Friday, January 27, 2012

The Modal Ontological Argument

What’s wrong with the ontological argument? That’s something I’ve been wondering. Now of course, as is the case with every theistic argument we give a generic name, the “ontological” argument is a type of theistic argument. I only intend to focus on Plantinga’s modal ontological argument (MOA). The MOA appears like this:

1. It is possible that a maximally great being exists.

2. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.

3. If a maximally great being exists in some possible world, then it exists in every possible world.

4. If it exists in every possible world, then it exists in the actual world.

5. Therefore, a maximally great being exists.

Many people dismiss this argument, thinking it’s some kind of parlor trick. However, it is an excellent example of modal reasoning. First, let us explain the argument and how the logic works.

A maximally great being is defined to be a being possessing maximal excellence, “where maximal excellence entails such excellent-making properties as omniscience, omnipotence and moral perfection.”[1] By (1), Plantinga means to say such an idea involves no incoherence, and is intuitively possible. That is, it really could be the case such a maximally great being exists. Most people would agree with this. The second premise just explicates the idea of possibility in a format called “possible worlds.” A possible world is a complete description of the way reality could be, down to the last detail, encompassing every proposition’s truth or falsehood in a consistent manner. Hence, if something truly is possible, then it exists in a possible world.

(3) is the premise that confuses the average layperson. Why should it be so that if a maximally great being exists in one possible world, he exists in all? Because such a being holds its greatness and excellence in a maximal way, it would do so in every possible world (else there would be a greater being displaying more excellence—namely, the one who existed in all possible worlds).

The fourth premise is just true analytically. The actual world belongs to the set of all possible worlds. This is because if the actual world were not possible, it would not be actual! But then (5) follows, and the maximally great being does in fact exist.

So it seems the crucial premise is the first one. Epistemically, one may say it is possible God does exist and possible he does not. However, we are interested in metaphysical possibility. It is on these grounds one must object. That objection can come in two forms: A. The concept of a maximally great being is incoherent,[2] or B. We do not (and/or cannot) know whether or not the concept of a maximally great being is metaphysically possible. With respect to (B), it’s not at all clear why we cannot justifiably intuit such a being is metaphysically possible (even if it’s not epistemologically compulsory that we do). With respect to (A), it seems the maximum values of what we would call “great-making” properties are coherent, and hence it follows they are metaphysically possible.[3]

John Feinberg, a Christian theologian, remarks on his interest in the ontological argument but seems to show agreement with its critics. He wrote, “what . . . [the ontological argument] proved is that a contingent being could not be God. Any being worthy of the title ‘God’ must be a necessary being.”[4] The philosophical rub Feinberg seemed not to catch, however, was this: in modal logic, a being or truth that is necessarily true means it is impossible not to exist. A necessary corollary or entailment of some being or truth being necessary is that if it does turn out to be false, it is necessarily so. So the MOA demonstrating the maximally great being’s necessary existence does more than give us a curious fact. Rather, it establishes that God’s existence is either necessary or impossible. Either the maximally great being is possible or impossible. This is why it is such a great argument!

                [1] J.P. Moreland and William Lane Craig, Philosophical Foundations for a Christian Worldview. (Downers Grove, IL: IVP Academic, 2003), 496.

                [2] Here, incoherence means the maximally great being has two or more properties or attributes that conflict with one another so that they cannot both be actual in the same being.

                [3] Again, without being able to explicate every property, it is difficult to force someone to accept the metaphysical possibility of the maximally great being. However, that would not be grounds to deny it. Further, even if we could explicate every property, it is only the lack of incoherence of which we are aware that allows us to hold our intuition.

                [4] John S. Feinberg, No One Like Him: The Doctrine of God. (Wheaton, IL: Crossway, 2001), 190. He was commenting on Anselm’s second formulation of the argument, but the MOA relies on the same conclusion on this point.
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  1. Is (2) correct because in order for something to exist, even a "maximally great being", it necessarily must exist in a world,
    -ie, a part of the definition of existence is that of a world to exist in,
    -ie, it is logically impossible for a maximally great being to exist apart from existing in a world, thus calling into question the definition of "world", meaning the definition of world necessarily includes "a world must exist for existence to be possible"

    But does my second 'ie', then, give us a tautology, or even an ad infinitum (is that right, or do I mean infinite regress)? A world is necessary for existence, but existence is necessary for a world? Or a world already exists, but in order for it to exist, it must have a world to exist in?

    Or am I just all sorts of confused??? Yeah, probably lol :P . . .but i am asking in all sincerity. . . FYI, I'm a VERY amateur philosopher, & I do think this and the Anselmic ont. arg. are valid.

  2. One thing that worries me about the argument is that I think you could replace all instances of "exists" with "does not exist" and you have opposing conclusions. It's not immediately clear which to favor without some further investigation. So, even if we grant the modal principle (and I know some have questioned it, like Tooley in Mind 1996? - can't remember the name) we still would have to focus our attention on the other arguments to see which is the right way to lean.

    There are also other routes to take in setting up an "anti" ontological argument. For example, I think the evil god could be turned into soemthing like this (though I prefer what I mentioned above). I ran this by Graham Oppy and he said it would require me to show that the evil god was on a doxastic par with the maximally great being. I think I might be able to do that, but again it gets us into all sorts of other arguments.

    So, it seems like the MOA isn't overly helpful, and that's its problem. It only offers guidance once we've come to strong conclusions via other arguments (and by then why do we need it?). Those are my two cents, anyway.

    1. Hello.

      Do you know how I could contact Graham Oppy, if he's not too busy?


