who has all power, all knowledge and all moral goodness exists (= epistemic possibility)
    (2’) it is possible that an agent who has all power, all knowledge and all moral goodness does not exist

    from (2)

    (3) God possibly exists
    (4) God necessarily exists (by S5 etc)
    (5) God exists in the actual world

    but from (2’)

    (3’) God possibly doesn’t exist
    (4’) God necessarily does not exist (or “It’s impossible that god exists” by S5 etc)
    (5’) God does not exist in the actual world.

    In your argument you simply ignore (2’) and its logical implications.You say you disagree that the epistemic possibility of X implies the possible non-existence of X, but that's the definition of epistemic possibility: possibly yes, possibly no.If as you say, the possible non-existence of X would just be an open question, then of course the possible existence of X is equally an open question under epistemic possibility. You may emphasise whatever you wish, but I may also emphasize whatever I wish.
    IOW If you believe that God possibly exists, then you believe that God exist and if you don’t , then you don’t.
    Is it really worth all the trouble of building a sophisticated argument only to show something as trivial as this?

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  8. When an argument turns to modal logic as one of its supports, I get leery or chary.

    Moreover, I'm no longer sure that God is "necessary" in just the way that Aristotle means that term. Sure, given that "the universe," which is contingent, exists, it is necessary that God, who is non-contingent, exists. But, I'm no longer convinced that God cannot not exist ... to put it crudely, I see no logical reason that God cannot "commit suicide" (which would cause all thigs to not be).

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  9. WVdA: "If ever someone succeeds in building a persuasive argument for the existence of God, ..."

    Done and done (with background)

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  10. Walter, that's not the definition of epistemic possibility. The term, "epistemic," denotes that one is rationally justified in believing something. If you are rationally justified in believing that something is red, that doesn't begin to imply that I am justified in believing the same object is not-red.

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  11. Walter Van den AckerDecember 12, 2010 at 2:15 AM

    Epistemic possibility means "for all we know, X could be true" and in most cases this entails "for all we know X could be false", otherwise it would be epistemic necessity: "for all we know, X is certainly true". Your some-more analogy says that it is possible that an all-powerful entity exists in all possible worlds and in the absense of further argument it also entails that the entity only exists in some possible worlds or even does not exist in any possible world. So my objection stands.

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  12. Again, that's not what is implied by "epistemic possibility." It's just like the fact that "some are" does not imply "some are not."

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  13. By the way, are you aware of the distinction between strictly logical necessities and broadly logical necessities? I only ask because this could be the root of one of our disagreements.

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  14. "are you aware of the distinction between strictly logical necessities and broadly logical necessities?"

    I for one am not, nor do I see how such a distinction is logically possible.

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  15. Walter Van den AckerDecember 12, 2010 at 10:51 AM

    Doug said:
    "some are" does not imply "some are not."
    That's not what i'm talking about, what I say is: "X may exist" implies "X may not exist", otherwise we could just as well say "X exists".
    e.g. "It is epistemically possible that there is intelligent life on other planets" entails "It is possible that there is no intelligent life on other planets", doesn't it?
    And I do not think the distinction between strictly logical and broadly logical necessities is relevant here. the broadly logically necessary existence of God cannot be proven by just looking at one possible world because the property "exists in every possible world" exceeds the scope of one possible world.

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  16. Walter Van den AckerDecember 12, 2010 at 10:55 AM

    WVdA: "If ever someone succeeds in building a persuasive argument for the existence of God, ..."
    Ilion said
    Done and done (with background)

    Interesting arguments, Ilion, if I can find some time I may post a comment in your blog, if you don't mind, of course.

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  17. Walter: "e.g. "It is epistemically possible that there is intelligent life on other planets" entails "It is possible that there is no intelligent life on other planets", doesn't it?"

    It doesn't. The latter is true given other background knowledge, but it's not true because of any implication of the former statement.

    Walter: "And I do not think the distinction between strictly logical and broadly logical necessities is relevant here. the broadly logically necessary existence of God cannot be proven by just looking at one possible world because the property 'exists in every possible world' exceeds the scope of one possible world."

    That's not what broadly logical necessity refers to. In any case, there's no reason to think that the epistemic possibility of one proposition implies the epistemic possibility of its negation.

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  18. Walter Van den AckerDecember 12, 2010 at 3:47 PM

    Doug said

    "That's not what broadly logical necessity refers to. In any case, there's no reason to think that the epistemic possibility of one proposition implies the epistemic possibility of its negation"

    Broadly logical necessity refers to existence in all possible worlds.

    And epistemic possibility, unless it is epistemic certainty, implies that the negation is possible. The fact that you say: "The latter is true given other background knowledge", refers to certainty, not to possibility. If the existence of other intelligent life forms is stated as an epistemic possibility it means that the person saying it isn't sure whether intelligent life forms exist elsewhere or not.
    But, that's the last thing I am going to say about this argument, I don't want to repeat myself.

