JOEL

I. F R I E D M A N

N E C E S S I T Y AND T H E O N T O L O G I C A L A R G U M E N T

INTRODUCTION

The Ontological Argument for God's existence was invented by St. Anselm ~ in the 1 lth Century and continues to find adherents even in the present day, though admittedly very few. St. Thomas Aquinas attacked this argument, claiming that it showed only that if God exists, then he necessarily exists. 2 Descartes, Spinoza, and Leibniz revived the Ontological Argument 3. According to them, God must exist, since his very essence involves existence, in the strong sense that from an adequate idea of God, his existence can be derived. More precisely, the Ontological Argument may be stated in the following distilled form (which is more or less a paraphrase of Leibniz' argument): God is, by definition, the subject of all (positive) perfections. Since existence is one of those perfections, it follows that if God can be consistently conceived at all, or if he is possible, then he must be conceived as having the perfection of existence, that is to say, he must be conceived as existing. Now God can be consistently conceived, or he is possible. Therefore, God must be conceived as existing, that is, God necessarily exists. Leibniz "perfected" the Ontological Argument by giving an additional, explicit "proof" that God is possible (though in my view, something very much like this proof is already implicit in Spinoza's Ethics, Part I, Proposition 10). 4 The British empiricists naturally rejected this heavily non-empirical Ontological Argument. Hume would have thrown it to the flames. Kant rejected it also, arguing that existence is not a predicate, or to put it more precisely, not a predicate which adds anything to the subject, s Frege and Russell both attacked the Ontological Argument, basing their attack on ideas from mathematical logic. 6 Their objections may be summarized as follows: (1) "existence" is used illegitimately as a first-order predicate; instead, it should be used as an existential quantifier, together with higher-order concepts, and (2) proper names and definite descriptions are misused. Note that (1) incorporates Kant's objection. In our sophisticated logical age, thanks in large part to Frege and Russell, the Ontological Argument appears logically frivolous, at least to many. It seems Erkenntnis 15 (1980) 301-331. 0165-0106/80/0153-0301 $3.10. Copyright 9 1980 by D. Reidel Publishing Co., Dordrecht, Holland, and Boston, U.S.A.

302

JOEL

I. F R I E D M A N

just plain wrong. Yet ironically, it can be given sophisticated formulations utilizing the tools of mathematical logic, in particular, modal logic. Thus, the Ontological Argument continues to fascinate contemporary non-believers, as well as believers, primarily because of its rich modal challenge. More recently, the Ontological Argument has been defended by Hartshorne, Malcolm, and Hubbeling. 7 Hartshorne gives an interesting modal version, utilizing Lewis' modal logic, to be dealt with below. Plantinga competently attacks Hartshorne's and Malcolm's versions, arguing persuasively that (3) modal fallacies are committed, s Plantinga also offers his own extremely rarefied and sophisticated yet formally valid reconstruction of the Ontological Argument, which he admits can only be believed to be sound. In a later article, 9 Hubbeling attempts to revise Hartshorne's argument, utilizing a modal version of Peirce's Law. However, I will show that Hubbeling's attempt comes to naught. I have myself reconstructed Spinoza's version of the Ontological Argument, utilizing primarily quantifier logic (with some modal logic and metalogic), together with various suppressed premises about possibilities. The argument as reconstructed is formally valid, but again, of questionable soundness. 1~ Thus, my reconstruction too comes to naught. Both Plantinga's reconstruction and my own are modal arguments de re. In this paper, however, I shall focus on Hartshorne's de dicto modal argument, which is formally valid in Lewis' Ss. (These distinctions will be explained in section 1). I shall then consider six senses of necessity, in particular, two senses of logical necessity, one sense of causal necessity, and three senses of metaphysical necessity. For all of these senses, I shall call into question either the truth of at least one of the premises or the truth of at least one of the axioms of modal logic itself. Finally, I shall consider Hubbeling's abortive attempt to revise Hartshorne's argument using a modal version of Peirce's law. The main conclusion to be drawn from all these considerations, including Plantinga's work as well as my own, is that it is probably impossible to formalize within a sound modal logic any traditional or semi-traditional version of the Ontological Argument in such a way that it is both formally valid yet has necessarily true, a priori known premises. I believe that any claim to the contrary is based on acute modal confusion. In another paper, however, I have argued that the mystic's Ontological Argument H (wherein God is defined as the maximally incomprehensible being, as opposed to the maximally perfect (infinite) being) fares much better, avoiding any such modal confusion, as well as the classical objections of Kant, Frege, and Russell. However, nominalists, and perhaps most mystics, will balk at the very abstract nature of such a maximally incomprehensible being.

NECESSITY 1.

AND THE ONTOLOGICAL

PRELIMINARY

CONSIDERATIONS

MODAL

SYSTEM

ARGUMENT

303

AND LEWIS'

Ss

In this section, I shall first consider various logical and modal distinctions, and then give a formulation of Lewis' Ss. As elementary as these distinctions may be, they can hardly be emphasized too much in a metaphysical paper. First, let us consider the distinction between formal validity and semantical validity. An argument is formally valid if and only if its conclusion is logically derivable from its premises, using only the inference rules and logical axioms of the system. Note that the notion of formal validity is a purely syntactical notion. On the other hand, an argument is semantically valid if and only if its conclusion is true in every model in which its premises are true. For the propositional and quantifier logics, it is well known that formal validity is provably equivalent to semantical validity. Another way of stating this is to say that the propositional and quantifier logics are consistent and complete. Moreover, though less well known, Lewis' Ss is consistent and complete, although one must assume a certain definition of "necessary truth in a model". ~2 Furthermore, Kripke has shown the consistency and completeness of quantified modal logic, again assuming a special definition of "necessary truth in a model". *a It should be emphasized that for modal logic, a different interpretation of the necessity operator may very well undo completeness, with some of the modal axioms turning out to be false as well. Secondly, let us consider the distinction between validity and soundness. An argument is sound if and only if it is not only valid but also all its premises are true. Thus, an argument might very well be valid, either formally or semanticaUy, but not be sound. Also, an argument might be sound but not necessarily sound or not known to be sound. Furthermore, an argument might be proved valid and yet not proved sound, even though it is sound. All these points will be of great relevance when we consider the Ontological Argument. Finally, a crucial distinction in modal logic is that between de dicto and de re necessity. De ditto necessity, as its Latin meaning indicates, applies to statements, whereas de re necessity applies to things. Thus, those versions of the Ontological Argument which attempt to prove the de d i t t o necessity of God have as their conclusion: "it is necessary that God exists", whereas those versions which attempt to prove the de re necessity of God have as their conclusion: "God exists as a necessary being". One can hardly emphasize enough that the logical structure of the two kinds of ontological arguments are radically different. Also, it should be noted that de re necessity (at least for definable things) is ultimately definable in terms o f de dicto necessity, as follows:

304 Def

JOEL

I. F R I E D M A N

x is (de re)-necessary if and only if there is a one-place formula S satisfied uniquely by x such that the existential quantification of S is (de dicto)-necessary, that is to say, ((3y)S(.v)) is necessarily true.

Here we see that de re necessity is defined in terms of metalogical notions as well. 14 The above definition seems to indicate that the notion of de dicto necessity is the more fundamental notion. However, suppose de dicto necessity could be defmed in terms of de re necessity. In that case, it would seem that neither notion of necessity would be more fundamental than the other, since then they would be mutually interdef'mable. In my opinion, however, de dicto necessity is not definable in terms of de re necessity. One reason is that de dicto necessity can be applied to statements of any form whatever, whereas de re necessity can only be applied to things, as a predicate. Yet, even if de dicto necessity were definable in terms of de re necessity, the former is still the clearer notion. Ever since Leibniz, we have a much better understanding of de dicto necessity (truth in every possible world, or alter~aatively, derivability from "identicals", (though the two explications may not be equivalent, as Kripke has argued against Leibniz)). Granted that philosophers may dispute over the details, still, de dicto necessity can, at least in certain contexts, be precisely defined within mathematical logic. (For example, the truth-functional necessities are just the tautologies, and the quantifier necessities are just the logical truths, that is, the statements which are true in every model). On the other hand, de re necessity is relatively unclear, unless defined as above. Indeed, some philosophers, notably Hume, have argued that it is a meaningless notion. Given these considerations, I think it is a philosophical gain to define de re necessity in terms ofdedicto necessity, but a philosophical loss the other way. Lewis' Modal System Ss

I now give a simple formulation of Lewis' Ss mentioning a few theorems for illustrative purposes as well. Ss is not only consistent and complete, but also decidable, that is to say, there is (in principle) a computer program which, for any statement of Ss as input, will output yes or no, depending on whether the statement is a theorem or not. Given these considerations, Ss is a useful system to work in, on, and about.