  3. Hello, thanks for commenting! Because your comment is so substantive and asks helpful questions, I allowed it to remain, but I just ask in the future to assign a first name (or even nickname) to the comment (see comment policy). :)

    The interesting feature about (2) is that it is true for just anything and everything that is possible. So the answer to your very first question is "yes." :) If something is possible, then it exists in a possible world. You touch on the right question when you then ask for the definition of a possible world. Note this is not like Star Trek or other science fiction whereby there's this actual place out there we call a possible world. Rather, it's just a complete state of affairs. It's saying that this is a way reality could have been. It's complete in its description by touching on every single proposition imaginable; it either claims it as true or false.

    Here is the easiest way to think about possible worlds: ask yourself what would a world look like in which JFK was never shot? You probably would think of the entire history of the world as remaining constant up to the point of JFK's presidency almost unconsciously. Say every last detail was the same except Lee Harvey Oswald got a tiny bit extra nervous, and missed on the shot. That one little detail of difference means we're discussing another possible world. So possible worlds can be almost identical to ours in their truths down to the littlest detail, except instead of typing this response with both hands I do it with one; they can be vastly different, so that the United States never even existed!

    Your questions also ask us to understand "exist." Here we're using a weak form of existence; we're not actually saying that such-and-such is in actuality. It's merely a manner of speaking, or another way of saying something is true. In that case, it does seem the second ie is a bit of a tautology. For if we have a possible world that does not exist in this weak sense, then it's not really a possible world after all. It would be an impossible world.

    I think your intuitions were right about this, and you'll be a better philosopher one year from now than you are today. Trust me, I've been there and I know, and I hope I am a better philosopher one year from now myself!

  4. Found the article. It's from Mind (1981) called Plantinga's Defence of the Ontological Argument. It's worth a read and raises great questions. Given that it was in 1981, I'm sure more has been said since then, but I haven't had much luck finding any new work on the subject referencing Tooley's paper.

  5. Hi Dr. Mike! :)

    You're absolutely right. Since God's existence is here considered necessary, then his existence is either necessarily true or necessarily false. That said, metaphysical necessity isn't like assessing the premises of an argument, where we weigh the evidences for and against and on the basis of that we proceed. Rather, if a premise stated to be metaphysically possible is coherent, then it is metaphysically possible (provided some other, necessary truth does not override it).

    It'd be interesting to see what such an argument would look like, and whether our intuitions really would comport in a similar way (or, what Oppy said :) ). Let me know if you do it or come across one already laid out. Law doesn't quite do it for me on the moral argument with his evil god hypothesis, for a variety of reasons I laid out in my critique of him on this blog.

  6. Hey Randy,

    “What’s wrong with the ontological argument?”

    A lot. Where to begin?

    (a1) Notions of 'maximal greatness' or 'metaphysical perfection', etc., are vacuous. What, exactly, does 'metaphysical perfection' mean? Notions of 'metaphysical perfection' really track one's pretheoretic prejudices than anything essential about anything.

    (a2) It is not at clear 'God' is a coherent concept. Query: “What, exactly, is 'God'?” Answer: “He is that being which is omniscient, omnipotent, and morally perfect.” Rejoinder: “Yes, but what, exactly, knows everything or can do anything? Omniscience, omnipotence, and moral perfection are all secondary attributes; what we need are primary attributes, such as 'composed of this molecular structure' or 'occupies this spatio-temporal location'.”

    Though, even if we relent on (a1) and (a2), we have:

    (a3) Classical theistic attributes of 'God' entail contradictions: E.g., omnipotence entails 'God' can create a being, S, with perfectly free will. Omniscience entails 'God' knows all of S's actions before S even wills to do them. Thus, S does not have free will.

    But here is the rub!:

    (a4) (i) Either the conclusion simply does not follow from (1) – (4) or (ii) the conclusion (5) begs the question relative to the S5 axiom. Consider: There are, in fact, many different notions of necessity and possibility. Among the many notions, we can distinguish two which are relevant to MOA: logical and epistemic.

    Logical necessity and possibility are explicated in terms of truth across possible worlds. That is, some sentence, A, is necessarily true at a world, w, if A is true at * every * world, possible relative to w; and some sentence, A, is possibly true at a world, w, if A is true at * some * world, possible relative to w.

    Epistemic necessity and possibility are a bit different. Some sentence, A, is epistemically necessary if it is known to be true, and A is epistemically possible if it could be true for all we know.

    (i) If the monadic operators employed in MOA are epistemic, (5) does not follow validly from (1) – (4), since (2) is false because, whilst it may be epistemically possible that S is true, it does not follow that S is true in some possible world; S may, in fact, entail a contradiction for all we know, or simply be false. Think of matters thus: It is epistemically possible that a mathematician should provide a proof for Goldbach's conjecture, which, if true, is necessarily true. However, it does not follow that in some possible world relative to our world Goldbach's conjecture is true.

    (ii) If the monadic operators employed in MOA are logical, whilst it follows validly from (1) – (4), (5) begs the question relative to S5. One can only assert- indeed, one must only assert- (1) only if one is also willing to assert (5), given S5. For, given S5, if one asserts 'it is possibly the case that it is necessarily the case that A', one essentially asserts 'it is necessarily the case that A'. In other words, given S5, (5) is contained explicitly in (1), which constitutes good ole petitio principii.

    The MOA is a ridiculously bad argument.

  7. Hi Aaron, thanks for the comments. You have a tendency to overstate your criticisms, though. ;)(a1) is only epistemic--we don't have to know all of the particular traits of a concept to understand the overall concept itself. (a2) is only true if we grant some kind of physicalism/naturalism, which is doubtful the theist will wish to do. However, (a2) is on the right track, as I discussed that one may deny (1) by stating such a concept is incoherent logically. But we await that argument. Such an argument must make at least two moves: 1. That there are two properties in contradiction when taken in a maximal way, and 2. The maximally great being possesses these properties (i.e. they are great-making). Even (a3) is just an assertion.

