Thomas Metcalf

Chris McHugh has developed a sophisticated modal ontological argument that attempts to avoid classic problems with modal ontological arguments[1]. In this post, I describe the major problem I have with accepting his argument.

Here's a statement of McHugh's argument in pseudosyllogism:

McHugh defines a Godlike* being as a being that possesses all of a specified series of "negative properties," properties that can't conflict with other properties of the "same kind." One of these properties is "non-contingency."

It should be obvious that the more controversial premise is 2. While the existence of something Godlike* is certainly epistemically possible, the question before us is whether we have good reasons to believe it's logically possible. McHugh's answer in the affirmative is based on the fact that negative properties are logically guaranteed not to conflict with each other. For example, "non-red" can never conflict with "non-blue" or "non-green", and certainly not with properties of different kinds such as "non-heavy" or "non-bright." Self-contradictory beings are impossible, but this entity is guaranteed not to be self-contradictory, so it cannot be impossible. The modus ponendo tollens goes through and our conclusion is that God is logically necessary.

Perceptive readers will have noticed an important implicit premise in the above argument. McHugh notices that self-contradictory beings are impossible; true, that, but are we justified in accepting the converse? The motivation to affirm premise 2 in the above argument may derive from an instance of Affirming the Consequent. If self-contradictory, then impossible is undeniable, as is its contrapositive if not impossible, then not self-contradictory -- yet it is fallacy to conclude therefrom not self-contradictory; therefore not impossible.

Here is McHugh's argument, revised and reconstructed to take into account the missing premise(s):

1) Either the existence of something Godlike* is logically necessary or logically impossible.
2a) If something is logically impossible, then it is self-contradictory.
2b) Something Godlike* is not self-contradictory.
2c) Therefore, it is not the case that the existence of something Godlike* is logically impossible.
3) The existence of something Godlike* is logically necessary.

It is my view that we are simply not in a position to accept 2a. Certainly, in terms of our experience, impossible beings are self-contradictory, but I suspect that for all of these entities, they're not defined to be non-contingent. Notice that for all of our "impossible" entities, there is nothing de dicto in their description that reports their alethic modal status.

I think it makes sense to say that the possibility conditions for would-be-necessary beings are far different from the possibility conditions for non-would-be-necessary beings. For a non-would-be-necessary being to fail to be possible, it must fail to exist in all possible worlds. But for a would-be-necessary being to fail to be possible, it only must fail to exist in one possible world. Therefore, the way would-be-necessary beings fail to exist is far different from the way non-would-be-necessary beings fail to exist. And therefore, we aren't justified in assuming if impossible, then self-contradictory. Even if McHugh's God isn't self-contradictory, it still may fail to be possible by failing to exist in some possible world.

There are a great many impossible beings that aren't self-contradictory. For example: the non-contingent entity that makes the sky green instead of blue; the non-contingent entity that's another satellite of earth but not the moon; the non-contingent entity that's a huge redwood forest growing in Central Park in New York City. All of these entities are impossible, but not because there's something internally inconsistent about them. Rather, they're impossible because they fail to exist in at least one possible world. There are even entities that seem to exist in the actual world but are in fact impossible: the Non-Contingent Eiffel Tower and the Non-Contingent Vladimir Putin, for example. The Eiffel Tower exists in the actual world, but the Non-Contingent Eiffel Tower doesn't, because it's impossible -- because it doesn't exist in every possible world.

With these considerations, I think it's clear that to be self-contradictory isn't the only way for an entity to be impossible. In fact, there are a great many impossible non-contingent entities that seem to exist in some possible worlds. Therefore, McHugh can't rule that a Godlike* being isn't logically impossible.

[1] Theism or Atheism: McHugh vs. Krueger
[2] Ibid.

Ernest Sparks

I see a problem with your analysis of McMOA:

(start)

If one resorts to an ensemble-of-possible-worlds interpretation of it, then why should any non-self-defeating entity not have a world of its own. What's a possible-worlds-ensemble good for if you can't imagine a non-self-defeating entity and let it thrive there in some possible-worlds, its existence statement among the truths for those possible-worlds.

(end)

On the other hand, I can't see why some possible-worlds can't be constructed so as to guarantee NO effectively-unlimited objects are in them. Also, I can imagine possible-worlds with demi-godlike-beings, unlimited with regard to all non-contingent-beings in those possible-worlds, but subordinate to a superior demi-godlike-being. I'll warrant that the formal McMOA, substituting a new existence assertion for his 'q' would carry. I can even imagine a whole infinite hierarchical chain of demi-godlike-beings in some possible-worlds, with NO final full-godlike-beings in them at all. I'll bet McMOA argument with such a substitute existence assertion would carry also. Is this ontological mayhem or no?

