Wednesday, September 7, 2011

An Argument from Existence

The following argument seems to me to be valid and sound.

1. If nothing exists necessarily, then there is a possible world in which nothing exists.

2. We cannot conceive of a possible world in which nothing exists.

3. Therefore, there is no possible world in which nothing exists.

4. Therefore, something exists necessarily.

(1) is not a reification, as though I am saying that something exists necessarily, and we call it “nothing.” Rather, the antecedent means that the category of things that exist necessarily is empty. If that is the case, then there is a possible world with nothing. Not simply a dead universe, but nothing: void of rocks, light, edges, anything.

(2) is very plausibly true as well. For although I can imagine a possible world of nothingness I cannot really conceive of it. Every time I try to think of a universe of nothingness, my mind instantly fills in some detail. A small beam of light, an edge to the nothingness (where something is), etc. Of course, from these two premises it follows analytically there is no possible world containing nothing. Then, by modus tollens, something does in fact exist necessarily.

Suppose one wishes to deny (2). In that case, he thinks it is entirely possible there is a world full of nothingness, and hence the antecedent of (1) is true. But here’s the interesting part: if there are no necessarily existing things, then to say that “X exists necessarily” is necessarily false. That is to say, there just is no possible world in which a necessary being exists if (1) is true! Hence, although one may deny (2) and feel very comfortable, he is also committed to the further proposition:

5. It is impossible for something to exist necessarily.

(5) is a much bolder claim than anything above, and it is a logical entailment of a denial of (2). I find it is much more plausible to think that there is no possible world of empty nothingness than to think there is such a world, and that it is impossible for that world to be occupied by a necessary being.

So what?, one may ask. This gets us a necessary being, but it may not be God. Fair enough. But it’s not very plausible to be the universe either. First, why could the universe not have been any different than it was? Couldn’t some of the quarks have been different? If the universe is necessary, the answer is “no.” It is easy to conceive of a universe that is identical save for one small fact (like a particular tiny rock on a particular asteroid being red instead of brown), but the universe’s necessity means not only would that not have happened, but that it was impossible! Second, a necessarily existing thing seems more plausibly to be the ground of all reality. It makes more sense to posit a maximally-great being than it does to posit a necessarily-existing universe. This argument does not get us all the way to the Christian God, or even necessarily to God. But I think it opens the door to consider that the first premise of the modal ontological argument (“it is possible that a maximally-great being exists”) is possible after all. If it is possible, then by modal logic, the conclusion “therefore, a maximally-great being exists” follows!
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  1. The problem I would have with this argument is in the first premise. By definition a "world" is a "existing thing". If there is a world at all, even a boundless vacuum, then something does exist. But that doesn't mean that something necessarily exists, because we can conceive of there being no world at all.

    What do you think?

  2. Hi James, thanks for the comment! I would say that I am going with the definition of a world in the same sense as a "possible world", which is to say just a complete description of the way reality could be. If there are no necessarily existing things, then all that exists are contingent objects. For any contingent object, there is at least one possible world--or state of affairs, in which it does not exist. It seems then there would be a state of affairs in which there were no objects. So a possible world being just a description is no different than saying "there is no world at all," where "world" is understood to mean an "existing thing." That's where I differ: I think that while we can imagine such a state of affairs that nothing exists whatsoever, we can't really conceive of reality holding a description of nothing. By definition, there's nothing to conceive of! That, coupled with the interesting corollary that we must believe that it is actually impossible for a thing to exist necessarily (and its further entailment that any posited necessary being or thing is impossible to exist), is strong enough for me to accept (2) rather than deny it. :)

  3. I think (2) is questionable, but I would focus on (1). As an aside, I think it would be more helpful to change the first "nothing" to something else; it can cause confusion (nothing exists necessarily when you mean something more like no thing).

    So, I'm just not sure that the conditional in (1) is true. To show my sense here, I'll reframe it a bit.

    Let's try considering (2) first, so we start with an assumption that there cannot be an empty world. Then we move on to the question of whether there is a necessary being (or a necessary thing). Well our first assumption doesn't actually support a necessary thing; rather, it supports something in every case. But that could be a completely different thing. So, it might be the case that some thing has to exist for any world to be possible without it being the same thing across all worlds.

    What you would have to defend is:

    Either there is some possible world in which nothing exists or some particular thing exists necessarily.

    It's not "something," but "some particular thing.' I think you'll have a hard time justifying that.

