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What are some objections to this form of the argument? It seems like the only premise that can be disputed is premise 1, but nobody has successfully disproven the possibility of a maximally great being.

  1. It's possible that a maximally great being exists. In other words, a maximally great being exists in some possible world.
  2. If a maximally great being exists in some possible world, it exists in every possible world.
  3. If a maximally great being exists in every possible world, then it exists in the actual world
  4. Therefore, a maximally great being exists in the actual world.

Support for premise 2: A maximally great being wouldn't be maximally great if it only existed in some possible world. To be maximally great it has to exist in every possible world.

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  • How do you justify premise 2?
    – Eliran
    Mar 25, 2017 at 10:23
  • 1
    If the Christianity site cannot do truth claims why exactly can the Phil site?
    – Neil Meyer
    Mar 25, 2017 at 13:01
  • 1
    No, it does not; the conclusion: "a maximally great being exists" is false, and thus the either the argument is not valid or some of the premises is false. Mar 25, 2017 at 14:28
  • 3
    It seems to me the modality in your argument is an idle wheel that does no work. Premise 1 is redundant, what you need is the conclusion of Premise 2, and the justification for it has nothing to do with Premise 1. It is roughly that otherwise MGB is not greatest "in every way". But if this reasoning works then it can be directly applied to the actual world, and the argument reduces to the old one of Anselm, no modality needed. It does not work because if it did it would prove too much, e.g. the existence of "maximally greatest" island, clown, carrot, etc., as Gaunilon pointed out to Anselm.
    – Conifold
    Mar 28, 2017 at 0:31
  • 3
    What does "great" mean?
    – Frank
    Apr 8, 2017 at 23:39

9 Answers 9

8

I understand your argument as follows:

  1. A maximally great being possibly exists.
  2. If a maximally great being possibly exists then it necessarily exists.
  3. If a maximally great being necessarily exists then it actually exists
  4. Therefore, a maximally great being actually exists.

Here is a reconstruction using modal logic:

  1. ◊∃xGx
  2. ◊∃xGx → □∃xGx
  3. □∃xGx → ∃xGx
  4. Therefore, ∃xGx

As written, the argument is valid; the conclusion does follow. Now for the premises.

Premise 3 is a logical truth, no problem there.

Premise 1, I take it, would be justified by claiming that a maximally great being is conceivable, and that it is therefore possible. That does seem plausible, but it is controversial whether conceivability entails possibility.

Premise 2 needs further support. You're assuming that if a maximally great being possibly exists then it necessarily exists, but you provide no justification for that. Possibility usually does not entail necessity, so you need some argumentation for this premise.

Finally, David Lewis provides a very good analysis of Anselm's modal ontological argument (which is somewhat similar to yours) in his paper Anselm and Actuality.

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  • 1
    For premise 2, I think the idea is that it's greater to exist in every possible world. Hence, if a being exists in fewer than all possible worlds, then it's not maximally great.
    – user18800
    Mar 27, 2017 at 21:54
  • What is the point of rephrasing the argument like this? Why not comment on the original premises?
    – ILoveJesus
    Apr 4, 2017 at 13:55
  • 3
    @ILoveJesus because you are making a modal argument and asking about the logical validity of the argument; why would translating it into modal logic be irrelevant? Modal logic gives a deductive proof system for modal arguments, which seems to be what you want to use to evaluate your argument.
    – Not_Here
    Apr 5, 2017 at 17:24
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The proof does not work, I think. Your problems are premises 1 and 2.

My main problem is with premise 1: it is possible for a maximally great being to exist. Why should we accept this?

There is the tempting notion, mentioned in Eliran's (considerably better) answer, that anything we can imagine must be possible; but there is a great deal to be said about the nature of possibility and the rational mind before we can accept this. And even if it were true, the principle can surely only applied to determinate ideas, not simply names. For instance I can talk a fair amount about a circular square, but there is no true picture of such a thing in my mind. The same could be said of a world without time. Perhaps the same is true of a maximally-great being. At the very least I do not have such a picture.

We want some additional explanation for premise 2. We must show that necessary existence is greater than contingent existence. Now intuitively this is easy, in that it seems to be true, but we probably want to say that greatness comes from predicates, and it's not clear that necessity is a predicate.