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  19. Broadly logical necessity and strictly logical necessity both refer to existence/instantiation in all possible worlds. The former is designated for those truths that are necessary, but not obviously necessary. Think of the proposition, "the prime minister is a prime number." That proposition is necessarily false, but not in the same way as X is ~X.

    My statement about background knowledge doesn't allude to any certainty. Rather, it is an informed skepticism about life on other planets given what we know to be true or likely true.

    Here is how we can show that the epistemic possibility of X doesn't entail the possibility of ~X. In order for something X to be true, X must be possible. This means that it must be actually possible. Now, in order for us to know that X is actually possible, we must have an epistemic status that corresponds to the actual possibility of X. This rationally justified belief is epistemic possibility. Hence, an actual possibility requires an epistemic possibility. But, the truth of X may very well be indubitable or at least known with a high degree of certitude, in which case ~X is not an epistemic possibility.

    Now, if you want to say that X is only an epistemic possibility, then we can talk about ~X being an epistemic possibility. However, the arguments I've been talking about seek to establish the actual possibility, and not only the epistemic possibility, of a maximally great being.

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  20. Walter Van den AckerDecember 13, 2010 at 4:21 AM

    Of course you seek to establish the actual possibility of a maximally great being, but your some-all analogy just does not do that. It only establishes epistemic possibility, and an atheist would only grant its epistemic possibility and is also justified in holding that a maximally great being is not actually possible.
    I e.g. am convinced that a maximally great being is not actually possible.
    So, all your argument says is that if you believe a maximally great being is actually possible, then it follows that said MGB is necessary and actually exists. And if you don't believe that an MGB is actually possible , it follows that said MGB is impossible and does not exist.
    But that's so obvious that I cannot think of any reason why anyone wants to go to the trouble of building this kind of argument. argument

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  21. Walter: "Of course you seek to establish the actual possibility of a maximally great being, but your some-all analogy just does not do that."

    This, of course, is what we disagree about.

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  22. "What the ontological argument shows, at the very least, is that the existence of God (where "God" is a maximally great being, not just a generic creator of the universe) is not merely a contingent matter"

    But since this is the first premise of your argument, I'm a bit puzzled how it can "show" this. It'd be question begging.

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  23. Hi Doug. I've been wondering about the argument. It seems formally valid. But anything like this seems formally valid:

    (1)It is proposed that a being X exists in all possible worlds.
    (2)X is possibly exemplified. That is, it is possible that there be a being that exists in all possible worlds. (Premise)
    (3)Therefore, possibly it is necessarily true that X exists.
    (4)Therefore, it is necessarily true that X exists. (By S5)
    (5) Therefore, X exists.

    This is the same form as Plantinga's ontological argument. Now it seems that we could use this argument to "prove" anything (x could be anything). Although one shouldn't deny an argument because one doesn't like the conclusion, that sort of conclusion is not what we want here.

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  24. It's true that the form of the argument is valid. In fact, that's one of the reasons Plantinga defends the ontological argument. Where parodies of the argument fall short is in the coherence of X. For example, if we replace X with Gaunilo's Island, it becomes evident that such a counter-argument would not really prove that a maximally great island exists. But, instead of this being an argument against the ontological argument, I think it turns out to undermine the coherence of a maximally great island. The question, then, is whether or not a maximally great being is a coherent idea. If it is, then it is not undermined by disanalogous arguments, such as Gaunilo's Island.

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  25. Mickey, the possibility premise can be denied. In this case, a maximally great being would be impossible. The very idea of a contingent maximally great being is, I think, quite manifestly absurd, especially if necessary existence is greater than contingent existence.

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  26. A couple of more possible objections. I really don't see any problems with the validity, or with S5, as some others might think.

    1) What do you think of the idea of a maximally *evil* being?
    2) What if nothing is necessary? For example maybe there is a possible world in which no being is instantiated? And we can rule out abstract objects by a deflationary theory of truth.

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  27. These are good questions. 1) I would argue that the very concept of a maximally great being is incoherent. For, necessary existence is thought to be a perfection, a very great good. Yet, to be maximally evil is to lack all and every good, which would include necessary existence. Hence, a maximally evil being cannot be shown to exist by S5.

    2) A whole lot can be said in reply to this latter question. Is it possible for a world to contain literally nothing? Would such a world even be considered a world at all? One of the reasons I don't think this is the case is that even granting that such a state of affairs is conceivable, conceivability does not always entail possibility. Where N = a necessary being exists, the argument is supposed to be that the conceivability,and therefore possibility, of ~N in conjunction with S5 demonstrates that ~N is true.

    One of the problems with this objection is that the exact opposite can be argued. After all, N is a conceivable state of affairs that, when in conjunction with S5, demonstrates that N is true. But, N and ~N cannot both be true. I think what this suggests is that the notion of conceivability entailing possibility is not always correct.

