Doxazo Theos

38 Responses to “A Successful Ontological Argument?”

1. Anonymous Says:
   July 5th, 2006 at 1:31 am

   This is a great post, well written and well put together. Thank you for taking the time to do this.

   emily

2. Alex Says:
   July 14th, 2006 at 7:15 am

   If you want a thorough, clear and concise summary of reasons why the modal ontological argument has not won widespread assent, you should read Peter van Inwagen’s articles “Ontological Arguments” and “Modal Skepticism.” Van Inwagen, by the way, is a colleague of Plantinga’s at Notre Dame (where I am a grad student in philosophy), and moreover, he is a theist.

   Van Inwagen would reject the burden of proof move that you make in favor of the ontological argument, and I have to agree with him. There isn’t anything on the side of the theistic supposition other than a whole lot of history, which is most likely irrelevant to the argument itself.

   Of course, I think that the ontological argument is sound (since I am a theist, and actuality implies possibility), but the ontological argument will not convince anyone unconvinced of the possibility of a maximally-great being.

3. Chad Says:
   July 14th, 2006 at 11:19 pm

   Thank you, Alex, for you comment!

   If you want a thorough, clear and concise summary of reasons why the modal ontological argument has not won widespread assent, you should read Peter van Inwagen’s articles “Ontological Arguments” and “Modal Skepticism.” Van Inwagen, by the way, is a colleague of Plantinga’s at Notre Dame (where I am a grad student in philosophy), and moreover, he is a theist.

   I am familiar with Van Inwagen, though not as familiar as I am with Plantinga. Most of what I’ve read of his (Inwagen) I’ve been either unsettled on or in sharp disagreement (but perhaps this claim is made in ignorance) with.

   Van Inwagen would reject the burden of proof move that you make in favor of the ontological argument, and I have to agree with him. There isn’t anything on the side of the theistic supposition other than a whole lot of history, which is most likely irrelevant to the argument itself.

   I don’t see how one who wants to criticize the main premise can avert the burden of proof. For it demands showing the idea of a maximally great being internally incoherent, which at least doesn’t appear to be prima facie. Because the property of maximal excellence (or the conjunction of any other of the divine attributes) doesn’t present itself as conspicuous in any obvious way, I think it’s reasonable to say the burden of proof is on the one who thinks so. If what I’m saying is wrong, however, who, if anyone, would bear the burden of proof with respect to the argument’s main premise then?

   Of course, I think that the ontological argument is sound (since I am a theist, and actuality implies possibility), but the ontological argument will not convince anyone unconvinced of the possibility of a maximally-great being.

   It would be silly to say the main premise cannot be rationally denied. So if that’s what you mean, I agree. Skeptics are free to reject this premise without appearing unwarranted for the rejection. But again, this just brings us back to Nielson’s argument and variants thereof, none of which have proven either philosophically successful or academically popular.

4. Keith Says:
   December 16th, 2007 at 3:16 pm

   Maximal greatness is defined in terms of maximal excellence, not the other way around. The possibility of there being any entity in any possible world that exhibits maximal greatness *depends on* the necessity of maximal excellence, and the likelihood of the possibility of maximal greatness’s being exhibited in any possible world must therefore be evaluated by evaluating the likelihood of the necessity of maximal excellence’s being exhibited in every possible world. Since the necessity of maximal excellence seems far from likely on its face, so does the possibility of there being any entity in any possible world that exhibits maximal greatness.

   (I also have reservations about defining a property of an object in an individual possible world in terms of its occurrence in all possible worlds; it seems to me that while individual objects in individual possible worlds would display, or fail to display, maximal excellence, it would only be the *ensemble* of possible objects displaying maximal excellence that would display maximal greatness, not any single possible object. But I haven’t yet digested Plantinga’s “essence” talk; and at any rate, my primary objection is in the previous paragraph.)

5. Chad McIntosh Says:
   December 17th, 2007 at 1:49 pm

   I largely agree with your above paragraph, only the necessity of maximal excellence seems quite likely to me. Rather than dabble into the evidential value of intuition, as some have done at this point, I think the best way to proceed here is by establishing (or, more likely, defending) the coherence of a maximally excellent being. None so far have succeeded in showing such a concept incoherent.

6. Keith Says:
   December 19th, 2007 at 11:25 am

   Even if my intuition agreed with yours (it doesn’t; I don’t see any logical contradiction introduced into a possible world by the nonexistence of a maximally excellent entity in that possible world, any more than you see a logical contradiction in a possible world in which one exists), I’d still find the argument dubious, even if only because it seems circular: It takes as a premiss the possibility of maximal greatness–which is logically equivalent to assuming the necessity of maximal excellence and, in Plantinga’s possible world semantics, the necessity of God’s existence–and derives from that the necessity of maximal greatness–which is again logically equivalent to the necessity of maximal excellence and of God’s existence.

   The move from the possibility of maximal greatness to its necessity is supposed to somehow convince us of the plausibility of belief in God–surely it’s plausible to believe that the existence of a being exemplifying maximal greatness is *possible*, even if it weren’t plausible to believe that such a being’s existence were *necessary*–but it doesn’t, because the two are logically equivalent, even though they don’t at first sight seem so (and therefore don’t *feel* so)–the premiss is logically equivalent to the conclusion.

   The same sort of move can be made with an argument for anything. Pick unicorns. Surely unicorns exist in some possible world. Now define a maximally great unicorn as one which exists in all possible worlds. Take as a premiss the possibility–the mere possibility–that some entity displays maximal greatness. If there is any possible world in which a maximally great unicorn exists, then it must exist in all possible worlds, since to be a maximally great unicorn is to be a unicorn in all possible worlds, and if unicorns exist in all possible worlds, then their existence is necessary, and if their existence is necessary, then their existence is necessary in all possible worlds. So, the existence of a maximally great unicorn is either necessary or impossible. But we’ve already agreed that it’s possible. So it’s necessary. Just like God’s.

   But, of course, there are no unicorns. The argument proves nothing. The argument shouldn’t even convince us that it’s reasonable to believe in unicorns. And similarly with Plantinga’s modal argument for the existence of God.

7. Chad McIntosh Says:
   December 23rd, 2007 at 6:59 pm

   The move from the possibility of maximal greatness to its necessity is supposed to somehow convince us of the plausibility of belief in God–surely it’s plausible to believe that the existence of a being exemplifying maximal greatness is *possible*, even if it weren’t plausible to believe that such a being’s existence were *necessary*–but it doesn’t, because the two are logically equivalent, even though they don’t at first sight seem so (and therefore don’t *feel* so)–the premiss is logically equivalent to the conclusion.

   Plantinga’s argument assumes

   (1) A maximally excellent being exists in every possible world

   is possibly true; that is, not incoherent. A being which has maximal excellence in every possible world have what Plantinga calls maximal greatness. Now the same modal status of (1) is applied to

   (2) Maximal greatness is possibly exemplified

   You are confusing epistemic possibility with metaphysical possibility as I distinguished them in the post. The proper distinction shows the key premises and the conclusions modally distinct, which in turn renders the argument non-circular. To challenge the argument would require showing either (1) or (2) not possibly true, or incoherent.

