How Not to Derive 'Is' from 'Could Be': Professor William Rowe on the Ontological Argument

How Not to Derive 'Is' from 'Could Be': Professor William Rowe on the Ontological ArgumentAuthor(s): Ralph KennedySource: Philosophical Studies: An International Journal for Philosophy in the AnalyticTradition, Vol. 55, No. 3 (Mar., 1989), pp. 293-302Published by: SpringerStable URL: http://www.jstor.org/stable/4320022 .

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RALPH KENNEDY

HOW NOT TO DERIVE 'IS' FROM 'COULD BE':

PROFESSOR WILLIAM ROWE ON THE

ONTOLOGICAL ARGUMENT

(Received in revised form 3 November, 1987)

I

Magicians are beings who can make the gods do what they want.1 They do not actually exist.

Could they actually exist? If our 'could' is meant to express a sufficiently broad sort of possibility,2 the answer would seem to be 'yes'. They don't exist in the actual world but it is possible that they should. Not everyone would agree, however. William Rowe, for instance, has claimed: "If no existing things are magicians then no possible things are magicans", a magican being something that exists in and is a magician in the actual world.3 Rowe thus appears to claim that nothing could be an actually existent magician unless something were an actually existent magician. Since nothing is an actually existent magician we must say that the concept 'magican' or 'actually existent magician' is not exemplified by any possible thing: nothing could be an actually existent magician.

This has a paradoxical sound, as Rowe admits: "We are inclined to think that only contradictory concepts like 'the round square' are not exemplified by any possible things."4 Indeed, it is not easy to think of what, other than some kind of internal incoherence, could account for a concept's not being exemplified by any possible thing. The account Rowe provides for 'magican'is:

... no possible object that doesn't exist will exemplify a concept like 'magican' in which

.existing' is included; and if there are no existing things which exemplify the other features included in the concept - for example, 'being a magician' in the case of the concept 'magican' - then no possible object that exists will exemplify the concept. Put in its simplest terms, if we ask whether any possible thing is a magican the answer will depend entirely on whether any existing thing is a magician.5

(Rowe is clearly using 'exist' and 'existing' in the sense of 'actually

Philosophical Studies 55 (1989) 293-302. C 1989 by Kluwer Academic Publishers.



294 RALPH KENNEDY

exist' and 'actually existing' here. Here would not deny, on the grounds that there are no magicians in the actual world, that 'magician who exists in beta', where beta is some nonactual world, is exemplified by some possible object.)

Rowe's remarks suggest what may be for some a rather surprising perspective on the following 'ontological argument' for the existence of magicans:

(OA) PREMISE. It is at least possible for there to be magicans.

(Alternatively: Possibly, there are actually existent magicians.)

CONCLUSION. There actually are magicans. (Alternatively: There actually are magicians.)

Since we know that the conclusion is false, we know that either the argument is invalid or the premise is false. A first look might well lead us to think, therefore, that the argument must be invalid, since the premise, asserting only the bare possibility that a certain definitely coherent concept is exemplified, seems to assert so little. But, if Rowe is right, the truth is just the other way around. The argument is valid, and (hence) the premise asserts every bit as much as the conclusion does.

Rowe notes as a corollary of his account of concepts like 'magican' that the principle

(N) for every concept F and possible world w: (a) F is satisfied in w

iff (b) if w were actual then something satisfying F would actually exist

would appear to be false.6 And it is easy to see why. If (N) were true then the premise of (OA) would be true: 'magican' would be satisfied in some possible worlds, since all worlds in which 'magician' is satisfied are such that if they were actual a magican would actually exist. If, then, Rowe is right about (OA)'s being valid, its conclusion would have to be true too: there would actually have to be magicans; magicians would actually exist. But the conclusion is not true.

Rowe calls concepts that, like 'magican', are counterexamples to (N) 'abnormal.'7



HOW NOT TO DERIVE 'IS' FROM 'COULD BE' 295

In this paper I shall take issue with Rowe's account of 'magican' and similar concepts. I shall argue that it is at least misleading to say flatly that arguments like (OA) are valid. In fact, they are ambiguous and valid only on a rather strained reading. I shall argue further that (N) is true - even truistic - on its only reasonable reading. The argument just sketched against (N) will be seen to owe its appearance of being valid to equivocation.