    It also seems as though the rest of the objection amounts to a reductionist, rather than deductive, view of the argument. No one thinks that one must realize, a priori, that a maximally great being exists in every possible world and hence is necessary. In fact, we may say what I said in the article above; where it seems that a being who is maximally great in a metaphysical sense (that is, has all perfections of metaphysics) is actually (metaphysically) possible if it is coherent. It can certainly seem coherent in principle without realizing, epistemically, every truth entailed by this other truth. In fact, it is upon this examination of entailments that we discover in fact it is greater to X than not-X. Perhaps on this examination we discover X is incoherent with respect to some other property the maximally great being must have; or perhaps we discover X is necessary existence. This is the issue here, not begging the question. After all, in every valid deductive argument the conclusion is contained in the major premise. That it can be reduced to contain its conclusion in no way means that we must assert the conclusion to assert the premise, even if the premise logically entails it. We may have independent grounds for asserting some premise whose logical entailments later lead us to reject it (or confirm it), and there's nothing amiss here.

    Finally, the first premise, even on a reductionist account, still amounts to asserting God's existence is either necessary or impossible. I would think that a relative few actually think God's existence is metaphysically impossible, but that is their right. Just as few would think his existence is necessary. However, I suspect more would think that it's at least possible he does exist, and think they have better epistemic justification (even if not warrant) for thinking it's more likely God's existence is possible than impossible, even in the metaphysical sense. But in that case, it follows one should embrace God's necessary existence. Epistemology flows from ontology, so that our views of a metaphysical possibility are always going to reflect an epistemic possibility as well (e.g., we won't say that we think X is metaphysically possible but that we also view X as epistemically impossible). I hope that helps, and I was typing this quickly as I am busy tonight, so please take this in a good-natured spirit. I do appreciate your contribution and thought-provoking comments!

  8. "{E.g., omnipotence entails 'God' can create a being, S, with perfectly free will. Omniscience entails 'God' knows all of S's actions before S even wills to do them. Thus, S does not have free will."

    That doesn't follow at all, Aaron. This is just another classical example of faulty reasoning. A barometer measures atmospheric pressure, but does not determine it. God measures future contingencies and decisions, but does not determine them.

    You are performing an immense, and unwarranted, leap of reasoning.

  9. Anonymous,

    If my reasoning is erroneous, your barometer analogy does not elucidate the error.

    'God' does not merely 'measure' future contingencies and decisions; rather, he causally effects outcomes through its divine foreknowledge and deliberate plan. In other words, in creating any state of affairs, due to its omniscience, 'God' knows that some other state of affairs will- indeed, must- obtain. Thus, in creating an agent,S, with free will, 'God' determines the actions and decisions of S. Thus, S is free and not free. QED.

    P.S. Randy, I expect to offer a substantive response to you tomorrow.

  10. Aaron, you know Molinism avoids such a problem nicely. :) Further, not all Christian theists accept that God has anything to do with an outcome insofar as free will is concerned. I look forward to the response!

  11. Correction: It is *purported* by some that Molinism avoids such a problem. As for 'God' having anything to do with the free will choices of its handiwork, well, it (1) arranged a state of affairs and (2) it knew what would inevitably result from the arrangement. (Mind you 'God' did not *need* to create anything.)

    So, if I permit my daughter to play in the kitchen (presumably I can bar her from playing in the kitchen), and I know that in so letting her play I greatly increase the likelihood that she will ingest a chemical product, I am responsible if she ingests a chemical product. This analogy is compounded vis-a-vis your deity.

  12. Hi Aaron. :) There's nothing in (1) and (2) that indicates causal responsibility which eliminates a free agent's action--at least not without begging the question. What we've described are necessary conditions (i.e., a necessary condition of my performing some act is that I exist, the universe exists, etc.), not also sufficient conditions (at least not in a complete sense). I still don't see any reason why foreknowledge would itself constitute the sufficient condition for an act. In fact, it seems just the opposite. The future act counterfactual constitutes the sufficient condition for God's foreknowledge in the strict sense (of all possibilities and would counterfactuals), while which truths are actual depend *both* on which counterfactuals are true and which world God chooses. The world which God chooses is only open to him in the event some counterfactuals are true and compossible. Interestingly, this analysis doesn't even need to be shown to be correct. Dialectically, this comes in response to the assertion that a maxmially great being is impossible.

    There's one further issue: it's not clear to me the proposed contradiction really is one after all. This is because omnipotence does not entail the ability to do just anything, but anything which is logically possible or feasible. Here's the dilemma: if we say omniscience renders free will impossible, and God possesses omniscience essentially, then it is not logically possible for God to create S after all. The other option is to say that it's not really impossible after all, and then the problem disappears. Now this raises the question of just when omnipotence dissolves into a mere description of consistency with any nature, and it's not a topic I wish to pursue too far just yet. As a result, I think this would not be my main objection as much as the preceding section would be.

  13. Randy,

    Re 'we don't have to know all of the particular traits of a concept to understand the overall concept itself.'

    The issue here is not about knowing all of the particular traits of a notion (whatever that amounts to) but rather about whether the notion * itself * makes any sense at all. I contend that notions of 'metaphysical perfection', 'maximal greatness', and other such utterances are meaningless- that is to say, they lack any coherent definition.