    There are also additional reasons for thinking that N is possible. Imagine someone takes the sum total of all contingencies C and asks, "is it possible for C to have an external cause?" Given that external causes in general are logically possible, it seems quite reasonable to infer that C possibly has an external cause. Yet, this cause cannot be contingent, since otherwise it would be part of C and therefore not external to C. Therefore, the possible external cause of C would have to be a necessary entity. From this is follows that a necessary entity possibly exists, and in conjunction with S5, this means a necessary entity exists.

    Notice what the skeptic cannot say at this point. He cannot build a counter-argument by saying that C possibly does not have an external cause. For, C's not having an external cause is logically consistent with the existence of a necessary entity. So, there's no valid inference to be made from C's possibly not having an external cause to the possibility of ~N. Make sense?

    My apologies for the somewhat lengthy post. It's just that I get into these discussions a lot like I get into Eagles games. :)

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  28. "2) What if nothing is necessary? For example maybe there is a possible world in which no being is instantiated?"

    That wouldn't be a world, would it? How can nothing be a world?

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  29. "Yet, to be maximally evil is to lack all and every good, which would include necessary existence."

    It seems to me that a hypothetical "maximally evil being" would lack even contingent existence.

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  30. No need to apologize. I love this stuff too! Yes, I noticed that N and ~N are both conceivable states of affairs, but not possibly both N and ~N, and thus conceivability does not imply possibility. Of course, this may have some more important and radical consequences later on.

    Your explanation all makes sense. It sounds similar to the Modal Cosmological Argument of yours that I first read. The only thing one could really say is that it is impossible that C have an external cause. I'm not sure how you could do that, but I remember one person you were discussing this with managed to try and do so.

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  31. Walter Van den AckerDecember 14, 2010 at 10:47 AM

    Doug said

    "1) I would argue that the very concept of a maximally great being is incoherent."

    I, too, think the very concept of a maximally great being is incoherent. Once again, we agree on something.

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  32. Doug said,

    "Mickey, the possibility premise can be denied. In this case, a maximally great being would be impossible. The very idea of a contingent maximally great being is, I think, quite manifestly absurd, especially if necessary existence is greater than contingent existence."

    I don't deny, Doug, that the premise can be denied. My point is that what you claim the ontological "shows" is more or less given in your first premise, and so it's question begging.

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  33. Actually, I thought about this some more, and it leads me to a couple more possible objections. There is a world where John who is five feet tall is 1*10^-x inches shorter. x could be any natural number. Now, there is an infinite set of natural numbers. Each of those worlds is possible and contingent. Thus an infinite number of contingencies (and possible worlds for that matter). But how can something cause an infinite number of things? This may have other ramifications I'm not thinking of right now.

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  34. Many thanks to Walter for pointing out my typo. What I meant to say was this: "1) I would argue that the very concept of a maximally evil being is incoherent."

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  35. Mickey: "I don't deny, Doug, that the premise can be denied. My point is that what you claim the ontological 'shows' is more or less given in your first premise, and so it's question begging."

    I'm not sure how that's question-begging. (1), in conjunction with S5, shows that a maximally great being is either necessary or impossible. Suppose instead that one accepts (1), but rejects S5. Not that there is any good reason to reject S5, but such a view, if correct, would lead us to believe that a maximally great being may exist contingently.

    Of course, I completely left S5 out for the sake of simplicity, but (1) stands or falls based on it.

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  36. awatkins: "Your explanation all makes sense. It sounds similar to the Modal Cosmological Argument of yours that I first read. The only thing one could really say is that it is impossible that C have an external cause. I'm not sure how you could do that, but I remember one person you were discussing this with managed to try and do so."

    What's interesting, though, is that even if it were impossible for C to have an external cause, that wouldn't establish the possibility of ~N.

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  37. Ilion: "That wouldn't be a world, would it? How can nothing be a world?" That's a fair point. Some people may object to this though, probably because it's so simple and actually makes sense!

    Still, even if we conclude that there is no "world" with nothing, all we can formulate is that "necessarily some undefined thing exists". From this it doesn't follow that "there is a necessary being."

    Take two worlds, w and w*. w contains an up quark. w* contains a down quark. In each of these worlds there is nothing they share in common. If we were working with sets, the intersection of the two sets would be an empty set.

    What can we conclude from this? Maybe that there are no necessary beings, such as we take N to be. For if there are at least two possible worlds with nothing in common, that means there is at least one possible world where N doesn't exist. And thus N is not a necessary being, nor could there be any necessary being.

    The way to reply is to do what Doug says, and propose an argument whereby the sum total of contingencies C is possibly externally caused by a necessary being N, then prove by S5 that N necessarily exists. And since w and w* don't contain N, they are impossible worlds, because whatever is necessary doesn't differ between possible worlds. If it differs in w and w* then they are impossible worlds.

    Jeez, sorry for wasting so much time!