  4. Hi Mike. :) I considered that. That is, I thought maybe it is simply the case that "necessarily, every possible world contains some object" rather than "some object exists necessarily." But I rejected the former ultimately.

    The reason is partially found in my above comment to James. For every contingent thing X, X is possibly non-existent. In terms of strict logic, there is a possible world in which no X exists. If no X exists and no necessary thing N exists, then there is a possible world devoid of any X or N, and hence is actually empty.

    If that is the case, and (2) holds, then it is true that in every possible world there exists something, of necessity. However, I think it is more than that. Here's why: again in light of the relevant conditions, this means it is impossible that there be a completely contingent world (that is, a world of completely contingent objects' non-existence [which is what it means to be contingent]). But then in that case, what is the alternative? Brute facts? I don't see why it must be the case for any contingent thing to exist in light of the non-existence of any other contingent thing. Moreover, it follows that for whatever that thing is, it could not have failed to exist. For it is necessary that it exists and not some other thing.

    I suppose it all boils down to whether or not we accept that contingently existing things can compossibly be non-existent, and what its explanation is as to its existence if one thing is required. One final thing: consider the thought experiment in terms of just the set of all contingent objects, so that nothing is described in terms of necessity. Suppose further there are three different objects in the whole set: A, B, C.

    Here are the worlds possible:
    1. A, B, and C exist.
    2. A and B exist, C does not exist.
    3. A and C exist, B does not exist.
    4. B and C exist, A does not exist.
    5. A exists, B and C do not exist.
    6. B exists, A and C do not exist.
    7. C exists, A and B do not exist.
    8. A, B, and C do not exist.

    Why is (8) impossible? What makes it the case that the objects A, B, C must exist in some combination or separation vs. not at all? One may answer this is because it is not possible to have an empty world. Yet that just assumes the conclusion is false (that it would be an empty world without any contingent objects). Contrariwise, I do not assert (1) is true because of the conclusion. Rather, I think (1) is true because I think that there's nothing inherently absurd about that state of affairs. Also, if nothing exists nececessarily, it still follows that it is logically impossible for any object to exist necessarily. A high metaphysical price to pay, I think.

  5. Hi, Randy.

    I'll start with the end. I think that we could say something exists necessarily without saying some being exists necessarily. Then, it wouldn't strike me as a high metaphysical price. If I were going to deny (2) I would probably want to say that some sort of space-time could always exist or logical rules that give us propositional truths or something very basic that does not involve any being (I think I said this in our last discussion).

    For the main point, I haven't been able to sort this out in my mind as clearly as I would like, but I'll try and just write it and see what happens. You say that (8) is logically possible, but then impossible. Maybe this is happening due to a stricter limitation as we move from logical possibility to metaphysical possibility? If that's the case, then it doesn't end in a contradiction. I think my response lies somewhere along those lines, but like I said, it's not completely clear to me yet. Something seems not quite right.

  6. Interesting take Mike (as usual)! Your point about distinguishing between some thing and some being is well-taken, and if I understand you correctly I'll submit to that. That is, just on the argument's premises alone, it could very well be some thing (like space time) or some being (like God or whatnot). That being said, I think there's better reasons to posit a God or a being than a particular object, and this argument may have potential regarding the modal ontological argument's first premise.

    I'm saying that (8) is logically possible, given the nature of contingent beings/things. I don't think it's possible to have a world of only contingent beings/things, but that is because I can't conceive (but I can imagine) a world of nothingness. Given these two premises, it follows that: there is no possible world containing only contingent beings/things. From this, it follows necessarily that: every possible world contains at least one necessary being/thing. Just my thoughts on it. :)

  7. Hi Randy,

    I have a couple of thoughts/questions:
    The first time I read premise (1) I construed it to mean that nothing necessarily exists. That is, necessarily, nothing exists, rather than "no existent thing exists necessarily."
    I think taken the way I initially took it, P1 is obviously false since it seems to entail the logical impossibility of something existing.
    Taken the other way, I think P1 is correct, perhaps by definition. A possible world is just, as you say, a description of the way reality might have been (that is, a logically possible though not necessarily a plausible description of reality). So right, if nothing which exists does so necessarily, this means that it is logically possible for any existent thing not to have existed. Which seems to means there is a logically possible world in which none of these things exists. Hence in such a world nothing would exist.

    My question concerns P2. You seem to be missing a premise somewhere here, and it might go like this: Any description of reality which we cannot conceive of cannot possibly be true. Or If we cannot conceive of X then X cannot be the case. This seems a somewhat necessary step to make between P2 and P3. The problem for me though is that this sounds suspiciously like an argument from ignorance. In what way does our failure or inability to conceive of a state of affairs show that that state of affairs cannot possibly be true? So that would be my main initial question.