NECESSITY AND THE O N T O L O G I C A L A R G U M E N T

305

I. Primitive symbols o f Ss - N (the necessity operator, flanked by sentences or formulas, not names of such); F, G J t (sentence constants); p~?r (propositional variables); 3, ~, &, v, -= (propositional connectives).

II. Formation Rules o f Ss - The modal-free well-formed formulas (wffs) of propositional logic are the atomic wffs of Ss. If S is a wff, then (NS) is also a wff. If S and T are wff, then (S ~ T), (~S), (S & T), (S V T), and (S -- 7") are all wff. III. Rules o f Inference o f Ss - MP (modus ponens). No special modal rule of inference is required. MP is the only propositional rule required, given the quantity of axioms of Ss, as formulated next. IV. Axioms o f Ss NS, if S is a tautology of propositional logic. Al N(S ~ 7") ~ (NS ~ NT) (modal distribution) A2 NS ~ S (necessity implies truth) A3 -NS ~ N - NS (necessity of non-necessity) Aa NA2, NAs, NA4 (necessity of axioms) As Note that axioms A1 -As are all axiom schemata, with infinitely many instances of each. That is why no substitution rule of inference is required. Moreover, because of AI ,As, and MP it follows that every tautology of propositional logic is a theorem of Ss. Note that a tautology is defined as a formalized statement which is true in every row of its truth table. It is also convenient to add the following: V. Definitions o f Ss DI PS -- ~ N - S ("P" for "it is possible that") D2 (S ~ T) -~ N(S ~ T) (" -~" for "strictly implies") Da CS =- ( - N S & ~ N - S ) ("C" for "it is contingent that") Given DI, which implies that if a statement is possible then its negation is not necessary, it is a theorem of Ss that if a statement is necessary, then its negation is not possible. Also, if a statement is true, then it is possible. Moreover, in Ss it can be shown that if a statement is necessary,then it is necessary that it is necessary. Furthermore, if a statement is possible (or impossible), then it is necessary that it is possible (or impossible). Again, if a statement is contingent, then it is necessary that it is contingent. Consequently, in Ss the modal

306

J O E L I. F R I E D M A N

status of any statement is itself necessary. Moreover, the rule O-S/.'. bNS) can be derived. Given these preliminary considerations, especially with regard to Ss, we are now ready to deal with the Ontological Argument, de dicta. 3.

HARTSHORNE'S

MODAL RECONSTRUCTION

ONTOLOGICAL

OF THE

ARGUMENT

In his book, The Logic o f Perfectian (page 51), Hartshorne gives a de dicta modal reconstruction of the Ontological Argument. He shows, in effect, that the de dicta necessity of God's existence can be logically derived in Lewis' Ss from two premises, both of which he regards as necessary or intuitively given. Premise 1 : it is possible that God exists (or as Hartshome comments, "Perfection is not impossible"). Premise 2: it is necessary that if God exists, then he necessarily exists (or as Hartshorne comments," 'Anselm's Principle': perfection could not exist contingently"). Hartshome's reconstruction of the Ontological Argument may thus be formulated as follows: is 0,4

1. PG 2. N(G ~ NG)[.'.(G & NG) (where "G" means "God exists")

Hartshorne's modal derivation, then, amounts to a derivation of the conclusion of OA from premises I and 2 of OA, using modal axioms and assumptions which can all be subsumed under Lewis' Ss. Hartshorne, however, does not explicitly work in Ss. (Note that Charles Jarrett, in his paper, "Spinoza's Ontological Argument", reconstructs Hartshorne's argument in Ss). Now consider the following variation of Hartshome's modal derivation. Here Lewis' Ss is used explicitly. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

PG N(G ~ NG) N((G ~ NG) ~ (~NG ~ ~G)) N(G ~ NG) ~ N ( ~ N G ~ ~G) N ( ~ N G ~ ~ V) N~NG ~ N~ G ~NG ~ N ~ N G ~NG z N ~ G ~ N - G ~ NG PG ~ N G

(premise) (premise) (A,) (3, A2, MP) (2,4, MP) (5,A2 ,MP) (A4) (7,6,PL) ("PL" means "propositional logic") (8,PL) (9, D l )

NECESSITY AND THE ONTOLOGICAL ARGUMENT

11.

NG

(I,IO,MP)

12.

NG 3 G G&NG

(A3) (11,12,PL) Q.E.D.

13.

307

Thus we see that OA, as a formal argument, is formally valid in Lewis' Ss. This is quite uncontroversial and is simply a result of formal logic. What is controversial, however, is the soundness of OA. As regards Premise 1, perhaps metaphysical perfection, or maximality, is impossible. Recall Russell's profound discovery that there must be different logical types and that not all existence can be comprehended in a single logical type. Now, if metaphysical perfection must comprehend all existence, then this seems to violate Russell's discovery. Thus we see a real difficulty in establishing Premise 1. One way out of this difficulty may be to regard metaphysical perfection as comprehending only all concrete existence, and not all the abstract logical types. In any case, the problem is not easily resolved, given Russell's discovery. As regards Premise 2, perhaps metaphysical perfection could exist de dicto contingently. I will grant that if God exists, then he exists at all times and is not caused by anything else. Thus, if God exists, he exists with de re causal necessity. However, I have real doubts whether he exists with de dicto logical necessity, or metaphysical necessity, or even with de dicto causal necessity. Surely one should distinguish the following two statements: (a) (b)

If God exists, then it is necessary that God exists, and If God exists, then God exists as a necessary being.

It seems to me that (a) is false under de dicto logical necessity, whereas (b) is true under de re causal necessity. Thus, (a) and (b) should not be confused with each other. In the next section, the various senses of necessity will be examined more systematically. For each sense of necessity, the two main tasks will be first, to determine whether Lewis' Ss (or an appropriate Finite fragment) is sound, and secondly, to determine whether in that sense of necessity (or possibility) God is necessary (or possible). In my view, neither Hartshome nor Malcolm nor Hubbeling have been sufficiently sensitive to the various senses of necessity. Thus, they modally blunder their way to God. The same may be said of Descartes, Spinoza, and Leibniz, but with this excuse: they were writing at a time before the invention of Ss and the sophisticated methods of mathematical logic.

308

J O E L I. F R I E D M A N

4. S Y S T E M A T I C

CRITICISM OF HARTSHORNE'S

MODAL RECONSTRUCTION

In this section, I shall consider six senses of de dicto necessity, and for each sense, examine Lewis' Ss as well as the premises of OA. The six senses of necessity are as follows: logical necessity in two senses: Carnapian sense and Kripkean sense causal necessity in one sense: derivability from empirical taws metaphysical necessity in three senses: derivability from metaphysical starting points (in three senses) Let us now consider each of these senses in turn.

A. logical necessity in the Carnapian sense Oef

S is logically necessary iff S is analytic (or L-true).

Oef

S is analytic iff S is logically derivable from the definitions and meaning postulates of the system.

Alternate Def S is analytic iff S is true in every model (or state description) in which the definitions and meaning postulates hold. (Note that the two definitions of analyticity are equivalent for first-order languages and first-order derivability) 16 Now consider the axioms of Ss, in the Carnapian sense of logical necessity. A~ A2

A3 A4 As

If S is a tautology, then S is analytic. If (S ~ T) is analytic and S is analytic, then T is analytic. If S is analytic, then S is true. If S is not analytic, then (S is not analytic) is analytic (in a higherorder sense). (A2-A4) are again analytic (in a higher-order sense).

It should be clear that A~-A3 hold under the two Carnapian definitions of analyticity (or Quine's definition for that matter). However, A4 and As present a special problem, because a higher-order sense of analyticity must be used. What is required is a recursively defined notion of nth-order analyticity, using an nth level metalanguage. Furthermore, the modal derivation of OA given in Section 3 of this paper has only a finite number of layers of " N " . Thus, only a finitely leveled fragment S~ of Lewis' Ss is required for the derivation of OA. S~ can then be interpreted, in a Carnapian sense, using the no-

NECESSITY AND THE ONTOLOGICAL

ARGUMENT

309

tion of nth-order analyticity. It is not at all clear that Ss itself can be strictly so interpreted. Thus, strictly speaking, I am interpreting only a Finitely leveled fragment of Ss sufficient for the derivation of OA. ~7 Given these considerations, A4 and As, as well as A~-Aa, hold for all their instances in S~, given the recursive Camapian interpretation of logical necessity indicated above. Now let us consider the premises of OA, interpreted in this Camapian sense. P~ P2

The negation of G is not analytic (in a first-order sense). " I f G is true, then G is analytic" is analytic (in a second-order sense).

