In his book, _Atheism: A Philosophical Justification_, Michael Martin
levels an attack on Charles Hartshorne's modal version of the ontological
argument for the existence of God. Even though Dr. Martin admits the
validity of the logical inferences involved in Hartshorne's proof, he
contends that the argument is unsound because of two faulty premises. This
paper is an attempt to obviate Martin's objections by correcting the
dubious premises of Hartshorne's argument. Instead of directly refuting
Professor Martin's objections, I will present a modified version of the
modal ontological argument that uses Hartshorne's basic logical structure.
It will be shown that the addition of two self-evident axioms and a change
in the definition of God will vitiate Martin's objections by making them
irrelevant.

Charles Hartshorne, in _The Logic of Perfection_, stated the modal
form of the ontological argument in this way,(3) where "q" = There is a
perfect being, "N" = It is logically necessary that, "~" = It is not the
case that, "v" = or, and "p -> q" = p strictly implies q.

(1) q -> Nq (Anselm's principle)
(2) Nq v ~Nq (excluded middle)
(3) ~Nq -> N~Nq (Becker's postulate)
(4) Nq v N~Nq (from 2 and 3)
(5) N~Nq -> N~q (from 1)
(6) Nq v N~q (from 4 and 5)
(7) ~N~q (intuitive postulate)
(8) Nq (from 6 and 7)
(9) Nq -> q (modal axiom)
(10) q (from 8 and 9)

Premise (1) is St. Anselm's principle that a perfect being can only
exist if its existence is logically necessary. Premise (7) is the
assumption that the existence of God is not logically impossible. Each of
the other premises is either a truth of logic, or is the product of a
logically valid deduction.

While accepting the validity of the logical structure of the proof,
Michael Martin argues that the proponent of this argument must
conclusively demonstrate the consistency of the God concept before one is
warranted in accepting premise (7). He writes:

"There seems to be little doubt that the argument is valid. The
crucial question is whether the premises are true. Clearly the most
important ones for our purposes are premises (1) and (7). On Hartshorne's
view, (7) is the hardest to justify. He recommends using one or more of
the theistic proofs that he claims demonstrate that perfection must be at
least possible. But this seems to have things backward. The theistic
proofs presume that the concept of God is coherent; they cannot
demonstrate it. Furthermore, ...there have been many attempts to show that
the concept of God is incoherent. Before one can claim that it is
coherent, one at least needs to show that these attempts have failed.
Hartshorne has not done this, and consequently premise (7) is
unjustified."

Dr. Martin continues the attack on the proof by attempting to infirm
premise (1). He claims that if Anselm's principle that a perfect being can
only exist by logical necessity is accepted, then one can use the logic of
the ontological argument to prove the existence of all sorts of absurd
"perfect" entities. He writes:

"It would seem possible to 'prove' the existence of the super
absolute evil one [a being like God in all ways except that it is
absolutely evil] by a modal argument identical to Hartshorne's, the basic
difference being the interpretation of q. Statement q would now mean 'A
perfectly evil being exists.' "

Even though Professor Martin's criticisms of the modal ontological
argument can be brought into question for various reasons beyond the scope
of this paper, I will accept them for the sake of argument and proceed to
show how a revised version of Hartshorne's proof can be formulated such
that it avoids these problems entirely. Hence, even if Martin's objections
are granted, the modal ontological argument will still be able to soundly
demonstrate that God exists. The new definitions and axioms of the
modified argument are as follows:

Definitions and Axioms

Definition (1) - A term is descriptive if and only if it characterizes the
nature of something by distinguishing it from some other conceivable
nature. [A descriptive term would be something like "red," "non-red, " or
some other distinguishing predicate that conveys information about the
nature of something. Note that the term "exists" is not a descriptive term
because it does not add to one's concept of the nature of something.
"Exists" functions as a judgment about some description that has already
been conceived and is therefore external to the description itself. A term
like "consistently described" is also non-descriptive because it is a
judgment about a description. Additionally, a term like "A or non-A" is
non-descriptive because it applies to absolutely everything conceivable
and conveys no distinguishing information at all about the nature of what
is being described.]

Definition (2) - A descriptive term is positive if and only if it is
understood through an act of direct conceptualization. [Terms like "fast",
"triangular," "blue," "hot," etc. are all positive because the mental act
involved in comprehending them is one of direct awareness.]

Definition (3) - A descriptive term is negative if and only if it is
merely the denial of the applicability of some positive descriptive term.
[Terms like "non-fast," "non-triangular," "non-blue," "non-hot" etc. are
all negative because they are simply denials of positive terms. Double
negatives like "not non-blue" will be considered to be positive since they
are logically equivalent to positive terms and thereby express more than
the mere denial of the applicability of some positive term.]

Definition (4) - Something is contingent if and only if its existence and
non-existence are both logically possible. [Something like the Statue of
Liberty, which can be coherently conceived to either exist or not exist is
contingent. The term "non-contingent" would apply to whatever exists by
logical necessity (if anything), and to whatever cannot be conceived to
exist (like square-circles).]