  8. Hi Daniel, thanks for your insightful comments! Yes, because of the nature and limits of language, (1) had to be explained in the paragraphs following the argument in order to avoid just this sort of confusion.

    Really, (2) is just the justification for (3), so that it could be reduced to a syllogism relying on modus tollens. I chose to put it in rather than leave it out, but you have highlighted an important point.

    A guide to logical or metaphysical possibility (though I recognize these two concepts are not exactly the same) is self-consistency and not contradicting any necessary truths (metaphysical or logical; in the latter case we would say it makes a situation logically impossible and in the former metaphysically impossible). It's the same type of reasoning inherent in objective moral values and intuition. While it is self-consistent to say there is a possible world where nothing exists (as discussed in the argument, in the comments above, and by yourself), it seems we cannot really conceive of a world where nothing exists at all. This is the same type of reasoning that gives us the strong response that it is really metaphysically impossible, after all, that a world exists in which we have a moral obligation to rape babies.

    This differs from an argument from ignorance in that we are not saying, "I don't know that there is such a world, therefore there isn't." Rather, we are using metaphysical intuitions. The downside of such usage is that if someone does not share the intuition, then he doesn't have a reason to believe it. But the curious thing is that I think most people do in fact have that intuition; they just don't think that it's sufficient to make the claim.

  9. Randy,

    Yes, I think most people share the intuition, but "the intuition" seems to be a failure to conceive of a certain state of affairs. A subset of arguments from ignorance is argument from incredulity, where the belief that a proposition is false is based on an inability to imagine it.

    I'm not satisfied that your argument sufficiently distinguishes itself at a crucial point from an argument from incredulity. I note that in your exposition of the argument, you use seem to use a failure of imagination as some grounds for thinking that "non-being" could be a possible world. You said things like "no matter how hard we try to conceive of nothing, we still imagine a boundary to it, or a beam of light, etc..." You said that your mind automatically fills in some detail, and I find that this is true for me as well. It is not even enough to imagine a great black expanse with no matter, since space and color are existent things!

    My problem is with the move from P2 to P3, and I maintain that a premise seems to be missing. It seems to me that the argument as formulated *has* to assume that nothing of which we fail to conceive can be an actual state of affairs, and I would want to see the justification for this assumption. If we take away this assumption, then we are left with P3 not following from P2, since our inability to imagine an empty world implies nothing about whether such a world could or could not exist.

    In actually though, I embrace the conclusion of the argument. I think that God exists necessarily. I just don't know how you can get to any necessarily existent entity on the basis of the argument you've outlined. You mentioned forming it as a modus tollens syllogism. Perhaps if you did that it would be more clear to me.

  10. Hi Daniel, thanks for your continued thoughts. :)I think this case, specifically does not rely on ignorance, but rather what we actually do. As you state, we conceive (I do not use these terms interchangably as you do, but I don't think it matters at this juncture) of something even when we try to imagine nothing. I think that it is this conception which gives us a bit of a metaphysical guide. What the problem seems to be is whether or not intuitions provide a guide to metaphysical reality, and I think they do.

    We do this all the time with moral intuitions. We don't really think it's possible, after all, that there is a world in which we are commanded and therefore morally obligated to rape babies. How did we get there? For some, they have the option of some kind of divine command theory. But many others who do not even embrace this theory nonetheless agree intuitively that such is wrong! I think they are justified in that intuition.

    I think the premise that an intuition as a guide to metaphysical truth is probably true; moreso than thinking that there are states of affairs that exist that cannot be conceived of. It's a bit like the first premise of the modal ontological argument. Suppose the idea of a maximally great being were to be inconceivable after all; upon its explanation, suppose no one really could conceive of it (though they could still imagine it was true). In that case, if it is not conceivable, in what way is it possible? Note that I am not asking for certainty, probability, or depth of knowledge. It seems, rather, the argument from ignorance would be on the one who affirms the opposite of the premise. That is, if one is saying "there are states of affairs that are inconceivable but are nonetheless true," by definition this is an argument from ignorance (ex. we can't know it is true, therefore it is [since if we knew it was true, we'd have conceived of it]). It's also important that I am not saying "if we have not conceived of X, then X is not metaphysically possible" where X is a state of affairs. Rather, I am saying "if we cannot conceive of X, then X is not metaphysically possible."