II

Since there are actually no magicians, and (OA) (if Rowe is right) is valid, it is imposible that there should be any magicans. But, as we have noted, there seem to be worlds such that if they were actual a magican would actually exist. The question thus arises: could any of these worlds be actual? I.e., we might say that although they are not actual it is not impossible that they should be actual. However, if we say that any of these worlds even could be actual it seems that we are saying that magicans could exist, which, translated into possible worlds talk is: magicans do exist in some possible world; or, the concept 'magican' is satisfied in some possible world. This is what Rowe does not want to say, so be will have to deny that any possible worlds in which 'magician' is exemplified even could be actual. Can this be reasonable? As Peter van Inwagen asks in a different context: ".. . what could be meant by calling a world 'possible' except that it is a world that might possibly be actual?" 8

Although this question may seem to be an embarrassing one for Rowe, it is by no means immediately decisive against him. There do seem to be reasons for saying that if a world is not actual then it could not be actual. At any rate, systems of modal logic that contain an 'actually' operator appear to be constructed along lines suggested by this thought.

For instance, John Pollock9 presents a system in which

r- a AP-

is valid, and Martin Davies10 presents a system in which one of the axiom schemata is:

AP- EAP.



296 RALPH KENNEDY

In either case, if we had as a premise that magicians didn't actually exist we could deduce that it was necessarily true that magicians didn't actually exist. Apparently, Rowe has company. But we should look a little more closely. Let P be any true sentence, e.g., 'the earth moves.' Davies notes that in virtue of the axiom just mentioned 'AP' will be necessarily true "in the sense of 'necessarily' which is expressed by ''."11 But he adds that it is natural to say: "in some sense of 'necessarily' (yet to be made precise) the sentence ... [rAP'] . .. is not necessarily true." 12 He then proceeds to define this other sense of 'necessarily'. In a somewhat similar vein, although Pollock says that

T -- o AP'

is valid, he adds that it is "counterintuitive that . . . ['Necessarily, grass is actually green'] ... should be true." 13 His solution is to say that the scope of the actuality operator is ambiguous and can "either include or be included in the scope of 'C' .. ." 14 When the operators are not subscripted the scope of the actuality operator includes that of the modal operator, and it is thus that rp - C AP' counts as valid. But the reason it does not follow from the fact that grass is green that 'Neces- sarily, grass is actually green' is true, is that the 'actually' in that sentence is most naturally interpreted as having narrow scope. I.e., instead of meaning

(3 w)(w is actual & a (grass is green at w))

the sentence means

O(]w)(w is actual & grass is green at w).'5

Finally, David Lewis also detects an ambiguity in the sorts of cases at issue. He analyzes 'actually' and its cognates as indexicals normally referring (rigidly) to the "world of utterance".16 Thus, if we say 'If Max ate less he would weigh less than he actually does' we mean that in certain worlds (the details don't matter here) in which Max eats less than he does in this very world he weighs less than he does in this very world. But a different approach is called for in 'If Max ate less he would actually enjoy himself more.' If we did not vary the approach we would have to construe this sentence somewhat as follows: certain worlds in which Max eats less than he does in this very world are worlds such that Max enjoys himself more in this very world than he does in them.




This is pretty much the opposite of what the sentence means. So in addition to the 'unshifty' sense of 'actually' in which it refers rigidly to the world of utterance, there is a 'shifty' sense in which it refers to whatever possible world is "under consideration'.17 The proper con- strual of 'If Max ate less he would actually enjoy himself more' is therefore: certain worlds in which Max eats less than he does in this very world are worlds in which he enjoys himself more than he does in this very world.

Lewis notes further that

The following is contingent: in the actual world, Caesar is murdered

and Let 'Alpha' name the actual world; Alpha might not have been actual

and Let 'Beta' name some nonactual world; Beta might have been actual

are true on a natural reading but not true if 'actual' always has its unshifty sense, whereas

There could have been objects other than those there actually are

and I could have been richer than I actually am,

though also true on a natural reading, would be false if 'actual' always had its shifty sense.18

Thus, our three philosophical logicians are in agreement about the following: there is a sense in which it is true to say 'Necessarily, the earth actually moves.' (There's a sense of that sentence in which it follows from the true sentence 'The earth actually moves.') But they would add that 'Necessarily, the earth actually moves' is ambiguous and is by no means true (or follows from 'The earth actually moves') on its most natural reading.

There is a lesson here that we can apply to Rowe's claim that (OA) is valid. The validity of (OA) comes to the same as the validity of:

(AO)

PREMISE. There are actually no magicians. CONCLUSION. Necessarily, there are actually no magicians.

Clearly, none of our three philosophical logicians would be willing to



298 RALPH KENNEDY

say flatly that (AO) is valid. They would say that whether (AO) is valid depends on how the conclusion is read; and they would say, likewise, that whether (OA) is valid depends on how the premise is read. If the 'actually' in that premise is read as having wide scope or as being unshifty, the conclusion follows; otherwise, it does not. It is thus misleading at best to say simply that (OA) is valid.