   The same sort of move can be made with an argument for anything. Pick unicorns. Surely unicorns exist in some possible world. Now define a maximally great unicorn as one which exists in all possible worlds. Take as a premiss the possibility–the mere possibility–that some entity displays maximal greatness. If there is any possible world in which a maximally great unicorn exists, then it must exist in all possible worlds, since to be a maximally great unicorn is to be a unicorn in all possible worlds, and if unicorns exist in all possible worlds, then their existence is necessary, and if their existence is necessary, then their existence is necessary in all possible worlds. So, the existence of a maximally great unicorn is either necessary or impossible. But we’ve already agreed that it’s possible. So it’s necessary. Just like God’s.

   But, of course, there are no unicorns. The argument proves nothing. The argument shouldn’t even convince us that it’s reasonable to believe in unicorns. And similarly with Plantinga’s modal argument for the existence of God.

   Relevant literature on Plantinga’s argument has for the most part rejected these parallel notions of maximally excellent unicorns and necessarily existent lions as adequate objections. The principle reason for this is because it is recognized that the properties that go to make up maximal excellence (omniscience, omnipotence, and moral perfection) have intrinsic maximum values which are not captured by unicorns, lions, or islands. Moreover, it is a dubious supposition that such objective, excellent-making properties can be applied to things like unicorns (much less pink ones) in the first place. The excellence of some unicorn seems to be a subjective matter—I think a blue unicorn would be far more excellent than a pink one.

   The concept of a necessarily existent pink unicorn fares no better. We can conceive of many possible worlds where pink unicorns could not have existed—namely, worlds where the property of pink is never exemplified or, more to the point, worlds without space and time. Just what it means to be a unicorn without space and time is incoherent; unintelligible at best. It is precisely for these reasons that the argument’s detractors moved from maximally great lions and islands to the concept of a quasi-maximally great being, which I’ve mentioned elsewhere.

   Also to note by way of implication—a proposition’s modal status alters its epistemic status. To use our current topic as an example, if the concept of a maximally-great pink unicorn is incoherent, then surely you wouldn’t assign the same epistemic status to that as you would to concepts that are coherent. Generally speaking, incoherent or unintelligible propositions, if believed, are easily shown unjustified. On the other hand, the task of showing coherent or intelligible ones unjustified is much, much harder. It is therefore a bit too simplistic to claim belief in God and belief in pink unicorns or Santa Clause are epistemically equivalent, as you do on your website.

   Thanks for the comment!

8. Keith Brian Johnson Says:
   January 2nd, 2008 at 2:38 am

   I do intend to reply to your post. However, for the moment, having missed whatever method of contacting you might be available here, I want to ask you if it would be OK to link to your blog and to quote some of our dialogue on my nascent blog (at http://www.blog.holycyclops.com )?

   Keith Brian Johnson

9. Chad McIntosh Says:
   January 2nd, 2008 at 4:14 am

   Absolutely! I would be delighted to be linked and to have our dialogue quoted. I’ll return the favor. I do apologize for not making contact easier–I guess I never realized I didn’t have any contact information available. I updated the “About Me” section with my e-mail address, or just click from here: mcintosh_chad@hotmail.com. Thanks Keith!

10. Keith Brian Johnson Says:
    February 24th, 2008 at 12:46 am

    I’m baaaaaaack! Sorry to have taken so long. I actually did start a blog, but I can’t seem to get it to look anything like what I’d like, so it’s in limbo for now. Anyway, about your reply….

    First, I’m not sure where you think I’m confusing metaphysical possibility with epistemic possibility. Explain?

    Second, I think that to focus on the known nonexistence of unicorns as disabling the unicorn counterexample is to miss the point; the point is that the form of the argument seems to enable the demonstration of the existence of something known not to exist (although one might reasonably ask whether or not unicorns really *are* known not to exist). But other discussions, with other people, have focused on intrinsically maximizable qualities, so I’ll give the example I’ve given elsewhere: A pure volume of water of some prescribed volume. Every other feature of the water can be specified, so that it does not vary from world to world; only the water’s purity (or impurity) varies. Clearly, this is maximizable, so one may speak of a maximally excellent volume of water as being completely pure. And one may then define maximal greatness as being the exemplification of maximal purity in all possible worlds. The Plantinga-style proof (in Lane’s formulation; I haven’t mastered Plantinga’s yet) will then prove that there is a pure volume of water (with other characteristics already fixed) in the actual universe. The objection will be raised that there might be universes with different physical laws, in which there is no water; but that’s OK. We’ll just restrict our consideration to the subclass of possible worlds in which physical law is as it is in this one. If need be, we can further restrict the subclass under consideration to the class of worlds in which there is an Earth. (Necessity and possibility would then be universal exemplification in this subclass and at least one instance of exemplification in this subclass, respectively.) What matters is the structure of the proof. (The unicorn case can similarly be restricted, but that wouldn’t handle the intrinsic maximizability issue.)

    Third, I’ve been told that the proof is intended not as a definite proof of existence but rather as a proof of the rationality of belief. But then we have to evaluate the key premiss P(MG)–i.e., N(ME). And since MG is defined in terms of ME’s modal status, ME’s modal status has to be adjudged before MG’s modal status is adjudged. (And note that although you say that incoherent or unintelligible propositions are generally easily shown to be unjustified, when we wind up with N(ME) and N(~MG) in opposition, it’s not so easy to show that either P(~ME) or P(MG) is incoherent or unintelligible.) MG, however, is an artificially-created property that converts contingency into either necessity or possibility; we may do something similar with any other contingent property. If maximal redness (MR) is defined to be the property of the exemplification of redness in every possible world (i.e., as N(R)), and if we make the seemingly harmless assumption P(MR), we have P(MR)=P(N(R))–>N(R). So, if maximal redness is possible, redness is necessary (just as P(MG) yields N(ME)); moreover, if P(~R), then in some possible world, red is not exemplified, then ~N(R), so ~MR, and since MR is either exemplified in all possible worlds or in none of them, we have N(~MR). So, we have that
    P(MR)–>N(R) and P(~R)–>N(~MR), in parallel with P(MG)–>N(ME) and
    P(~ME)–>N(~MG). But surely we’re not going to start saying that various contingent properties are either necessary or impossible? No, I think somewhere there must be a problem with defining the modal status of a property’s exemplification as a *property*, or perhaps with the application of our normal intuitions about possibility and impossibility to such a property. In any event, clearly MR is defined in terms of R, so we must evaluate R’s modal status *first*. Since we accept P(~R), we do not accept MR, so we must accept N(~MR). Similarly, accepting P(~ME) leads us to accept N(~MG). We haven’t ruled out the existence of a maximally excellent being in so doing; we’ve only shown that maximal greatness cannot be exemplified by a merely contingent being. (Now, if one had some reason to think that maximal greatness *was* exemplified….)