    Re '(a2) is only true if we grant some kind of physicalism/naturalism'

    We both recognize the existence of physical objects and processes, use the same language, and possess the same sensory and cognitive organs, all of which permit you and I to come to an agreement about the definition of the supermajority of terms like 'electron', 'molecule', 'species', 'monochromatically colored balls', 'operetta', etc. Indeed you and I can understand a great number of never before uttered sentences, such as “The blue jay in your backyard lived a sedate life until one morning it decided to pick up an elephant by its ears and fly it across the Pacific to New Zealand in order to watch the aura australis” because we both understand the observable conditions under which we would either assert or deny the sentence.

    Every term, even the theoretical terms or science, with the exception of logical vocabulary (e.g., 'and', 'or', 'if-then', etc.), must admit of observation criteria for either its assertability or deniability. So, e.g., you can neither assert nor deny the sentence 'Goshes distim gosteks' because you do not understand the observable conditions under which you would do so. That is, the sentence, for you, is without meaning. Now, via stipulation, synonymy, ostentation, etc., we could identify the meaning of the sentence, but this amounts to nothing more than identifying the observable conditions under which one would assert or deny the sentence.

    'God' presents a glaring lacuna for the theist, because, as I said, he is using the same language and possesses the same sensory and cognitive organs as the non-cognitivist. The the non-cognitivists insists that, unlike almost every other term, 'God' has not been given a proper definition in terms of observable conditions of assertability. * This * is the problem and it in * no way * presumes physicalism.

  14. Continued...

    Re (a4)

    You do not understand my argument. The argument is straightforward: Nobody asserts 'it is possible that it is necessary that' p under S5 if they do not already wish to assert 'it is necessary that' p. (I will use monadic operators L and M for 'it is necessary that' and 'it is possible that', respectively.) In S5 one may substitute every occurrence of 'ML' p for 'L' p salve veritate. Hence, premise (1) may be represented thus:

    p = 'a maximally great being exists'

    (1a) 'ML' p & (1b) 'L' p

    and the conclusion (5) thus:

    (5a) 'L' p & 'ML' p

    In other words, the conclusion (5) is stated explicitly in the first premise (1). Thus, the conclusion begs the question. Given S5, nobody asserts (1) who does not also want to assert (5). Of course, the issue is whether it is possible the a necessary being exists. So, if S5 is the appropriate modal logic for logical necessity, when one asserts (1) though wishes to deny (5), one must object that the monadic operator in (1) does not pick out logical possibility and rather point out that it denotes epistemic possibility. That is, it is epistemically possible that a 'maximally great' being exists, which is to state nothing more than the humble claim that it is conceivable that one should hear an argument which convinces one that such a being exists.

    However, if (1) picks out epistemic possibility, (5) does not follow validly from the premises. Thus. MOA fails. As an aside, if you are inclined, you should read E.J. Lemmon's paper 'Is There Only One Correct System of Modal Logic?' ('Proceedings of the Aristotelian Society, Supplementary Volume 33: 23-40). In it Lemmon provides a good overview of various notions of necessity. You can obtain the paper via JSTOR.

  15. P.S.

    I took no offense at anything you typed. I enjoy exchanging comments with you on blog and hope we can meet up to talk about this stuff in person, too.

  16. Hi Aaron, I've enjoyed the discussion so far! :)

    As to God's coherence, it seems you are referring to semantic content. Or are you referring to metaphysical coherence? If the latter, I don't know of anyone who will grant that up front. If the former, it seems quite understandable to suggest at least one maximally-great making property (such as, being the locus of all goodness, or being the most perfect being morally) that has obvious intent or meaning. I don't think "observable" has any essential function in meaning. For instance, I've never observed assertions. Now I have observed people making assertions, but never assertions themselves. It doesn't then follow assertions have no semantic content. Forgive me, but the examples given as essential to (a2) implied physicalism, and thus I thought this was the major thrust.

    With respect to your last set of comments, I think Craig has said it best. Allow me to reproduce, in my next comment, his address of a virtually identical situation.

  17. Dr. Craig:"Second, you confuse necessity de re with necessity de dicto. Necessity de re is the necessity of a thing (res); necessity de dicto is the necessity of a statement (dictum). The first premiss of the ontological argument asserts that a certain statement is possible, namely, the statement that a maximally great being exists or that maximal greatness is exemplified. It is not the statement, "It is possible that it is necessary that a maximally excellent being exists." That statement involves the iteration of two modalities de dicto. If we let G be the proposition "A maximally great being exists," the first premiss should be symbolized: ◊G.

    Third, you confuse logical equivalence with synonymity. To say that “Possibly, a maximally great being exists” is, indeed, logically equivalent to saying that “Possibly, it is necessary that a maximally excellent being exists.” But these statements do not mean the same thing. It is the meaning of a statement that is relevant to its epistemic status for us, not its logical entailments. A statement may seem true to us even though we are quite unaware of its logical implications. It is therefore a mistake to say that "’possibly necessary’ is the same thing as ‘necessary,’" if by “is” you mean “means.” So it is a mistake as well to think that because ◊□G ↔ □G, the first premiss of the argument “reduces” to □G. It’s not a matter of reduction but deduction! The whole point of the ontological argument is to show that in asserting the possibility of the existence of a maximally great being one has committed oneself to its actual existence. The nature of a deductive argument is that the conclusion is implicit, stashed away, as it were, in the premises, waiting to be made explicit by means of the logical rules of inference. One typically believes that ◊□G without first believing that □G; at least one needn’t first believe that □G and then on that basis infer that ◊□G. One’s modal intuitions may support the belief that ◊□G, and then one may realize that that is logically equivalent to and so entails that □G, and so one comes to believe that a maximally great being exists.

    In a nutshell: the logical equivalence of the conclusion of the ontological argument to its first premiss just shows that it’s a valid deductive argument, not that it’s question–begging."