Given the above considerations regarding Russell's discovery of logical types, I maintain the following: if P~ is true, then God cannot comprehend all the logical types nor incorporate them into his being; moreover, if God does not comprehend or incorporate all the logical types, and furthermore, if he is, in essence, concrete or at least has some concrete aspect, then P~ is plausibly true. Let us consider this in more detail. Suppose God does comprehend or incorporate all the logical types. Then God is an arbitrarily abstract being, even if he has some concrete aspect. In such a case, God would be of the highest logical type. However, as Russell showed in his famous paradox, there cannot be a highest logical type. This is logically impossible. It is no use to ask whether God transcends all the logical types. That too is logically impossible, since everything is of some logical type or other. Also, it is impossible for God to k n o w all the logical types, at least not discursively, since then God would have in his mind a single language describing all the logical types. However, this too is impossible, as Russell showed. Note Tarski's analogous result that there cannot be a single metalanguage for all languages. God, therefore, cannot have such an ultimate language in his mind. Therefore, if God does so comprehend or incorporate all the logical types, then the negation of G is analytic, and PI is false. On the other hand, suppose God is not arbitrarily abstract, that is, does not comprehend or incorporate all the logical types, and suppose further that God is in essence concrete or has some concrete aspect. That is to say, it follows from his essence (or definition) that he has this concreteness. Then, in my view, it is far-fetched to regard atheism about such a concrete God as analytically true, since concrete existence, if embedded in a consistent abstract structure, cannot be disproved from definitions and meaning postulates alone. Consequently, P~ is plausibly true under these conditions. From the above considerations, we may conclude that if God, in essence,

310

JOEL

I. F R I E D M A N

has any concreteness, then PI is plausibly true if and only if God is not arbitrarily abstract, that is, does not comprehend or incorporate all the logical types. Now let us consider P2. It seems to me that if God, in essence, has any concreteness, then P2 is plausibly false, for the reason (similar to that given above) that concrete existence cannot be logically derived from definitions and meaning postulates alone. Indeed, how could such concrete theism, any more than its negation, be analytically true? Concreteness is contingent. What def'mitions and meaning postulates could yield even a partially concrete God? In my view, it cannot be derived from mere definitions and meaning postulates that something concrete rather than nothing concrete exists. However, if this be challenged (as Hartshorne did challenge it in a letter to me), then I reply that it cannot be derived from mere definitions and meaning postulates that more than 10,000 meager concrete things exist (or more than two meager concrete things, for that matter, say two quarks). For, there might have been only 10,000 meager concrete things in existence (or perhaps only two). Yet, if God has any concreteness, then surely 10,000 meager concrete things are not anough concrete material for him. Therefore, such a concrete God could not be derived from definitions and meaning postulates alone. I will leave this for Professor Hartshorne and others to ponder. In any case, for all we know, there might have been nothing concrete in existence. Note that (3x)(x = x) is a theorem of standard quantifier logic with identity, but that (3x)(x is concrete & x = x) is not such a theorem. In first-order logic, the variable "x" ranges over first-order individuals, but such individuals don't have to be concrete objects, either physical or mental. First-order individuals may be abstract, for example, abstract sets. Thus, one should not identify first-order individuals with concrete individuals. With this in mind, it is more understandable that (3x)(x = x) is a theorem of logic, but not (3x)(x is concrete &x =x). Moreover, I don't see how the addition of mere definitions and meaning postulates could help. On the other hand, if God, in essence, had no concreteness; in other words, if God, in essence, were purely abstract, and moreover was not arbitrarily abstract (that is, did not include all the logical types); then P2 would be plausibly true, and so would PI- However, such an Abstract God has only some analogy with the God of Western (and even Eastern) tradition. This purely abstract, wholly non-concrete, mystical God would constitute a "change of subject" for most philosophers (including Hartshorne), whether in the mainstream or not. (See my paper, "The Mystic's Ontological Argument"). It should be emphasized here that my distinction between abstract and

NECESSITY AND THE ONTOLOGICAL

ARGUMENT

311

concrete aspects of God is radically different from Hartshome's distinction9 In the Logic o/Perfection (see Chapter 2, Section 8, page 63), Hartshorne distinguishes logical levels of God's existence and argues that on the abstract level of perfection, God's existence is necessary, but on the concrete level of exemplification, God's existence is contingent. Thus, for Hartshome, God has an abstract as well as a concrete aspect. God as abstract being is necessary whereas God as concrete being is not. Still, God must necessarily have some concrete aspect or exemplification, according to Hartshome, even though the particular concreteness he has is contingent. This is very important. To reiterate: it follows from the essence (or def'mition) of Hartshome's God that there exists some concrete aspect or exemplification of God, even though the particular concreteness he has does not follow from his essence. Admittedly, this is a non-traditional view. In any case, Hartshorne's abstract-concrete distinction is different from my own. His comes closer to the distinction between bare existence and full existence (for actual beings). Also, it seems to me that Hartshome's God, even though he has an abstract aspect, does not comprehend or incorporate all the logical types (in Russell's sense). Thus, from the above considerations, P2 is plausibly false for Hartshome's semi-traditional God. For, since it cannot be logically derived from definitions and meaning postulates alone that there exists any concrete existence whatever, it follows that Hartshome's God cannot be logically derived in this way, even if he exists. 9 Given the above considerations, the main conclusion is that if God, in essence, has any concreteness, then in the Carnapian sense of logical necessity, (P~ & P2) is plausibly false, or at least cannot be known to be true. To reiterate the argument: such a concrete God is either arbitrarily abstract or he is not. If he is arbitrarily abstract, then P~ is false, though P2 is vacuously true. And if he is not arbitrarily abstract, then P2 is plausibly false, or cannot be known to be true, though P~ is plausibly true. In either case, (P~ & P2) is plausibly false, or cannot be known to be true. Therefore, we may conclude that OA is not known to be sound, given the Carnapian sense of logical necessity.

B. logical necessity in the Kripkean sense De/"

S is logically necessary iff S is true in every possible world.

Here the notion of possible world is not in any way to be identified with the notion of model or state description. Indeed, there are good grounds for regarding Carnapian logical necessity as non-equivalent to Kripkean logical necessity (which might not be possible if the above identification were made). Kripke has emphasized the great difference between these two notions. ~a

312

J O E L I. F R I E D M A N

Now let us consider the axioms of Lewis' Ss in the sense of Kripkean logical necessity. Al A2 A3

A4 As

If S is a tautology, then S is true in every possible world. If (S ~ 7) is true in every possible world and S is true in every possible world, then T is true in every possible world. If S is true in every possible world, then S is true. If S is not true in every possible world, then (S is not true in every possible world) is true in every possible world. (A2-A4) is true in every possible world.

It should again be clear that A~ -Aa hold under the Kripkean notion of logical necessity. Moreover, I think Kripke would regard the complex predicate, "true in every possible world" as a strongly rigid designator, that is, as a designator which names the same property in every possible world. 19 Given this consideration, it follows that A4 holds. Furthermore, similar considerations show that As also holds. Note that with this notion of necessity, it is not necessary to introduce any finite fragment of Ss. Thus, all the axioms of Ss hold in the sense of Kripkean logical necessity. Next consider the premises of OA, interpreted in this sense. PI P2

G is true in some possible world. " I f G is true, then G is true in every possible world" is true in every possible world.

It should first be noted that G contains only the individual constant "God", which may be regarded as a rigid designator, according to Kripke. 2~ However, there is no reason to think that " G o d " is a strongly rigid designator, unless one builds necessity into the very definition of God, a move I regard as bordering on the philosophically frivolous. Thus, we should distinguish rigid from strongly rigid designators as follows: a rigid designator names the same thing in every possible world in which that thing exists, whereas a strongly rigid designator names the same thing in every possible world. That is to say, a strongly rigid designator is a rigid designator which also names in every possible world. It seems to me that the term "God" is not a strongly rigid designator, even if it is a rigid designator. It is indeed highly questionable, given Kripke's notion of possible world, that if God exists, he exists in every possible world. Let us examine this more carefully. Unless God is intrinsically woven into the very notion of possible world (as for example with Leibniz), I don't see how any concrete God, either in the traditional sense or in Hartshome's semitraditional sense, can exist in every possible world. If God is so woven, then