III

We noted earlier that it appeared to be a corollary of Rowe's account of concepts like 'magican' that the principle

(N) for every concept F and possible world w: (a) F is satisfied in w

iff (b) if w were actual then something satisfying F would actually exist

was false. 'Magican' appeared to be a counterexample to (N) - an 'abnormal' concept.

We have found that Rowe's claim that (OA) is valid needs qualifying. Does this mean, in view of the fact that the ostensible validity of (OA) was appealed to in the argument against (N), that 'magican' is not a counterexample to (N) after all?

The short answer is 'yes', but some argument will be necessary. We have granted that (OA) is valid on one interpretation, and it is con- ceivable that that is all that is needed to make the argument against (N) work. I shall now argue that that is not so.

My strategy will be first to set out in detail what I take to be19 the argument against (N) and then to show why, on our analysis of (OA), this argument fails. It runs as follows:

(AN) (1) Some possible world is such that if it were the actual world then

there would be magicans in the actual world - the concept 'magican' would be satisfied in the actual world. Comment: possible worlds contain magicians. If the actual

world contained magicians they would be magicans as well. So if any possible world containing magicians




were the actual world there would be magicans in it, the actual world.

(2) 'Magican' is satisfied in some possible world; i.e., it's possible that magicans exist. Comment: This appears to follow by (N) from (1). According

to (1) some world, call it 'w*', is such that if it were the actual world then 'magican' would be satisfied in the actual world. Thus, if (N) is true, 'magican' is satisfied in w*.

(3) Magicans actually exist, and hence magicians actually exist. Comment: According to (OA), if it's even possible for there to

be magicans then there actually are magicans. And of course anything that is actually a magican is actually a magician. So if (2) is true so is (3).

We know that (3) is false and that (1) is true, so if (OA) really is valid, (N) must not be true.

The first thing to note is that (AN) really can't be any good because the proposition, (N), which it purports to refute is, on its only reasonable reading, the merest truism. In arguing for this point and others to come in this section I shall rely on David Lewis's way of understanding the ambiguity of the crucial sentences. I believe my arguments could be recast without too much difficulty in Davies' or Pollock's terms.

(N) may be read either shiftily or unshiftily, but it seems that the latter alternative is not reasonable. Suppose we were to understand (N) unshiftily. The clause (b) - 'if w were actual then something satisfying F would actually exist' would come to: 'if w were identical to ? then something satisfying F would exist at ?', where '?' is a name of the actual world. It's hard to see what this could mean other than that something satisfying F does exist at (. (N) would thus say that for every concept F and world w F is satisfied in w if and only if something satisfying F does exist at ?. The concept 'unicorn' (or 'magician' for that matter) would be a counterexample. Clearly such a blatantly false versior of (N) is not what Rowe intended to refute. He says specifically that 'unicorn' is a 'normal' concept, i.e., not a counterexample to (N).20

The remaining possibility is that (N) is to be understood shiftily. Clause (b) is then to be read somewhat as follows: 'Let the possible



300 RALPH KENNEDY

world under consideration be w; then something satisfying F exists in the possible world under consideration.' This in turn would seem condensable to: (c) something satisfying F exists in w. (N) construed thus shiftily turns out to be the merest truism: for all concepts F and worlds w, F is satisfied in w if and only if something satisfying F exists in w. Something must indeed be wrong with any argument against this!

But what exactly is wrong with (AN)? First, consider whether (2) really does follow from (1) by (N). In

some sense of course it does; but (1) is ambiguous, and clearly the explicit occurrences in it of 'actual' and 'actually' must be read shiftily in order for (N), as we are understanding it, to license deriving (2).

Suppose then the explicit occurrences of 'actual' and 'actually' in (1) are read shiftily. Is (1), so read, plausible? The trouble with that question is that (1) is still ambiguous, made so by the occurrence in it of 'magican'. 'Magican', meaning 'actually existent magician', can itself be read either shiftily or unshiftily in (1) - i.e., with the 'actually' in it read either shiftily or unshiftily. If it is read unshiftily, (1) is not plausible. What made (1) plausible was that magicians exist in some possible world w*, so that if w* were actual then magicians would exist in it, the actual world. We have no reason at all to say that if w* were actual then magicians would exist in 0! But that is just what would be implied by saying that, on an unshifty reading of 'magican', 'if w* were actual then there would actually be magicans' is true. The required reading of (1) thus appears to be shifty with respect to all occurrences of 'actual', explicit and implicit.

Finally, if 'magican' in (1) is read shiftily then to avoid equivocation we must read 'magican' in (2) shiftily as well. But, as we have seen, (3) follows from (2) by (OA) only if 'magican' in (2) is read unshiftily.

