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1970:

Lewis, "Anselm and Actuality". The key critique
of ontological arguments. All ontological arguments are either invalid or
question-begging; moreover, in many cases, they have two closely related
readings, one of which falls into each of the above categories.

1974:

Plantinga, The Nature of Necessity. Plantinga's
"victorious" modal ontological argument.

1995:

Gödel, Collected Works Volume III.
Gödel's ontological argument.

2. Taxonomy of Ontological
Arguments

According to the taxonomy of Oppy (1995), there are seven
major kinds of ontological arguments, viz:

definitional ontological
arguments;
conceptual (or
hyperintensional) ontological arguments;
modal ontological
arguments;
Meinongian ontological
arguments;
experiential ontological
arguments;
mereological ontological
arguments; and
Hegelian' ontological
arguments.

Examples
of each follow. These are mostly toy examples. But they serve to highlight the
deficiencies which more complex examples also share.

1. God is a being which has every
perfection. (This is true as a matter of definition.) Existence is a perfection. Hence God exists.

2. I
conceive of a being than which no greater can be conceived. If a being than
which no greater can be conceived does not exist, then I can conceive of a
being greater than a being than which no greater can be conceived namely, a
being than which no greater can be conceived that exists. I cannot conceive of
a being greater than a being than which no greater can be conceived. Hence, a
being than which no greater can be conceived exists.

3. It
is possible that that God exists. God is not a contingent being, i.e., either
it is not possible that God exists, or it is necessary that God exists. Hence,
it is necessary that God exists. Hence, God exists. (See Malcolm
(1960), Hartshorne (1965), and Plantinga (1974) for closely related arguments.)

4. [It
is analytic, necessary and a priori that] Each
instance of the schema "The F G is F" expresses a truth. Hence the
sentence "The existent perfect being is existent" expresses a truth.
Hence, the existent perfect being is existent. Hence, God is existent, i.e. God
exists. (The last step is justified by the observation that, as a matter of
definition, if there is exactly one existent perfect being, then that being is God.)

5. The
word God' has a meaning that is revealed in religious experience. The word
God' has a meaning only if God exists. Hence, God exists. (See
Rescher (1959) for a live version of this argument.)

6. I
exist. Therefore something exists. Whenever a bunch of things exist, their
mereological sum also exists. Therefore the sum of all things exists. Therefore
God the sum of all things exists.

7. God
must exist.

Of
course, this taxonomy is not exclusive: an argument can belong to several
categories at once. Moreover, an argument can be ambiguous between a range of readings, each of which belongs to different
categories. This latter fact may help to explain part of the curious
fascination of ontological arguments. Finally, the taxonomy can be further
specialised: there are, for example, at least four importantly different kinds
of modal ontological arguments which should be distinguished. (See, e.g., Ross (1969) for a rather different kind of modal
ontological argument.)

3. Characterisation of Ontological
Arguments

It is not easy to give a good characterisation of
ontological arguments. The traditional characterisation involves the use of
problematic notions analyticity, necessity, and a priority and also
fails to apply to many arguments to which defenders have affixed the label
"ontological". (Consider, for example, the claim that I conceive of a
being than which no greater can be conceived. This claim is clearly not
analytic (its truth doesn't follow immediately from the meanings of the words used
to express it), nor necessary (I might never have entertained the concept), nor
a priori (except perhaps in my own case, though even this is unclear
perhaps even I don't know independently of experience that I have this
concept.)) However, it is unclear how that traditional characterisation should
be improved upon.

Perhaps
one might resolve to use the label "ontological argument" for any
argument which gets classified as "an ontological argument" by its
proponent(s). This procedure would make good sense if one thought that there is
a natural kind ontological arguments which our practice carves out, but for
which is hard to specify defining conditions. Moreover, this procedure can be
adapted as a pro tem stop gap: when there is a better definition to
hand, that definition will be adopted instead. On the other hand, it seems
worthwhile to attempt a more informative definition.