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  38. Doug: "What's interesting, though, is that even if it were impossible for C to have an external cause, that wouldn't establish the possibility of ~N."

    I must be missing something here. If we take a scenario like above with two worlds with nothing in common, and we haven't proven N by saying C has an external cause (or some other way), then why is ~N impossible?

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  39. Walter Van den AckerDecember 15, 2010 at 7:35 AM

    Awatkins69 said

    "Your explanation all makes sense. It sounds similar to the Modal Cosmological Argument of yours that I first read. The only thing one could really say is that it is impossible that C have an external cause. I'm not sure how you could do that, but I remember one person you were discussing this with managed to try and do so."

    Of course it is impossible that C has an external cause IF necessary beings cannot exist. If one believes that only contingent beings can exist, then the sum total of all contingent beings CANNOT have an external cause.
    So, any argument that sets out to prove that necessary beings are possible can only succeed provided one already assumes from the outset that such beings are not impossible. That's why virtually all ontologucal arguments are question-begging.
    Doug says in this respect
    "For, C's not having an external cause is logically consistent with the existence of a necessary entity. So, there's no valid inference to be made from C's possibly not having an external cause to the possibility of ~N. Make sense?"

    Actually there is a valid inference from C's possibibly not having an external cause to the possibility of ~N. If C does not have an external cause then that does not automatically mean that N does not exist. However it's hard to see why, if there is a possible world Wc in which C does not have an external cause, there is any need for N in Wc. And if there is no need of N in that world, that means there is a possible wold without N (because Wc can exist on its own). One could say that we have already defined N as existing in Wc, but then Wc1 would be exacrly the same world as Wc but without N. Since N plays no active role in Wc, Wc1 is a possible world too.

    BTW
    Doug said:
    "I would argue that the very concept of a maximally evil being is incoherent."

    That depends on how you define evil. I don't think e.g. it is possible to show that a maximally great being who approves of mass murder, child abuse, rape etc is impossible. After all, who is to say that such a being cannot be "great". That would assume a standard of morality independent on God. If however, as Christians claim to get out of Euthrypho's dilemma, morality is dependent on God, then it can take any form. There is no reason why there couldn't be a possible world where all these things are actually good becaase God approves of them.

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  40. WvdA:Of course it is impossible that C has an external cause IF necessary beings cannot exist. If one believes that only contingent beings can exist, then the sum total of all contingent beings CANNOT have an external cause.

    So, any argument that sets out to prove that necessary beings are possible can only succeed provided one already assumes from the outset that such beings are not impossible. That's why virtually all ontologiucal arguments are question-begging.


    You’re in over your head, aren’t you?

    What you’re really asserting is that “virtually all ontological arguments are question-begging” ... because you refuse to be persuaded by any of them, because *you* refuse to acknowledge that a non-contingent being is possible, much less necessary.

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  41. Hey Doug, do you think Russell's paradox is applicable here?

    We know that Russell's paradox says that the "set of all regular sets" is a paradox, because if it is a set of all regular sets, and is itself regular, it will contain itself.

    The same thing follows with C the set of all contingencies. If it contains all the contingencies, and is itself contingent, then it contains itself. And this is absurd of course, and the set is undefined. We can't do anything with an undefined set, and we certainly can't say it's possibly externally caused.

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  42. Walter: "Of course it is impossible that C has an external cause IF necessary beings cannot exist. If one believes that only contingent beings can exist, then the sum total of all contingent beings CANNOT have an external cause."

    That's a fairly good point, although someone might say that assuming a necessary being is impossible is question begging as well.

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  43. Doug said,

    "I'm not sure how that's question-begging. (1), in conjunction with S5, shows that a maximally great being is either necessary or impossible."


    The first premise of your argument along with S5 does not "show" that a maximally great being ( God) is either necessary or impossible. That's the premise itself! Perhaps Platinga's argument shows this, but your argument does not. To see this, consider your argument:


    1. God is either necessary or impossible. (Definition)

    2. God is not impossible. (Premise)

    3. Therefore, God is necessary. (From 1 and 2)


    Just what do you think the first premise states?




    Doug said,

    "Suppose instead that one accepts (1), but rejects S5. Not that there is any good reason to reject S5, but such a view, if correct, would lead us to believe that a maximally great being may exist contingently."

    If one accepts your premise (1), he cannot also consistently think that God is contingent. This has nothing to do with S5. There's just only three existential modalities: Impossibility, necessity and contingency. This is not something one can deny by denying S5.

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  44. "Of course it is impossible that C has an external cause IF necessary beings cannot exist. If one believes that only contingent beings can exist, then the sum total of all contingent beings CANNOT have an external cause.
    So, any argument that sets out to prove that necessary beings are possible can only succeed provided one already assumes from the outset that such beings are not impossible. That's why virtually all ontologucal arguments are question-begging."

    Modal ontological arguments do not intend to show that a necessary being is possible. Instead, they intend to show that a necessary being exists. Given this, I'm unsure where there's a question begged.