NECESSITY AND THE ONTOLOGICAL

ARGUMENT

313

PI can be immediately challenged. However, as opposed to Leibniz and others, a possible world, in Kripke's sense, is not ontologically dependent on God's mind. A possible world is a metaphysical entity (or perhaps a metaphorical entity) rather than a theological or logical entity, though it is not like an isolated foreign planet, a disanalogy Kripke is fond of making. Now I can conceive a world without a concrete God, since I can conceive a world without any concrete existence at all, or at least a world with only two meager concrete things (or perhaps 10,000). Therefore, there is a possible world without such a God. Perhaps nominalists would reject such possible worlds as too abstract. Indeed, I am not sure what Kripke's views are regarding the ontological status of possible worlds. In any case, as I interpret his notion of possible world, God does not have to exist in every possible world, even if he exists in this world (given of course that God is not defined as the perfect necessary being). It follows from this that there are no metaphysical principles which logically imply God's existence and which are true in every possible world. This by no means excludes some metaphysical principles from being true in every possible world. As an example, consider metaphysical definitions or metaphysical meaning postulates. I regard these as true in every possible world (see below), yet by previous considerations of Carnapian necessity, they do not logically imply God's existence. On Kripke's notion of possible world, logical and ma.themathical principles, as well as certain metaphysical principles, are true in every possible world, but not metaphysical principles in general. Consider, for example, the metaphysical principle that the ultimate laws of nature are simple. Surely this is false in some possible world, though hopefully not in our world. Given the above considerations, the main conclusion to draw is that P2 is false or at least not known to be true, though PI is true, provided that God, in essence, has some concreteness and also is not arbitrarily abstract, in the previously considered sense. If God is arbitrarily abstract, then PI is false and P2 is vacuously true, as before. In any case, given the traditional or semi-traditional concrete God, (P~ & P2) is false, or at least not known to be true, in the Kripkean sense of logical necessity. Digression: consider the statement, "God is omniscient". This statement is true in every possible world in which "God" names God (given the concrete notion of God). Thus, "God is omniscient" is Kripkean necessary, according to the Kripkean definition of bare necessity. 2~ However, it does not follow that "God is omniscient" is true in every possible world, since "God" might not name God in some possible worlds, by above considerations. Therefore,

314

JOEL

I. F R I E D M A N

"God is omniscient" is not Kripkean logically necessary. Here we see an example of the f'me distinction between Kripkean bare necessity and Kripkean logical necessity. As regards G, it is a more controversial matter whether G is bare Kripkean necessary. One may argue that existence statements should be treated no differently than ordinary subject-predicate statements, in applying bare Kripkean necessity. Thus, on this view, G is bare Kripkean necessary. To see this more deafly, note that G is logically equivalent (in free logic) to "(3x)(x = God)"; moreover, there is something identical with God, in every possible world in which "God" names God. Therefore, "(~tx)(x = God)", and hence G, has bare Kripkean necessity. I am not arguing that we should interpret bare Kripkean necessity in the above manner. However, if we do, then (P~ & P2) becomes plausibly true. For, God exists in some possible world (provided God is not arbitrarily abstract). Moreover, if God exists, then he exists in every possible world in which the term "God" names God. Furthermore, this statement itself is plausibly true in every possible world. Hence, under this interpretation of bare Kripkean necessity, (P~ & P2) is plausibly true and may be regarded as known a priori. However, something else is now wrong, namely, both A2 and A3 of Lewis' Ss become questionable. Consider A3 first. Just because a given statement is true in every possible world in which its terms name their intended denotations, it doesn't follow that its terms name in our world and that the statement is true in our world, that is, true. However, suppose we require rigid designators to name in our world. Then A3 would no longer be questionable. Still, A2 would remain questionable. Let us consider A2 in more detail, under the assumption that rigid designators name in our world. If (S ~ 7") is true in every possible world in which its terms name what they name in our world, and if S is true in every possible world in which its terms name what they name in our world, it doesn't follow that T is true in every possible world in which its terms name what they name in our world. To see this more clearly, suppose S has a proper name which T does not have, so that the terms of S name in fewer possible worlds than the terms of T. Then it might well turn out that (S D T) and S are true in these fewer possible worlds, yet that T is false in a different possible world in which its terms name what they name in our world, but in which not all the terms of S so name. For concreteness, consider the following example: let S be the statement, "Albert Einstein is a male human", and let T be the statement: "there is a

NECESSITY

AND THE ONTOLOGICAL

ARGUMENT

315

male human". Clearly, S and (S ~ T) are true in every possible world in which their terms name what they name in our world. For, being male (at least at birth) and being human are natural kinds which are part of Einstein's essence, at least on Kripke's view. Moreover, (S ~ 7') is an instance of existential generalization, provided "Einstein" names Einstein. On the other hand, T is not true in every possible world in which its terms name what they name in our world, since "male" and "human" are logically separable. To see this, let W be a world in which there are non-human males and non-male humans, but no male humans. This is clearly possible. Now in such a world, the natural-kind terms of Tname what they name in our world, yet Tis false in W. Thus, we have a counterexample. However, if this counterexample be doubted, consider the general form which any counterexample of this kind must take in order to falsify Modal Distribution under bare Kripkean necessity9 Find an individual e belonging to two distinct natural kinds M and H, which are part of the essence of e, and which are logically separable, that is, there is at least one possible world in which something has M but not H, and something else has H but not M, but nothing has both M and H. Also, it is presupposed that "M" and " H " are rigid designators. 9No doubt, this difficult case deserves more consideration, but I shall not pursue it further in this paper. I leave it to the reader to find a more satisfactory counterexample, using the above form. Also, the reader may well wonder how much of a notion of necessity is bare Kripkean necessity, if it violates Modal Distribution, especially since all the other notions of necessity considered in this paper do satisfy Modal Distribution9 Given the above considerations, and given that we accept some counterexample to A2, we may conclude that (P~ & P2) is plausibly true, indeed, known a priori to be true, in the sense of bare Kripkean necessity (as interpreted above), but that Lewis' Ss, especially A2, is not plausibly true or known a priori to be true, in this Kripkean sense9

C. causal necessity Def

S is causally necessary if and only if there are initial empirical conditions C such that S is derivable (in the broad sense of allowing def'mitions and meaning postulates) from (Lo & C), where Lo represents the empirical laws of nature, whatever they are.

316

JOEL

I. F R I E D M A N

First, it should be noted that this notion of causal necessity is certainly not the intended one in Hartshorne's modal reconstruction of the Ontological Argument. However, I include it for the sake of completeness, as well as for its own interest. It is intrinsically interesting whether the axioms of Ss (or a finite fragment thereof), as well as the premises of OA, are known a posteriori in the sense of causal necessity. Perhaps a new Cosmological Argument is forthcoming. Moreover, consideration of causal necessity will be useful for subsequent consideration of metaphysical necessity. Secondly, it should be emphasized that empirical laws of nature, by their very nature, are testable by the methods of science. That is their distinguishing characteristic. On the other hand, metaphysical principles are not so testable, though they may be more closely related to testability than many philosophers think. (Obviously, I am presupposing that Lo is non-empty). The question whether testability should be negatively def'med in terms of Popperian falsifiability or positively defined in terms of Carnapian confirmability, or else def'med in some other way, is a question beyond the scope of this paper. Let us now consider the axioms of Ss (or a finite fragment thereof) in the sense of causal necessity. A] A2

Aa A4

As

If S is a tautology, then S is derivable from (Lo & C), for some initial conditions C. If (S ~ 7) is derivable from (Lo & C1 ), and S is derivable from (Lo & C2), then T is derivable from (Lo & C), for some initial conditions C, namely, for C = (C1 & (72). If S is derivable from (Lo & C), then S is true. If S is not derivable from (Lo & C), for any initial conditions C, then (S is not derivable from (Lo & C), for any such C) is derivable from (Lo & C), for some initial conditions C. (A2-A4) is derivable from (Lo & C), for some such C.

It should be clear that A~ and A2 are true, given this notion of causal necessity. For, even if Lo is empty, there are empirical initial conditions. As regards Aa, consider that Lo is true because truth is part of the very notion of empirical law of nature, at least as I am using it. Also, C is true because truth is part of the notion of initial condition, as I am using it. Thus, (Lo & C) is true, and hence Aa holds, by the truth-preserving property of derivability. It should be noted here that the notion of truth I am using is the informal counterpart to Tarski's formal semantical notion of truth. This informal notion of truth

NECESSITY

AND THE ONTOLOGICAL

ARGUMENT

317

may be regarded as implying a minimal correspondence theory. The main point is that it is a semantical notion, not a syntactical notion. As regards A4 and As, similar considerations as for Carnapian logical necessity are required here. (S is causally necessary) needs to be interpreted recursively, to take account of the various layers of the causal necessity operator. Then, as before, a finite fragment S~, as well as OA, can be recursively interpreted, in this sense of causal necessity. Given these qualifications, A4 and As, as well as A~-A3, plausibly hold for all their instances in S~. However, this may require that L0 and C have various meta-levels capable of expressing meta-laws (such as Einstein's Principle of Relativity) and recta-conditions (such as experimental conditions involved in sociological experiments about experiments), respectively - a plausible assumption, in my view. Furthermore, Lo may be infinite (though C is assumed finite), but it is presupposed that Lo can be recursively enumerated, another plausible assumption, in my view. Consider the premises of OA, interpreted in the sense of causal necessity defined above, with the appropriate qualifications. PI P2

The negation of G is not derivable from (Lo & C), for any initial conditions C. " I f G is true, then G is derivable from (Lo & C), for some such C" is derivable from (Lo & C), for some such C.