    Now of course I recognize that you are not affirming there are such states of affairs that are inconceivable, but rather saying there is no reason to believe that such are not possible. So long as one holds an intuition that has not been shown to be unjustified, I don't think he should have any problem in holding it to be true.

  11. Randy,

    I agree with much that you say, especially concerning the value of intuitions. And I even intuit that nothingness could never be an actual state of affairs. My concern is that intuition alone does not seem sufficient to show this to someone who does not share the intuition already. As such, the argument may serve to strengthen the degree to which one holds nothingness to be an impossible state of affairs (provided they already intuit that it is an impossible state of affairs), but it seems to have difficulty with people who do not (or say they do not) share that intuition. This is not a fault of the argument, per se. The moral argument has some of the same difficulty.

    The second concern is, as I said, that it does seem to be very similar to an argument from incredulity. Perhaps you would simply deny that an argument from incredulity is fallacious? But here, wouldn't you have to grant the atheist some points, because they (and many Christians) seem to powerfully intuit that evil is a problem for God's existence?

  12. Randy,

    (I hope you do not mind my sporadic comments throughout various posts- you have so much interesting stuff on which to comment.)

    Conceivability is a much too poor guide to possibility. That aside, we *can* conceive of worlds where, say, only three blue colored swans exist in a single pond. Likewise we *can* conceive of complete emptiness- nothing. But in the latter case your intuition is, of course, that one thing exists, namely, you, the conceiver. However, if this is true, then you must conclude that you, the conceiver, exists in the world with only three blue colored swans in a pond, and in the world with only three blue colored swans in a pond with a cardinal flying overhead... and so forth ad infinitum. By implication, then, it follows that in all possible worlds, you, the conceiver, exist, in which case you would be a necessary being. So, it seems that we can conceive of plenty of worlds in which we do not exist, and also a world in which no thing exists.

    More simply, let us define- as is commonly done- a world as a set of all statements (or propositions, if you believe in such things) which can be stipulated truly at that world. So, a world which nothing exists would be maximally described by the statement: 'No thing obtains.'

    (I would argue that not even god exists in the world maximally described by the statement 'No thing obtains.')

  13. Hi Aaron, I do not mind. I have been thinking about this a lot. I would go a little further within the definition of a possible world by maintaining it is a maximal state of affairs. I think conceivability (as opposed to imaginability) is a good guide to logical possibility, provided there are no necessary truths which it would contradict. With that in mind, I would reject that I can conceive of nothing; rather I can merely imagine it.

    I agree we can conceive of a world where only three blue swans exist in a pond (though I think this is impossible, but only because I already believe in the necessary truth that God exists). I also do not think my intuition is that something exists, and it's me; but rather merely that something exists!

    If the intuition holds, the proposition "something exists" has de dicto necessity I think. The trouble with this argument may be that it does not seem to establish de re necessity of a being; it may be subject to the criticism in one of the comments above that all that results is the necessary truth of the statement, "in every possible world there is at least one thing X in existence," where X may vary from world to world. It would be up to me to show why X would be the same in each possible world, something I think may be accomplished through other arguments from contingency.

  14. Randy,

    I am curious about your definition of a possible world (df. 'a maximal state of affairs'). If by 'a maximal state of affairs' you mean: 'a state of affairs which is describable by a maximally consistent set of propositions, which is obtained by taking the set of every proposition which can be asserted and affirming or denying each one (if in the process we affirm A and not-A, either directly, or indirectly by affirming B which entails not-A, then the world is impossible),' then we agree. However, if by 'a maximal state of affairs' you intend something else, then I would like to know what that is. On to 'conceivability' versus 'imagination.'

    In what sense relevant to metaphysical possibility do 'conceivability' and 'imagination' differ? I take it that by 'imagination' you mean something like 'a convenient and particular mental representation,' yes? Certainly 'conceivability' is often used in this sense, so, by 'conceivability' you mean something else, no? [Your clarification above of (2) does not help me here.]

    Setting the above aside pro tem- which is really immaterial to what I have to say here- you say 'I agree we can conceive of a world where only three blue swans exist in a pond,' but then assert that you cannot 'conceive' [I choose to scare quote 'conceive' until it is given a more precise definition] of a world in which no thing exists. This strikes me a problematic; consider the following:

    Let us call the world which contains only three blue swans in a pond W1. Thus, W1 is a non-empty set which contains four objects: three blue swans and one pond. We subtract one object (any one you like) and obtain W2, a non-empty set which contains three objects. We subtract again and get W3, and again and again until we have subtracted all the objects and obtain W5, an empty set. Now, (W1 – W5) can each be describable by a maximally consistent set of propositions [W5 is describable via the proposition 'No thing exists;' in nuce, the proposition 'No thing exists' is true at W5].