    Fourth, I think the concept of Santa Claus is quite coherent, or at least can be made so with only a little effort. It might involve an invisibility shield surrounding the North Pole, and an antigravity device for his sleigh and reindeer, and a Star Trek-style transporter to get into and out of houses, and a bag that reaches into a fourth spatial dimension so as to be effectively bottomless, and a time dilator so that he can get all around the world in one night, and so on; but it’s hardly a logical contradiction.

    Invisible pink unicorns, of course, constitute a joke, and are aimed at those religious believers whose God-beliefs are self-contradictory. I don’t imagine that all believers have self-contradictory beliefs.

    Keith Brian Johnson

11. Keith Brian Johnson Says:
    February 24th, 2008 at 12:48 am

    I am curious–and this, I think, turns out to be an important question–are existence-propositions, like “Tigers exist,” supposed to be part of possible-world descriptions, or are only descriptive propositions, like “Tigers are striped,” supposed to be part of possible-world descriptions?

    Keith Brian Johnson

12. Chad McIntosh Says:
    April 22nd, 2008 at 5:22 pm

    Thanks, Keith, for your challenging reply! I apologize for the delayed response.

    First, I’m not sure where you think I’m confusing metaphysical possibility with epistemic possibility. Explain?

    Actually, you didn’t conflate the two. As I looked back on our discussion, it seems we agree on the modal status of the propositions in question. However, just because “the premiss is logically equivalent to the conclusion” (where I understand ‘logically equivalent’ to mean ‘operative in the same modal domain’), this does not mean the argument is circular or question-begging. We can look further into why if you dispute this claim, but I’m assuming you’ve read Plantinga’s seminal article on the ontological argument, in which he explains why quite well.

    Second, I think that to focus on the known nonexistence of unicorns as disabling the unicorn counterexample is to miss the point; the point is that the form of the argument seems to enable the demonstration of the existence of something known not to exist (although one might reasonably ask whether or not unicorns really *are* known not to exist).

    I did not merely assert the known nonexistence of unicorns; I distinguished the modal status of the existence of unicorns from the sort of being relevant to Plantinga’s argument. For, as I pointed out, unicorns do not possess intrinsically great-making qualities. Moreover, your point that “the form of the argument seems to enable the demonstration of the existence of something known not to exist” fails to acknowledge the modal restrictions under which Plantinga’s argument is crafted. Presumably, if it were true that

    (P) ◊□∃x[Fx] → □∃x[Fx]]

    then according to one’s standard ontology,

    (O) Any world in which a singular proposition is true, is one in which there is such a thing as its subject, or in which its subject has being if not existence

    which, as you note, would allow for the “demonstration of the existence of something known not to exist,” which is absurd. This is why Plantinga’s argument is constructed not with possible objects, but properties. In fact Plantinga takes (O) to be false, replacing it with a restricted ontological principle:

    (O_R) Any world in which a singular predicative proposition is true, is one in which its subject exists

    in which case (P) would only hold for propositions which predicate properties of their subjects (as opposed to propositions which deny properties of them). Objects known not to exist (or not known to exist) do not have properties predicated of them and so can’t be candidates for (P), and hence, not for (O_R) either. But what does exist and is possibly true are the stories according to which unicorns (and other objects known not to exist) exist, not unicorns (and other objects known not to exist) themselves. Therefore it is false to say that “the form of the argument seems to enable the demonstration of the existence of something known not to exist.”

    You go on to very perceptively observe that one “might reasonably ask whether or not unicorns really *are* known not to exist.” This is precisely why God cannot be as easily dismissed as unicorns as a possibly existing object; because we can reasonably ask whether or not it is known that God does not exist. However, your point is overstated because we cannot as reasonably ask such a question about unicorns (once again distinguishing their epistemic likelihood). Only a quick look at the history of philosophy up to the present will show you that. At any rate, this is a moot point because, as I said, the argument does not concern itself with possible objects (however reasonable their knowability is), but properties. Your next objection focuses on just this.

    But other discussions, with other people, have focused on intrinsically maximizable qualities, so I’ll give the example I’ve given elsewhere: A pure volume of water of some prescribed volume. Every other feature of the water can be specified, so that it does not vary from world to world; only the water’s purity (or impurity) varies. Clearly, this is maximizable, so one may speak of a maximally excellent volume of water as being completely pure. And one may then define maximal greatness as being the exemplification of maximal purity in all possible worlds. The Plantinga-style proof (in Lane’s formulation; I haven’t mastered Plantinga’s yet) will then prove that there is a pure volume of water (with other characteristics already fixed) in the actual universe.

    The problem facing this parody is the intuitive implausibility of there possibly being a necessarily existent example of pure water. Sure, purity is an intrinsically maximizable property, but for your example to be equivalent to the argument at hand it would have to have as its main premise

    (1) Possibly, there is a necessarily existing example of pure water

    which, in contrast to the main premise in Plantinga’s argument, seems clearly false. There aren’t any samples of water that exist necessarily. Do you have an argument for (1)? This is to ask precisely the same thing you did of the maximal greatness: “Now, if one had some reason to think that maximal greatness *was* exemplified”. Thankfully, there are reasons to think maximal greatness is exemplified! Again, just take a brief look at the history of philosophy up to the present on that point. Therefore any intuitive misgivings we may have regarding maximal greatness are significantly wavered, whereas they are not for (1).

    If I’m not mistaken, your third objection rested on that assumption—that there weren’t independent reasons for thinking maximal greatness is possibly exemplified—and of course I do not expect you to think there are, as I do. This is why, as you pointed out, many take this argument to be a rationally acceptable proof of theism as opposed to rationally compelling one. But so long as you’ve been unable to counter the argument’s soundness, Plantinga’s argument may therefore be seen as contributing to the rational acceptability of theism.

13. LauLuna Says:
    May 24th, 2008 at 8:22 am

    This comment is perhaps a bit naive but let me make it anyway.

    As I see it, assessing the argument ultimately amounts to assessing the soundness of the concept of ‘a being that necessarily possesses omnipotence, omniscience and moral perfection’. That is, a being that is necessarily maximally excellent, i.e. a being that is so in all possible worlds.

    If ‘necessarily possessing P’ is intepreted as ‘possessing P by definition’ or even perhaps ‘possessing P by essence’ everything remains in the intensional (with ’s’) realm of concepts and I have nothing to object to.

    But the possible world semantics completely alters this. According to it, ‘necessarily possessing P’ involves ‘possessing P in the actual world (among others)’; hence it involves ‘existence’.

    Kant’s distinction between formal predicates (existence, necessity, possibility, and other categorial predicates) and material predicates (empirical, sensory predicates) is called for here. There are restrictions on the form in which a formal predicate can be a component, a feature contained in a concept’s intension.

    Existence as a feature in a concept’s intension is tricky because it seems to permit inferring ‘real existence’ from merely thought or attributed existence. As when I infer that ‘existent unicorns’ exist.