Now P~ seems plausibly true, since atheism does not seem to be a scientific thesis, though one can never be sure in the long run. Our knowledge of this depends on the future development of science. For all we know, the term "God" may someday become a theoretical term of science, and the negation of G may be derived from (Lo & C), however implausible this may seem now. As regards P2, this seems highly questionable. Given that G is true, is it a scientific truth? Can G be derived from Lo, together with initial conditions C?. Again, this depends on the empirical laws of nature. As mentioned above, the term "God" may someday become a theoretical term of science, and G, rather than the negation of G, may be derived from (Lo & C). But how probable is this? 1 would say about as probable as for atheism. Still, P2, though highly questionable, is an attractive doctrine about the "naturalness" of God, a view akin to Spinoza's. Perhaps scientists should keep their minds open to it, however improbable it may seem at present. In any case, P2 is surely not known to be true, either a priori or a posteriori. Therefore, a fortiori, (P~ & P2) is not known either, and we see how questionable is the empirical soundness of OA in the sense of causal necessity.

318

J O E L 1. F R I E D M A N

D. metaphysical necessity (in three senses) Def I

Def2

Def 3

S is metaphysically necessary (in sense 1) iffS is logically necessary (in either the Carnapian or Kripkean sense), and moreover, S contains at least one metaphysical term essentially. S is metaphysically necessary (in sense 2) iffS is logically derivable from at least one true metaphysical axiom (together with definitions and meanings postulates). S is metaphysically necessary (in sense 3) iffS is logically derivable (using definitions and meaning postulates) from the Principle of Sufficient Reason (PSR), together with a certain maximality axiom Mo, to be discussed below.

Note that some other hallowed metaphysical principles might have been chosen instead of PSR and 34o. In any case, these definitions are motivated in part by Leibniz' notion of metaphysical necessity. Also, Definitions 2 and 3 could have been given a Kripkean version, in addition to their Carnapian version, but I chose just one version for simplicity's sake. Let us consider each sense of methaphysical necessity, in turn, and the axiom of Ss, as well as the premises of OA, in that sense.

(1) metaphysical necessity in sense 1 Def Def

Def

ml

A2

S is a primitive-term statement iff S contains only primitive terms, as opposed to defined terms. Let S be a primitive-term statement. Then S contains a metaphysical term t essentially iff S is not intensionally equivalent to any primitive-termstatement not containing t. (Admittedly, the notion of a metaphysical term is not all that clear). Let S be a non-primitive-term statement. Then S contains a metaphysical term t essentially iff S is not intensionally equivalent to any primitive-term statement not containing t or not containing the primitive definiens of t, in case t is non-primitive, where those definientia contain at least one metaphysical term essentially (previous definition). If S is a tautology, then S is logically necessary and contains at least one metaphysical term essentially, say m. If (S ~ T) is logically necessary and contains m I essentially, and S is logically necessary and contains m2 essentially, then T is logically necessary and contains some m essentially.

NECESSITY AND THE ONTOLOGICAL

A3 A4

As

ARGUMENT

319

If S is logically necessary and contains m essentially, then S is true. If S is not logically necessary or does not contain any m essentially, then (S is not logically necessary or does not contain any m essentially) is logically necessary and does contain some m essentially. (A2-A4) is logically necessary and contains some m essentially.

Clearly, A~ and A2 are both false unless we restrict S and T to statements which contain metaphysical terms essentially. So let us do that. Under such a restriction, AI-Aa clearly hold. Moreover, under this restriction, A4 also holds. To see this, note first that the disjunct, (S does not contain any m essentially), gets cancelled, and thus previous considerations regarding logical necessity apply. Moreover, the statement, (S is not logically necessary or does not contain any m essentially), is not only logically necessary, but also contains at least one metaphysical term essentially, namely the term, "logically necessary". This is so whether Kripkean or Carnapian logical necessity is intended. To justify this claim, it should be noted that on Kripke's use,the definition of "logically necessary" contains the metaphysical term, "possible world" (essentially); moreover, on Carnap's use, the def'mition of "logically necessary" contains the metaphysical term, "meaning postulate" (essentially), though Carnap would have denied this. Still, on my notion of metaphysical, "meaning postulate" is a metaphysical term, since "meaning" is metaphysical. Given these considerations, A, (or all instances of A4 in S I ) holds, as before. Similar considerations show that As (or all instances in S ~) also holds. Therefore, Ss (or a f'mite fragment thereof) holds in sense 1 of metaphysical necessity. Now consider the premises of OA, in this sense. Pt P2

the negation of G is not logically necessary or does not contain any rn essentially. " I f G is true, then G is logically necessary and G contains some m essentially" is logically necessary and contains some rn essentially.

For preliminaries, it should first be noted that "God" is clearly a metaphysical term occurring in the statement G. Secondly, it should be noted that "God" is not a primitive term, in either the traditional or semi-traditional sense, since "God" is invariably defined in one way or another. Thus, G is not a primitive-term statement. The next question to consider is whether G contains the metaphysical term "God" essentially. According to the above definition given, we must primarily consider whether or not G is intensionally

320

JOEL

I. F R I E D M A N

equivalent to any primitive-term statement not containing the primitive, metaphysical definiens of "God". In my view, G is not so intensionally equivalent, though this is difficult to decide with certainty. It seems to me that the traditional or semi-traditional notion of God is not reducible to non-metaphysical notions, at least not at present, given that "God" is not a theoretical term of empirical science. Therefore, "God" must be defined in terms of certain primitive metaphysical terms which occur essentially in the definiens of God. In that case, G will not be intensionally equivalent to a primitive-term statement not containing this metaphysical definiens. Therefore, G will contain the metaphysical term "God" essentially, as defined above. Moreover, it follows that the negation of G will also contain "God" essentially. For, if the negation of G were intensionally equivalent to a statement not containing the definiens o f " G o d " , then G would be intensionally equivalent to the negation of that statement, also not containing the definiens of "God". Hence, G would not contain "God" essentially, contrary t O the previous conclusion. Therefore, we may conclude the following: since it is plausibly true that "God" is not reducible to non-metaphysical terms (at least at present), it is plausibly true that the negation of G contains "God" essentially. It might even be claimed that this is known a priori, but that is more controversial matter. With these preliminaries taken care of, let us now consider PI 9Given that the negation of G contains "God" essentially, we may cancel the second disjunct of PI, obtaining the following statement: the negation of G is not logically necessary. This statement was considered previously in the Carnapian and Kripkean senses of logical necessity, and the same considerations apply here. Now consider P2- Clearly, P2 implies the following statement: if G is true, then G is logically necessary. Again, this statement was considered previously, and the same considerations apply again. Therefore, we may conclude the following: (PI & P2) in sense 1 of metaphysical necessity logically implies (P~ & P2) in the Carnapian or Kripkean senses of logical necessity. Moreover, it was previously shown that (PI & P2) in these latter senses is not known to be true. Consequently, it follows that (P~ & P2) in sense 1 of metaphysical necessity is also not known to be true. Therefore, 0,4 is not known to be sound, in this sense. (2) metaphysical necessity in sense 2 A1

If S is a tautology, then 3 is derivable from some true metaphysical axiom, say M.

NECESSITY AND THE ONTOLOGICAL

A2

ARGUMENT

321

I f ( S ~ T) is derivable from true Ml , and S is derivable fromtrue M2, then T is derivable from some true M, namely M = CM~ &

M2). A3 A4 As

I f S is derivable from true M~, then S is true. If S is not derivable from any true M, then (S is not derivable from any true M) is derivable from some true M. (A2-A4) is derivable from some true M.