My hangup is on the whole alethic modal machinery itself. I notice there is a whole literature of debate on modal logic enlargements of standard quantificational logic and the (sometimes) proclivity for reification of possible-beings out of thin air, when enabled beyond the Simplest Quantified Modal Logic system. My standing metaphor is the basic mathematical model of a system of statements and their component relations. The interpretation objects come from a base set and the interpretation relations (entuples) come from the natural superstructure {1} of that basic set. Interpreting statements of the form 'necessarily f(x)' or 'possibly f(x)' by escaping the model and plying the paint brush across it just seems, well, an awful long stretch of the idea of interpretation.

Did I say that I don't much like how McMOA elevates simple 'q -> Nq' to the stronger 'N(q -> Nq)'. That produces 'Nq v N-q', which is just a way of saying 'Pq -> Nq'.{2} Imagine: from harmless-looking 'q -> Nq' to the brink, 'Pq -> Nq'. The opposition is necessarily forced to work the minor premise.

But I'm just learning all this as of the McMOA posting, so I probably have a long way to go. I must thank Mr. McHugh for posing this problem. On the other hand, maybe I should be doing something else, like sleeping normally.

Thanks,
ernie

{1} s-0 := basic set of objects;
---- s-1 := *power* (s-0 *union* *power*(s-0))
---- s-2 := *power* (s-1 *union* *power*(s-1))
---- ...
---- s-i := *power* (s-i *union* *power*(s-i)) for any positive integer i
---- ...
---- superstructure := *union-indexed-by-i-over-all-positive-integers (s-i)

{2}Pq (possibly-q) := ~N~

Family Man

I don't think the first premise holds much water either. Why can't a god be logically possible, but non-existent?

Ernest Sparks

Here (,naively):

'possibly McHugh-godlike-being exists' means 'for some possible-world w, 'McHugh-godlike-being exists' is True for w.

This means 'McHugh-godlike-being properties hold in w for some x in w, which means 'some x is non-contingent' is True for w.

Falsify 'McHugh-godlike-being necessarily does not exist' using the assumption of this tack ('possibly McHugh-godlike-being exists'); then that leaves the other alternative 'necessarily McHugh-godlike-being exists' as True in w.

'necessarily McHugh-godlike-being exists' interprets as 'McHugh-godlike-being exists in every possible-world w' of the possible-worlds-ensemble. So, in particular, 'necessarily McHugh-godlike-being exists' must be True in the designated actual world'.

In short, a run-of-the-mill godlike-being might not exist, but not a McHugh-godlike-being.

HRG

I would not call this a fact, because every property can be made to "sound" negative. As soon as properties P and Q make up a complete dichotomy (e.g. transparent and absorbant, necessary and contingent), P is equivalent to non-Q and Q to non-P. And I could of course define "eulb" as "any color but blue", which makes blue into non-eulb.

IOW, I don't believe that the concept of "negative property" is well-defined; thus McHugh cannot guarantee consistency by his argument.

Regards,
HRG.

HRG

Why so timid ? I would at least index over the countable ordinals!



Regards,
HRG

Bill Snedden

Another very cogent comment, Thomas. :notworthy: Here are some thoughts, not as well organized, of my own:

I'm somewhat suspicious of an entity that can only be defined negatively; by what it's not. It seems to me that if existence is a second-order predicate, arguing that "something" exists without specifying what "it" is is not really arguing much of anything at all.

After all, if I tried to describe my wife by only telling you what she was *not* (not tall, not ugly, not blonde, not older-than-me, etc), I don't think you'd get a very good picture of my wife. If you asked me if I was married and I said, "I'm not not-married," you might even wonder if she existed at all.

I question also the property of "non-natural". This seems to beg a sort of question: do the terms "natural" and "supernatural" actually represent distinctions that exist in reality, or are they equivocations?

In addition, I wonder about the property of "non-deficiency." A determination of "deficient" would seem to imply a value judgement, which would require some sort of standard of comparison. But what standard? Especially if this entity is going to be, at some later point, set up to be the standard?