Definition (5) - God is that to which no positive descriptive term can be
applied. [This is the traditional mystical conception of God as a being
the nature of which transcends anything that can be directly conceived.
Alan Watts writes:

"Negative terms are used of the ultimate Reality simply because it has
none of the dimensions of the individual and finite realm, as one might
say of colour that it is neither long nor short, high nor low, round nor
square, rough nor smooth."

Since no positively conceived descriptive term can be applied to God, "He"
must be considered to be non-contingent, non-finite, non-spatial,
non-temporal, not dependent on anything else, etc.

Axiom 1- If no positive descriptive term can be applied to God, then the
concept of God is free from contradiction. [At first this may seem
surprising, but a thought experiment will prove it to be true that no
single descriptive negation or conjunction of descriptive negations is
ever able to consume all of logical space to yield a contradiction. Of
course, negations of non-descriptive terms like "A or non-A" yield
contradictions immediately, but the axiom only applies to the negations of
descriptive terms.]

Axiom 2 - If the concept of God is free from contradiction, then it is not
logically necessary that God does not exist. [In other words, if God is
consistently described then the existence of God is logically possible.]

The New Argument

q = God exists.
d = No positive descriptive term can be applied to God.
f = The concept of God is free from contradiction.
N = It is logically necessary that
~ = It is not the case that
v = or
p -> q = p strictly implies q
Axiom 1 - d -> f
Axiom 2 - f -> ~N~q

(1) q -> Nq (from the denial of contingency implied in the definition of
God)
(2) Nq v ~Nq (excluded middle)
(3) ~Nq -> N~Nq (Becker's postulate)
(4) Nq v N~Nq (from 2 and 3)
(5) N~Nq -> N~q (from 1)
(6) Nq v N~q (from 4 and 5)
(7) d (from the definition of God)
(8) f (from 7 and Axiom 1)
(9) ~N~q (from 8 and Axiom 2)
(10) Nq (from 6 and 9)
(11) Nq -> q (modal axiom)
(12) q (from 10 and 11 )

By means of this new version of the argument, Martin's criticisms are
entirely circumvented. The issue of proving the logical possibility of the
existence of God is no longer a difficulty since the consistency of the
God concept is guaranteed by the self-evident truth of Axiom 1.
Furthermore, the argument cannot be parodied because it only works for
something that is conceived strictly in terms of negations (namely God).
Any attempt to develop a parody, like a "perfect devil," would require the
introduction of some positive descriptive predicate into the idea, thereby
bringing the parody concept outside the protection of Axiom 1.
Here is a less formal version of the proof in ordinary language:

(1) If no positive descriptive term can be applied God, then the concept
of God is free from contradiction. (Axiom 1)
(2) No positive descriptive term can be applied to God. (by definition)
(3) The concept of God is free from contradiction. (from 1 and 2)
(4) It is not logically necessary that God does not exist. (from 3 and
Axiom 2)
(5) God cannot exist contingently. (implied in the definition of God)
(6) Either God necessarily exists or necessarily does not exist. (implied
from the denial of contingency)
(7) It is logically necessary that God exists. (from 4 and 6)
(8) God exists. (from 7)

Objections and Replies

Objection I - It is not legitimate to conclude the existence of something
solely through reference to its definition. An ontological commitment is
never part of a description; it is simply the positing of what has been
described. As such, affirmations of existence are always extrinsic to
definitions because they are judgments applied to descriptions, and can
never be part of the descriptions themselves. One can only conclude the
existence of something via empirical processes, and never through mere
reflection on a definition. Consider the Kantian criticism of the
ontological argument, which shows that the term "existence" can never be a
factor in a definition:

"By whatever and by however many predicates we may think of a thing - even
if we completely determine it - we do not make the least addition to the
thing when we further declare that this thing is. Otherwise, it would not
be the same thing that exists, but something more than we had thought in
the concept; and we could not, therefore, say that the exact object of my
conception exists."

Reply I - The above objection does not militate against the argument for
the existence of God that has been presented here. This is because the
description of God, in and of itself, implies no ontological commitment.
"Non-contingency" only implies that the being in question either
necessarily exists or necessarily does not exist. Since the ontological
status of God remains indeterminate even though contingency has been
denied, it follows that one cannot rightly say that the definition of God
contains a judgment of existence within itself. It is only when one
combines the definitional denial of contingency with the (necessarily
synthetic) judgment of the logical possibility of God's existence that one
ends up with a proof of the existence of God. Hence, it follows that the
Kantian criticism has no power against this version of the ontological
argument.

Objection II - It is not possible for a being to exist by logical
necessity. For example, one can conceive of a possible world in which
there exists nothing but air and iron filings. Therefore, the existence of
God is not logically necessary.

