Friday, August 06, 2010

Plantinga Answers Miller

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 Just for grins I sent part of Miller's argument against the modal argument to Plantinga to see what he would say. Here's the bit I sent:


Some ontological arguments have a cleverer premise to replace the old one.
Old Premise: It is possible that God exists.
New Premise: There is no contradiction in the existence of God.  In other words, God is "consistent."
The old premise logically follows from the new one.  If you're familiar with symbolic logic, I hope you already knew this.  If not, here is a simple proof.

Suppose that the old premise is false; it is not possible that God exists.  The statement "If P, then Q" is always true if P is false.  Likewise, the statement "If God exists, then Q" is always true, because God doesn't exist.  It's true even if Q is a contradictory statement (ie "God is blue and not blue").  Therefore, the new premise is false; the existence of God implies a contradiction.

If the old premise is false, then the new premise is false.  Equivalently, if the new premise is true, then the old premise is true.

But now we will run into another problem of translation.  I will distinguish between two kinds of consistency.
Self-consistency:  The object has no contradicting properties in its definition.
Logical consistency: The object implies no contradictions.
Proponents of the ontological argument often expect me to disprove the self-consistency of God.  Perhaps they expect me to argue that God's omnipotence contradicts its omniscience, or something like that.  But they fail to realize that I don't have to.  The proof requires logical consistency, not self-consistency.

Self-consistency is not sufficient to establish logical consistency.  For an object to be logically consistent, not only must its definition be properly formed, but the world must cooperate.  (More precisely, the set of "possible worlds" must cooperate.)  Suppose that the world does not cooperate, and the object does not exist.  If the object does not exist, then the existence of the object implies a contradiction.  Namely, it implies that the object both exists and does not exist.  I didn't even have to look at the definition of the object.

Of course, I don't know whether the world cooperates with the ontological proof or not.  The proponents have no idea either, but think they do.

Philosophers ought to teach themselves some mathematics. In geometry, there is a famous axiom called the Parallel postulate.  It is famous because many mathematicians thought they could prove it.  Modern mathematicians know that it is impossible to prove, because there is no contradiction in assuming it false.  Likewise, it is impossible to disprove.  The Parallel postulate is self-consistent.  The negation of the Parallel postulate is also self-consistent.  But in any given geometrical system, only one can be true.  Thus, only one can be logically consistent.


 I thought just for grins I'd put up Plantinga's answer. This he sent to me in private email and he sent permission for me to post it.




I'd say that a proposition is *logically consisstent* if it's not possible to deduce a contradiction from it in ordinary *first order) logic.  Obviously the existence of God is logically consistent.  But note everything that is logically consistent is possibles in the broadly logical sense: false arithmetical propositions for example, are logically consistent but impossible in the broadly logical sense.  The question of the ontological argument is whether the existence of God is possible in the broadly logical sense.  If it is, then it is also actual and also necessary.

As for the parallel postulate, it might very well be necessary in the broadly logical sense--which is all you can say for the other axioms on geometry.  When people say it isn't provable, they mean that it isn't deducible from the other axioms--but that (I think) is also true of each of the other axioms.

4 comments:

miller said...

Plantinga’s answer isn’t especially clear.

The first thing he obfuscates is his definition of “logically consistent”. He defined it as something from which we cannot deduce a contradiction. In my definition, I just said it’s something that does not imply contradiction, and I said nothing about whether it is deducible. Geez, now I need to distinguish between “logical consistency” as defined by me and “logical consistency” as defined by Plantinga. Why’s he got to make it more difficult than it already was?

How are false arithmetical propositions logically consistent. Aren’t they provably false?

What does it mean to be “possible in the broadly logical sense”?

And did he just say that the argument doesn’t work? Am I reading it right? This is how I’m parsing it:
God is logically consistent.
Not everything that is logically consistent is possible in the broadly logical sense.
The ontological argument requires that God be possible in the broadly logical sense.

He’s right about mathematical axioms though. The interesting thing is that instead of the parallel postulate, you can actually take a different axiom which is mutually inconsistent with the parallel postulate. Then you get a whole new kind of new geometry.

Metacrock said...

yes I would like him to say more. But I'm not sure how far to push the envelope. When he feels he's too taxed to respond any further he just doesn't answer back.

Metacrock said...

The first thing he obfuscates is his definition of “logically consistent”. He defined it as something from which we cannot deduce a contradiction. In my definition, I just said it’s something that does not imply contradiction, and I said nothing about whether it is deducible. Geez, now I need to distinguish between “logical consistency” as defined by me and “logical consistency” as defined by Plantinga. Why’s he got to make it more difficult than it already was?


gee it's really quite a struggle to decide which I think has more epistemic authority, you are he? wow how do I decide gee lets see, do you have a Ph.D.? do you teach at Notre Dame? Do you have a reputation among philosophers as one of the top men in metaphysics in this age?

It's such a hard question, who knows more, you are or he?

Metacrock said...

that was a factious answer ;-)