    I'm also unsure if you're relating this causal stuff to the ontological argument. if you are, i'm unsure why. No ontological argument uses a causal premise; these are a posteriori arguments while the ontological argument is a priori.

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  45. Mickey, I think the first premise has a lot of "unpacking" to do, as it were. You're right that there are only three modalities. We might begin by actually providing a defense of the first premise:

    Prove A: A maximally great being is either necessary or impossible. (E.g. a maximally great being cannot be contingent.)
    Assume ~A: A maximally great being can be contingent.
    ~A --> B: If a maximally great being can be contingent, then a maximally great being would not be maximally great.
    ~B: A maximally great being must be maximally great.
    ~~A: by modus tollens.
    Therefore, A: A maximally great being is either necessary or impossible.

    I regret listing (1) as a definition, since the proponent of the ontological argument also argues that necessary existence is a great-making property, via (~A --> B).

    The confusion between the ontological argument and the cosmological argument is my own fault. I brought up causality to illustrate how one might further reason that a necessary being is possible.

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  46. Walter, it's important to keep in mind that the modal cosmological argument (MCA) does not start out by simply asserting the possible existence of a necessary being. Rather, this is a conclusion that is inferred from the fact that things can, and arguably quite often, have external causes. This principle is then applied to C, which explains why a necessary being possibly exists. To reject the premise that C possibly has an external cause, without any justification, seems to be an elementary case of special pleading.

    As for a maximally evil being, which is it? Is a necessary being (good, evil, or whatever) possible or not? Moreover, the situations you mention still aren't maximally evil. Even Hitler didn't kill his own mother. With respect to the Euthyphro Dilemma, be careful not to confuse dependency with contingency.

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  47. Alfredo: "I must be missing something here. If we take a scenario like above with two worlds with nothing in common, and we haven't proven N by saying C has an external cause (or some other way), then why is ~N impossible?"

    Assuming these two worlds are possible, then that would establish ~N. Of course, ~N would also require that C cannot even possibly have an external cause, which is quite position to have to defend.

    What I was talking about was that N may exist even if N is not the cause of C. Do you see what I mean here? If one tries to counter the MCA by stating that C possibly does not have an external cause in, say, w1, then N may still exist in w1, but in such a way that N is not causing C. So, it's not enough for the skeptic to turn around the causal/possibility premise. Rather, he/she must go further by arguing that C cannot have an external cause.

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  48. I'm glad you brought up Russell's Paradox, since it allows me to clarify something. When we define C as the sum total of all contingencies, we're restricting those contingencies to concrete objects. One shouldn't think of C as a mathematical set, but simply as a large collection of concrete objects that makes up a large concrete object, much like how the parts of a house construct a relatively large concrete object (the house itself).

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  49. Walter Van den AckerDecember 16, 2010 at 6:41 AM

    Ilion said:

    "You’re in over your head, aren’t you?"

    I don't think so.

    "What you’re really asserting is that “virtually all ontological arguments are question-begging” ... because you refuse to be persuaded by any of them."

    I'm not asserting anything and I will be persuaded by any argument that is persuasive.

    ", because *you* refuse to acknowledge that a non-contingent being is possible, much less necessary."

    I don't know whether a non-contingent being is ACTUALLY possible, and what's more: nobody knows this. There are good arguments against the Christian God's being non-contingent and it isn't even sure if anything can be non-contingent.

    Mickey said:
    "Modal ontological arguments do not intend to show that a necessary being is possible. Instead, they intend to show that a necessary being exists. Given this, I'm unsure where there's a question begged."

    If a necessary being is ACTUALLY possible it exists. So, to be succesful OA's have to prove that necessary beings (or the kind of NB's they set out to prove) are ACTUALLY possible. But the OA given by Doug does not do that, it jumps from yes/no possibility (possibly N, possibly ~N) to actually possible N. that's why it is question-begging.

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  50. Walter Van den AckerDecember 16, 2010 at 7:04 AM

    Doug said:

    "Prove A: A maximally great being is either necessary or impossible. (E.g. a maximally great being cannot be contingent.)
    Assume ~A: A maximally great being can be contingent.
    ~A --> B: If a maximally great being can be contingent, then a maximally great being would not be maximally great.
    ~B: A maximally great being must be maximally great.
    ~~A: by modus tollens.
    Therefore, A: A maximally great being is either necessary or impossible"

    This illustrates why OA's are question-beggiçng most of the time. This 'proof' you present here, which is dreived from Anselm's OA is already question-begging on its own, for a maximaaly great being CAN be contingent if necessary beings are impossible.
    So by stating that a maximally great being would not be maximally great if it were contingent, you beg the question. Maximally great is as great as something can maximally be.

    "Walter, it's important to keep in mind that the modal cosmological argument (MCA) does not start out by simply asserting the possible existence of a necessary being. Rather, this is a conclusion that is inferred from the fact that things can, and arguably quite often, have external causes."

