## 1. History of Ontological Arguments




|  |  |
| --- | --- |
| 1078: | St. Anselm, *Proslogion*. Followed soon after by
Gaunilo's critique *In Behalf of the Fool*. |
| 1264: | St. Thomas Aquinas, *Summa*. Criticises an argument which
somehow descends from St. Anselm. |
| 1637: | Descartes, *Discourse on Method*. The argument of
Discourse 4 is further elaborated in the *Meditations*. The
*Objections*--particularly those of Caterus and
Gassendi--and the *Replies* contain much valuable
discussion of the Cartesian arguments. |
| c1680: | Spinoza, *Ethics*. Intimations of a defensible
mereological ontological argument, albeit one whose conclusion is not
(obviously) endowed with religious significance. |
| 1709: | Leibniz, *New Essays Concerning Human Understanding*.
Contains Leibniz's attempt to complete the Cartesian argument by
showing that the Cartesian conception of God is not inconsistent. |
| 1776: | Hume, *Dialogues Concerning Natural Religion*. Part IX is
a general attack on *a priori* arguments (both analytic and
synthetic). Includes a purported demonstration that no such arguments
can be any good. |
| 1787: | Kant, *Critique of Pure Reason*. Contains famous attack
on traditional theistic arguments. Three objections to "the
ontological argument", including the famous objection based on
the dictum that existence is not a predicate. |
| 1831: | Hegel, *Lectures of 1831*. In these lectures, Hegel says
that "the ontological argument" succeeds. However, he does
not make it clear what he takes the premises of "the ontological
argument" to be; and nor does he make it clear what it would be
for "the ontological argument" to succeed. Some scholars
have claimed that the entire Hegelian corpus constitutes an
ontological argument. |
| 1884: | Frege, *Foundations of Arithmetic*. Existence is a
second-order predicate. First-order existence claims are meaningless.
So ontological arguments--whose conclusions are first-order
existence claims--are doomed. |
| 1941: | Hartshorne, *Man's Vision of God*. Defence of modal
ontological arguments, allegedly derived from *Proslogion
3*. |
| 1970: | Lewis, "Anselm and Actuality". A 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: | Godel, *Collected Works Volume III*.
Godel's ontological argument. |
| 2004: | Sobel, *Logic and Theism*. Detailed critique of
ontological arguments. See, especially, chapters 2-4, pp.
29-167. |



For a useful discussion of the history of ontological arguments in the
modern period, see Harrelson 2009. 


## 2. Taxonomy of Ontological Arguments



According to a modification of the taxonomy of Oppy 1995, there are
eight major kinds of ontological arguments, viz: 


1. definitional ontological arguments;
2. conceptual (or hyperintensional) ontological arguments;
3. modal ontological arguments;
4. Meinongian ontological arguments;
5. experiential ontological arguments;
6. mereological ontological arguments;
7. higher-order ontological arguments; and
8. 'Hegelian' ontological arguments;



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



Note: No example is provided of a 'Hegelian' ontological
argument. There is no extant discussion that states clearly the full
set of premises of a 'Hegelian' ontological argument. (See
Redding and Bubbio 2014 for recent discussion of this point.)


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. Say that a God-property is a property that is possessed by God in all
and only those worlds in which God exists. Not all properties are God
properties. Any property entailed by a collection of God-properties is
itself a God-property. The God-properties include necessary existence,
necessary omnipotence, necessary omniscience, and necessary perfect
goodness. Hence, there is a necessarily existent, necessarily
omnipotent, necessarily omniscient, and necessarily perfectly good
being (namely, God).



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. Uses of Ontological Arguments



Before we turn to assessment of ontological arguments, we need to get
clear about what the proper intended goals of ontological arguments
can be. Suppose we think of arguments as having advocates and targets:
when an advocate presents an argument to a target, the goal of the
advocate is to bring about some change in the target. What might be
the targets of ontological arguments, and what might be the changes
that advocates of these arguments aim to bring about in those targets?




Here are some proposals; no doubt the reader can think of others: 


1. The targets might be atheists, and the goal might be to turn them
into theists.
2. The targets might be agnostics, and the goal might be to turn them
into theists.
3. The targets might be theists, and the goal might be to improve the
doxastic position of theists.
4. The targets might be professional philosophers, and the goal might
be to advance understanding of the consequences of adopting particular
logical rules, or treating existence as a real predicate, or allowing
definitions to have existential import, or the like.
5. The targets might be undergraduate philosophy students, and the
goal might be to give them some sufficiently frustrating examples on
which to cut their critical teeth.



In the coming discussion, it will be supposed that the targets are
atheists and agnostics, and that the goal is to turn them into
theists. Suppose that an advocate presents an ontological argument to
a target. What conditions must that arguments satisfy if it is fit for
its intended purpose? A plausible suggestion is that, minimally, it
should make the targets recognise that they have good reason to accept
the conclusion of the argument that they did not recognise that they
have prior to the presentation of the argument. Adopting this
plausible suggestion provides the following criterion: a successful
ontological argument is one that should make atheists and agnostics
recognise that they have good reason to believe that God exists that
they did not recognise that they have prior to the presentation of the
argument. Note that this criterion has a normative dimension: it
adverts to what atheists and agnostics should do when presented with
the argument. 



There is an important discussion to be had about whether we should
suppose that the targets of ontological arguments are atheists and
agnostics, and that the goal is to turn them into theists. However, it
is simply beyond the scope of this entry to pursue that discussion
here. 