  18. It seems to me quite trivial to find a counter example to 3. A universe that consists of a circle with a particle going around it forever is a possible universe. It is boring, and it doesn't include a maximally great being.

  19. Hi Dr. P, thank you for your comment! (3) isn't really being negated directly here, but (1). Allow me to explain. First, I'll refer you back to the article for a discussion of why something that necessarily exists does so in every possible world. Hence, your world is not really a possible world at all inasmuch as it's not a complete description of reality. Now you may reply, but it just is a logically possible state of affairs!

    There are two quick responses. First, in order to be a possible world, it must satisfy at least two criteria: a) be coherent (self-consistent) and b) have no contradictory necessary truth. Your world fulfills (a) but not (b). Second, your world can only fulfill both criteria if and only if God's existence is impossible, metaphysically speaking. But since no presenter of the argument will grant you that up front, it's a non-starter as an objection. I hope that helps!

  20. Randy,

    I am preparing a longer reply to your most recent comments regarding Dr. Craig's (missing-the-point) comments. I expect to post the reply as semi-article over at the Florida Student Philosophy Blog. However, if you wish, I can post it simultaneously here.

  21. Thanks Randy, but no, that doesn't help. My toy world is not our world, but it is clearly a possible world.

  22. Dr. P, since whether or not it is a logically possible world is the very point under contention, your sentence here functions only as a bare assertion. Until you demonstrate that the possible world is a complete description of the way reality could be, including every proposition or its negation, it just doesn't work. My point is that it is less than clear it is a possible world. You might be confusing epistemic possibility with metaphysical possibility.

  23. I can provide a complete mathematical description of this world. That should be sufficient to asses the truth value of any proposition. Would this help clarify the issue?

  24. Hi Dr. P. Since we're speaking in terms of modal logic, what we need is an explication of what, exactly, the claim is, which premise or premises that would negate of the argument, and why we should take that claim as true. I'm not sure that mathematics is up to the task with respect to modal considerations--or at least the ones here. But maybe. :)

    I think we should tease out the claims stated and/or implied by your original comment. It is suggested a circle with a particle going around it is a logically possible world, or a logically possible state of affairs. It is also asserted, however, that this claim affects premise 3.

    This means you may embrace one or more of the following propositions:
    1. Necessary existence is not a great-making property.
    2. A maximally-great being is impossible.
    3. Necessary existence does not mean existence across all possible worlds.

    If you embrace none of these propositions, and in fact think them all false, then it follows inescapably that:
    1a. Necessary existence is a great-making property.
    2a. A maximally-great being is possible.
    3a. Necessary existence does mean existence across all possible worlds.

    But then, (1a-3a) necessarily and inescapably imply the truth of the modal ontological argument. So what we need to know is which of the three (and how many) you disagree with, and why. It is only then we may truly evaluate whether or not your possible world (let's call it "P World") is indeed possible.

  25. My claim is

    1p) P World is possible

    Your cliam is

    2a) A mixmally-great being is possible

    I will attempt to show whatever you require to defend my claim. However, whatever you require for my claim should also be required for yours. For example, if I must show that mine is free of contradiction, I'd like you to show that yours is free of contradiction. Is that fair?

  26. Hi Dr. P. I certainly think the example is fair. And it's also fair and good that I be able to provide some reason to believe my claim. I hesitate to embrace the condition only due to dialectics: that is, (1p) is a suggested defeater for at least one of the premises of the argument (ostensibly, [1]). However, I don't see anything dialectically off about accepting the condition, so I do so tentatively. ;)

  27. I guess I should start by catching up with you in the defense of my claim in the original post you (or Alvin) offer thee supports for the claim that a MGB is possible.

    A) "...such an idea involves no incoherence....."
    B) Such and idea " intuitively possible."
    C) "Most people would agree with this."

    If you want me to show that the A is true for my claim, I'd like to know exactly what it means. (Is the idea of a largest prime number incoherent? There is no such thing, but the idea makes sense.)

    My claim satisfies B.

    C should be backed up with polling data if this is an important point. If you have polling data, I will do a pole to support my claim as well.

    What would you like me to do to support my claim at this point?

  28. Hi Dr. P. In order for a world to be considered metaphysically possible, it only need meet two criteria: coherence and no necessary truths entailing its nonexistence.

    "Coherence" just means a lack of an internal logical contradiction. P World clearly passes this test.

    "No necessary truths entailing its nonexistence" just means what it says: there is no truth out there, impossible to be false, that, if true, would make such a state of affairs false. So, while "the prime minister is a prime number" meets the coherence test, it fails the necessary truths test (as its just necessarily false that a person can be an abstract object), and thus any world containing this proposition is in fact an impossible world.

    So does your world meet the "necessary truth" test? Well I don't know, let's see. Dialectically, P World is suggested as a defeater for the idea of a maximally-great being. But if the maximally-great being in fact exists, then P World cannot pass the "necessary truth" test. If we simply assume P World passes the "necessary truth" test, we are begging the question against the MOA.

    So what to do? I would attack the coherence of the maximally-great being (MGB). Showing its incoherence shows P World is possible. But then, P World's use in the argument is nullified, for it would be the coherence criticism against the MGB doing all of the work.

  29. I want to make sure I understand the word "coherent." The idea of a greatest number is incoherent because it contains a logical contradiction. If N is the greatest number then N+1 is a greater number, contradicting the premise that N is the greatest number. Am I using coherent correctly here?

  30. Hi Dr. P. It is very close. What we mean by incoherence is strict logical possibility, or free from self-contradiction. So in taking a concept, we examine whether there are concomitant properties that are incompatible with each other. So in your example, the concept is the greatest number. There's nothing inherently contradictory in saying there is a greatest number. However, another necessary truth, which is that N can be added with 1, and such a number is greater than N, shows it to be contradictory.