    So, why, exactly, is W5 an impossible world? [Recall, an impossible world is a world which entails a contradiction.] It seems to me to be clear that the intuition which engendered your initial post cannot be employed to reject the (rough) argument outlined here. To claim otherwise in this context would be to beg the question.

  15. Hi Aaron, yes that is how I would describe a possible world (in fact, this is exactly how I have seen it described in my reading). As to conceivability and imaginability, I qill quote Craig on this issue: "A thousand sided polygon is unimaginable, but it is hardly inconceivable. Conceivability is taken to be co-extensive with metaphysical possibility." Something that can be imagined is not sufficient for metaphysical possibility, and I can indeed imagine an empty space, so to speak. But I can't conceive of there just being nothing! Now one may say he does not share my intuition, or one may say my intuition is wrong; but in the case of the former, that need not trouble me, and in the case of the latter, we'd need some other argument as to why this particular intuiton is incorrect.

    I admit, as I have used "imagine" and "conceive" it seems I conflated the two, as even in the very same comment I went on to assert that I didn't think it possible after all (if I granted that God exists as a necessary being). But as I mentioned, even subtracting that, I don't see W5 (that is, an empty world) as truly conceivable; for in order to accept the subtracting of objects to nothing we'd just have to accept the denial of the conclusion.

    In essence, I think what the W5 argument shows is that its possible that these particular objects do not exist, and I think that's right. But if we mean, then, that there is a world such as W1 where only contingent beings exist, I would probably disagree. But then it is incumbent upon me to show why I think (2) is true. Instead of that, I appeal to intuition--which, strictly speaking, does not show anything to be true, but rather is how I know some proposition to be true. One who does not share my intuition, then, may not see a reason to accept (2). (this mirrors my discussion with Daniel on this topic above)

  16. Randy,

    Re: Intuition

    I am not sure what intuition is if not one's own personal pre-theoretic prejudice, so, suffice it to say that I reject intuition as being evidence for anything, let alone as justifying beliefs.

    Re: Imagination and conceivability

    I figured this is the distinction you were going to make. But I do not think this distinction helps, for just there are many things that are conceivable which are not imaginable, it seems to me clear that everything that is imaginable is also conceivable. That is, the set of everything which is imaginable is a proper subset of the set of all things conceivable, which would make all imaginable things possible. Thus, if W5 is imaginable (which you accept), then W5 is conceivable, and thus possible.

    Moreover, much that is possible is also not conceivable (e.g., superpositions, virtual particles, wave-particle duality, Hilbert spaces, etc.).

    Oh well! I simply think the question is being begged here. (Of course, in the spirit of full disclosure I should say that I don't believe in abstracta or necessarily existing entities of any sort.)

  17. Hi Aaron, I would disagree with the imaginability being itself conceivable. For I can imagine many things that I don't think I conceive properly of; I can imagine a bachelor who is married, but to conceive of it requires something I cannot do (namely, understand the concepts behind "bachelor" and "married"). Or another example, perhaps much more pertinent: I can imagine that no God exists, but if God is a necessary being, I cannot truly conceive of it (for to conceive of his nonexistence is just to say that there is a possible world in which he does not exist, which is just to say that he doesn't exist [at least not necessarily]). This is why I say conceivability/metaphysically necessary truths are such a guide.

  18. Randy,

    I certainly cannot construct a mental representation of a married bachelor. Neither can I construct a mental representation of a ball (monochromatically) red colored all over and (monochromatically) green colored all over. Can anyone construct a mental representation of a logical impossibility? I don't think so. (Attempts have been made: cf. Graham Priest's short story 'Sylvan's Box')

    We may be at an impasse here, so I will leave any last word with you, but I much prefer we efface ourselves of all talk of imagination and conceivability and instead define logical / metaphysical possibility in terms of the describability of maximally consistent sets of propositions / statements.

    P.S. I am curious to read your response to two short essays I authored over at the Florida Student Philosophy Blog. (1) The Moral Trilemma of the Omnibenevolent Abrahamic god and (2) An Argument Against Rational Belief in the Resurrection of Jesus.

  19. P.P.S. Eamon is me ('Eamon' is a pun on my daughter's pronunciation of my name).


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