To recap:

  1. We don't know that intelligibility implies possibility

And

  1. We don't know that "maximally-great being" is a truly intelligible concept

So

  1. We don't know that it is possible for a maximally-great being to exist.

What's more,

  1. We don't know that necessity is a predicate

Which means

  1. We don't know it is greater to exist necessarily than contingently

Therefore

  1. The proof fails.
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  • The argument does not fail just because we are not 100% sure of the things you mentioned. All that's necessary is for the premises to be more plausible than their negations. So your conclusion is false.
    – ILoveJesus
    Apr 5, 2017 at 16:38
  • 3
    It's not a proof if it does not in fact prove anything. It may well be a valid argument, but that is a long step away from a proof. Roughly, you need uncontroversial premises for a proof.
    – Canyon
    Apr 5, 2017 at 17:00
  • 1
    You're right, I used the word "proof" in the title. Oops.
    – ILoveJesus
    Apr 5, 2017 at 17:05
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The proof fails in the very first step. You try to justify this step in your initial explanation, but let's just put this explanation as part of the proof.

  1. Nobody has successfully disproven the possibility of a maximally great being.
  2. It's possible that a maximally great being exists.

You are basically fallaciously playing with the word "possible" here. What you've proven is that it's "possible" in the sense that "we do not know whether or not a maximally great being exists" i.e. the possibility is derived from uncertainty. However, you then try to jump to

  1. In other words, a maximally great being exists in some possible world.

which requires you to establish a different meaning of possible--specifically, "in the set of all possible worlds, there is at least one in which a maximally great being exists." In this case, the possibility is derived from nonzero probability.

If your incorrect line of reasoning was valid, we could literally prove any mystery/uncertainty of the universe with it.

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In a "round-about way" you are saying the same thing (using circular logic).
Let me rephrase:
1. It is possible that God Exists, (an assumption)
4. Therefore, God exists. (an unfounded assertion).
In other words, just because something is possible, does not necessarily make it so!

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  • That's not what I'm saying. That's what premises 2 and 3 are for.
    – ILoveJesus
    Apr 5, 2017 at 16:25
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Breaking an informal argument into explicit steps is only half the battle; you also have to define your terms. In particular, this will often reveal that an "obvious" assumption is anything but . . .

. . . as it does in this case. You've edited to stipulate that statement (2) is justified by the definition of "maximally great being," so is implied by statement (1). OK, that's fine, but that depends on what you mean by "maximally great being." Whether or not the possibility of a maximally great being is plausible (let alone true) depends on what that phrase means precisely, and that's something you haven't even tried to do.

So you can indeed make (2) justified by choosing a sufficiently strong meaning for "maximally great being," but then that makes (1) extremely objectionable: given that maximal greatness now quantifies over all possible worlds, why on earth should such a thing be possible at all? ("Given any thing, I can imagine a better thing . . .")

And "nobody has successfully disproven the possibility of a maximally great being" is not a justification for (1) being a "reasonable" assumption at all. Nobody has yet disproved the possibility of a counterexample to the Riemann hypothesis; is that a reasonable assumption to make?


OK fine, a comment on the last sentence: in mathematics people do prove "conditional" results, e.g. "If the Riemann hypothesis is false, then [something]." However, the hypothesis is part of the result: we do not claim to have proved [something]! So you can perfectly reasonably claim the conditional result "If the existence of a maximally great being is possible, then there is a maximally great being," but (a) that's not much of a surprise, and (b) you'll still need to define "maximally great being."

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I assume your argument here is based on Plantinga's work. If so, a key thing you are ignoring is the primary axiom on which the argument relies, 'Axiom S5'. The modal operator states something along the lines of:

If it is possible that something is necessarily true, it must (logically) therefore be necessarily true in at least one possible world. If something is necessarily true in at least one possible world, it (logically) must be necessarily true in all possible worlds.

To demonstrate this, you could use a basic math sum as an example. It is possible that 2 + 2 = 4 is necessarily true, which means that in at least one possible world, 2 + 2 = 4 is necessarily true. However, if 2 + 2 = 4 is necessarily true in at least one possible world, it must also be necessary in all possible worlds.

