joel i. friedman, the mystic's ontological argument

North American Philosophical Publications

The Mystic's Ontological ArgumentAuthor(s): Joel I. FriedmanSource: American Philosophical Quarterly, Vol. 16, No. 1 (Jan., 1979), pp. 73-78Published by: University of Illinois Press on behalf of the North American PhilosophicalPublicationsStable URL: http://www.jstor.org/stable/20009742 .

Accessed: 10/09/2014 07:34

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

University of Illinois Press and North American Philosophical Publications are collaborating with JSTOR todigitize, preserve and extend access to American Philosophical Quarterly.

http://www.jstor.org

This content downloaded from 109.228.107.138 on Wed, 10 Sep 2014 07:34:02 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=illinois

http://www.jstor.org/action/showPublisher?publisherCode=napp

http://www.jstor.org/action/showPublisher?publisherCode=napp

http://www.jstor.org/stable/20009742?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


American Philosophical Quarterly Volume 16, Number i, January 1979

IX. THE MYSTIC'S ONTOLOGIGAL ARGUMENT JOEL I. FRIEDMAN

IN

this brief paper, I present the mystic's version of the Ontological Argument for God's existence.

While this new version has its own difficulties, I believe it does not suffer from the logical deficiencies of the traditional Ontological Argument.

To qualify as an

ontological argument, an argu? ment must start with some definition of God, as a

premise, and together with additional a priori premises, finish with the existence of God, as a conclusion.1 No empirical premises

are allowed.

Throughout the centuries, since St. Anselm, the

traditional Ontological Argument, in its various

versions, has been attacked by various philosophers (Aquinas, Hume, Kant, Frege, Russell, and recently

Plantinga), but also defended by various philos? ophers (Descartes, Spinoza, Leibniz, and recently

Hartshorne and Malcolm). Thus, we are not dealing with an easy topic.

The traditional Ontological Argument may be stated simply as follows :

i. God is defined as the subject of all perfections. 2. Existence is a

perfection.

3. Hence, God cannot be conceived as not having existence.

4. Therefore, God necessarily exists.

This argument may be taken as representative of

the various versions of the traditional Ontological

Argument. To our modern logical ears, it admittedly has a horrible sound. For, how can God be heard

from Logic alone? Nevertheless, the argument does

have versions which are considerably sophisticated,

though it is not my intention in this paper to examine

any of these arguments in detail.2

Instead, I will note that the traditional Ontological Argument has been charged with at least the fol?

lowing logical deficiencies :

(i) "Existence" is used as a predicate illegit? imately (Kant)

(ii) Proper names and definite descriptions are misused (Russell)

(iii) Modal fallacies are committed (Plantinga)

It is my contention that the mystic's Ontological Argument does not suffer from the above deficiencies, although it has its own difficulties. In this paper, I am not going to show that the traditional Ontological

Argument does suffer from the above deficiencies. Rather, I shall show that the mystic's Ontological Argument does not so suffer. Indeed, I have been

scrupulous (a) in not using "existence" as a primitive predicate, but only as an existential quantifier, (b) in not

misusing proper names or definite descriptions, but always proving the appropriate existence and

uniqueness conditions, and (c) in not committing modal fallacies, but using only a single uncon troversial principle of modal logic (see below).

The mystic's Ontological Argument may also be stated simply as follows :

i. God is defined as the maximally incompre? hensible being.

2. Necessarily, something is incomprehensible. 3. Hence, necessarily, there is a

maximally in?

comprehensible being. 4. Therefore, God necessarily exists.

Admittedly, this is a mere sketch of an argument, but the fuller argument is given below. For now, it

will be useful to work from this more sketchy argument. Let us consider each line in its turn.

Line 1?"God is defined as the maximally incom?

prehensible being."