    Nevertheless, IF necessary beings are not possible then C cannot have an external cause. So, if one does not believe or even if someone isn't sure whether necessary beings can exist, then he cannot say that C (actually) possibly has an external cause.

    "As for a maximally evil being, which is it? Is a necessary being (good, evil, or whatever) possible or not?"

    I don't know, and nobody does. But if a necessary being is possible, there is no reason why it cannot be 'evil'


    "Moreover, the situations you mention still aren't maximally evil. Even Hitler didn't kill his own mother."

    Yes, but I could add all of that if you wish. The fact is, that if God showed up and told you he was in favour of all 'bad' things, you would have no argument to show that he wasn't a truly maximally great being.


    "With respect to the Euthyphro Dilemma, be careful not to confuse dependency with contingency."

    I don't. The fact that you seem to think your dependency/contingency distinction works against atheist criticism of the argument from morality shows that you misunderstand this criticism. But that's for another debate.

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  51. A.Watkins: "2) What if nothing is necessary? For example maybe there is a possible world in which no being is instantiated?"

    Ilíon: "That wouldn't be a world, would it? How can nothing be a world?"

    A.Watkins: "That's a fair point. Some people may object to this though, probably because it's so simple and actually makes sense!"

    There is generally a lot of that going around. Sometimes, it almost seems the default state, at least among those who like to think of themselves as deeper thinkers than everyone else.

    A.Watkins: "Still, even if we conclude that there is no "world" with nothing, all we can formulate is that "necessarily some undefined thing exists". From this it doesn't follow that "there is a necessary being."

    But then, I’m not an Aristotelian, and I increasingly am having doubts about the over-all soundness of his metaphysical conclusions.

    A.Watkins: "Take two worlds, w and w*. w contains an up quark. w* contains a down quark. In each of these worlds there is nothing they share in common. If we were working with sets, the intersection of the two sets would be an empty set.

    What can we conclude from this?


    Perhaps we can conclude that we’re not thinking clearly? For:
    1) sets are mental constructs, they are imaginary;
    2 ) there are no such things as intersections of two (or more) worlds. This is definitional.

    A.Watkins: "Still, even if we conclude that there is no "world" with nothing, all we can formulate is that "necessarily some undefined thing exists". From this it doesn't follow that "there is a necessary being."

    Actually, what we should say is more this: “If anything contingent exists, then necessarily something non-contingent exists as either its proximate or ultimate cause.” This non-contingent something may or may not be “necessary,” in the sense meant by Aristotle and his followers, but we don’t appear to have enough information to make an informed decision of which it is.

    At the same time, when/if the contingent something that we’re talking about is “the world,” then, necessarily, the non-contingent something/cause is “outside” the world.

    And, further, if “the world” we’re talking about contains selves who are rational beings, then, necessarily, the non-contingent something, which is the cause of the world, and which is “outside” the world, is not a ‘which,’ but a ‘who.’

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  52. Have any of you asked yourselves whether "non-contingent being" is (necessarily) equivalent to "necessary being" (understood as "that which cannt not exist")? And, if they are equivalent, on what grounds do we know it to be so?

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  53. Walter: "This illustrates why OA's are question-beggiçng most of the time. This 'proof' you present here, which is dreived from Anselm's OA is already question-begging on its own, for a maximaaly great being CAN be contingent if necessary beings are impossible."

    We have already discussed this at some length. Naturally, I think the above objection is quite weak.

    Walter: "Nevertheless, IF necessary beings are not possible then C cannot have an external cause. So, if one does not believe or even if someone isn't sure whether necessary beings can exist, then he cannot say that C (actually) possibly has an external cause."

    But why say that when, in fact, we know that every other contingent thing is at least possibly caused? Take the keyboard you're typing on. If, for the sake of argument, you were asked whether it even possibly had an external cause, I would hope you would answer with an emphatic, "yes." Why should C be the exception to the rule?

    Walter: "I don't know, and nobody does. But if a necessary being is possible, there is no reason why it cannot be 'evil'"

    As it's been pointed out, evil is a privation of a good. A maximally great being would have to necessary existence and moral perfection. Parodies of a maximally evil being don't work for the reason that they are incapable of correctly utilizing S5.

    Walter: "Yes, but I could add all of that if you wish. The fact is, that if God showed up and told you he was in favour of all 'bad' things, you would have no argument to show that he wasn't a truly maximally great being."

    No, I would just conclude that it wasn't God who was telling me those things.

    Walter: "I don't. The fact that you seem to think your dependency/contingency distinction works against atheist criticism of the argument from morality shows that you misunderstand this criticism. But that's for another debate."

    On the contrary, it's not that we misunderstand the criticism. Rather, the problem is that we understand the criticism so well that it's easy to show where the fallacy lies.