    The trick consists of taking as a concept what in fact is an assumption:

    When I add ‘existence’ to ‘horse+white+having horn…’, I merely suppose or imagine the unicorn (as I had previously devised it) existent; I merely set a hypothesis. I build no new concept. ‘Existent unicorn’ is an assumption, not a concept.

    Consequently, all I can infer is: ‘if there are existent unicorns, then they exist’.

    Similarly, ‘maximally excellent being that is such in all possible worlds’ is an assumption, not a concept.

    And certainly, if a maximally excellent being exists in all possible worlds, then it exists in the actual world.

14. Keith Brian Johnson Says:
    July 15th, 2008 at 6:01 pm

    “If ‘necessarily possessing P’ is intepreted as ‘possessing P by definition’ or even perhaps ‘possessing P by essence’ everything remains in the intensional (with ’s’) realm of concepts and I have nothing to object to.

    “But the possible world semantics completely alters this. According to it, ‘necessarily possessing P’ involves ‘possessing P in the actual world (among others)’; hence it involves ‘existence’.”

    “When I add ‘existence’ to ‘horse+white+having horn…’, I merely suppose or imagine the unicorn (as I had previously devised it) existent; I merely set a hypothesis. I build no new concept. ‘Existent unicorn’ is an assumption, not a concept.

    “Consequently, all I can infer is: ‘if there are existent unicorns, then they exist’.”

    Well said, LauLuna! I have long used a similar line of argument against St. Anselm’s Ontological Argument, but possible-worlds semantics have left me feeling that something was going wrong but not quite knowing what. It is unclear to me whether a “possible world” is supposed to be a “conceivable world,” in which existence is merely conceived-of existence (like the “existence” of a conceived-of-as-white-and-horned-and-solid-unicorn) or is something more. It seems to me that a “possible world” is a possible *description* of a world; but the question then arises: Is “X exists” part of the description of a world? If “unicorns exist” is part of the description of some possible worlds but not of others, then “unicorns have horns” is part of the description of some possible worlds but not of others. Conceptually, however, “unicorns have horns” is analytic; it is necessarily true of a unicorn that it have horns. Similarly, it seems as though a maximally excellent being could exist in some worlds but not in others. Its being omniscient would be necessarily true; but that wouldn’t give it necessary existence. (My favored way of putting this is to say that apparently existence-implying properties do not imply existence–the fact that one conceives of a unicorn as horned, apparently implying its existence [since nothing nonexistent can be horned], doesn’t actually imply its existence.)

    What the ontological argument seeks to do is to make necessary existence a property, like hornedness, so that it will be necessarily true of any existent necessarily existent being that it is necessarily existent. But it is a curious feature of this “property” that if it is possibly exemplified, then it is necessarily exemplified. (Even if unicorns were horned in every world in which they existed, so that we could say that unicorns were necessarily horned, we would not be guaranteed that unicorns existed in every possible world or that necessary hornedness were exemplified in every possible world, even if we accepted that unicorns existed in some possible world. But a necessarily existent entity, if it exists in any possible world, exists in all of them, or so the argument goes.) I do wonder, though, if necessary existence isn’t a property of the collection of all possible worlds rather than of any single possible world, however; and if it is, it’s hard for me to see how it is exemplified by any single possible world.

    On to Chad’s reply.

15. Keith Brian Johnson Says:
    July 15th, 2008 at 9:49 pm

    Chad:

    I agree that O(R) is an improvement over O. I don’t yet see how your objection runs, because I don’t know what your P means. It looks like “If it is possible that it is necessary that it is (possible or necessary, as one wishes) that there exists an x exemplifying F-ness, then it is necessary that it is (possible or necessary, whichever was chosen in the antecedent) that there exists an x exemplifying F-ness.” More simply, it looks like S5’s conversion of “possibly necessarily” to just “necessarily.” But I can’t tell.

    I will ask why “But what does exist and is possibly true are the stories according to which unicorns (and other objects known not to exist) exist, not unicorns (and other objects known not to exist) themselves” doesn’t apply equally well (if it does apply) to God and to the stories according to which God exists.
    ————
    Maximal excellence (ME) appears to be a logically contingent property. Perhaps “maximal excellence is exemplified” is tautologous; perhaps it is self-contradictory; but as a logical matter, it *appears* that the exemplification of ME is contingent. Hence, P(ME) and P(~ME) both appear to be true. But then maximal greatness (MG) is not exemplified. And because of how MG is defined, ~MG—>N(~MG).

    Why should one accept the premiss that MG is possibly exemplified, when it appears that ME is only contingently exemplified and that, therefore, MG is necessarily *not* exemplified?

    The argument, in fact, appears superfluous: One appears to need independent reason for thinking that ME is tautologous (so as to have reason to change his assumption that N(~MG) into the argument’s premiss P(MG)); but if one lacks such reason, the ontological argument fails, while if one has such reason, he doesn’t need the modal ontological argument in the first place.

    You do say, “Thankfully, there are reasons to think maximal greatness is exemplified! Again, just take a brief look at the history of philosophy up to the present on that point”; is this intended as a statement that there are reasons to think that “maximal excellence is exemplified” is a logical tautology? If what you have in mind is metaphysical necessity rather than logical necessity, how would you characterize a metaphysically necessarily true proposition that was not logically tautologous, and what reasons do you have in mind? My own brief look at the history of philosophy reveals lots and lots of unjustified bald assertions and of bad (although often convoluted) reasoning and of wishful thinking on the part of theists (although not only theists have been guilty of such things).

16. Keith Brian Johnson Says:
    July 15th, 2008 at 10:09 pm

    About the perceived question-begging nature of the argument: Plantinga gives the example

    (P1) Either 5+7=13 or God exists.
    (P2) It is false that 5+7=13.
    (C) Therefore, God exists.

    While this is a valid argument, what seems to be wrong with it is that no one who didn’t already accept (C) would accept (P1). At first sight, this seems not to be the problem with Plantinga’s “Victorious” argument, since one might accept P(MG) without already accepting that ME was exemplified in the actual world. However, when one notes that P(MG) is logically equivalent to N(ME), he can see that no one who understood it would accept it without already accepting that ME was exemplified in the actual world. Perhaps that is why it sometimes seems question-begging.

17. Keith Brian Johnson Says:
    July 18th, 2008 at 1:48 am

    I’ve been thinking about possible worlds and their objects a bit. Remember Plantinga’s principle: O(R) “Any world in which a singular predicative proposition is true, is one in which its subject exists.” But what does the word “exists” mean here?

    “The number nine is composite” is true in every possible world, if it is true in any. But while the number nine is a linguistic object or a conceptual object, I’m hardly willing to grant it any meaningful kind of metaphysical existence; when I say that the number nine is necessarily composite, I am saying something about how we have agreed to use the word “nine,” and something about the concept of nineness, but I’m unwilling to say that there’s a really existing number nine to which is being ascribed compositeness. Similarly, we may so define “God” as to make maximal excellence part of the concept of Godness, so that “God is maximally excellent” says something about how we have agreed to use the word “God” and about the concept of Godness, without our thereby committing ourselves to the existence of a metaphysical God-object.