Here the traditional theist will object that this is not his definition of God. He will charge the mystic

73

1 This is admittedly a rather broad conception of "ontological argument," but will serve for the purposes of this paper. St. Anselm is generally credited with the invention of the traditional Ontological Argument. See Anselm's Proslogion, Chs. II-IV, translated in,

The Ontological Argument, ed. by Alvin Plantinga (Garden City, NY, 1965), pp. 3-6. 2 Cf. Alvin Plantinga, The Nature of Necessity (Oxford, 1974), Ch. X, pp. 196-221. Plantinga attacks various versions of the

Ontological Argument (for example, Malcolm's, Hartshorne's, and others). He then offers his own extremely rarified and sophisticated reconstruction. However, he admits that his version, even though valid, can only be believed to be sound.

In my 1977 paper, "Was Spinoza Fooled"by the Ontological Argument?" to appear in Philosophia, I gave a reconstruction of

Spinoza's Ontological Argument, with two versions. One version is invalid, though its premises are logically necessary. The other version is valid, but alas, its premises are not logically necessary. I am convinced that one cannot have it both ways, as regards the traditional Ontological Argument.



74 AMERICAN PHILOSOPHICAL QUARTERLY

with giving a merely stipulative definition, not a real

definition of God. However, from the mystic's point

of view, this is not a mere stipulative definition.

Indeed, it is not properly speaking a definition at

all, in any first-order sense. Rather, the mystic

regards God as essentially undefinable, incom?

prehensible, and unnamable. Thus, God can at most

be defined only by a higher-order definition. And

that is how Line i should be regarded, as a higher order definition. Yet, once this distinction is made, the mystic has a

right to regard Line i as more than

a stipulative definition. He and his fellow mystics use the term "G?d" in a way that makes Line i

more than a stipulation. Indeed, mystics are just

as

faithful to their usage of the term "God" as traditional

theists are to theirs.

Such mystics, though a minority, can be found in the history of Western Philosophy, as well as

Eastern Philosophy, though there is more variety than implied above. For, the notion of incompre? hensible has various meanings, thus making for

various kinds of mystics. For example, the Jewish Helenistic philosopher Philo held that "it is wholly

impossible that God according to His essence should

be known by any creature"; rather, God "is un?

namable and ineffable and in every way incom?

prehensible."3 Still, Philo believed in the God of the

Bible, who created the world by willing it (see footnote 3). Other mystics, such as certain Buddhists or Taoists, would object to such an anthropomorphic description of God. (See Lao Tzu's Tao Te Ching and

Stcherbatsky's, The Conception of Buddhist Nirvana.) Still, given some notion of an incomprehensible

God, I am attempting to give

a plausible version of

the Ontological Argument, more plausible,

at least,

than the traditional Ontological Argument.

Line 2?"Necessarily, something is incompre?

hensible."

Even if something is incomprehensible, it may well be wondered whether this is not an empirical

matter. If the statement, "something is incompre?

hensible," does require empirical justification, then Line 2 is false.

Consider therefore the following a priori justifi? cation of Line 2 : We should not limit ourselves to the world of concrete things, but consider also the

world of abstract sets, properties, relations, etc. Then

Line 2 becomes much more plausible. For, given the

results of Mathematical Logic, not everything in the

abstract world can be comprehensible, at least, not

to us finite creatures. For example, given Russell's

open-ended types, we cannot comprehend all the

types, as a whole4 ; given Tarski's proof of the un

definability of truth (in formal languages) in general, we cannot comprehend truth, in general5; and

finally, given Cantor's proof of non-denumerably infinite sets, we cannot comprehend every set, since

there are only a denumerably infinite number of

names and definitions.6 Thus, in the abstract world,

much is incomprehensible, and necessarily so.

And not only in the abstract world. For, if we

regard the physical space of our concrete world as

intensively infinite, that is, as having infinitely many concrete points (and corresponding

to Car?

tesian co-ordinates in abstract space), then it is

quite plausible to regard this concrete infinity as

non-denumerable, since the points in abstract space

are, as Cantor showed, in one-one correspondence

with the set of real numbers, which is non-de?

numerably infinite (see footnote 6). Thus, not every concrete point could be comprehended, since not

every concrete point could be defined. However,

even if there were only a denumerably infinite number of points in concrete physical space, still,

there would be a non-denumerably infinite number

of subsets of such points. This again by one of

Cantor's famous theorems.7 Thus, not every subset

of points in physical space could be comprehended, since not every subset of points could be defined.