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  54. Walter Van den AckerDecember 17, 2010 at 2:05 AM

    Doug said

    "We have already discussed this at some length. Naturally, I think the above objection is quite weak."


    Yes, of course it sounds weak to somebody is convinced that impossible entities are greater than possible ones, but I'm still hoping that someone visisting this blog is capable of seeing the obvious absurdity of that position. If not, then so be it.

    "No, I would just conclude that it wasn't God who was telling me those things."

    I'm sure you would think that, but the question was: is this conclusion logically justified? What if 'God' says you're wrong and throws you into hell for blasphemy?

    "Rather, the problem is that we understand the criticism so well that it's easy to show where the fallacy lies."
    That would not be a problem. But your reply above makes it abundantly clear that you completely miss the point.

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  55. At this point, we've gotten to another completely different argument, which is actually a modal cosmological argument (MCA) for a necessary being. I've thought of all the real decent objections I could find against that, though I'm still a little worried about Russell's paradox, because we should be able to think of any aggregate as a set. But I think it's probably sound. The MCA is useful because it proves that necessary existence is possible, and this combined with the some-all analogy argument for the possibility of God shows us that God exists.

    Walter: I'm wondering why you assume that a necessary being is not possible, and that therefore C is not possibly caused. Do you think (1) it is possible for nothing to exist? Or do you think that, (2) necessarily, some undefined thing exists? That is, do you think that every possible world contains at least one contingent being, but there are no possible worlds with necessary beings? If it's either of these things, can you give an argument for these views that you find compelling? Also, if you think (1), can you explain why something actually exists rather than nothing? If you believe (2) can you explain why there must be at least one thing and why (1) is not possible?

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  56. Walter: "Yes, of course it sounds weak to somebody is convinced that impossible entities are greater than possible ones, but I'm still hoping that someone visisting this blog is capable of seeing the obvious absurdity of that position. If not, then so be it."

    Rather, having a perfection is greater than not having it.

    Walter: "I'm sure you would think that, but the question was: is this conclusion logically justified? What if 'God' says you're wrong and throws you into hell for blasphemy?"

    What if a bachelor were married? In order for God to be God, He must be good. Yes, this conclusion is justified.

    Walter: "That would not be a problem. But your reply above makes it abundantly clear that you completely miss the point."

    If you feel that I have missed your point, perhaps you could explain what it is instead of just dismissing my objection as a "misunderstanding" on my part.

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  57. Walter Van den AckerDecember 17, 2010 at 7:43 AM

    Awatkins69 said
    "Walter: I'm wondering why you assume that a necessary being is not possible, and that therefore C is not possibly caused."

    I don't assume that a necessary being is not possible. In fact I used to think that an necessary being was possible, but I don't think there is any way to knwo whether or not necessary concrete entities are possible for the simple reason that nobody has any clue as to what 'ingredient' or 'power' would make a being necessary.

    It's not that C is not possibly caused, it's that C is possibly not caused. The possibility stated here is what I would call epistemic possibility, but maybe that's not the correct term. It's 'possibly yes/ possibly no'.
    After all, some contingent things are demonstrably uncaused.

    "Do you think (1) it is possible for nothing to exist?"

    Maybe, yes. I think it is epistemically possible, but I do not know whether it(s actually possible.
    But consider world W1, which contains nothing but one immaterial being which is almost completely inert. There is no reason why W1 would not be possible. And yet W1 does not contain anything that could be described as 'God'. So, God does not seem to be necessary.


    "Or do you think that, (2) necessarily, some undefined thing exists?"

    That's also an epistemic possibility.

    "That is, do you think that every possible world contains at least one contingent being, but there are no possible worlds with necessary beings?"

    How would it be possible to determin whether a being existing in some possible world is a necessary being? To determine whether something is necessary we must of course look at all possible worlds. I just think that, as long as there is no contradiction in a world where a certain enetity does does not exist, we have to assume it's not a necessary being.


    "If it's either of these things, can you give an argument for these views that you find compelling? Also, if you think (1), can you explain why something actually exists rather than nothing?"

    I don't think there is an explanation for why something exists rather than nothing. I believe the principle of sufficient reason is self-defeating.

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  58. "If a necessary being is ACTUALLY possible it exists."


    Since possibility extends to all worlds, if it is actually possible, then it's possible in all worlds. Given S5, whatever is possible necessary is necessary, yes. And whatever is necessary, exists. But we shouldn't think that modal OAs intend to show that God is possiblly necessary; that's only half the battle.


    [quote]So, to be succesful OA's have to prove that necessary beings (or the kind of NB's they set out to prove) are ACTUALLY possible.[/quote]

    Given S5, they could show this just by showing or arguing for the possibility of a necessary being.


    [quote]But the OA given by Doug does not do that, it jumps from yes/no possibility (possibly N, possibly ~N) to actually possible N. that's why it is question-begging."[/quote]

    That's not question begging. Whatever is possible in one world is possible in any other. That's S5.