    Incoherence would be like saying "I am a married bachelor" or "I went to the store and I did not go to the store" or some such, with respect to statements. Incoherence with respect to concepts like the maximally great being would be to say that two or more properties are incompatible with each other, in much the same way as the above statements.

  31. "Maximally-great" does not directly contradict "Being" so the MGB is a coherent idea. Can you show that it does not contradict other necessary truths?

    The idea of maximal-greatness is fraught with peril, even in very well defined contexts like integers and real numbers. Consider these six coherent ideas:

    1. Greatest integer
    2. Greatest real number
    3. Greatest negative integer
    4. Greatest negative real number
    5. Greatest non-positive integer
    6. Greatest non-positive real number

    All of them are coherent, but only half of them actually exist.

    If you want your MGB to exist, you are going to have to be very carefully. In particular, I think that MGB is only possible if beings' greatness is bounded from above. I.E. there is some finite amount of greatness, G, such that every possible being's greatness is less than or equal to G.

    P World isn't anything special, so it is less vulnerable.

  32. Hi Dr. P. That of course is not the discussion. You said P World is a possible world and that it includes no MGB. I asked you to show that it is. So far, nothing has even been offered.

    Additionally, what's interesting is that all subjects have their modalities necessarily. This means if something is possible, its impossibility is impossible. How does that figure in here? I propose MGB, pending coherence test and necessary truth test. You propose P World, stating this world does not include MGB and is possible. But then, you see, it is a necessary truth, and hence MGB would fail the necessary truth test. That's how one fails or passes the necessary truth test: if there's a necessary truth that overrides it, it fails.

    With a maximally-great being, it would be incoherent if two or more properties essential to that being (i.e., great-making properties) are logically contradictory. So you wouldn't take the two terms of the concept as much as you would take the properties of that being. I would also like to add we mean great making properties in a maximal way with respect to quality or value. This may or may not entail quantity, but quality is the key to metaphysics.

    So, I ask: why should we think P World is possible as a defeater to the MOA?

  33. We agree that both MGB and P World are coherent. Neither has been shown to meet the "necessary truth" test. Is that where we stand?

  34. Sorry, I just reread your last comment and it appears that we agree that P World is coherent, but we have not agreed that MGB is coherent. It looks like showing coherence could be a challenge given the multifaceted and unquantifiable nature of greatness. Am I reading you correctly?

  35. Hello Dr. P. Because I am big on dialectical consistency and honesty (and I like to avoid long discourses if at all possible), I must ask you to deal with the issue directly. Please show why P World is a logically possible world, or make some argument as to why a maximally great being is impossible, or I will not approve any further comments. Thanks!

  36. For general interest, it should be explained that "no necessary truths entailing its nonexistence" simply means "it is not the case that there are any such truths." It does not require nor indicate that a survey of every necessary truth must be done; it only requires the state of affairs being no necessary truth ontologically. Epistemologically, we can say its possible so long as we do not know of any such truths and we are not "sticking our heads in the sand;" at such time as we are presented such a necessary truth, then we can move from there. :)

  37. Hey Randy! Sorry I have been away for a while! I won't be making any comments on your post but just wanted to say I have enjoyed reading your comments back and forth, along with Aaron's comments. This is quite a mind expanding discussion! With no intellectual struggle of some sort, I won't grow in this way. So thanks again and feel free to call me sometime :)

  38. Hi Ben! Thanks for the comment and I probably will--so busy over here lately. :)

  39. Randy,

    I'm having trouble understanding premise 3--namely, how can the property of 'greatness' be attributed to the property of 'existence'? Either something exists or it does not. There are not varying degrees of existence or non-existence. Rather, to say something exists is to assert a fact about the actual state of affairs, so it seems silly to attach 'greatness' to 'existence'.

  40. Hi Quinn. With respect to "greatness," what we mean here is what constitutes a great-making property. This is helpful because it's not as though we think properties themselves have properties. Rather, it is simply a matter of definition. With respect to "greater," we mean metaphysical greatness. Now existence is not regarded (in general) to be a property (although some contemporary philosophers are now questioning what, exactly, Kant uses to get to that conclusion). But let's grant it for now.

    Now in one sense you are correct: something either exists or it does not. But in another sense you would be incorrect if you mean there are not different modalities of existence. After all, somethings (like you and I) exist contingently. However, necessary existence is quite different. It means it exists across all possible worlds, and could not fail to exist (its existence is impossible to be false). It seems obvious that necessary existence is certainly metaphysically greater than contingent existence, for if we compare two hypothetical beings that both contain all great-making properties (properties it is better to have than to lack, metaphysically) in a maximal way, yet one is contingent and one is necessary, the necessary one displays his maximally great making properties in more and varying possible worlds than the contingent one. This means the necessary one "outshines" the contingent one in this respect.

    Moreover, any claim of greatness to anything will simply be asserting a fact of an actual state of affairs, so I'm not sure how the criticism follows. Would things only be considered great if what was being described was possible but not actual?

    So, existence is not what we consider to be a great-making property, but necessary existence is.

  41. So, is it possible to conceive of a maximally-great being whose existence is contingent?

  42. Not upon reflection of what it means to be maximally great (maximal greatness means having great-making properties taken in a maximal way; necessary existence is considered great-making; nothing can both necessarily exist and contingently exist).

  43. That's what I was getting at. Thanks.

  44. Hi Quinn. I guess I do not understand what you were getting at, unless you mean that the argument entails God's necessary existence, in which case I wholeheartedly agree.