Here we see that incomprehensibility in the abstract

world may very well transfer over to the concrete

world.

3 Cf. H. A. Wolfson, Philo (Cambridge, Mass., 1947), vol. 2, pp. 110-113. I am indebted to my colleague, Neal Gilbert, for

digging up these gems. 4 Cf. Bertrand Russell, "Mathematical Logic as based on the Theory of Types" (1908), reprinted in Logic and Knowledge, ed. by

R. C. Marsh (London, 1956), pp. 59-102. 5 Cf. Alfred Tarski, "The Concept of Truth in Formalized Languages" (1931), translated by J. H. Woodger, in Logic, Semantics,

and Metamathematics (Oxford, 1956), pp. 152-278. In this paper, Tarski shows that no consistent formal language is capable of having

an adequate definition of truth within that language itself, though an adequate definition in a richer language can always be given.

These results show that no general definition of truth, adequate for every formal language, can be given.

6 Cf. Georg Cantor, Contributions to the Founding of the Theory of Transfinite Numbers (1895-1897), ed- anc^ tr- DY P- Jourdain (New

York, 1915 and 1955). Some non-denumerably infinite sets can be comprehended, for example, the set of real numbers since there is

a formula for defining this set. However, not every real number (regarded as a decimal sequence) can be comprehended, since by

Cantor's result, there are real numbers which have no formulas for generating or defining them. Such real numbers are incomprehensible. 7 Ibid. Cantor proved that given any denumerably infinite set, the set of all its subsets will be non-denumerably infinite.



THE MYSTIC S ONTOLOGICAL ARGUMENT 75

It may well be that the concrete world is incom?

prehensible in its own right. For example, physical atoms may be so infinitely complex that they are

truly incomprehensible to finite creatures. Neverthe?

less, if this is so, it seems to be an empirical question, and hence, not sufficient to justify Line 2. On the other hand, whether physical space has non-de?

numerably many points seems to be a conceptual

matter and not an empirical question. Thus,

whether there necessarily are any incomprehensible concrete things seems to depend

on whether there

necessarily are any incomprehensible abstract things.

Admittedly, this is subject to debate. At this point, I should say a word about the

notion of incomprehensibility. Any given incompre? hensible thing can always be comprehended in a

higher-order way, for example, "the incompre? hensible thing I am now thinking about." More?

over, any given incomprehensible thing can

always be "comprehended" under logical or tautological properties, for example, the property of self

identity and the property of having or not having F.

Thus, what makes anything incomprehensible is that it cannot be comprehended under first-order,

"non-logical" properties. However, one cannot

identify the incomprehensible with the (first-order) undefinable. For, primitive notions are

certainly

undefinable, by definition, yet they are often compre? hended, whether abstractly or concretely (for example, the

membership relation in set theory and

yellowness as a phenomenon). Also, I do not think we should identify the incomprehensible with the undefinable and unintuitable, since we may be able to intuit what is incomprehensible. However, consider the following tentative definition of the

incomprehensible :

Definition x is incomprehensible if and only if x is first-order undefinable and unperceivable, and x also has

no examples or instances (or perhaps good

analogies) which are either definable or per? ceivable.

Incomprehensible sets or points would fulfill this definition. Possibly this definition is inadequate, and it may even be the case that the notion of incompre? hensible is itself incomprehensible.

Admittedly, much more could be said about the notion of incomprehensible, but I shall let the matter rest here.

Line 3?"Necessarily, there is a maximally in?

comprehensible being."

Given line 2, together with a certain principle of whole-formation, we may infer the existence of

the non-empty whole of all and only the incompre? hensible things. This whole is not a class or set, but

rather a discontinuous whole containing as parts all

and only the incomprehensible things. In this way, we may avoid Russell's Paradox.8 This whole is nevertheless infinite.