To counter this axiom, with this example, you would have to argue why a world in which 2 + 2 does not equal 4 is a logically tenable possibility. This is fruitless though, because at this point you're arguing against a predefined set of terms, that are almost universally uncontroversial. The same can be said of Plantingas ontological argument and his concept of maximal greatness. The only way you might squeeze out of Axiom S5 as having these implications is if you, like James Garson, argue that necessary and possibility don't mean what Plantinga intends.

When the effect of this axiom is taken into account, the modal ontological argument can no longer be said to be begging the question, or circular reasoning. It simply demonstrates that if it is possible that the existence of a god-like being is necessarily true in one possible world, it's existence is simply necessary (in all possible worlds, of which ours is one).

Depending on your conclusions about the internal consistency of the definition of maximal greatness, this argument succeeds in proving that a maximally great being is either necessary (and thus god exists), or impossible (and thus god does not exist).

The problem with unicorns and pizza, and other silly replacements of maximal greatness is that there is nothing intrinsically "great" about any of them, especially in the sense that Plantinga means.

I'd strongly encourage you too study his argument more closely.

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A better formation of the argument would go as follows:

Premise 1: "Either God exists or God does not exist."

Premise 2: "If God exists, then it is necessary that God exists."

Premise 3: "If God does not exist, then it is impossible that God exists."

Preliminary Conclusion: "Either it is necessary that God exists or it is impossible that God exists."

Premise 4: "It is impossible that God exists if and only if the concept of God is self-contradictory."

Premise 5: "The concept of God is not self-contradictory."

Preliminary Conclusion: "It is not impossible that God exists."

Final Conclusion: "It is necessary that God exists."

Notes: Premises 2 and 3 are supportable by logical arguments of their own. The arguments can be stated or not stated. Premise 5 needs to be proved. I hope this helps!

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TL,DR: you must define your terms before using them.

Long version:

Just what does "maximally great" mean ? (Or even "great", in a theological context, for that matter...) As long as this concept of maximal greatness is not rigorously defined, any proposition derived from it is tainted and suspicious.

It follows from the vagueness of the premise 1 that premise 2 is meaningless as well. "Maximally" introduces the idea of a limit to greatness, without specifying what or where this limit is. Why should the aptitude of existing in multiple worlds (for whatever that means, again...) be within the limits of maximal greatness ? It might be impossible to exist in many worlds, why not? We have never observed a maximally great being or multiple worlds, therefore we can't possibly know. In all fairness premise 2 can't be granted as fact.

0

As noted by other users, this argument seems to be a version of Alvin Plantinga’s so-called Victorious Modal Ontological Argument for the Existence of God (presented at the end of Plantinga’s book The Nature of Necessity). There is a lot I could say about it, but, space being limited, I want to focus on what I view as the argument’s fundamental problem. Also, not knowing how much knowledge of modal logic’s symbolism I can assume, I’ll use “N” and “P” for “necessarily” and “possibly.” I’ll also abbreviate “a maximally great being exists” (or, in Plantinga’s way of speaking, “maximal greatness is exemplified”) as “MGE.” “P(MGE)” and “N(MGE)” will then mean “possibly, a maximally great being exists,” or equivalently “at some possible world, a maximally great being exists,” and “necessarily, a maximally great being exists,” or equivalently, “at all possible worlds, a maximally great being exists.” (Rather nonstandardly, I’ll use “A(MGE)” for “a maximally great being actually exists.”) To begin with, at least, I won’t worry here about what I view as the problematic definition of the property of maximal greatness as the necessary exemplification of maximal excellence but will simply assume its legitimacy, taking its use as a way of expressing the noncontingency of God’s existence used by Charles Hartshorne (the Hartshorne and Plantinga versions of the argument look very different but are essentially the same at their cores—as is Norman Malcolm’s and as are the rather lengthy Robert Maydole arguments I’ve seen). A maximally great being’s either necessarily existing or necessarily failing to exist—its existing at all possible worlds or at none—is then an expression of its noncontingency, which I will here treat as a premise (as the argument given does). First, I'll show that something must be wrong with the argument; second, I'll say what I think is the fundamental problem with it.