    We could say that propositions ascribing properties to numbers just aren’t included in possible worlds, because numbers don’t exist, and that compositeness is never exemplified by any object in any possible world. In that case, why should we include propositions ascribing properties to God? P(MG) seems to commit us either to accepting that God is conceived of as maximally excellent, just as the number nine is conceived of as composite, without committing us to God’s actual existence, or to accepting that God is a really existing object (because it is the subject of a true singular predicative proposition in at least one possible world, given the premiss P(MG)) but that the number nine is also a really existing object (because it, too, is the subject of a true singular predicative proposition). I see nothing to distinguish between the cases of God and the number nine as regards metaphysical existence, as opposed to merely linguistic or conceptual existence.

18. Ulrich Says:
    August 2nd, 2008 at 6:24 am

    I believe that all ontological arguments are fundamentally unsound, and I’d like to give the following deduction to prove my point. It is intended to “mirror” the last version of Plantinga’s argument given in the post.

    (1′) It is possible that a maximally great being does not exist.
    (This is the complement of (1), and at this point of the argument, we must accept it as true because otherwise we’d assert the necessary existence of such a being, which however is what we are yet trying to prove.)

    (2′) If it is possible that a maximally great being does not exist, then a maximally great being does not exist in some possible world.
    (3′) If a maximally great being does not exist in some possible world, then it exists in no possible world.
    (Just like (2) and (3), by definition of possibility and necessarity.)

    (4′) If a maximally great being exists in no possible world, then no maximally great being exists.
    (Obviously.)

    So, by using the very same reasoning, we can prove the non-existence of God. It should be obvious that any argument that can both verify and falsify some proposition must be flawed. The flaw is, in this case, that it uses a definition of “maximally great being” that implies said being’s existence. However, defining something into existence is not permitted. Consider this little example:

    Definition: Let P be the biggest prime number that exists.

    Now, since Euclid we know that there are infinitely many primes, each bigger than the previous one. There is no existing number that meets the criteria of P. But, by definition, P does exist - we have a contradiction.

    Definitions are not permitted to make statements about the existence of whatever they define; the existence of any defined object or entity must be established independently. The ontological argument violates this rule, which is why it is invalid.

19. Chad McIntosh Says:
    August 2nd, 2008 at 11:31 pm

    Thanks for the comment, Ulrich.

    I think you’re being a bit hasty in judging all ontological arguments unsound on the basis of your one deduction! Indeed, even if the deduction you outline above succeeded, all that would show is that particular ontological argument unsound. It would say nothing to countless other contemporary versions (Hartshorne; Malcolm; Maydole–and keep your eye out for Maydole, who’s work in this area has not yet impacted the scene in the way I think it soon will, perhaps more so than Plantinga’s. See Maydole’s “The Modal Perfection Argument for the Existence of a Supreme Being” Philo 6 [2003] 299-313), or even classic versions with contemporary defenders (Adams).

    But is your deduction a sound counter? I think not. First, your

    (1′) It is possible that a maximally great being does not exist

    is not the negation (or compliment) of

    (1) It is possible that a maximally great being exists

    Instead, it is an entirely different premise with an entirely different modal structure. Where MG is Maximally Great and the diamond is the possibility operator, the modal structure of (1) is

    (1) ◊∃x[MGx]

    whose counter is simply

    (1*) ~◊∃x[MGx]

    whereas the modal structure of your (1′) is

    (1′) ◊~∃x[MGx]

    which, as you see, is quite different from (1*). (1′) amounts to a conceptual confusion between predicative and impredicative propositions, entailing there are possible but nonexistent objects. But this has real problems. The devil’s in the details, but in short you’re confusing

    (P) ~◊ p (not-possibly p)

    with

    (Q) ◊ ~p (possibly not-p)

    Second, even when you do get the modal structure right (i.e., (1*)), the argument is not a counter to the original argument’s soundness until you show (1*) to be true. Do you have an argument for the truth of (1*), namely, that it is not possible that a maximally great being exists? Otherwise, (1) seems entirely possible and so it goes through.

    Third, the argument is not guilty of defining an object or entity into existence because, as I noted to Keith above, the argument doesn’t concern itself with possible objects but properties (namely, the property of maximal greatness).

20. Ulrich Says:
    August 4th, 2008 at 3:42 am

    Hi Chad,

    even if (1′) is not the logical negation of (1), I still hold that it is a valid premise that cannot be dismissed a priori: because doing so would assume that _its_ negation is the only option. However, said negation is ~◊~∃x[MGx], which is the logical equivalent to ☐∃x[MGx] - a statement which implies the proposition you are trying to prove, so asserting it here amounts to circular reasoning (”God exists because God exists”). Hence, I don’t see why my deduction would not be a valid counter.

    Regarding your third objection: MG implies necessary existence, ie. a MG being cannot possibly not exist - by definition. The whole argument just consists of rewriting the - seemingly harmless - “It is possible that a MG being exists” to “A MG being exists”, using _only_ the above property from the definition of MG. I call that ‘defining into existence’.

21. Keith Brian Johnson Says:
    August 6th, 2008 at 1:02 am

    How does the argument not assume N(ME)? And how does such an assumption in the proof of ME[a] prove anything other than that a necessarily exemplified property is exemplified in the actual world, leaving the question of the reasonableness of assuming its necessity unaddressed?
    ————–
    I don’t know what’s showing up on your screen, but on mine, apparently superfluous boxes are appearing. Do they have some meaning here?

22. Ulrich Says:
    August 6th, 2008 at 2:59 am

    The boxes (aside from the one meaning “necessarily”, of course) probably have to do with your browser’s character encoding and are not supposed to be there.

    On the topic:

    We have a proposition: ∃x[MGx]. We want to prove the truth value of this proposition. Before we have done so, we must not make any assertions about this truth value, hence both ◊∃x[MGx] and ◊~∃x[MGx] must be considered true statements: If we were to consider ◊∃x[MGx] to be false, we’d thereby assert ☐~∃x[MGx] and thus also ~∃x[MGx]. Conversely, if we dismissed ◊~∃x[MGx], we’d assert ☐∃x[MGx] and thus also ∃x[MGx]. Doing either would be anticipating the proof, and result in circular reasoning.

    Now, Plantinga’s argument starts with ◊∃x[MGx] and deduces ∃x[MGx]. My argument starts with ◊~∃x[MGx] and deduces ~∃x[MGx]. These two results obviously contradict each other, which means something must be wrong with them. Now, since both arguments use the exact same logic, one cannot be wrong while the other is right. Either both deductions are wrong (then Plantinga’s argument is already refuted), or both are right, in which case something else must be wrong. As I see it, the only remaining possibility is an invalid definition of MG, and indeed I think it is fairly obvious that any definition implying the necessary existence of whatever it defines will always end up in a contradiction like this (unless we can somehow _independently_ demonstrate the necessary (non-)existence of that whatever).

