The Nachlass of A.N. Prior
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Department of Information Studies - University of Copenhagen
Department of Communication and Psychology - Aalborg University

The Ontological Argument (Fragment 2)

By Arthur N. Prior on NA/NA/1965

This text has been transcribed and edited by David Jakobsen and Peter Øhrstrøm

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The Ontological Argument (Fragment 2)by A.N. Prior {Page 4}(2) Some cogitable (or possibile) is a really existing unicorn
(3) Some unicorn really exists. Here, indeed the first premiss is logically true, so that the substantial argument is that from (2) to (3), and this too seams obviously valid. It is like (2) Some tramp is a blond sailor. (3) Some sailor is blond 3. The stock answer is that ”existence isn’t a predicate,” so that (2) and (3) aren’t properly representable as x (Tx & Fx & Rx) and x (Fx & Rx). How then, are they representable? The
standard way of representing “Tame lions exist” and “Lions exist” would be by x (Tx & Lx)(“Something is a tame lion”) and x Lx (“Something is a lion”) respectively; the existence here is not carried by a predicate but by the quantifiers. So our argument ought to be worded (2) Something is a cogitable (or possibile) and is perfect (or is a unicorn).
(3) Something is perfect (or is a unicorn). But this, being of the form (2) x (Tx & Px) (3) x Px, is still valid. However, there now seems very little reason to accept the premiss. For, real existence being carried by the quantifiers, the argument now means {Page 5} (2) Something real is a cogitable (or a possibile)
and is perfect (or is a unicorn) (3) Something-real is perfect (or is a unicorn) 
This text has been edited by David Jakobsen and Peter Øhrstrøm. The original MS is kept in the Prior collection at Bodleian Library, Oxford, Box 11. The original page numbers have been put in {...}. All underlinings in the text are Prior’s. Clearly, something is missing in the beginning of the text.
And who will grant that something real is both a cogitabile(or a possibile and perfect (or a
unicorn)? 4. To this refutation, however, it might be replied that it is “is a cogitabile” (or a possibile) rather
than “is real” that “isn’t a predicate”, and that quantifiers don’t carry existence with them as logicians say they do, or at all events they needn’t, or at all events they could be quantifiers that don’t. Why not let our quantifiers range over the whole realm of cogitabilia (or possibilia), and then
distinguish the real as that sub-class of those which possesses real existence? Bringing back R for this last, we could use x for this more liberal quantifier, and define the
original x (“Something real” as follows: D1. xFx = x (Rx & Fx), i.e. “Something-real is F” means “Something-imaginable (or Something-possible) is real and is F”, This turns the argument into the following: (1) x (Rx & Px) (2) x Fx i.e. “Something-imaginable (or something-possible) {Page 6} is real and perfect, and something-real is perfect”, or “something-imaginable (or possible) is a real dragon, Something-real is a dragon.” 5. But does this make any difference? Isn’t the premiss still as obvious false or questionable as the conclusion. “For some imaginable (or possible) x, x is a dragon and really exists” – why should anyone swallow this? Well, an argument of sorts can be put up for it. It can be imagined that there
are real dragons, or that there really are dragons, and it is possible that there should be real dragons,
or that there should really be dragons. Indeed, to imagine that there really are dragons, or that there
are real dragons, and to imagine that there are dragons, would seem to come to the same thing. And
if we imagine that there really-are dragons, doesn’t it follow that there imaginably-is a real dragon, i.e. that some imaginable-thing is a real-dragon? If we use I for “It is imaginable that”, the principle
here appealed to seems to be (A) Ix Fx x Fx and so, in particular (taking Dx & Rx for our Fx) in (A)), (B) Ix (Dx & Rx) x (Dx & Rx) Indeed, seems we have the equation x Dx = x(Dx & Rx) = x (Dx & Rx & Rx) = x(Dx & Rx) {Page 7} this gives us, with (B) (C) Ix Dx = Ix (Dx & Rx)x(Dx & Rx)
Indeed, Anselm’s original argument for “Some cogitabile is perfect” seems to have moved more or
less along these lines. But (C) with D1 immediately gives us (D) IxDx xDx, and the ontological argument is restored (for dragons as well as for God). It is clear, indeed, that we cannot escape (D) if we have both (A) and D1. Which (if not both) shall we give up? 6. Current logical taste would seem to be against D1, i.e. against treating the real as a simple sub-class of the imaginable or the possible. And maybe this prejudice is well-founded; I do not want to argue for D1. But I do want to argue against (A). It is clear that one imaginable state of affairs is that there should (really) be only one object, i.e. it is imaginable that there should (really) be an such that for any (real) , is the same object as ; or in symbols (E) Iy(y=x) But from this and (A) we could infer (F) y(y=x), i.e. there is an imaginable object with which all real objects are identical; and this surely doesn’t follow from (E). Even less does this follow: (G) y(y=x), where y is the dual of y, and means “For all imaginable ”, so that (G) means that there is an {Page 8} imaginable-object with which all imaginable-objects are identical. I say “even less” because if all imaginable-objects are identical with then all real objects are, since the real is a sub-class of the imaginable. What (E) means, but neither of the other means, is that there is an imaginable situation in which there is a real x, i.e. real in that situation, such that all the y’s that are real in that situation, are identical with x. Without the operator I, but only a quantifier binding all imaginable objects and another binding all real objects (i.e. really real ones), this proposition is inexpressible. Similarly, of course, with “possible”. It is possible that there should be only one object, Mx (x = y). But there is no possible-object (if we are going in for those things) such that either (i) every possible-object or even (ii) every real-object, is identical with that possible-object; i.e. where Fx is y(x = y), we have MxFx but not xFx. •  University of Copenhagen •  Aalborg University •