It should be emphasized that the whole of all

incomprehensible things may very well be mixed and contain both abstract and concrete things, together. Thus, it may contain incomprehensible sets of numbers, as well as

incomprehensible points in physical space, and even

possibly, incomprehen? sible physical objects. Such a mixture of abstract and concrete objects would be discontinuous indeed, but it would not be a class, in any case, at least not

in the abstract sense. It would be an individual

thing, perhaps fit to be a god. Now since all the parts of this maximal whole are

incomprehensible, it seems plausible enough to

regard this whole as itself incomprehensible. Granted that a whole might be comprehensible even though some of its parts were incomprehensible, still, it could

hardly be comprehensible if no part of it were

comprehensible. That would be asking a lot. More?

over, it should be clear that the whole of all in?

comprehensible things is maximally incompre?

hensible, given that it is incomprehensible at all.

It could not be any more incomprehensible, since

everything that is incomprehensible is a part of it.

Also, by the logic of whole formation, the whole of all subwholes of this whole could not be formed.

Thus, it is reasonable to regard this incomprehensible whole of all incomprehensible things as maximally

incomprehensible.9 It might be objected that the mystic would never

countenance any such maximal mixture of abstract

and concrete things, but rather insist that his in?

comprehensible God must be wholly concrete.

8 Uninhibited use of the Principle of Class Formation leads to Russell's paradox of the class of all non-self-membered classes.

This paradox may arise anew unless we inhibit the formation of the class of all incomprehensible things. Instead, we may introduce a principle of whole-formation, which will yield the whole of all incomprehensible things. Such a whole is not subject to the standard set theoretical operations, and thus Russell's Paradox can be avoided, even though this whole contains all incomprehensible classes, as well as the purely concrete things. For a discussion of analogous mixed hierarchies, see my paper, "Proper Classes as members

of Extended Sets," Mathematical Annals, vol. 183 (1969), pp. 232-240. 9 I admit that this paper commits the sin of omitting any treatment of the logic of wholes.




Therefore, it might be argued that my notion of the

mystic's God is not the usual one. In answer to this,

let me first ask a question. Is the usual mystic articulate

enough to assert, one way or another, that his in?

comprehensible God is wholly concrete? Secondly, I answer more

positively, that even if the usual

mystic's God is wholly concrete, still, his God would

be part of my maximally incomprehensible whole.

Thus, my reconstruction would comprehend his

notion. Finally, I answer that at least some unusual

mystics, or mystical metaphysicians, have counte?

nanced an "abstract God," for example Plato.

Thus, I would say that my mixed maximally in?

comprehensible whole has some analogy to Plato's

Form of the Good. For, the Form of the Good,

according to Plato, comprehends both abstract

forms (ideas), as well as concrete objects (such as

the sun), and indeed, makes possible their existence.

See Plato's, "The Good as Ultimate Object of

Knowledge," in the Republic. Also, my maximally

incomprehensible whole has some analogy with

Spinoza's God (which he identified with Nature),

just because this whole is maximal. However,

Spinoza's God, though maximal, is not incompre? hensible, since It is defined in Definition 6, Part I of

the Ethics (in a first-order way). In any case, I am

influenced by both Plato and Spinoza, a rather

mixed pair of philosophers at that (even if they are

not strict mystics). In my view, though many questions may legit?

imately be raised here, Line 3 has a certain plau?

sibility. So long as it is consistent to conceive such a

maximally incomprehensible whole, it is as reason?

able to assert (or postulate) its existence as it is to

assert (or postulate) the existence of abstract infinite sets or classes.

Line 4.?"God necessarily exists."

This line follows from Lines 1 and 3, together with the assumption that necessarily, there is at most one maximally incomprehensible thing. This as?

sumption seems to me

quite plausible. For, given two wholes which both contained as parts all and

only the incomprehensible things, these wholes

would be indiscernible (in the logical, as opposed to

the psychological sense). Thus, by the Principle of

the Identity of Indiscernables, they would be identical. It seems quite reasonable to apply this

principle to wholes, though it is somewhat ironic to talk about discerning incomprehensible things.