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  59. Walter: I was more wondering whether you think (1) or (2) is *actually* possible. I'm not really concerned about epistemic possibility. I want to call them X and Y instead now. I'll also add hypothesis Z.

    X = "There is one possible world where no entity exists."

    Y = "Necessarily, there is some contingent being."

    Z = "A necessary being exists."

    Which one do you think to be the case, "metaphysically" speaking? Not worrying about epistemic possibility here.

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  60. Walter Van den AckerDecember 18, 2010 at 8:04 AM

    Mickey:

    "Since possibility extends to all worlds, if it is actually possible, then it's possible in all worlds. Given S5, whatever is possible necessary is necessary, yes. And whatever is necessary, exists. But we shouldn't think that modal OAs intend to show that God is possiblly necessary; that's only half the battle."

    Yes, but they must first show that God is actually possibly necessary, and the point is: they don't, at least not the ones I'm familiar with and most certainly not this one.

    "Given S5, they could show this just by showing or arguing for the possibility of a necessary being."

    No, they couldn't, they have to argue for the actual possibility of a necesary being and that entails arguing that the NB exists in a possible world. Not just that a very powerful being exists in one possible world, but that a very powerful being that exists in all possible worlds exist in one possible worlds. And that's a very big burden.

    "That's not question begging. Whatever is possible in one world is possible in any other. That's S5."

    No, actually that is not true, whatever is necessary and is possible in one world is possible in any other. The difficulty is proving that such a being is actually possible, and Doug's argument does not do that.
    And the question-begging lies in the fact that one has to assume that a NB is possible before one can conclude that it is possible. That's question-begging, it's even circular.

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  61. Walter Van den AckerDecember 18, 2010 at 11:20 AM

    Awatkins69 said

    "Walter: I was more wondering whether you think (1) or (2) is *actually* possible."


    The point is, that IMO it is at this moment impossible to say whether some things are ACTUALLY possible or not.
    But I'll try to answer your question the best I can.

    X = "There is one possible world where no entity exists."

    There are arguments against the possibility of a completely empty world, but I do not really find them convincing, so, at this moment I would say that world X is a possible world.

    Y = "Necessarily, there is some contingent being."

    I think this is a contradiction. A contingent being is not neceesary and cannot exist necessarily.
    At this moment, I think that it is possible that there is at least one possible world with only one contingent being.

    Z = "A necessary being exists."

    There is no conclusive evidence against this, but it would contradict world X . So either X
    is impossible or Z is.
    And what I have been trying to say here all along, both are epistemically possible but of course only one of them can be actually possible. And I don't think there is any way to know this. The ontological arguments I am familiar with, including Doug's, all start by asssuming Z is a possible world, but if we don't assume that, we cannot arrive at the conclusion that the necessary being in question exists.

    Which one do you think to be the case, "metaphysically" speaking? Not worrying about epistemic possibility here.

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  62. Sorry, Walter. I guess I didn't clarify with Y. X,Y, and Z are all mutually exclusive options, metaphysically speaking.

    Basically, what I mean by Y, is that in every possible world, there is at least one undefined contingent entity. So all that means is that there is no possible world where absolutely no being is instantiated. On Y, however, there are also no beings which are common to all possible worlds. In other words, each world has at least some entity, but that entity isn't necessarily the same in all possible worlds.

    Makes sense? If so, which of the three propositions is true, X, Y, or Z? If not, I'll try to clarify.

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  63. Walter Van den AckerDecember 19, 2010 at 1:27 AM

    Awatkins69

    I know what you mean and the problem is that X, Y and Z are all epistemically possible, but, as you say, since they are mutually exclusive, only one of then is actually possible.

    Which one? I really do not know, and therein lies the main problem of OA's: if the above question ("Which of these 3 is actually possible?") cannot be answered, the conclusion: "God is necessary", or "God exists" or even "An unidentified necessary being exists" is not justified.

    That pretty much summarizes my position. I think I've said all I wanted to say concerning this argument, so, unless someone has a specific question, I will probably not be commenting here again.

    Best wishes to all


    Walter

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  64. No offence, Walter, but you have quite a lot of confusion here. I won't get to it all, but consider something you said: "

    "No, actually that is not true, whatever is necessary and is possible in one world is possible in any other."

    This was said in response to my claim that whatever is possible in one world is possible in all other worlds. I told you that this was a trait of S5. You denied this. But why? Refer to your textbooks on modal logic, walter. It's an axiom of the logic, S5.

    This is what it looks like: ◊G→□◊G

    You can wiki it, too. I'm not wrong.

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  65. Walter Van den AckerDecember 22, 2010 at 4:10 AM

    Mickey said

    "This is what it looks like: ◊G→□◊G"


    Yes, you are right here.

    But it does not really change things. If something is actually possible it is possible in all other worlds. But that does not bring us any further. The burden is still on the person claiming that something is possible to prove that it is actually possible and not merely epistemically possible.

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