Fallible wrote:So are we waiting for Thommo to rock up, or what?

VazScep wrote:Is the property of being supreme even coherent? I'm not sure. It might be that this notion of "greater-than" in the argument gives an ordering with no maximum. Perhaps no matter how great a thing we conceive, we can always conceive of something greater, in which case, supremacy is impossible. Talking about a supreme being is like talking about the greatest natural number. It might be that "Greatest natural number" and "supreme" are both absurd properties.

IIzO wrote:Seriously wth is "perfection" ?

Thommo wrote:Wondered about this too, it does seem like an absolute bar on this argument accomplishing anything with such an important concept just left open.

The same criticism applies to a lesser extent to the other open term of "a property that it is better to have than not". In itself it seems like perfection is already defined as a subclass of truth via the axioms M1-M3,

VazScep wrote:

Thommo wrote:Wondered about this too, it does seem like an absolute bar on this argument accomplishing anything with such an important concept just left open.

I think all of these arguments revolve in some way around taking terms of art out-of-context and assuming they can be applied rigorously. I'm not going to be surprised if this process leads us to strange conclusions such as "God exists". I wouldn't be surpised if it leads us to the very strong conclusion "Contradictions are true." That's how semantic paradoxes work after all. But semantic paradoxes are fun and there's usually a lot to say about them, which is why I'm happy to give Maydole's argument the time of day.

The same criticism applies to a lesser extent to the other open term of "a property that it is better to have than not". In itself it seems like perfection is already defined as a subclass of truth via the axioms M1-M3,

It's defined as a subclass of satisfiability, as I showed above, and as Maydole formally "proves" in the appendix (*). But I think you might have some deeper insight into this. M1 and M2 are indeed fundamental properties of truth and satisfiability: preservation under entailment and refutation under negation. In terms of propositions, M1 and M2 require truth. In terms of properties, M1 and M2 require satisfiability. It might be interesting to replace M2 with the equivalent:

M1) ◻(∀x. P x → Q x) → Perfect P → Perfect Q
M2a) Perfect P → ⋄(∃x. P x)
M2b) ∃P. ¬Perfect P

In other words, we can change M2 to say: a) every perfection is possibly satisfiable; b) something is not perfect. If we run your analysis and think about truth instead, M2a says that something is true and M2b says that something is not true. In other words, we have more than one truth value.

(*) The proof is entirely trivial. At best, the symbolic proofs just obfuscate. But I think this is almost point. If you regard M1 and M2 as a substantial way towards a semantics for truth-predicates, then M3 is just the claim "there might be a supremacy". Now supremacy is a conjunction of modal denials. It asserts its own necessity, which means we can skip right from "there might be a supremacy" to "there must be a supremacy." These steps are unimpressive. In fact, the proof of necessity of a supremacy does not make use of the "greater-than" notion, only the placement of modal operators. The notion of "greater-than" is only needed to get uniqueness, and even that's just the trivial matter of realising that the maxima of any order-relation is always unique.

The problem is that we now want to charge the argument with "question-begging." But I suspect this is the charge of "triviality." Because a trivial conclusion is just an elaboration of one's premises, and you are question-begging it any other way. And Maydole's argument is trivial. Don't be fooled by the dense symbolism and large number of proof steps. That's just a problem with formal logic which makes me baffled why philosophers bother with it: it causes even very simple proofs to explode in length (technically, the proof that 1000 != 1001 requires over 1000 proof steps in formal number theory).

Unfortunately, I don't have a rigorous definition of "trivial". The phrase probably communicate nothing more than a subjective unimpressed. So I'm not sure how to argue against someone who thinks Maydole's got a good argument. I still think the premises are interesting, otherwise I wouldn't be talking about them. And again, they show that modal logic has ways to formulate ontological arguments that defeat the usual "existence isn't a predicate" objection. But like I said in the last thread, don't come here looking for a convincing argument for God.

mindyourmind wrote:Maydole, in Blackwell's Companion to Natural Theology, first disses Anselm's effort, inter alia calling one of the propositions a "...somewhat muddled argument for the bogus proposition .."

[Anselm] situated his argument in the context of the Great Chain of Being: an ancient principle for thinking about the world that ranks kinds of things according their degree of reality (roughly and readily). The idea goes back at least to Plato, and is not a theological construct of Christianity. In Book VI of The Republic Plato argues for a heirarchy of objects of knowledge, with images or reflections (known through imagination) at the bottom, followed by the everyday objects of sensory perception (known by mere opinion), then the abstract objects of geometrical and mathematical reality (known through formal reasoning) and, at the top, the perfect Forms (known, ironically, through a quasi-mystical sort of direct understanding -- albeit one that has to proceed through the formal knowledge of mathematics and science).