23. Chad McIntosh Says:
    August 6th, 2008 at 12:04 pm

    It’s astonishing to me how much confusion surrounds this argument!

    even if (1′) is not the logical negation of (1), I still hold that it is a valid premise that cannot be dismissed a priori: because doing so would assume that _its_ negation is the only option. However, said ∃x[MGx] -∃x[MGx], which is the logical equivalent to ☐negation is ~◊~ a statement which implies the proposition you are trying to prove, so asserting it here amounts to circular reasoning (”God exists because God exists”). Hence, I don’t see why my deduction would not be a valid counter.

    What you have a problem with, then, is not the argument, but quantified modal logic. What is most telling is your first sentence, “even if (1′) is not the logical negation of (1), I still hold that it is a valid premise that cannot be dismissed a priori: because doing so would assume that _its_ negation is the only option.” Because the concept of a maximally great being does not seem incoherent in the least, then we can say that possibly, a maximally great being exists. Indeed, most philosophers agree that if God’s existence is even possible, then he must exist. Another way of putting this is to say that if God is not logically impossible, then God exists necessarily. To counter the argument you must show that that it’s impossible that God exists (i.e., (1*)), not that it’s possible that God does not exist (i.e., (1′)). Again, this point deserves stressing. The negation of (1) does not enjoy the same modal status because the concept of a maximally great being does not seem incoherent in the least, whereas its proper negation, (1*), requires it to be. If you want to maintain that (1) and (1*) are modally equivalent, then you need to provide an argument for (1*), showing that the concept of maximal greatness is incoherent, like the concept of a married bachelor or a round square. I would suggest giving up on (1’), because it’s not, to my knowledge, the negation of a key premise in any modal ontological argument.

    Regarding your third objection: MG implies necessary existence, ie. a MG being cannot possibly not exist - by definition. The whole argument just consists of rewriting the - seemingly harmless - “It is possible that a MG being exists” to “A MG being exists”, using _only_ the above property from the definition of MG. I call that ‘defining into existence’.

    Again, this response doesn’t appreciate quantified modal logic. On the basis of well-formed formulas such as

    □∃x[Fx] ~ ◊∀x[Fx v Gx]

    ∃x[□Fx]

    ◊□∃x[Fx] → □∃x[Fx]]

    you add certain axiom schemes such as the following

    (T*) □ A → A
    (B*) A → □ ◊ A
    (S4*) □ A → □ □ A
    (S5*) ◊ A → □ ◊ A

    which, in turn, serves to guide possible-worlds semantics. On this John Divers observes that “taken at face valve, a typical possible-worlds semantic theory appears to generate at least the following substantial modal metaphysical commitments: There is a modal reality, and it consists in the existence of possible worlds and the possible individuals that exist in them.” (“The Modal Metaphysics of Alvin Plantinga” in ed. Deane-Peter Baker, Alvin Plantinga [Cambridge, 2007], 73). Of course you can dispute whether this standard modal practice is legitimate. I encourage you to crack open any standard text on modal logic. If not, then we can take it to shed light on things’ existence based on their respective concepts (or definitions).

    In any case, I’ve always thought the “you can’t define something into existence” retort to the ontological argument was rather like the “what caused God” and “who designed the designer” retorts to design and cosmological arguments. What they all have in common is an apparent knee-jerk reaction that betrays sophistication.

    How does the argument not assume N(ME)? And how does such an assumption in the proof of ME[a] prove anything other than that a necessarily exemplified property is exemplified in the actual world, leaving the question of the reasonableness of assuming its necessity unaddressed?

    In short, The argument doesn’t assume N(MG) because N(MG) is a consequence of P(MG). Because N(ME) is not assumed, your second question is moot.

24. Keith Brian Johnson Says:
    August 6th, 2008 at 2:45 pm

    Chad: My next post used to be part of this one, but I decided it was too important to be left as merely part of a post.

    (1) P(MG)=(by def.) P(N(ME))=(by logical equivalence) N(ME) Therefore, N(ME) *is* being assumed.

    (2) It’s unclear to me how P(~MG) involves possible but nonexistent objects, in Plantinga’s sense, or involves a confusion between predicative and impredicative singular statements. P(~MG) simply states that there is a possible world in which the property of maximal greatness isn’t exemplified.

    (3) If the concept of a maximally great being doesn’t seem to you to be incoherent, does the non-exemplification of maximal greatness strike you as incoherent? It’s not at all obvious to me why there shouldn’t be some possible world in which maximal greatness isn’t exemplified–it doesn’t seem self-contradictory to me. Moreover, as Plantinga points out, maximal greatness is a universal property–either it is exemplified in all possible worlds, or in none. Hence, either N(MG) or N(~MG), and P(MG)=N(MG) and P(~MG)=N(~MG). One can’t finesse the necessity involved by writing simply P(MG) and pretending to have gotten around that necessity.

    However, as to its incoherence…. If maximal greatness were to be exemplified in every possible world, that would mean that every possible description of reality included maximal greatness. But it’s *easy* to conceive of a description of reality that does *not* include maximal greatness. Hence, maximal greatness is *not* necessary; and, since it is a universal property, it is not exemplified at all.

    It is *not* similarly easy to conceive of a description of reality that does include maximal greatness. That’s because such a description of reality would include the exemplification of maximal excellence in every possible world, but we know that it’s easy to conceive of a possible world in which maximal excellence isn’t exemplified.

    (4) I don’t see why possible-worlds semantics commits one to the existence of objects in possible but nonactual worlds, any more than talking about unicorns commits one to the existence of unicorns or talking about numbers commits one to the existence of numbers. The conceivable is not the actual.

    I reiterate that it’s my next post that I view as the truly important one.

25. Keith Brian Johnson Says:
    August 6th, 2008 at 2:50 pm

    This, I think, is the important point:

    If one begins with some premiss p; then conjoins premiss q, and from the two derives conclusion c (so that (p^q)–>c, where p alone would not suffice to derive c); and if the premiss r conjoined with p would lead to the conclusion not-c (so that (p^r)–>~c, where p alone would not suffice); then, in beginning with premiss p and then explicitly conjoining premiss q, one is implicitly conjoining ~r. I.e., conjoining premiss q to premiss p involves implicitly conjoining the negations of any premisses which, conjoined with p, would lead to ~c.

    More simply put, if p^q leads to c and if p^r leads to ~c, then p^q assumes ~r and p^r assumes ~q.

    Now, if we put Plantinga’s definitions and other assumptions into one premiss p, and then assume P(MG), so that (p^P(MG))–>God exists; and if we then note that (p^P(~MG))–>God does not exist; we see that assuming both p and P(MG) implicitly assumes ~P(~MG)–i.e., N(MG). (Similarly, assuming both p and P(~MG), as in Ulrich’s version, implicitly assumes ~P(MG)–i.e., N(~MG).)

26. George Renner Says:
    August 6th, 2008 at 11:03 pm

    I find it telling that nobody has taken up the challenge of making a case for (1*). Instead, all I see is split hairs and straw men.