Focus
on the case of ontological arguments for the conclusion that God exists. One
characteristic feature of these arguments is the use which they make of
"referential vocabulary" names, definite descriptions, indefinite
descriptions, quantified noun phrases, etc. whose ontological commitments
for occurrences of this vocabulary in "referential position"
non-theists do not accept.

Theists
and non-theists alike (can) agree that there is spatio-temporal, or causal, or
nomic, or modal structure to the world (the basis for cosmological arguments);
and that there are certain kinds of complexity of organisation, structure and function
in the world (the basis for teleological arguments); and so on. But theists and
non-theists are in dispute about whether there are perfect beings, or beings
than which no greater can be conceived, or ;
thus, theists and non-theists are in dispute about the indirect subject
matter of the premises of ontological arguments.

Of
course, the premises of ontological arguments often do not deal directly with
perfect beings, beings than which no greater can be conceived, etc.; rather,
they deal with descriptions of, or ideas of, or concepts of, or the possibility
of the existence of, these things. However, the basic point remains:
ontological arguments require the use of vocabulary which non-theists should
certainly find problematic when it is used in ontologically committing contexts
(i.e not inside the scope of prophylactic operators such as "according
to the story" or "by the lights of theists" or "by the
definition" which can be taken to afford protection against unwanted
commitments).

Note
that this characterisation does not beg the question against the possibility of
the construction of a successful ontological argument i.e., it does not lead
immediately to the conclusion that all ontological arguments are
question-begging (in virtue of the ontologically committing vocabulary which
they employ). For it may be that the vocabulary in question only gets used in
premises under the protection of prophylactic operators (which ward off the
unwanted commitments.) Of course, there will then be questions about whether
the resulting arguments can possibly be valid how could the commitments turn
up in the conclusion if they are not there in the premises? but those are further questions, which would remain to be
addressed.

4. Objections to Ontological Arguments

Objections to ontological arguments take many forms. Some
objections are intended to apply only to particular ontological arguments, or
particular forms of ontological arguments; other objections are intended to
apply to all ontological arguments. It is a controversial question whether
there are any successful general objections to ontological arguments.

One
general criticism of ontological arguments which have appeared hitherto is
this: none of them is persuasive, i.e., none of them provides those who
do not already accept the conclusion that God exists and who are reasonable,
reflective, well-informed, etc. with either a pro tanto reason or an
all-things-considered reason to accept that conclusion. Any reading of any
ontological argument which has been produced so far which is sufficiently
clearly stated to admit of evaluation yields a result which is invalid, or
possesses a set of premises which it is clear in advance that no reasonable,
reflective, well-informed, etc. non-theists will accept, or has a benign
conclusion which has no religious significance, or else falls prey to more than
one of the above failings.

For
each of the families of arguments introduced in the earlier taxonomy, we can
give general reasons why arguments of that family fall under the general
criticism. In what follows, we shall apply these general considerations to the
exemplar arguments introduced in section 2.

(1)
Definitional arguments: These are arguments in which ontologically committing
vocabulary is introduced solely via a definition. An obvious problem is that
claims involving that vocabulary cannot then be non-question-beggingly detached
from the scope of that definition. (The inference from By definition, God is
an existent being' to God exists' is patently invalid; while the inference to
By definition, God exists' is valid, but uninteresting. In the example given
earlier, the premises licence the claim that, as a matter of definition, God
possesses the perfection of existence. But, as just noted, there is no valid
inference from this claim to the further claim that God exists.)

(2)
Conceptual arguments: These are arguments in which ontologically committing
vocabulary is introduced solely within the scope of hyperintensional operators
(e.g. believes that', conceives of', etc.). Often, these operators have two
readings, one of which can cancel ontological commitment, and the other of
which cannot. On the reading which can give cancellation (as in the most likely
reading of John believes in Santa Claus'), the inference to a conclusion in
which the ontological commitment is not cancelled will be invalid. On the
reading which cannot cancel ontological commitment (as in that reading of John
thinks about God' which can only be true if there is a God to think about), the
premises are question-begging: they incur ontological commitments which
non-theists reject. In our sample argument, the claim, that I
conceive of an existent being than which no greater being can be conceived,
admits of the two kinds of readings just distinguished. On the one hand, on the
reading which gives cancellation, the inference to the conclusion that there is
a being than which no greater can be conceived is plainly invalid. On the other
hand, on the reading in which there is no cancellation, it is clear that this
claim is one which no reasonable, etc. non-theist will accept: if you doubt
that there is a being than which no greater can be conceived, then, of course,
you doubt whether you can have thoughts about such a being.