A "perfectly evil being" could fail to be non-deficient, as could a "perfectly non-functional automobile" or a "perfect psychopathic killer". Literally any entity could fail to be deficient, depending upon the definition of such an entity as definition determines the standard against which deficiency is measured. Who wants to worship a perfectly insane, perfectly evil, perfectly ignorant, god?

McHugh seems to recognize that there's a bit of a problem here, sort of involving both of these issues, when he acknowledges that his construction cannot avoid parody by the addition of "non-good" or "non-powerful" traits. He maintains that this causes no problem for the theist and seeks refuge in the "traditional" apophatic conception of god. However, such a conception is, quite literally, incoherent. How exactly is the appeal to the incoherency of an entity expected to salvage an argument for its existence?

I would also say that even this appeal to an apophatic conception should be seen as presenting some serious problems for the apologist who holds God as either being or setting a moral standard for humanity. How can an apophatic deity serve as a moral standard or be believed to communicate such to his followers if its impossible to use moral language in describing it? Doesn't it really follow that such a view should lead one to moral skepticism? After all, if "good" doesn't really encompass "true goodness", and if "true goodness" necessarilly also encompasses what we consider to be evil (as it must do if McHugh's objection is granted), then how are we to be able to truly discern good from evil?

McHugh ends this "defense" with the statement, "This negative understanding of the divine nature seems to present us with a deity that is eminently more worthy of worship than is a being the essence of which can be encapsulated in one of our empirically derived positive concepts."

D'oh!

Let me see if I understand this. An entity that may or may not correspond to what I believe is "good", may or may not be "powerful", may or may not be "knowing" and may or may not approach any conceptions I have whatever is somehow more worthy of worship than one I can conceive of positively?

Yikes!

Finally, as McHugh grants that the attempt to parody his argument by adding "non-good" and "non-powerful" succeeds, would it fare as well by adding "non-conscious" and "non-self-aware" to the list of negative properties. I can't immediately see why not, but if so, what have we got? The universe. Bing!

Regards,

Bill Snedden

Llyricist

Did I miss the proof that #1 was NOT a false dichotomy? On it's face, it sure seems like one.

Seems to me that valid dichotomies using those terms would be:

a) Something is either logically possible or logically impossible
or
b) Something is either logically necessary or logically unnecessary

For number 1 to be true it must be that logically possible = logically necessary. SINCE WHEN???

I will first admit that IF something is logically necessary then it must be logically possible but I can't see the converse as being valid at all (i.e. if something is logically possible it MUST be logically necessary.) .

Ernest Sparks

HRG,

you: Why so timid ? I would at least index over the countable ordinals!

I guess I'm just a slug (garden mollusk). The suspect the intention where this construction was lifted from wanted a guarantee that all model relations used would have finite order type.
Come to think of it, some infinite sequences might be desirable among the modeling relation-sets.

you: I don't believe that the concept of "negative property" is well-defined

I've thought some about this. Here is a quantified modal rendering of the contingency/non-contingency predicates:

c(x) {x is contingent} := ((P(Ey)x = y) ^ (P(z)~(x = z)))
{contingent: possibly something is x and possibly everything is not x}

Then, ~c(x) {x is non-contingent} = ((N(y)~(x = y)) v (N(Ez)(x = z)) is easily demonstrated.
{non-contingent: necessarily everything is not x or necessarily something is x}

Which one is really "negative"? They contain an abiding interior symmetry regarding '=' and '~'.

ernie

Thomas Metcalf

Originally posted by Ernest Sparks :

Ha. I like "McMOA." Sounds like the sort of thing I could get with fries and a coke for $4.99.

I'm perfectly happy to grant that for contingent beings. But non-contingent beings, as I described in my post, are a different matter all together. Remember, even if something like God existed in some possible world, this would be no guarantee that a Godlike* being is possible. For it to be possible, it must exist in every possible world. So even if there were a non-self-defeating entity that was Godlike* minus non-contingent in some possible world, this would be no guarantee that a Godlike* being is possible.

But its existence statement couldn't be among the truths "for" those possible worlds. Its existence statement must range over possible worlds. So we can certainly imagine a non-self-defeating entity such as a Godlike* being existing in a possible world, but that's not enough to guarantee that it's actually a possible being -- it must in fact exist in all possible worlds to be possible.

Well. I took intermediate logic autumn quarter and got a good grade in it, but my mind hasn't made the synaptic connections yet to be comfortable in conceptualizing the statements you make below. I understand all of it, carefully, except for the notion of a superstructure.