27. Dmitry Chernikov Says:
    August 6th, 2008 at 11:59 pm

    Chad, my opinion of the Plantinga’s argument has not changed since I posted On the Modal Ontological Argument. I think

    (a) that it indeed begs the question that maximal greatness is possibly exemplified — I find it easy to deny this key premise: again, if maximal greatness is impossible, then it is impossible that any being has maximal excellence in every possible world: ~PN(a maximally excellent being exists) = N~N(God exists) = NP(God does not exist) = P(God does not exist) = “there is a possible world in which God does not exist” = (since God’s existence is possible) “God is contingent” -> “we don’t know that God exists in the actual world”;

    (b) that it tries to demonstrate that God exists in the actual world by trying to show that God exists necessarily — an enormous overkill;

    (c) that it should not even be called an ontological argument, because it bears no similarity to Anselm’s original formulation of it.

    You write that the argument claims that “a maximally excellent being is conceptually coherent and possibly exemplified.” Well, of course it is. It is a maximally great being which we have no reason to claim is possibly exemplified. Just go through the modal logic transformations, and you will see that ~P(maximally great being) entails no contradiction but is fully equivalent to the proposition “God is contingent.” And Plantinga’s argument simply asserts that P(maximally great being); it does not prove it. Now perhaps in any world Anselm’s original argument will show that the meaning of the term “God” entails that God exists. In the post where you invited me to this discussion I explain Aquinas’s objection to it, but for now I leave it to the reader to decide whether this objection succeeds. Even if it does, perhaps there is a way to rehabilitate the ontological argument. But Plantinga certainly has not done so.

28. Dmitry Chernikov Says:
    August 7th, 2008 at 12:35 am

    In other words, you don’t gain anything from expressing the proposition “God exists necessarily” (from which you deduce that God exists actually) in the sneaky and tricky yet logically equivalent way “P(a maximally great being exists).” It is true that a “possibly X” is a very weak statement — all you have to do is find one measly little world in which X — and that’s where our proposition derives its apparent plausibility. But why believe that it is possible? If you answer, “because it is conceptually coherent,” then I will reply “that is not clear at all until you transform this statement into something less convoluted.” And that’s, again, “God exists necessarily,” hardly a self-evident proposition.

29. Ulrich Says:
    August 7th, 2008 at 2:41 am

    Chad,

    I don’t think I have a problem with quantified modal logic. I do have a problem with the claim that possible existence should be a sufficient condition for necessary existence. After all, it’s the other way around in general - P(A) is a necessary condition for N(A) (for some statement A), yet by no means sufficient. The exemption made here for “maximal greatness” looks like a big case of special pleading to me, and I’m curious about how many philosophers (aside from the likes of Plantinga) really support it.

    Obviously, my objection does not apply if you accept P(MG) -> N(MG), but then I see no reason for accepting it.

    George,

    in fact, I find ~P(MG) quite attractive because I somehow don’t believe _any_ being might exist in every possible world. But I don’t see a way to prove this.

30. Ulrich Says:
    August 7th, 2008 at 8:16 am

    Sorry for double-posting, but I’d just like to point out one thing: the original argument seems not to rely on the characteristics of “God” (i.e. the notion of “maximal excellence”) at all, only on his alleged necessity. Consider this abstract version:

    (1) An object is said to be A if it has the property [insert some property here].
    (2) An object is said to be maximally A if it is A in every possible world.
    (3) Maximal A-ness is possibly exemplified, ie. a maximally A object exists in some possible world.
    (4) If a maximally A object exists in some possible world, it exists in every possible world.
    (5) Hence, maximal A-ness is necessarily exemplified.
    (6) Hence, A-ness is necessarily exemplified.

    A could be “blue”, “cold”, anything whatsoever (as long as we can give a coherent definition of it).

    Blueness is possibly exemplified - no doubt about it. Is it necessarily exemplified? I don’t think so - just imagine a possible world with no light at all. Where’s the error? Probably at (3) - maximal blueness is not possibly exemplified. This seems to be a very important point to me: even if A-ness is possibly exemplified, it does not follow that _maximal_ A-ness is. In fact, “maximal A-ness is possibly exemplified” is equivalent to “A-ness is necessarily exemplified” - a highly categorical claim that should require a much more involved proof than a mere possibility or actuality claim.

    Back to the ontological argument: Following the above template, P(MG) is equivalent to the claim that “Maximal excellence is necessarily exemplified”. A _very_ bold assertion, I’d say. So bold in fact that I’m willing to dismiss it on the spot unless given some really solid evidence for it. So far, I haven’t seen any.

    George,

    aside from the above, how about proposing that “Maximal _excellence_ is not actually exemplified”? I believe there are some pretty good arguments out there for this kind of proposition, and if it is true, then so is ~P(MG).

31. Keith Brian Johnson Says:
    August 8th, 2008 at 1:28 am

    Ulrich: Here is the reasoning that P(MG)–>N(MG): P(MG) means that in some possible world, say W[MG], MG is exemplified. So, in W[MG], N(ME) is exemplified (since MG=N(ME) by definition). The exemplification of N(ME) in W[MG] means that in W[MG], it is true that ME is exemplified in every possible world. But if it is true in W[MG] that ME is exemplified in every possible world, then it is true in every possible world that ME is exemplified in every possible world. Hence, “ME is exemplified in every possible world” is true in every possible world–i.e., “N(ME)” is true in every possible world–so N(ME) is exemplified in every possible world. Hence, N(N(ME)), or N(MG). I note Plantinga’s observation that MG is what he calls a “universal” property: Either it is exemplified in every possible world or in none of them.

    Chad: Plantinga misdefines the property of maximal greatness. His (and other theologians’) idea is that not only does God, if he exists, exemplify maximal excellence (omniscience, omnipotence, moral perfection), but he necessarily exemplifies ME, in that God cannot exist in any possible world while not exemplifying ME. The problem is that this does not mean that God exemplifies ME in every possible world; it only means that God exemplifies ME in every possible world *in which God exists* (i.e., in every possible world in which ME is exemplified). In whatever worlds ME is exemplified in, God exists and is the entity exemplifying ME. However, there might be worlds in which God does not exist–in which ME is not exemplified at all. Naturally, in all possible worlds, God must still be *conceptualized* as exemplifying ME: That ME is (part of?) the definition of God means that God is conceptualized as exemplifying ME whenever God is conceptualized; the *concept* of God necessarily includes the *concept* of ME (this is also what a legitimate Anselmian proof would say). However, that MG=N(ME) is exemplified by God assumes that God exists in every possible world (because it assumes that ME is exemplified in every possible world, with God being the exemplar of ME), and this is too much to claim.

    Plantinga is welcome to define MG as N(ME) if he wishes to, but since N(ME) entails the actual existence (rather than conceptual) existence of God in every possible world, and since it is easy to imagine worlds in which God does not exist (i.e., in which ME is not exemplified), “ME is exemplified in every possible world” seems manifestly false, so that it is false that MG is exemplified in any possible world.