  45. No, I'm still not convinced by it as a whole, but that third premise was a point of confusion that you clarified well. I do still think there may be some problems with the first premise, however these I my ideas are not clear enough to present at the moment.

    I apologize for the informality of my questions and thoughts--I am by no means well-versed in philosophy, I merely have an interest in the subject.

  46. Well I am glad to have had the discussion! If or when you would want to come by and comment on anything, including this subject again, feel free. :)

  47. Comment nickname: "Fran and Kengo #1."

    I've already offered a detailed rebuttal of ontological arguments elsewhere. There are 4 core problems with Plantinga's version of the argument: 1) it un-informatively begs the question, 2) it is susceptible to Gaunilo-type counterexamples (especially examples involving deities that are more likely to exist than the God theists normally wish to argue for), 3) the phrasing of the first premise misleads people into applying the incorrect epistemic standards, and 4) every positive and negative atheist argument serves as a rebuttal of the argument's first premise, while virtually no theistic arguments (even purely epistemic arguments) can adequately support premise 1.

    Of course, there are other issues (ad hoc theistic definitions of "greatness", maximal greatness may be incoherent, arguments against possible world semantics as an accurate model of modality [a criticism I do not subscribe to, by the way], theistic equivocations between the "maximally excellent being" and the "maximally great being", theistic equivocations between metaphysical necessity/metaphysical impossibility and logical necessity/logical impossibility [i.e. conceptual coherence/conceptual incoherence], etc.). But any one of the four main criticisms I mentioned are enough to completely rebut the argument.

  48. Hello, this was kind of a drive-by, and some of these were addressed above. As to (1) it doesn't beg the question, for it doesn't demand that one accept the maximally excellent being exists ("maximally excellent" for Plantinga refers to a being that has all great-making properties exemplified in a maximal way); moreover arguments don't beg any questions. As to #3, people can use whatever modal rational intuitions they would need to affirm (1); if they find some reason later to go back and deny it, they may. #2, none are offered, so we needn't worry about that, and #4, dialectically, is subject to the modal argument's conclusion (apply this standard to literally every other modal argument, for instance). After all, if the MOA is successful, then whatever atheistic arguments there are, unless they demonstrate incoherence we shouldn't prefer them over the MOA; it is whatever is the most plausible. Finally, you overstate the case that the first premise cannot be justified; what you may mean is that no one would be compelled to accept (1). But that is no problem of the argument.

  49. Hi Randy!

    According to Richard M. Gale premise three, the "possibility premise", begs the question. He stated that one only has the epistemic right to accept the premise if one understands the nested modal operators, and that if one understands them within the system S5—without which the argument fails—then one understands that "possibly necessarily" is in essence the same as "necessarily". Thus the premise is invalid because the conclusion is embedded within it.

    What do you have to answer to this?

  50. Hello Alex, thanks for the comment!

    In Plantinga's formulation, premise 3 is, "3. If a maximally great being exists in some possible world, then it exists in every possible world."

    It's important to note that premises don't beg the question; people do. So, the crucial question is whether or not I can assert (3) on grounds independent of, epistemologically, the conclusion that a maximally-great being exists. And in fact, we may do just that.

    For we define a maximally-great being (MGB) as a being who possesses all great-making properties taken in a maximal way (where a "great-making property" is a property it is metaphysically better to have than to lack). In my above article, I say, "Why should it be so that if a maximally great being exists in one possible world, he exists in all? Because such a being holds its greatness and excellence in a maximal way, it would do so in every possible world (else there would be a greater being displaying more excellence—namely, the one who existed in all possible worlds)."

    Now then, knowing this definition, we can proceed forward and realize that we have a necessary being. But the epistemological flow does not state "necessary being, therefore necessary being," but rather "MGB, therefore all GMP; X is GMP; therefore MGB has X," where X is ultimately turns out to be necessary existence. Now one can go back and deny (1), but in order to avoid begging the question against the argument, one would have to have a reason to deny that MGB is possible, after all.

    Moreover, it is simply a feature of deductive argumentation for the conclusion to be within the major premise. In fact, if it is not contained within the premise, then the argument is patently invalid! So the so-called "reductionist objection" against the MOA ends up either misunderstanding the reasons for affirming (3) or misunderstanding deductive arguments (or both). Does that help at all?

  51. Granted, but I tend to take a thomistic stance on this. I believe in the doctrine of divine simplicity and think that God's existence is indisociable from his nature. So this would mean that for your argument to work we would have to conceive of the nature of God, yet this means we would have to know of his existence (Since his existence must be indisociable from his nature). And this seems rather a dubious entreprise. If God's act of existence was different from its nature then we would need ''something'' else to actualize this act of existence, because nothing that is ''form'' can cause its own act of existence. In short the argument fails because for it to work we should know of the nature of God to be able to conceive of it, which is just to say ''knowing his existence''.

  52. Well, it seems obvious that to say "God's existence is indisociable from his nature" seems to say something about his other properties as well (namely, that they are all identical). But that aside: the objection only works if we accept the presuppositions behind them. At worst, all that follows is that a Thomist cannot accept the modal ontological argument. But as there are plenty of non-Thomists (myself included), namely atheists, I think they aren't provided a way of escape.

  53. I think there is a problem with premise 1; or more specifically the notion of 'greatness' or even 'excellence' used here. Namely, you have to justify the possibility that two objects can be compared for how much greatness they have in any sense.

    Imagine if I asked 'which is greater, an apple or a Porsche'. How would you even attempt to answer that question without appealing to contingent facts or relative factors?

    The notion that some things are greater then other *sounds* intuitive, but I've never seen an account that wasn't basing this claim on human prejudices.