It should again be emphasized that the notion of truth I am using here is a semantical notion, not a syntactical one. Also, derivability is truth-preserving, that is to say, any statement derivable from a true statement is again true. As regards the notion of metaphysical axiom, this must be relativized to a particular system, say one's favorite system, since there is no general way of def'ming such a notion. Another difficulty with the notion of metaphysical axiom is that even within one's own system, it is often difficult to distinguish a metaphysical axiom from a metaphysical meaning postulate. Thus, for simplicity's sake, we may suppose that all metaphysical meaning postulates are metaphysical axioms, but not conversely. Furthermore, granted that one's metaphysical meaning postulates are true, how can one know that one's other metaphysical axioms are also true? This is a severe difficulty. But then, so is it with most any synthetic axiom. With these considerations in mind, let us consider A~. Clearly, A~ holds, provided there is at least one true metaphysical axiom, certainly a plausible assumption, given my inclusion of metaphysical meaning postulates among the axioms. As regards A2, one must assume that if M~ and M2 are metaphysical axioms, then (M ~ & M2 ) is also a metaphysical axiom. This may be adopted purely as a matter of convention, and is unobjectionable so long as we do not require non-redundancy among the axioms. Therefore, assuming this convention, A2 clearly holds. Also, As clearly holds by the truth-preserving property of derivability. As regards A4, this presents a special problem. First of all, it must be assumed that one's metaphysical axioms can be recursively enumerated, a plausible enough assumption. Then in enumerating these axioms, one must be able to derive certain non-derivability statements. Furthermore, since the notion of truth is involved in these statements, one must have a definition of truth or else certain axioms about truth, in order to derive these non-derivability statements involving truth. However, this should present no real obstacle, so long as higher-order metaphysical axioms are available in one's system. Thus, A4 (or its instances in S~) is plausibly true and may be regarded as known a priori. Similarly for As (or its instances in

322

JOEL

I. F R I E D M A N

S~). Therefore, Ss (or some finite fragment thereof) plausibly holds and may be regarded as known a priori, in sense 2 of metaphysical necessity. Consider now the premises o f O A . P~ P2

The negation of G is not derivable from any true M. "If G is true, then G is derivable from at least one true M" is derivable from at least one true M.

I regard P1 as very questionable. For, if atheism is a metaphysical truth (a logical possibility in my view), then there is no reason to believe that this truth is not derivable from any true metaphysical axiom. Thus, the negation of G might very well be derivable from some true M. In that case,P~ would be false. Note that this is the first time that PI has been seriously called into question (at least under the traditional or semi-traditional notion of God). On the other hand, ironically enough, P2 is now plausibly true. For, given that G is true, the Principle of Sufficient Reason (PSR) is also true, and indeed, may be taken as a true metaphysical axiom. Then, according to Spinoza and Leibniz, G derivable from PSR, 22 although this is itself controversial. However, what will surely clinch the derivation is the axiom stating that the (possibly inf'mite) series of causes or reasons has a maximal, and hence "necessary" element. This auxiliary axiom may be called M0. Then it should be uncontroversial that G is derivable from (PSR & M0). (I owe this point about Mo to Professor George W. Roberts). Thus, if G is true, then (PSR & Mo) is also true, and G is derivable from a true metaphysical axiom. This statement about derivability and truth should itself be derivable from some true metaphysical axiom, given previous considerations. Therefore, for the first time (except for the digressive case of bare Kripkean necessity), P2 plausibly holds, in sense 2 of metaphysical necessity (under the traditional or semi-traditional notion of God). However, since P~ is so questionable, it follows that (P~ & P2) is not known to be true, and therefore, that OA is not known to be sound, in sense 2 of metaphysical necessity. (3) metaphysical necessity in sense 3. This is the sixth and last sense of necessity I shall consider in this paper. Let usexamine the premisesofOA first. PI P2

The negation of G is not derivable from (PSR & Mo). "If G is true, then G is derivable from (PSR & Mo)" is derivable from (PSR & Mo).

Here Mo is the maximality axiom stating (as mentioned above) that the possibly infinite series of causes or reasons has a maximal element.

NECESSITY AND THE ONTOLOGICAL

ARGUMENT

323

Given that (PSR & Mo) is consistent, then since G is derivable from (PSR & Mo), it follows that the negation of G is not derivable from (PSR &Mo). Thus, P~ holds, provided that (PSR & Mo) is consistent, a plausible assumption, in my view. For, it is certainly possible that everything has a cause or reason and that the series of causes or reasons has a maximal element. As regards P2, we have by above considerations, that if G is true, then G is derivable from (PSR & Mo), and moreover, this statement itself is derivable from (PSR & Mo), using definitions and meaning postulate as well. Thus, P2 is plausibly true and may be regarded as known a priori. Therefore, for the first time (except for the digressive case of bare Kripkean necessity), (P~ & P2) is plausibly true and may be regarded as known a pr~ri. Since OA is formally valid, should we now regard G as known a priori? Indeed, doesn't a formally valid argument transform a priori knowledge of its premises into a priori knowledge of its conclusion? The answer is surely yes, provided the knower really does know all the premises, as well as the a x i o m s , and also has followed the deduction. However, in the above case, something has been left out, namely a consideration of the axioms of Ss (or some finite fragment thereof). These have been presupposed, yet have not been checked to see whether they are known a priori, in sense 3 of metaphysical necessity. It turns out for the first time (except perhaps for the digressive case of bare Kripkean necessity) that A3 may no longer be regarded as plausibly true or known a priori, in this sense, though the other axioms may be so regarded. Consider the following: A3

If S is derivable from (PSR & Mo), then S is true.

Here A3 may not be regarded as known a priori unless (PSR & Mo) is known a priori, a questionable assumption, in my view. For, (a) it is quite possible that not everything has a cause or reason, since there may well be an element of irrationality in nature, and (b) even if PSR is true,Mo may be false, since the series of causes or reasons may extend infinitely into the past, thus having no first or maximal element. However, if one insists, like Leibniz, on the cause or reason of the entire inf'mite series, then I reply that given such a super-cause or super-reason, a new series of super-causes or super-reasons may also extend infinitely; and so on, such that all these various levels of causes and reasons actually exhaust all the ordinal numbers (finite and infinite). In this case also, Mo would be false. It is for this reason that Cantor's invention of set theory destroyed the validity of Leibniz' version of the Cosmological Argument. Consequently, I do not regard (PSR & Mo) as known a priori, and hence A3 may not be so regarded. Indeed, if (PSR & Mo) is false, then false

324

JOEL

1. F R I E D M A N

statements are derivable from (PSR & Mo). For example, G is derivable from (PSR & Mo) and hence ~ a y very well be false. In fact, if (PSR & Mo) is false , then G is false, since (PSR & Mo) is equivalent to G. Hence A3 would be false. Given these considerations, we may conclude the following: OA (as a twopremise argument) is formally valid in Lewis' Ss (or a finite fragment thereo0. Moreover, OA is sound, in sense 3 of metaphysical necessity. However, not all the axioms of Ss are plausibly true and known a priori, in this sense. In particular, A3 fails. Thus, we cannot conclude that God's existence is known a priori, even if (P~ & P2 ) is known a priori. So close, yet so far away! 1 believe a similar result would foUow, if (PSR & Mo) were replaced by any other hallowed metaphysical principles. Therefore, not really so close, indeed very far away! Given the six senses of necessity considered in tiffs section, we have seen that there is no sense in which all the axioms of Ss (or a f'mite fragment thereof), together with the premises of OA, are plausibly true and known a priori. In the first five senses of necessity, all these axioms may be regarded as known a priori, but then at least one of the premises o f OA fails. In the sixth sense of necessity, both premises of OA may be regarded as known a priori, but then at least one of the axioms fails. In other words, the very soundness of Ss (or a t'mite fragment thereof) collapses, in sense 3 of metaphysical necessity. A similar thing happens for bare Kripkean necessity. I conclude (by induction?) that there is no single interpretation of necessity which would give us an a priori known sound OA and an a priori known sound Ss (or finite fragment thereof). Therefore, I conclude that Hartshome's modal reconstruction of the Ontological Argument fails. S.

HUBBELING'S

USE OF MODAL

PEIRCE'S

LAW

Hubbeling has attempted to revise 23 Hartshome's modal reconstruction by eliminating the troublesome Premise 2 of OA and introducing instead a modal version of Peirce's Law, or as he calls it, Modal Peirce's Law. Before dealing with this attempt, let us consider the following: Peirce's Law

((q ~ p) ~ q) z q

This is a well-known and interesting tautology, especially because it is not derivable in the Positive Propositional Logic. 24 Most positive tautologies are so derivable.

