Tuesday, January 01, 2008

Rufus's Third Ontological Argument

In their article, "Richard Rufus's Reformulations of Anselm's Proslogion Argument" [International Philosophical Quarterly (47) 3, September 2007], Richard DeWitt and R. James Long run into something of a snag over the interpretation of the third argument given. That argument, as they translate it, is this:

Let it be posited that a does not exist and yet that it can be thought. I say the following: whatever can be thought and does not exist, if it were to exist, would not be that than which a greater cannot be thought; a can be thought, and does not exist: therefore a, if it were to exist, would nto be that than which a greater could not be thought. Therefore, if a were to exist, a would not be a--which is absurd to say.

This is a tangled sort of argument, since it makes statements about what a (where is the thing that fits the description "that than which no greater can be thought", supposing that it does not exist, would be if it were to exist. And I think it trips DeWitt and Long up a bit. They hold that the conclusion is a (purported) contradiction, "if a were to exist, a would not be a"; which, as they note, is not a contradiction at all, and merely implies that a does not exist. Moreover, Rufus says that this argument is an argument "in the fourth mood of the first figure", and they say, "we can find no reconstruction of this passage that resembles any valid syllogism, or any valid argument--syllogistic or not" (p. 336). They conclude that it is defective, and that some logical mistake has been made.

Without ruling on whether the argument is defective, I think it's fairly easy to see what Rufus has in mind when we calls the argument an argument "in the fourth mood of the first figure". The argument is clearly the following:

(1) No (T & -E) is GNC.
(2) Something, namely a, is (T & -E).
(3) Something, namely a, is not GNC.
(4) a is GNC.
(5) a is not a.
(6) a is not (T & -E).

[T = something able to be thought; E = something that exists; GNC = that with regard to which a greater is not conceivable.] (1) is a premise; (2) is the supposition for reductio. (3) follows by Ferio, which is, indeed, the fourth mood of the first figure. (4) is definitional. (5) follows from (3) and (4) by substitution of definition. (6) is the conclusion by reductio ad absurdum.

Where DeWitt and Long go wrong is in taking the intended conclusion to be "if a exists, then a is not a"; but this is, I think, to confuse Rufus's subjunctive conditional with an indicative conditional. 'a exists' is not the antecedent of an implication; it is merely a condition supposed for the sake of the argument. The interpretation of this condition is very tricky because it is nested within an opposing condition. The overall supposition of the argument is that a does not exist; it then proceeds, given this supposition, to argue what would occur on (secondary) supposition that it exists. The point of this secondary supposition, I take it, is that all that Rufus wants to argue at this point is that "if a can be thought at all, it is necessary that a exist" (which is how he introduced the previous argument); and the assumption (again, I am assuming) is that something cannot be 'thought at all' if, supposing it existed, it would be an existing contradiction. And the thrust of the argument is that either a cannot be thought at all or it exists. So the esset that keeps recurring seems to me to be a clarifying qualification rather than anything essential to the structure of the argument.

Whether or not there is a defect in the argument, I don't think the argument can be accused of formal defect. It is valid; and Rufus is right that the argument (setting aside purely definitional matters) is a Ferio syllogism used for reductio.

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