Monday, September 27, 2010

A Perfectly Cromulent Inoculation against Plantinga's Proof

I have already tackled Alvin Plantinga's modal form of the ontological argument in a previous post, but I've never been entirely satisfied with my response. I was pondering it again today, and I think I have come up with a better rebuttal -- although it's more an "inoculation" than a rebuttal, as I will explain.

The most controversial aspect of Plantinga's argument is not the S5 axiom -- although, frankly, I apparently don't understand formal logic enough to see how the S5 axiom is possibly supportable, it seems to me to lead to obviously absurd results -- but rather, the acceptance of the possibility premise. To review, Plantinga's possibility premise is that "Maximal greatness is possibly exemplified", where maximal greatness is defined thusly: "It is proposed that a being has maximal greatness if it has maximal excellence in every possible world." (The definition of maximal excellence is not important for the purposes of this post) It has been argued that Plantinga is engaging in a form of begging the question here, in that when the listener agrees to this premise, she is agreeing to far more than she realizes.

Plantinga's response is that one could say this about any logical argument. And admittedly, he has a point: it is usually not fair to agree to a set of premises, and then when those premises lead to a result which one finds distasteful, to go back and revise the key premises until the result no longer holds. Otherwise, one could never mount any sort of logical argument whatsoever -- the premises would just be altered.

And thus I propose my inoculation against Plantinga's proof. This is a "proof" of sorts, which, via series of arguably objectionable premises, attempts to reach a result which is patently absurd. The point is that if a person rejects any of the premises in this proof, it makes it impossible for that person to agree to Plantinga's possibility premise. Thus, they are inoculated.

I start with a definition:

1. It is proposed that a proposition is perfectly cromulent if that proposition is true in all possible worlds.

And right off the bat, let's toss out our first premise:

2. There exist one or more propositions which are perfectly cromulent. (premise)

So what we are doing here is clarifying what we mean by "possible worlds". I would argue that if we want to take "possible worlds" at its face, then we must reject this premise. And I'm sure it is clear that if one rejects the premise at (2), one must also reject Plantinga's possibility premise -- for, if it maximal greatness were exemplified, then the statement "There exists a maximally excellent being" would be perfectly cromulent, and if (2) is false, there cannot be any perfectly cromulent statements.

But let's say we have a narrower definition of "possible worlds". Let's move on with another suggested premise, this time one we hope the listener will accept.

3a. If we can imagine a possible world in which proposition P is false, then P cannot be perfectly cromulent. (premise)

This really doesn't narrow the definition very much at all, but it does so in an important way. If a person agrees to premise (3a), then in regards Plantinga's argument, they have two choices: She can insist that she cannot even imagine a world without a maximally excellent being (in which case Plantinga's proof is superfluous!), or else she can admit that she can imagine such a world, in which case Plantinga's possibility premise once again breaks down: We can imagine a world with no maximally excellent being, therefore the proposition that "a maximally excellent being exists" is not perfectly cromulent, therefore the premise that "maximal greatness is exemplified" cannot be true.

Okay, so let's say the premise was rejected. Instead, let's substitute the negation.

3b. Even if we can imagine a possible world in which proposition P is false, P may still be perfectly cromulent. In other words, the imagined possible world is not actually a possible world.

I am having trouble imagining that a person might make this argument, but I want to cover as many bases as possible. It seems to me, however, that if one accepts premise (3b), it is rather hard to escape the next premise:

4. If a given proposition P is not proven to be false, then it is possibly perfectly cromulent.

If this premise is rejected, then I submit that the onus is now on the other person to say how we ever would determine whether a proposition is possibly perfectly cromulent. However, a person who has gotten this far and then rejects this premise is now free to agree with Plantinga's possibility premise if they wish.

Of course, if the premise is accepted, then we rapidly reach an absurd result:

5. For any given proposition P that has not been proven to be false, it is possibly necessarily true.
6. For any given proposition P that has not been proven to be false, it is necessarily true. (By that wily S5)
7. All propositions that have not been proven false are true.

Yes, one can still thread the gauntlet and agree with Plantinga's possibility premise. But most people won't -- and that's exactly the point. This forces people to clarify exactly what they are agreeing to before they accept Plantinga's premise.

Please, anyone who actually knows philosophy or logic, tell me where I went wrong!


  1. I can't get past premise 1 of the Ontological argument.

    Omnipotence and omniscience are both logical absurdities, and "wholly good" is a subjective concept which is not defined logically.

    All the following premises fail (at least) because premise 1 is invalid (if not for other reasons as well).

  2. Yeah, I pretty much agree with that. It's difficult, because the concept of "possible worlds" seems to me to be endlessly problematic. (It's that same ambiguous "possible worlds" concept that allows David Chalmer's interesting-but-flawed argument in favor of dualism) Do we mean by "possible worlds" anything that we can imagine? Is it the distributed set of true/false values for every conceivable proposition? (In which case that would allow logically contradictory, even unimaginable possible worlds) Is it the set of all worlds that would not violate our current understanding of the laws of the universe?

    The Wikipedia article on the philosophical concept of "possible world" is of no help to me here.

    Oh, and incidentally, I think that if Wikipedia has defined "possible world"'s relation to modal logic properly, than my initial objection to Plantinga's proof -- that he was actually creating a hierarchy of possible worlds of possible worlds -- was right to begin with. According to Wikipedia, in modal logic:

    Possible propositions are those that are true in at least one possible world

    If that is true, than Plantinga has abused modal logic like a Catholic priest with a choirgirl. Maximal greatness is a trait that applies to multiple possible worlds. So when he says "Maximal greatness is possibly exemplified," if I substitute the definition of "possibly" in modal logic (according to Wikipedia) and his definition of maximal greatness, we get this meaningless bullshit:

    "In at least one possible world, there is a being who exhibits maximal excellence in all possible worlds."

    What the fuck does that even mean? Nothing.

    So perhaps this post was superfluous, and my initial objection to Plantinga's proof was spot on.

    I really need to find a modal logic expert to talk with about this. I must have something wrong here, because this seems like a basic flaw in Plantinga's application of the S5 axiom -- if I were correct, surely other philosophers would have called him on it?

  3. Of course, even if the Ontological argument was valid, my response would be, "So what?".

    OK, we would've proven the existence of a Maximal being (as opposed to a Predacon being, I guess) about which we know absolutely nothing other than it logically exists. Would this knowledge serve any useful purpose? Would this be a reason pray to said unnamed maximal being?

    Not really. Assuming an all powerful, all knowing, perfect being (a concept which is illogical in and of itself), it seems illogical to think that we could affect its thought processes or actions. That would imply an imperfect being requiring our input in order for it to make a maximal decision. This assumes it is possible for us to have an actual free will of our own that wasn't entirely the result of (and thus directed by) the creator.

    Ontological argument: Multi-yawn.

  4. Yeah that whole "perfectly good" thing has been nothing but a logical headache for religion. You've got thousands of years of tradition supporting the idea of jealous, capricious gods for whom begging and supplication seem like a might good idea, and then you try to superimpose this "But actually there's only one of them, and He's a really nice guy!" thing onto it... doesn't work out so well logically.