Even though direct knowledge of Plato's work was a bit rare in Anselm's day, this idea and its descendents were very influential. A thinker is only as good as the best reasoning principles at his disposal for the time he lives in, and for Anselm, the Great Chain was state of the art. If it seems silly to the modern eye, I suggest that a rough contemporary analogue, and one as likely to seem hilariously quaint in a few hundred years, is the currently widespread notion of a Great Chain of Disciplines -- sociology or psychology at the top, physics or math at the bottom.

Anyhow, what looks like a great hole in his argument -- indeed, what is a great hole when the argument is taken out of context -- is the assumption that the scenario described as God existing only in the mind should be understood as a degenerate case of God's really existing. That is, the argument requires that we compare two modes of God's existence and ask which would be greater -- when it seems perfectly obvious that the first scenario is not one which God exists in a diminished sort of way, but rather one on which God just plain old does not exist.

You don't get the required comparison between God, existing merely in the mind, and some actually existing old sock, for instance, because really there is no first thing to be part of that comparison. "Only the idea of Santa exists": that's not equivalent to saying that Santa exists in a diminished sort of way, namely, as an idea. It's a way of saying there is no Santa -- none at all.

Well, for Anselm, existing as an idea is precisely a degenerate form of genuine existence. That's what the Great Chain embodies: a picture of heirarchical reality on which a thing can exist merely as an object of thought, or have moreover a form and constitution independent of thought. Those are two ways for an object to exist, two distinct degrees of reality it could have, depending on where it falls on something like Plato's line.

This is an idea that has remarkably little to recommend it, all things considered. Many ideas that seem good at the time turn out to have this defect. Descartes also makes heavy and unqualified use of something like the GCB in his argument for God in the Third Meditation. But this was much later than Anselm, by which time the principle was widely doubted, or at least recognized as flawed for use in just the kind of ways Descartes wanted to use it. Which is why the Meditations came into the world with a big boot mark on its ass -- the commentaries published with the very first edition pointed out the ways in which his GCB-ish reasoning was not state of the art. But at the time he wrote, in assuming the Great Chain, Anselm was just an educated man of his time relying on a widely accepted but unreliable premise. This doesn't give us a reason to accept his argument, of course -- Gaunilo was able to put pressure on Anselm's reasoning even with a broad GCB framework -- but it does suggest that he was not a purveyor of the gross invalidities that contemporary Modal Yodelers display.

He concludes by stating the bleeding obvious himself :

"Ontological arguments are captivating. They convince some people but not others. Our purpose here was not to convince but simply to show that some ontological arguments are sound, do not beg the question, and are insulated from extant parodies."

VazScep wrote:That's as I'd hoped, and I would agree that ontological arguments are captivating and the more we can say about them the better, even if we always smell something fishy about them. But I'm not convinced he's met his stated goals. Aside from begging the question, I'm thinking it can also be parodied. Maybe Maydole addresses this, but could you not go: Define X as the apple pie which is more delicious than all other possible apple pies and such that no other possible apple pie is more delicious than it. Assume X is perfect.

mindyourmind wrote:How anyone can read this stuff and then find Jesus I don't know. I know that is not really what Nat Theology claims to want to do, but read Blackwell's and see how the magic gets done.

Thommo wrote:

VazScep wrote:That's as I'd hoped, and I would agree that ontological arguments are captivating and the more we can say about them the better, even if we always smell something fishy about them. But I'm not convinced he's met his stated goals. Aside from begging the question, I'm thinking it can also be parodied. Maybe Maydole addresses this, but could you not go: Define X as the apple pie which is more delicious than all other possible apple pies and such that no other possible apple pie is more delicious than it. Assume X is perfect.

I haven't read into any attempts at parodies or rebuttals, so I may be heading in blind here, but it certainly does indeed look like any redefinition of supremity to any purported ordering with a maximum element should do the trick.

Matt_B wrote:

mindyourmind wrote:Maydole claims that his argument should be immune against parody, but I cannot agree, mostly along the lines you have indicated as a general attack.

I'd think that its only defence against parody is how long and convoluted it is. It's much harder to be witty when you're rambling on for several pages.

Thommo wrote:In response to Vazscep above:-

I suppose that the real question is what specifically is it about the modal logic that Maydole constructs that bridges the gap between satisfiability and truth, I have to admit that the exact detail was beyond me (my best logic days are alas behind me). I wondered if it had anything to do with the Barcan formula since the various expositions of the argument always seem to make a large song and dance out of the "controversial" nature of this axiom. The cynic in me suggests that this is true showmanship and misdirection though and the magic is done elsewhere.