As the argument stands, we may symbolize it as

  1. P(MGE) (possibility premise)
  2. If P(MGE), then N(MGE) (noncontingency premise) 2a. N(MGE) (2, 1, modus ponens)
  3. If N(MGE), then A(MGE) (modal premise—that which is necessarily true
    is actually true—modal axiom T)
  4. Therefore, A(MGE) (3, 2a, modus ponens)

But changing “P(MGE)” to “P(not-MGE)” (which, I note, is not the same as not-P(MGE)) yields the atheistic argument

1*. P(not-MGE) (possibility-not premise) 1**. not-N(MGE) (1*, duality) 2*. If P(MGE), then N(MGE) (noncontingency premise) 2a*. not-P(MGE) (2*, 1**, modus tollens) 2a**. N(not-MGE) (2a*, duality) 3*. If N(not-MGE), then A(not-MGE) (modal premise—that which is necessarily
true is actually true—modal axiom T) 4*. Therefore, A(not-MGE) (3*, 2a**, modus ponens)

(“Duality” refers to what in any classical modal logic amounts to logical equivalence. “Possibly, p” and “not necessarily not-p” is one duality; “necessarily, p” and “not possibly not-p” is another. As long as we are applying a classical modal logic—like Plantinga’s S5—the use of duality should be thought of as not changing anything but the form of a modal sentence—the way it “looks.”) Lines 1** and 2a** are merely rewritings of one statement into an equivalent form for the sake of applying modus tollens or modus ponens later; they are not new premises. Lines 3 and 3* are simply substitution instances of the modal axiom T, “if Np, then p.” All that has changed from the first argument to the second is that “P(MGE)” has changed to “P(not-MGE).” Instead of the first premise’s being that a maximally great being’s existence is possible, we have the new premise that a maximally great being’s nonexistence is possible. (Foreshadowing: But, if neither MGE nor not-MGE seems self-contradictory, why shouldn’t both be possible?)

One can also create parallel arguments for any other proposition thought to be noncontingent. Philosophers usually consider mathematical truths to be necessary truths. We do not know whether Goldbach’s conjecture is true or is instead false, but it must be one or the other, and if mathematical truths really are necessary truths, then either Goldbach’s conjecture is necessarily true or it is necessarily false. Using “GB” for “Goldbach’s conjecture is true,” we may then write the argument

  1. P(GB) (possibility premise)
  2. If P(GB), then N(GB) (noncontingency premise) 2a. N(GB) (2, 1, modus ponens)
  3. If N(GB), then A(GB) (modal premise—that which is necessarily true
    is actually true—modal axiom T)
  4. Therefore, A(GB) (3, 2a, modus ponens)

Voilà! We have proven the truth of the Goldbach conjecture without doing any mathematics! But….

1*. P(not-GB) (possibility-not premise) 1**. not-N(GB) (1*, duality) 2*. If P(GB), then N(GB) (noncontingency premise) 2a*. not-P(GB) (2*, 1**, modus tollens) 2a**. N(not-GB) (2a*, duality) 3*. If N(not-GB), then A(not-GB) (modal premise—that which is necessarily
true is actually true—modal axiom T) 4*. Therefore, A(not-GB) (3*, 2a**, modus ponens)

And behold! We have now proven not only the truth of the Goldbach conjecture but also its falsity! And without doing any mathematics!

(This might be a good place to note that the relevant kind of possibility is not subjective but is objective. Were it subjective, the contingency premise would be judged false by anyone who was not already convinced of the truth of N(MGE). Its being objective renders the plea “But surely, it’s at least a millionth likely that MGE, or a billionth likely, or a trillionth likely—and therefore P(MGE) must be true” pointless—just as “But surely, it’s at least a millionth likely that GB, or a billionth likely, or a trillionth likely—and therefore P(GB) must be true” pointless. Not to mention that “Surely, it’s at least a millionth likely that, etc.” could just as easily be said of P(not-MGE) and of P(not-GB), so that it doesn’t decide between P(MGE) and P(not-MGE) or between P(GB) and P(not-GB).)

I hope that these parallel arguments are enough to convince you that something must be wrong with the ontological argument originally given. Next, I'll say what I think fundamentally goes wrong with it.

If we can see that something must go wrong with the ontological argument given—essentially, Plantinga’s so-called Victorious modal argument—what goes wrong with the argument given?

If changing only the premise P(MGE) to the premise P(not-MGE) allows the conclusion of A(not-MGE) instead of the conclusion A(MGE)--if P(MGE) and P(not-MGE), when combined with the noncontingency premise, result in contradictory conclusions—then we must suspect that something about the combination of the two premises must be to blame. We could, of course, simply jettison the noncontingency premise—in fact, I find it dubious—but if we keep it, what goes wrong?