There is thus no reading of (AN) such that all of the following obtain: (1) is plausible; (2) follows from (1); (3) follows from (2).21

NOTES

* I would like to thank Professor Rowe for reading an ancestor of the present paper and corresponding with me on the topic. If I have managed finally to get things right, much of the credit is his. I would like also to thank Professors Charles Chihara and Win-Chiat Lee for their helpful comments.




I My dictionary (Webster's New International Dictionary, 2nd ed., unabridged (Merriam: Springfield, Mass. 1959), entry for 'magic', p. 1469), says among other things that magic is the "art, or body of arts, which claims or is believed to be able to compel a deity or supernatural power to do or refrain from doing some act...." My peculiar definition thus simply takes these claims or beliefs quite seriously, refusing to counte- nance as a genuine magician anyone who doesn't have the powers in question. It should become clear in the text why I want a sense of 'magician' in which there aren't actually any magicians - nothing turns on whether the word is ever ordinarily used in such a sense. 2 Cf. Alvin Plantinga's: 1974, The Nature of Necessity (Oxford), pp. 1-9, on "broadly logical" senses of possibility and necessity. 3 Rowe, William: 1985, 'The Ontological Argument', in Joel Feinberg (ed.), Reason and Responsibility, 6th edition (Wadsworth), p. 15. 4 Ibid.

Ibid. 6 Rowe, William: 1986, 'Modal Versions of the Ontological Argument', in Louis P. Pojman (ed.), Philosophy of Religion: An Anthology (Wadsworth), p. 70. I have taken slight liberties with Rowe's text here. He says: ". . . a normal concept C of a being or kind of being is satisfied in a given possible world just in case, were that world actual, that being or a being of that kind would exist." He then claims that not all concepts are normal. This comes to the same as saying that there are counterexamples to (N). I Ibid. 8 van Inwagen, Peter: 1980, 'Indexicality and Actuality', The Philosophical Review LXXXIX, No. 3, p. 424. 1 Pollock, John: 1984, The Foundations of Philosophical Semantics (Princeton), pp. 86-88. 'A' is the actually operator. I' Davies, Martin: 1981, Meaning, Quantification, Necessity (London). See Chapter IX, passim. I Ibid.,p. 224. 12 Ibid., p. 224. Throughout this paper square brackets indicate insertions by the present author. 13 Pollock, op. cit., pp. 86/7. 14 Ibid., p. 88. 15 Ibid.,p.87. 16 Lewis, David: 1983, 'Anselm and Actuality', in Volume I of his Philosophical Papers (Oxford 1983). See especially Postscript B. Also cf. Lewis: 1986, The Plurality of Worlds (Oxford), pp. 94-95. 17 Lewis, 'Anselm and Actuality', Postscript B. In discussing the sentences about Max, I gloss over certain peripheral issues. For instance, Lewis would not talk about Max in other worlds but about his counterparts there; and in using the expression 'in certain worlds' I merely allude to the vexed question of which possible worlds are relevant to the truth of a counterfactual conditional. 18 Ibid. 19 Rowe nowhere sets out in detail an argument against (N): (AN) is my best guess on the basis of what he does say as to what his reasons for rejecting (N) are. See also note 21. 20 Rowe, 'Modal Versions of the Ontological Argument', p. 70. 21 A referee for this Journal has suggested an argument against (N) that may at first appear very different from (AN). The idea is that we should distinguish between being actual and being actual in W: "Any object in W is actual in W - this is just to say that were W actual that object would be actual. But an object in W is actual only if it in fact exists. Similarly, any magician in W is a magican in W - this is just to say that were W



302 RALPH KENNEDY

actual it would be a magican. But a magician in W is a magican only if it in fact exists." Thus, although 'magican' is satisfied in no possible world, we must nevertheless admit that there is a world W that contains a magican-in-W, and this in turn is just to say that there is a world W such that if it were actual something would satisfy 'magican': 'magican' is therefore a counterexample to (N). I think this argument and (AN) succumb to pretty much the same criticism. Note that the present argument relies on the equivalence of 'There is an object in W such that if W were actual that object would be a magican' and 'Some object in W is a magican-in-W.' In the former sentence 'magican' may be read either shiftily or unshiftily, and only if it is read shiftily does the equivalence hold. (This is the point of the antepenultimate paragraph of this paper.) But if 'magican' is read shiftily here we don't have a counterexample to (N), since 'Nothing is in any possible world a magican' (or "magican' is satisfied in no possible world') is true only on the unshifty reading of 'magican'.

Department of Philosophy, Wake Forest University, Winston-Salem, NC 27109, U.S.A.



How Not to Derive 'Is' from 'Could Be': Professor William Rowe on the Ontological Argument

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