    You seem to want a demonstration of the incoherence of MG in order to establish that P(MG) is false. You seem to think that MG would have to be a self-contradiction in order for it not to be metaphysically possible–in order for it not to be exemplified in some possible world. But MG is not a within-world property; it is an across-world or transworld property–it is a property of the entire ensemble of possible worlds–and such a property needn’t be incoherent in order not to be exemplified in any possible world. Consider the property of necessary redness (N(R)). There is nothing incoherent about the concept of necessary redness–there would be no logical contradiction in redness’s being exemplified in every possible world. It’s just *false* that it is. Surely, there are possible worlds in which redness is not exemplified, and that is enough to doom N(R). (Or, you might say that since there are possible worlds in which redness is not exemplified, P(~R) is true, so ~N(R) is true, and since N(R) would contradict ~N(R), N(R) is not true. The contradiction is not in the concept of necessary redness; rather, the contradiction is with a state of affairs in some possible world. Similarly, it sure seems as though there are possible worlds in which ~ME is exemplified, as ME hardly seems tautological and ~ME hardly seems self-contradictory; so we have P(~ME); so we have ~N(ME); so N(ME) is not true. N(ME) would contradict the state of affairs in possible world(s) in which ME was not exemplified.)

    All of that, along with the fact that using Plantinga’s definitions and other premisses (collectively “p”) and then accepting the premiss P(MG) requires implicitly accepting the premiss ~P(~MG)=N(MG) (since p^P(~MG) would result in the conclusion that God did not exist–the contradictory conclusion to the one gotten from p^P(MG)), should be good reason not to accept Plantinga’s argument as actually victorious.

32. Dmitry Chernikov Says:
    August 8th, 2008 at 9:22 pm

    To conclude my response, it is conceivable that God exists necessarily and that P(a maximally great being exists); and it is conceivable that God exists contingently and that ~P(a maximally great being exists); but Plantinga’s argument gives us no means to adjudicating which pair of propositions is true. In other words, conceptual coherence buys you conceivability not possibility.

33. Ulrich Says:
    August 10th, 2008 at 3:27 am

    Keith: Perfect. I think that is the ultimate refutation of the ontological argument, and I’m quite curious how its supporters are going to respond.

    I was on the wrong track at first - I actually had realized the definition of MG implied P(MG) -> N(MG), but I was too dead set to show that something was wrong with this definition instead of just challenging the crucial premise. Only in my previous post I finally got the idea right.

34. LauLuna Says:
    November 15th, 2008 at 1:56 pm

    After my post on 24th May I’ve been reading more on modal ontological arguments because I was surprised by the contention of many proponents that although Anselm’s original argument was unsound, the modern modal argument is not so, or at least is not so for the same reasons as Anselm’s is.

    For example, Malcolm and Hartshorne claim that even if ‘existence’ is no predicate that could contribute to a being’s essence, ‘necessary existence’ is indeed such because even if existence adds no perfection, necessary existence does intuitively contribute to a being’s perfection, so that it should be part of a perfect being’s essence.

    Refuting this requires more Kantian resources. Kant interpreted modality as a relation between the cognizant subject and the known object (the known proposition): being necessary for a proposition is just being categorized as necessary by the subject’s reason. If Kant is right, then modalities can’t contribute in any way to the ontological content of a being.

    But using more specific Kantian resources subtracts force from the counterargument.

    Furthermore it seems that Gödel’s version of the argument can escape Frege’s criticism. You know that Frege rejected the (non modal) ontological argument on the grounds that existence (and necessary existence) is not a property of individuals but of predicates, i.e. a higher order property.

    Inspecting the logical form of Gödel’s ontological proof one can see that it does not even need to assume that necessary existence is a first order predicate (that is, a predicate of individuals): Gödel could have treated necessary existence as a second order predicate, i.e. as a predicate of properties or predicates (just the way Frege had required) and as a predicate of individuals only in a round-about way.

    I try to explain this.

    An essence of an individual x is for Gödel a property possessed by x and that entails (i.e. necessarily implies) all of the properties possessed by x. An individual x has necessary existence iff its esence is necessarily instantiated, says Gödel.

    Now, it seems we can develop Gödel’s argument by attributing necessary existence only to essences, that is, by substituting ‘necessary instantiatedness’ for ‘necesary existence’.

    Define Godlikeness as an essence entailing such and such perfections and possessing necessary instantiatedness.

    If Godlikeness is instantiated, then it is necessarily instantiated, because it possesses necessary instantiatedness: necessary instantiatedness is actualized as soon as Godlikeness is.

    In the modal system S5 this entails that if Godlikeness is not instantiated, then it is not possibly so. So, assume that Godlikeness is possibly instantiated and it follows (in S5) that it is instantiated, hence necessarily so.

    Perhaps Godlikeness, so defined, is not possibly instantiated but this is another question.

    To confront the Gaunilo’s kind of counterargument (i.e. define the unicorn’s essence so that it possesses necessarily instantiatedness and infer that the unicorn necessarily exists) it could be argued that it is simply not the fact that the unicorn’s essence so defined is possibly instantiated, since the necessary instantiatedness attributed to it may be incompatible with some properties entailed by it such as temporality, spatiality, etc. It could be argued that being temporally, spatially etc. instantiated is incompatible with being necessarily instantiated, and finally that necessary instantiatedness is only possible for Godlikeness.

    We usually admit that a property of individuals be included in the definition of an individual but, must we admit that a property of properties be included in the definition of an essence such as Godlikeness? Or must an essence be defined just by its content (by the properties it entails) so that existence or necessary existence is something that may or may not supervene on it but can by no means be used to shape its definition?

    The modal version of the ontological argument, it must be granted, is not so easy to defeat. Still I’m inclined to side with Kant or with what I assume Kant would have countered.

    But suppose we have found a way to make plausible that

    1. if God exists, then God necessarily exists,
    2. God possibly exists,
    3. S5 is sound.

    Then we have made plausible that God necessarily exists. Can we achieve 1. without including necessary existence in God’s concept?

    Perhaps we can. Think of God as the ultimate rational fundament of all the existing. Surely if such a fundament exists, it exists necessarily.

    I think that would have pleased Leibniz, yes, especially him.

35. LauLuna Says:
    November 15th, 2008 at 2:06 pm

    I’d very grateful if responses to my post would also be sent to laureanoluna at yahoo.es

    Thanks

36. Chad McIntosh Says:
    November 16th, 2008 at 8:28 pm

    Thanks, Lauluna, for the comment!

    Unfortunately, I’ve so little time lately that I don’t think I’d be able to put together a researched response, at least any time soon. Perhaps Keith will have something to say? Thanks for the comment, nonetheless. If I find more time to devote to this argument, I’ll pick back up here with your comment.

37. Clailkreask Says:
    April 6th, 2010 at 1:14 am

    Greets everyone!

    I just wanted to say hi to everyone

    Cheers!

    [URL=http://thegroceries.blogspot.com/ - [IMG - http://openvpn.net/archive/openvpn-users/2005-05/pngd55nFojmJX.png/IMG - [/URL -

38. thurman7bc Says:
    August 7th, 2010 at 8:58 am

    Stop hack the program!!!

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