The noncontingency premise makes the following true: either N(MGE) or N(not-MGE). If N(MGE), then P(MGE) is also true, but P(not-MGE) is not; if N(not-MGE), then P(not-MGE) is true, but P(MGE) is not. This is by design: Hartshorne argued that it was not possible for God to merely happen to exist, or to merely happen not to exist. Plantinga’s maximal greatness was designed to bring about that same noncontingency. But notice that then P(MGE) is equivalent to N(MGE), and notice that then P(not-MGE) is equivalent to N(not-MGE). If MGE is possible, then not-MGE is not; if not-MGE is possible, then MGE is not. The noncontingency premise collapses possibility and necessity for a maximally great being.

But then the premise P(MGE) is equivalent to N(MGE), and any reason to think that P(MGE) is true is also reason to think that P(not-MGE) is false. That’s not usually how the justification of a claim of possibility works. Here, though, sufficiently strong reason to think that P(MGE) is also sufficiently strong reason to think that N(MGE) (and to think that not-P(not-MGE)). But if one had sufficiently strong reason to think that P(MGE) as to accept P(MGE) (and therefore to go ahead and use the argument), he would also have to have sufficiently strong reason to think that N(MGE); and if he had that, he wouldn’t need the ontological argument. And if one did not have sufficiently strong reason to think that N(MGE), he wouldn’t have sufficiently strong reason to think that P(MGE); and lacking that, he couldn’t use the argument. The argument is therefore either superfluous (if one already has sufficiently strong reason as to accept N(MGE)) or toothless (if one does not already have sufficiently strong reason as to accept N(MGE)). And as a practical matter, that’s what’s fundamentally wrong with it.

There are, of course, other things one might notice about it. One might notice that if neither “possibly, a maximally great being exists” nor “possibly, a maximally great being does not exist” (neither P(MGE) nor P(not-MGE)) seems self-contradictory, and yet if one of them must be not only false but necessarily false, then it seems that some statements can be necessarily false without being self-contradictory. One may then choose among options: (a) one of the two really is self-contradictory despite not seeming to be, or (b) the premise of God’s noncontingency is false, or (c) for some statements, being necessarily false does not imply being self-contradictory. (Anyone wanting to keep (c) will then have to choose between (a) and (b).) As the same issue arises in the arguments involving Goldbach’s conjecture, and would do so in any argument having a similar noncontingency premise, option (b) has to be a more general option—perhaps that no non-tautologies are necessary truths and no non-contradictions are necessary falsehoods, thereby avoiding that sort of noncontingency premise altogether.

Or, one might think of the term “possible worlds” not as denoting worlds but as denoting world-descriptions, and he might think of its being impossible for an entity described one way as exemplifying a property defined in terms of how it is described in other ways. So, for instance, one might think that a tiger could be described as striped, because stripedness is a within-world property, but he might think of it as illegitimate to describe a tiger as striped at every possible world, i.e., world-description, even if he thought that tigers were indeed striped at every possible world, because although he might think of “Necessarily, tigers are striped” as true—he might think of “At every possible world (i.e., world-description), tigers are striped” as true—he might think of “Tigers exemplify necessary stripedness” as badly phrased, saying something nonsensical. He might suppose the necessity of tigers’ being striped to be a feature of the collection of world-descriptions rather than a feature ascribed to tigers in any individual world-description. One might think of Plantinga’s move from maximal excellence—maximal power, maximal knowledge, maximal goodness, or whatever one wants to include in the term—to necessary maximal excellence (which constitutes maximal greatness), thought of as a property of an object at a possible world rather than as characterizing the entire collection of world-descriptions, as simply illegitimate.

But the fundamental problem—that the argument is either superfluous or toothless—remains, even if one keeps the noncontingency premise in place and doesn’t worry about anything else that could be noticed about the argument. Because of the collapsing of possibility and necessity and the consequent equivalence between “P(MGE)” and “N(MGE),” so that sufficient justification for accepting the former must also be sufficient justification for accepting the latter, you can’t use the argument unless you don’t need it, and if you need it, you can’t use it.

(I don't mind the copying of my posts elsewhere, but please attribute them to "Keith Brian Johnson (MindWalk)")

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