It should also be noted that Line 4 requires only a

single, and uncontroversial, principle of Modal

Logic, namely, the Distribution Principle: if an

argument is valid (or if the connection between the

premises and the conclusion is necessary), then if the

premises are necessary, then so is the conclusion

necessary. This Distribution Principle of Modal

Logic can hardly be questioned. In my argument, I

incorporated the claims of necessity into some of the

premises themselves, namely, in Lines 2 and 3.

Since Line 1 is a definition, it should also be re?

garded as necessary. Hence, the conclusion follows,

using the Distribution Principle. Now I need not have incorporated the claims of necessity into any of the premises. I might first have presented an

argument valid in the quantifier logic (with identity and descriptions), then argued further that since the premises of the argument are necessary, so is the

conclusion necessary. This would have made the

structure of the argument clearer, by separating the

quantificational reasoning from the modal reasoning. This can actually be carried out. The following

argument is valid in the quantifier logic and makes

explicit much of the reasoning given above. Indeed,

this argument can easily be symbolized in the

quantifier logic. (See the Appendix for logical details.)

The Mystic's Ontological Argument

1. God is the maximally incomprehensible being

(mystic's definition of God). 2. Something is incomprehensible (plausible premise).

3. There is exactly one whole having as parts all and

only the incomprehensible things (instance of the

Principle of Whole-Formation).

4. A whole is non-empty if and only if it has at least one

part (definition).

5. There is exactly one non-empty whole having as

parts all and only the incomprehensible things

(2, 3, 4, QL ( =

Quantifier Logic, with Identity and

Descriptions)). 6. If all the parts of a non-empty whole are incom?

prehensible, then that whole is also incomprehen? sible (plausible premise).

7. The non-empty whole having as parts all and only the incomprehensible things is itself incompre? hensible (5, 6, QL).

8. A whole is maximally incomprehensible if and only if

it is incomprehensible, and everything which is

incomprehensible is part ofthat whole (definition).

9. There is a maximally incomprehensible thing

(5.7,8,Q?). 10. There is at most one maximally incomprehensible

thing (plausible premise, using Identity of Indis?

cernibles). 11. There is exactly one maximally incomprehensible

thing (9, 10, QL). 12. Therefore, God exists (1, 11, QL).



THE MYSTIC'S ONTOLOGICAL ARGUMENT 77

(Note that Line 12, the conclusion, does not require "exists" as a primitive predicate.)

I have finished the first part of the argument,

showing that the above is valid in the quantifier logic. The second part of the argument contains

premises stating the necessity of Lines 1, 2, 3, 4, 6,

8, and 10, together with a conclusion stating the

necessity of Line 12. This modal argument is then

valid, by the Distribution Principle. Hence, the

validity of the mystic's Ontological Argument. It should be clear that the mystic's Ontological

Argument escapes the logical deficiencies mentioned above. Let us see if this is true.

As regards (i), I have not used "existence" as a

predicate illegitimately, since it occurs only once in the proof,

as a predicate, namely, in Line 12, and

there only as a shorthand, non-primitive predicate. It could easily have been eliminated. "Existence"

has been used primarily as an existential quantifier throughout the proof. Thus, I have avoided (i).

As regards (ii), I have not misused proper names or definite descriptions. For, there are only two

occurrences of one proper name and two occurrences

of two definite descriptions, in the entire proof. "God" occurs in the first and last lines of the proof.

The first occurrence occurs in the definition of

"God," and is intended to carry no existential import at this point. The last occurrence of "God" occurs

in the conclusion and does carry existential import, but by this time, such existential import has already been proved. Moreover, the two occurrences of

the two definite descriptions in the proof are, "the

maximally incomprehensible being," in Line 1, and "the non-empty whole having as parts all and only the incomprehensible things," in Line 7. The first definite description occurs in a definition and is

intended to carry no existential import. The latter definite description does carry existential import, but it occurs

only after the corresponding existence

and uniqueness conditions have been proved, by Line 5. Thus, neither proper names nor definite

descriptions have been misused in the above argu? ment. Therefore, I have avoided (ii).