(3)
Modal arguments: These are arguments with premises which concern modal claims
about God, i.e., claims about the possibility or necessity of God's attributes
and existence. Suppose that we agree to think about possibility and necessity
in terms of possible worlds: a claim is possibly true just in case it is true
in at least one possible world; a claim is necessarily true just in case it is
true in every possible world; and a claim is contingent just in case it is true
in some possible worlds and false in others. Some theists
hold that God is a necessarily existent being, i.e., that God exists in every
possible world. Non-theists do not accept the claim that God exists in the
actual world. Plainly enough, non-theists and necessitarian theists disagree
about the layout of logical space, i.e., the space of possible worlds. The
sample argument consists, in effect, of two premises: one which says that God
exists in at least one possible world; and one which says that God exists in
all possible worlds if God exists in any. It is perfectly obvious that no
non-theist can accept this pair of premises. Of course, a non-theist can allow
if they wish that there are possible worlds in which there are contingent
Gods. However, it is quite clear that no rational, reflective, etc. non-theist
will accept the pair of premises in the sample argument.

(4)
Meinongian arguments: These are arguments which depend somehow or other on
Meinongian theories of objects. Consider the schema The F G is F'. Naive
Meinongians will suppose that if F is instantiated with any property, then the
result is true (and, quite likely, necessary, analytic and a priori). So, for
example, the round square is round; the bald current King of France is bald; and so on. However,
more sophisticiated Meinongians will insist that there must be some restriction
on the substitution instances for F, in order to allow one to draw the obvious
and important ontological distinction between the following two groups: {Bill
Clinton, the sun, the Eiffel Tower} and {Santa Claus, Mickey Mouse, the round
square}. Choice of vocabulary here is controversial: Let us suppose (for the
sake of example) that the right thing to say is that the former things exist
and the latter do not. Under this supposition, existent' will not be a
suitable substitution instance for F obviously, since we all agree that there
is no existent round square. Of course, nothing hangs on the choice of
existent' as the crucial vocabulary. The point is that non-theists are not
prepared to include god(s) in the former group of objects and hence will be
unpersuaded by any argument which tries to use whatever vocabulary is used to
discriminate between the two classes as the basis for an argument that god(s)
belong to the former group. (Cognoscenti will recognise that the crucial point
is that Meinongian ontological arguments fail to respect the distinction
between nuclear (assumptible, characterising) properties and non-nuclear
(non-assumptible, non-characterising) properties. It should, of course, be
noted that neither Meinong, nor any of his well-known modern supporters e.g.
Terence Parsons, Richard Sylvan ever endorses a Meinongian ontological
argument; and it should also be noted that most motivate the distinction
between nuclear and non-nuclear properties in part by a need to avoid
Meinongian ontological arguments. The reason for calling these arguments
"Meinongian" is that they rely on quantification over or reference
to non-existent objects; there is no perjorative intent in the use of this
label.)

(5) Experiential
arguments: These are arguments which try to make use of externalist' or
object-involving' accounts of content. It should not be surprising that they
fail. After all, those accounts of content need to have something to say about
expressions which fail to refer (Santa Claus', phlogiston', etc.). But,
however the account goes, non-theists will insist that expressions which
purport to refer to god(s) should be given exactly the same kind of treatment.

(6)
Mereological arguments: Those who dislike mereology will not be impressed by
these arguments. However, even those who accept principles of unrestricted
composition i.e., who accept principles which claim, e.g., that, whenever
there are some things, there is something which is the sum or fusion of all of
those things need not be perturbed by them: for it is plausible to think that

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