NECESSITY AND THE ONTOLOGICAL

ARGUMENT

325

In his first efforts, 2s Hubbeling applied Peirce's Law itself to Hartshome's OA, focusing on the following instance: (1)

((a ~ NG) ~ G) ~ G

He argued, in effect, that Hartshorne (assuming PG) proved G from the impli. cation between G and NG, that is, proved the antecedent of the Peirce's Lawinstance (1). Therefore, by Peirce's Law, G follows (assuming PG). Now if Hubbeling had been right, he would have proved God's existence from the possibility of God, thereby justifying the Ontological Argument (excluding senses 2 & 3 of metaphysical necessity). However, as pointed out by E_M. Barth in her article,26 'Philosophy of Religion and the Reality of Models for Modalities', Hartshorne (assuming PG) actually used the strict implication (G ~ NG), not the mere material implication (G ~ NG). Thus, Barth claims that not Peirce's Law, but the following invalid modal formula would be needed: (2)

((G ~ NG) ~ G) ~ G

In Hubbeling's later article,27 'The Meaningfulness of Metaphysics within Certain Systems', he agrees with Barth that the modal formula (2) is not valid and that Peirce's Law itself is not adequate to revise Hartshome's modal reconstruction. HloweveL Hlubbeling offers a modal version of Peirce's Law, which he argues is both valid and sufficient to revise Hartshome's OA. Consider the following modal formula introduced by Hubbeling (I have used a slightly different notation): Modal Peirce's Law (MPL) ((q ~ p) ~ q) ~ q (or N(N((q ~ p) ~ q) ~ q))

Now Hubbeling is right about the validity of MPL, though I shall omit its proof in Ss. Also, Hubbeling uses the following instance of MPL: (3)

((G ~ NG) ~ G) ~ G (or N(N((G ~ NG) ~ G) ~ G))

In his attempt to revise Hartshome's modal derivation of OA, Hubbeling seems to argue that Hartshome's derivation shows the following: 2s (4)

PG ~ ((G ~ NG) -~ G) (or N(PG ~ N((G ~ NG) ~ G)))

What this amounts to is that PG strictly implies the antecedent of the MPLinstance (3). Therefore, from MPL and (4), it follows that PG strictly implies G. In other words, God's existence follows from the possibility of God. Thus, if Hubbeling could establish (4), he would indeed have succeeded in revising

326

J O E L I. F R I E D M A N

Hartshorne's model reconstruction, eliminating the troublesome Premise 2 of OA. However, since the argument (PG/.'.G) has an easy counterexample in Ss, one may use the above considerations as a reductio argument for the conclusion that Hartshorne's proof does not show (4), and that (4) cannot be valid in Ss. The easy counterexample is the following: replace G by S, where S is the statement, "Pegasus exists". Then S is false, yet PS is true. There is a possible world in which Pegasus exists. Thus, (PG/:.G) has S as a counterexample, or more precisely, the argument form (Pq/:q) has S as a counterexample. S can also be used to invalidate (4) more directly. Let (4)S be the result of replacing G by S in (4). Suppose that (4)S is valid in Ss. Since PS is true, we have by (4)S that ((S ~ NS) ~ S) is true. Now since S is false, (S ~ NS) is vacuously true; and since (S ~ NS) strictly implies S, it follows that S is true also. Consequently, S is both true and false. This is a contradiction and shows that (4)S is not valid in Ss after all. Consequently, (4) is not valid either. Why Hubbeling may have accepted (4) can perhaps be explained by noting that the following similar modal formula is valid in Ss : (5)

PG ~ ((G ~ NG) ~ G)

(or N(PG ~ N(N(G ~ NG) ~ G))))

Note the similarity between the consequent of (4) and that of (5). Though (5) is valid in Ss, the consequent of (5) is not identical with the antecedent of the MPL-instance (3). Hence, G cannot be derived from PG, using (3) and (5), as opposed to (3) and (4). Thus, Hubbeling may have (unconsciously) confused (4) and (5). Given these considerations, we see why Hubbeling does not succeed in eliminating the troublesome Premise 2 of Hartshorne's OA, using Modal Peirce's Law, though he deserves credit for introducing Modal Peirce's Law. CONCLUSION

The Ontological Argument may be reconstructed as a formally valid de dicto argument. However, I have argued in this paper that in any fixed sense of necessity, either the premises of this argument or else some axiom of modal logic itself cannot be known to be true. In a way, the classical objections of Kant, Frege, and Russell were misplaced, since they did not address themselves to the modal weakness of the Ontological Argument. Hartshorne deserves credit for answering these classi-

NECESSITY AND THE ONTOLOGICAL ARGUMENT

327

cal objections with his formalized OA. Also, the charge o f formal invalidity is met by Hartshome. (Similarly for Plantinga's ratified formalization and my own formalization o f Spinoza's Ontological Argument). However, what cannot be met by Hartshorne, Malcolm, and Hubbeling is the charge o f modal confusion, especially confusion about the soundness o f the Ontological Argument. Malcolm, in his article, 29 'Anselm's Ontological Arguments', is especially guilty o f confusing de re causal and de re logical (metaphysical) necessity, as Plantinga so competently shows. (However, Malcolm deserves much credit for distinguishing the trivial existence predicate from the non-trivial necessary-existence predicate). In any case, I believe the considerations of this paper have confirmed Plantinga's original conclusion that modal confusion is at the heart o f the Ontological Argument. Therefore, students o f philosophy would benefit from the following: RULES FOR AVOIDING MODAL CONFUSION (i) (ii) 9 (iii)

de re necessity should be clearly distinguished from de dicto necessity. logical, causal, and metaphysical necessity, in their various senses, should be clearly distinguished. strict implication should be clearly distinguished from material implication.

I conclude this paper with a theological remark: if God exists, he does not look with favor upon modal confusion. University o f California, Davis

NOTES * This paper was inspired by Professor Wallace Matson's treatment of Hartshome's modal reconstruction of the Ontological Argument, in his paper, "Steps Toward Spinozism", delivered before the University of California, Davis Tercentenary Spinoza Symposium, in March 1977. 1 realized then, and claimed as much, that there is no single sense of necessity in which all the premises and axioms come out unquestionably true. Also, Plantinga's work has certainly inspired me to write this paper. See Anselm's Proslogion, Chapters II-IV, translated in Plantinga (1965)., pp. 3-6. 2 See selections from Aquinas', Summa Theologica, translated in Plantinga (1965). 3 See Descartes' Meditation V; Spinoza's Ethics, Part l, Propositions 7 and 1 l; and finally, Leibniz', New Essays Concerning Human Understanding, 714.

328

J O E L 1. F R I E D M A N

4 This was pointed out to me by Mr. Mark Boman. If one considers Proposition 10 of Part I of the Ethics, this should become more plausible: "Each attribute of a single substance must be conceived through itself''. Therefore, it would seem consistent to hold that a single substance has all attributes, since no one of them could in any way affect or "contradict" the others. All are (positive) perfections, as Leibniz would say. Now, since God is (more or less) defined by Spinoza as the substance with all attributes, it would seem consistent to hold that God exists, or in other words, that God is possible. Spinoza, however, never gave any such explicit argument, as far as I know. s See selections from Kant's Critique of Pure Reason, in Plantinga (1965), page 61. Kant states, " 'Being'..." is obviously not a real predicate; that is, it is not a concept of something which could be added to the concept of a thing". s In my view, the elimination of "existence" as a predicate in formal language gave Frege and Russel confidence that they could similarly eliminate "existence" as a predicate in philosophical language. Similarly, their treatment of descriptions in formal language gave them confidence that they could similarly treat descriptions in philosophical language. Such transferability is still a working hypothesis for a great number of analytic philosophers today, except that there is probably a greater appreciation of the differences between formal language and philosophical language. See Hartshorne's, The Logic of Perfection, page 51; see Malcolm's (in)famous 1960 article, 'Anselm's Ontological Arguments', in Plantinga (1965), pp. 136-159; and see Hulsbeling's, 'The Meaningfullness of Metaphysics within Certain Systems', in Erkennthis 9 (1975) 401-409. Also, see his Language, Logic, and Criterion: .4 Defense o f NonPositivistic Logical Empiricism, Amsterdam, 1971. s See Plantinga's book, The Nature of Necessity, Chapter I0, Section 6. Also, see Sections 7-8. Finally, see his treatment of Malcolm's version of the Ontological Argument in The Ontological Argument, edited by Plantinga, pp. 160-171. 9 This refers to the 1975 article cited in note 7. 19 See my paper, 'Was Spinoza fooled by the Ontological Argument?', to appear in Philosophia, 1980. ~1 See my paper, 'The MystiCs Ontological Argument', American Philosophical Quarterly, January 1979. 12 For a thorough treatment of Lewis' S s and other modal systems, see Hughes and Cresswell's, Introduction to Modal Logic, London 1968. 12 See Kripke's articles, 'A Completeness Theorem in Modal Logic', Journal o f Symbolic Logic, 24 (1959), pp. 1-15, and 'Semantical Considerations on Modal Logic' (1963), in Reference and Modality, edited by L. Linsky, pp. 63-72. ~4 Plantinga gives a similar though less metalogical definition in his article, De Dicto et De Re (1969). is Hartshorne in his book, The Logic of Perfection, page 51, does not literally start with premises I and 2 as in this paper, but gives a more "dispersed" formal proof. 16 By G6deFs Completeness Theorem for First-Order Quantifier Logic, a statement S of a first-order language is logically derivable from a set K of first-order statements if and only if S is true in every model in which K is true. Thus, i f K is the set of def'mitions and meaning postulates under consideration, then it should be clear that the two definitions of analyticity axe equivalent. On the other hand, by G6del's Incompleteness Theorem for