As regards (iii), no explicit modal terms whatever are used in the first part of the argument. In the second part of the argument, only the clearly valid

Distribution Principle of Modal Logic is used.

Hence, I have avoided (iii). Thus I claim to have avoided the logical de?

ficiencies of (i)-(iii), in presenting the mystic's Ontological Argument.

It must be admitted that other difficulties have

arisen, especially in regard to the logic of wholes, and the mixture of abstract and concrete objects.

However, I intended more to raise such difficulties rather than to resolve them, in this paper. Still,

I would go so far as to claim that the mystic's

Ontological Argument is more plausible than the traditional Ontological Argument, just because it avoids the logical deficiencies of (i)-(iii), yet does not commit any obvious logical howlers. Thus, I

maintain that the mystic's God, as opposed to the traditional God, can plausibly be derived from Logic alone (in some

expanded sense of "Logic").

Since the mystic is not interested in conceptual activity, qua mystic, but only in pure experiencing, I have taken it upon myself to do the job he is not inclined to do, namely, to give a rational reconstruction

of his belief in an incomprehensible God. Given this

reconstruction, the mystic may say, with more

justification than St. Anselm, that only the fool denies in his heart the Incomprehensible.10

University of California!Davis Received November 2, 1977

I now symbolize the mystic's Ontological ment, within the quantifier logic.

Scheme of Abbreviation Mx?x is maximally incomprehensible g?God Ix?x is incomprehensible

Wx?x is a whole

Appendix

jrgu- Pxy?x is a part of y Ex?x is empty

Symbolic Argument i. g=(tx)Mx (definition) 2. (3x)Ix (plausible premise) 3. (l^iWx & (y)(Pyx = Iy)) (instance of Prin?

ciple of Whole-Formation) 10 I am indebted to Mr. John Garibaldi, a student in my introductory philosophy class, for giving me the main idea of this paper.

In class, he asked the question whether the existence of an incomprehensible being follows from the idea of an incomprehensible being. This got me thinking about the mystic's version of the Ontological Argument.




4- (Va:) ( Wx => ( ~ Ex =

(3y) Pyx) ) (conditional defi?

nition) 5. {3iX)(Wx8l -Ex 8l ?1y)(Pyx = Iy) (2,3,4, QL) 6. ?ix)((Wx&~Ex&. ?iy)(Pyx=>/#))=>Ix) (plau?

sible premise) 7. 7(n*)(W*& ~Ex& ??y){Pyx

= Iy))(5,6,QL)

8. (\/x)(Wx^(Mx=(Ix & ?iy){Iy^Pyx)))) (con? ditional definition)

9. (3*)Ai*(5,7,8,?I) 10. ?ix) Ci y) (Mx & My^>x=y) (plausible premise,

presupposing Identity of Indiscernibles) 11.

(31x)Mx(g, 10, QL)

12. {3x)(x=g) (i, ii, QL (free logic))

It should be noted that here, we have a "free

logic" approach to definite descriptions. However, I could just as well have used a Russell-Quine approach, by replacing Lines i and 12 by the

following :

i'. (Vx)(Gx =

Mx) (where "Gx" means "xgodizes") 12' (3 x)Gx

(See Quine's classical article, "On What There

Is.")11

11 Reprinted in E. Nagel and R. Brandt (eds.), Meaning and Knowledge (New York, 1965), pp. 289-297. Also, B. Russell, "On

Denoting," ibid., pp. 78-87. Also cf. B. van Fraassen and K. Lambert, Derivation and Counterexample (Encio, 1972), Ch. 7, pp. 148-162, in

which free logic is fully developed.



joel i. friedman, the mystic's ontological argument

Documents