    1. Normally I don't allow anonymous comments, but I would like to take your critique, which I have heard before, and make it a blog post. I'll reply to this again when it is up. Thanks for the interaction!

  54. The first statement of the Ontological Argument is:

    "It is "possible" that a maximally great being exists".

    If we substitute the meaning of the word "possible" as it is used in this argument ("possible" means "true in some possible worlds"):

    "It is "true in some possible worlds" that a maximally great being exists".

    This is a statement of supposition. The basis for the assertion needs to be explained.

    1. Thanks for commenting! Now, there are two ways one can construe the possible/possible worlds relationship. One: something X is possible if X appears in a possible world. Two: Something X appears in a possible world if X is possible. I subscribe to the latter account (that is, something has its modality de re and doesn't somehow gain it from being in a possible world (in other words, I'm not a Lewisian modal realist).

      Now with that out of the way, I do wonder if you read the article, since I say, "By (1), Plantinga means to say such an idea involves no incoherence, and is intuitively possible. That is, it really could be the case such a maximally great being exists. Most people would agree with this."

      Now you may not think this is successful, but it is indeed an explained basis (i.e., it is an intuitive belief). I've written a little more about intuitions and the ontological argument specifically, so you can always use the search feature to check that out. I hope this helps!

  55. My concern is with the usage of the word "possible" in statement 1. In this statement, "possible" means "in at least one possible world". But the Maximally Great Being either exists or does not exist - and if the Maximally Great Being exists, it exists in all possible worlds. Thus the Maxiomally Great Being exists "necessarily" if it exists at all. The Maximally Great Being cannot exist "possibly". So because the word "possible" is referring to the Maximally Great Being, it must be replaced with the word "necessary" because the Maximally Great Being cannot exist "possibly, only "necessarily".

    1. Hello, thanks for the comments! I think there's a fundamental modal confusion going on. As you note, "possibly" can reference existence in at least one possible world (minimally, it means it is metaphysically possible that God exists), and from that we eventually derive the conclusion that God necessarily exists. But it's a modal mistake to thereby claim God doesn't exist possibly. On that, you're using "possibly" to mean "contingently." But the problem is that by negating God's possible existence, based on the initial definition, this is contradictory to God's necessary existence. Think about it this way: if God exists in all possible worlds, then he exists in at least one. Given modal logic, if God exists in at least one world, then he exists in all of them--but this is because of what it means to be maximally great, as we discover.

      You don't have to know the mode of existence in order to affirm the first premise. You can, of course, but it's not needed. Further, you can always "go back" if you think it's not really possible that God exists after all; or you can refrain from affirming the first premise if you're not sure whether or not it's possible. But one caveat: if the only reason you do so is because you feel the conclusion is undesirable or that you don't know it, that would be an instance of question-begging. It's just a matter of deduction and modal logic that yield the conclusion, so if one is inclined to accept the first premise, he must have a good reason for rejecting or refraining later on!

  56. I have not studied Modal Logic or Metaphysics, but have a basic understanding. I also understand that which is sometimes called Axiom S5. I am not questioning the logic of the argument - just the premise. I am not referring to God but the MEB and the MGB. Your piece omits the two definitions normally included:

    1. A being has maximal excellence in a given possible world W if and only if it is omnipotent, omniscient and wholly good in W; and
    2. A being has maximal greatness if it has maximal excellence in every possible world.
    3. It is possible that there is a being that has maximal greatness. (Premise)
    4. Therefore, possibly, it is necessarily true that an omniscient, omnipotent, and perfectly good being exists.
    5. Therefore, (by axiom S5) it is necessarily true that an omniscient, omnipotent and perfectly good being exists.
    6. Therefore, an omniscient, omnipotent and perfectly good being exists.

    (from 1 and 2) A being has "maximal greatness" if it "is omnipotent, omniscient and wholly good in every possible world".
    (by definition) "it is possible" means "it is the case that in at least one possible world".
    (hence 3) "It is the case that in at least one possible world" that there is a being that "is omnipotent, omniscient and wholly good in every possible world"

    This makes little sense. In any case, your statement "it is metaphysically possible" means nothing in actuality - a problem of context.

    The other issue with this premise is that Maximal Greatness is a label/name that is applied as a consequence of the Maximally Excellent Being existing in all possible worlds, including ours. The Maximally Excellent Being must exist in all possible worlds before this argument is considered. This existence is established in one of two ways (1) empirically or (2) pre-supposition. It has not been established empirically so it is by pre-supposition unless you have another way in which it has been established?

    My issue remains with the premise (your statement 1). To ask my question another way - how was the premise thought of? What prompted the claim? Is it pre-supposition? It certainly was not empirical. Whatever the source of the statement, it must be true to be a premise, thus it must be provable in its own right. It must be provable prior to its usage in this argument.

    Now I guess you will respond that this is all in the Modal Logic. But at some point this has to relate to actuality. It is my contention that any construct or tool that is used in Modal Logic (and Metaphysics) to "prove" the existence of the MGB/MEB must be valid to the same extent in actuality; otherwise in this case Modal Logic (and Metaphysics) is of no use for actuality. Do we have a problem of context - an attempt to impose a conclusion of Modal Logic on actuality? (sorry if I seem to rant...)

    1. Hello,

      Yes, this is just a consequence of deduction in modal logic (the conclusion is contained in the premises); if it didn't, just as in literally every deductive argument, it would be manifestly invalid.

      However, you do ask a really good question, in that: what is the support for premise 1? It seems to me that as long as it seems to someone that this kind of being could exist, then this is prima facie support for (1). Intuitions, is what I'm getting at. These aren't defeasible, by any means, but they are helpful.


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