NECESSITY AND THE O N T O L O G I C A L A R G U M E N T

329

Second-Order Logic, the two def'mitions of analyticity are not equivalent for secondorder statements, or in higher- order logic. This is important for Caruap, as opposed to Quine, since Carnap often def'mes analyticity in terms of derivability in higher-order logic. i~ To interpret Sn, one must first define Carnapian logical necessity in terms of nthorder analyticity, and then recursively define nth-order analyticity. Consider the following sketch: if S has n-1 layers of "N" (for n ;~ 1), then S is logically necessary iffS* is nth-order analytic, where S* is the result of eliminating the n-1 layers of "N" in S by replacing each subformula (NS') of S by (S' is ith-order analytic), where S t has (i-1) layers of "AT". The required definition of nth-order analyticity is given recursively by using metalanguages up to level n to define the finite orders of analyticity contained therein. The corresponding statements about such lower level analyticity are all derivable in an nth-level metalanguage, using definitions and meaning postulates. is See Kripke's seminal papers, (i) 'Naming and Necessity' in Semantics of Natural Language, edited by Davidson and Harman, Dordrecht-Holland, 1972, especially pp. 261-264; and (ii) 'Identity and Necessity', in Naming, Necessity, and Natural Kinds, edited by Schwartz, Ithaca, 1977; also see my paper, 'Carnapian Analyticity and Kripkean Necessity', forthcoming. ,9 Kripke has a lot to say about rigid designators in his seminal paper, 'Naming and Necessity', especially Lecture III, wherein he treats not only proper names but also natural-kind predicates and logico-mathematical predicates as rigid designators. 2o Kripke normally regards proper names as rigid designators. On the other hand, a proper name may be used as a disguised description. In that case, it is not treated as a rigid designator, l think Kripke's mature view is that a given proper name is in some contexts a rigid designator and in other contexts a disguised description. Thus, proper names and descriptions must be distinguished according to their 'referential' use and their 'attributive' use. See Kripke's, 'Naming and Necessity', as well as Keith Donnellan's paper, 'Reference and Definite Descriptions' (1966), in Naming, Necessity, andNatural Kinds, ibid., pp. 4265. 2~ Kripke's notion of necessity is given in the seminal articles already mentioned above. For Kripke, as I interpret him, a statement may be necessary even though it is not true in every possible world. It only needs to be true in every possible world in which its proper names (or natural-kind predicates) name their intended denotations. On the other hand, a statement is logically necessary ff and only ff it is true in every possible world. Thus, as l interpret him, Kripke distinguishes between bare necessity and logical necessity. See my paper, Bare Kripkcan Necessity, to appear. 22 The Principle of Sufficient Reason was stated both by Spinoza and by Leibniz and was central to their writings. Leibniz gave arguments to show that PSR is equivalent to G. See his papers, 'Necessary and Contingent Truths' and 'First Truths' in Smith and Grene (1940). Also, see Spinoza's alternate demonstration of P,I ('God necessarily exists'), in the Ethics, Part I. 23 See Hubbeling's paper, 'The Meaningfulness of Metaphysics within Certain Systems',

Ibid. 24 See Church's, Introduction to Mathematical Logic, p. 161. 2s See Hubbeling's book, Language, Logic and Criterion, Ibid. In Erkenntnis 9 (1975), p. 397.

330

JOEL I. FRIEDMAN

2~ See Hubbeling's paper, 'The Meaningfulness of Metaphysics within Certain Systems', Ibid., especially pp. 404-405. 2s Ibid., p. 406. 2, See Malcolm's article, 'Anselm's Ontological Arguments', in Plantinga (1965), especially pp. 144-147, and also p. 155. REFERENCES Barth, E.M., 'Philosophy of Religion and the Reality of Models for Modalities', Erkennthis 9 (1975), pp. 393-399. Carnap, Rudolf, Meaning and Necessity, University of Chicago Press, Chicago, (1947, 1956). Church, Alonzo, Introduction to Mathematical Logic, Princeton University Press, Princeton, 1956. Davidson, Donald and Gilbert Harman (eds.), The Logic of Grammar, Dickenson Publishing Co., Encino, Caliornia, 1975. Descartes, Ren~, Meditations on First Philosophy in Descartes Selections, R.M. Eaton (ed.), Charles Scribner's Sons, New York, 1927. Donnellan, Keith, 'Reference and Definite Descriptions' (1966) in Schwartz (1977). Frege, Gottlob, The Foundations of Arithmetic, translated by J.L. Austin, Harper's, New York, 1950 (original 1884). Friedman, Joel I., 'Was Spinoza Fooled by the Ontological Argument?', to appear in Philosophia, 1980. Friedman, Joel [., 'The Mystic's Ontological Argument', American Philosophical Quarterly, 16 (1979), pp. 73-78. Friedman, Joel I., 'Carnapian Analyticity and Kripkean Necessity', to appear. Friedman, Joel I., 'Bare Kripkean Necessity' (1980), to appear. Hartshorne, Charles, The Logic of Perfection, Open Court, LaSaUe, 1962. Hubbeling, H.G., 'The Meaningfulness of Metaphysics within Certain Systems', Erkennt. his 9 (1975), pp. 401-409. Hubbeling, H.G., Language, Logic, and Criterion: A Defense of non-Positivistic Logical Empiricism, Born N.V. Publishing Co., Amsterdam, 1971. Hughes G.E. and M.J. Cresswell, An Introduction to Modal Logic, Methuen and Co., London, 1968. Jarrett, Charles, 'Spinoza's Ontological Argument', Canad. Journ. of Philosophy, 6 (1976), pp. 685-692. Kripke, Saul A., 'A Completeness Theorem in Modal Logic', JSL, 24 (1959), pp. 1-15. Kripke, Saul A., 'Semantical Considerations on Modal Logic' (1963), in Linsky (1971), pp. 63-72. Kripke, Saul A., 'Naming and Necessity' (1970 lectures), in Davidson and Harman (1972), pp. 253-355. Kripke, Saul A., 'Identity and Necessity' (1971), in Schwartz (1977), pp. 66-101. Leibniz, Gottfried W., New Essays Concerning Human Understanding, translated by A.G. Langley, Open Court, Chicago 1916. Lewis, Clarence 1., A Survey o f Symbolic Logic, University of California Press, Berkeley, 1918.

NECESSITY AND THE ONTOLOGICAL ARGUMENT

331

Linsky, Leonard (ed.), Reference and Modality, Oxford University Press, Oxford, 1971. Malcolm, Norman, 'Anselm's Ontological Arguments' (1960), in Plantinga (1965), PP. 136-159. Matson, Wallace, 'Steps Toward Spinozism', delivered before the UC, Davis Tercentenary Spinoza Symposium, March 1977. Plantinga, Alvin, (ed.), The Ontological Argument, Doubleday-Anchor, Garden City, N.Y., 1965. Plantinga, Alvin, The Nature o f Necessity, Clarendon Press, Oxford, 1974. Plantinga, Alvin, "De Dicto et De Re' (1969), in Necessary ?'ruth, R.C. Sleigh Jr. (ed.), Prentice-Hall Inc., Englewood Cliffs, N.J., 1972, pp. 152-172. Russell, Bertrand, 'On Denoting', Mind 14 (1905). Russell, Bertrand, 'Mathematical Logic as Based on the Theory of Types' (1908), in Logic and Knowledge, R.C. Marsh (ed.), George Allen and Unwin, London, 1956. Schwartz, Stephen P. (ed.), Naming, Necessity, and Natural Kinds, Comell University Press, Ithaca, 1977. Smith, T.V. and Marjorie Grene, From Descartes to Locke, University of Chicago Press, Chicago, 1940. Spinoza, Benedict, Ethics, J. Gutmann (ed.), Hafner Publishing Co., New York, 1949. (Also see Everyman's Library edition, with an introduction by G. Santayana, 1910). Spinoza, Benedict, Opera Posthuma, C. Gebhardt (ed.), Carl Winter, Heidelberg, 1925. St. Anselm, Proslogion, reprinted in part in Plantinga (1965). Manuscript submitted 5 October 1979 Final version received 30 April 1980