Reply II - It is not possible to coherently conceive of the world
described above. Any conceivable world would necessarily be subject to all
logical/conceptual laws and mathematical truths. As such, the concept of
God would be a consistent concept (because of the conceptually inescapable
truth of Axioms 1 and 2), and would still imply the denial of contingency
as a matter of definitional truth. From these simple facts, the existence
of God can be deduced using nothing but truths of logic. When one makes
the objection that they can conceive of a world with nothing but certain
concrete objects, they are ignoring the implications of abstract
reasoning, and are not recognizing that the conclusions derived as a
matter of conceptual necessity are present in all possible worlds. Such
hidden conceptual implications are rationally inescapable even though they
are not immediately evident.

Objection III - If God can only be conceived in terms of negations, then
there is no difference between God and absolute nothingness.

Reply III - The difference is that God is defined as a transcendental
entity, the nature of which cannot be conceptualized, whereas nothingness
is just the absence of any nature at all. God's nature cannot be conceived
because of its radical transcendence, whereas the nature of nothingness
cannot be conceived because there is simply nothing to conceive. There is
an obvious difference in meaning between "A hypothetical entity the nature
of which transcends positive concepts" and "nonexistence." The
identification of the two is ruled out a prioi.

Objection IV - If the nature of God can only be conceived through
negation, then one cannot predicate God as "necessarily existing" because
that would be a directly conceived descriptive predicate.

Reply IV - Necessity is actually a negative descriptive predicate even
though there is no explicit "non" in the term. It is understood simply
through the denial of the attribute of contingency.

Objection V - Contingency could just as well be taken to be a negative
predicate; it could be understood as the denial of necessity. Therefore,
necessity would be a positive term after all.

Reply V - Any term that is logically equivalent to a negative term is also
negative. For example, if one uses the word "grue" to mean "non-red," then
the term "grue" is logically equivalent to a negative term, and is
therefore negative even though it does not seem to be so on the surface.
Similarly, the idea of "necessity" is logically equivalent to the act of
denying the possibility of something. Consider that a given proposition X
is necessarily true if and only if the complement of proposition X is
logically impossible. Since the idea of necessity is equivalent to the
recognition of the impossibility of something, and since the notion of
impossibility is clearly a negative one, it follows that the idea of
necessity is also negative. The notion of contingency, on the other hand,
merely serves to affirm the possibility of two complementary propositions
and, as such, is a positive term since possibility is a directly
understood idea.

Objection VI - The concept of necessity can be expressed positively as "A
given proposition X is necessarily true if and only if X is true in all
possible worlds." Since there is no need to invoke "impossibility" in that
formulation, it follows that necessity is really a positive term.
Reply VI - If one says "X is necessarily true" is to be interpreted as "X
is true in all possible worlds," then one is making a universal statement,
which always proceeds from the denial of the existence of something. In
this case, it would be a denial of the existence of a possible world in
which X is false. David Kelley, in The Art of Reasoning, writes:

"We use a minus sign for a universal statement because it is a denial of a
particular statement. A particular statement asserts the existence of
something - an S that is P, an S that is non-P. A universal statement
asserts the nonexistence of something. 'No S is P' asserts the
nonexistence of Ss that are P. 'All S are P' asserts the nonexistence of
Ss that are non-P. This feature of a statement is called its valence.
Particular statements have a positive valence because they assert
existence; universal statements have negative valence because they assert
nonexistence."

Thus it follows that the statement "X is true in all possible worlds" is
negative because, being universal, it is logically equivalent to the
denial of the existence of a possible world that does not contain
proposition X. In other words, the idea of necessity is logically
equivalent to an act of denial (as was detailed in Reply V). Since any
term that is logically equivalent to a negation is negative (surface
appearances notwithstanding), it follows that "necessity" is a negative
term.

Objection VII - It seems that the notions of contingency and necessity are
judgments that apply to propositions and therefore are not descriptive
predicates. For example, when one says "God necessarily exists," the term
"necessarily" is a judgment about the judgment of God's existence. As
such, it is twice removed from the realm of description. Given this fact,
it must be concluded that the definition of God presented here is improper
because it makes use of the non-descriptive term "non-contingent."

Reply VII - It is certainly the case that those terms are used as
judgments about propositions, but they can also be used as descriptive
predicates. For example, if the proposition "Dogs exist" is admitted to be
a contingently true proposition, then one must also admit that there is
something about the nature of dogs that causes propositions about their
existence to be contingently true. It is this determining characteristic
of dogs that is being conceptualized when the term "contingent" is used as
a descriptive predicate. "Contingency," used in the descriptive sense, is
that property of a being that causes propositions about its existence to
be contingently true.

Conclusion

It has been shown that Hartshorne's modal version of the ontological
argument can be modified such that it is rendered immune to all of Michael
Martin's criticisms even if their truth is granted. Until some better
criticism emerges, it must be concluded that the modal ontological
argument succeeds at demonstrating the existence of God.

Christopher McHugh