## 5. 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 license 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; all non-theists reject the claim that God
exists in the actual world. The sample argument consists, in effect,
of two premises:


* God exists in at least one possible world.
* God exists in all possible worlds if God exists in any.



A minimally rational non-theist cannot accept both of these premises
- they entail that God exists in every possible world whereas a
minimally rational non-theist maintains that there is at least one
possible world in which God does not exist. Given that a minimally
rational non-theist says that there is at least one possible world in
which God does not exist, such a non-theist can offer a parallel
counterargument with the following two premises:


* God fails to exist in at least one possible world.
* God exists in all possible worlds if God exists in any.



These premises entail that God exists in no possible world, and hence
that God does not exist in the actual world. Considered together, the
argument and the counterargument just mentioned plainly do not give
anyone a reason to prefer theism to non-theism, and nor do they give
anyone a reason to prefer non-theism to theism. So the sample argument
is unsuccessful: it doesn't supply an all-things-considered
reason to prefer theism to non-theism (just as the counterargument
doesn't supply an all-things-considered reason to prefer
non-theism to theism).



(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 sophisticated 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 piece of 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
pejorative 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 the conclusions of these arguments have no religious
significance whatsoever--they are merely arguments for, e.g., the
existence of the physical universe.



(7) Higher-Order arguments: The key to these arguments is the
observation that any collection of properties, that (a) does not
include all properties and (b) is closed under entailment, is possibly
jointly instantiated. If it is impossible that God exists -- as
all who deny that God exists suppose, on the further assumption that,
were God to exist, God would exist of necessity -- then it cannot
be true both that the God-properties are closed under entailment and
that there are properties that are not God-properties. Those who take
themselves to have good independent reason to deny that there are any
gods will take themselves to have good independent reason to deny that
there are God-properties that form a non-trivial collection that is
closed under entailment.



Even if the forgoing analyses are correct, it is important to note
that no argument has been given for the conclusion that no ontological
argument *can* be successful. Even if all of the kinds of
arguments produced to date are pretty clearly unsuccessful--i.e.,
not such as ought to give non-theists reason to accept the conclusion
that God exists--it remains an open question whether there is
some other kind of hitherto undiscovered ontological argument which
does succeed. (Perhaps it is worth adding here that there is fairly
widespread consensus, even amongst theists, that no known ontological
arguments for the existence of God are persuasive. Most categories of
ontological argument have some actual defenders; but none has a large
following.)



Many other objections to (some) ontological arguments have been
proposed. All of the following have been alleged to be the key to the
explanation of the failure of (at least some) ontological arguments:
(1) existence is not a predicate (see, e.g., Kant, Smart 1955, Alston
1960); (2) the concept of god is meaningless/incoherent/ inconsistent
(see, e.g., Findlay 1949); (3) ontological arguments are ruled out by
"the missing explanation argument" (see Johnston 1992; (4)
ontological arguments all trade on mistaken uses of singular terms
(see, e.g., Barnes 1972; (5) existence is not a perfection (see almost
any textbook in philosophy of religion); (6) ontological arguments
presuppose a Meinongian approach to ontology (see, e.g., Dummett
1993); and (7) ontological arguments are question-begging, i.e.,
presuppose what they set out to prove (see, e.g., Rowe 1989). There
are many things to say about these objections: the most important
point is that almost all of them require far more controversial
assumptions than non-theists require in order to be able to reject
ontological arguments with good conscience. Trying to support most of
these claims merely in order to beat up on ontological arguments is
like using a steamroller to crack a nut (in circumstances in which one
is unsure that one can get the steamroller to move!).



Of course, all of the above discussion is directed merely to the claim
that ontological arguments are not dialectically
efficacious--i.e., they give reasonable non-theists no reason to
change their views. It might be wondered whether there is some other
use which ontological arguments have--e.g., as Plantinga claims,
in establishing the reasonableness of theism. This seems unlikely.
After all, at best these arguments show that certain sets of sentences
(beliefs, etc.) are inconsistent--one cannot reject the
conclusions of these arguments while accepting their premises. But the
arguments themselves say nothing about the reasonableness of accepting
the premisses. So the arguments themselves say nothing about the
(unconditional) reasonableness of accepting the conclusions of these
arguments. Those who are disposed to think that theism is irrational
need find nothing in ontological arguments to make them change their
minds (and those who are disposed to think that theism is true should
take no comfort from them either).


## 6. Parodies of Ontological Arguments



Positive ontological arguments--i.e., arguments FOR the existence
of god(s)--invariably admit of various kinds of parodies, i.e.,
parallel arguments which seem at least equally acceptable to
non-theists, but which establish absurd or contradictory conclusions.
For many positive ontological arguments, there are parodies which
purport to establish the non-existence of god(s); and for many
positive ontological arguments there are lots (usually a large
infinity!) of similar arguments which purport to establish the
existence of lots (usually a large infinity) of distinct god-like
beings. Here are some modest examples: 



(1) By definition, God is a non-existent being who has every (other)
perfection. Hence God does not exist.



(2) I conceive of a being than which no greater can be conceived
except that it only ever creates *n* universes. If such a being
does not exist, then we can conceive of a greater being--namely,
one exactly like it which does exist. But I cannot conceive of a being
which is greater in this way. Hence, a being than which no greater can
be conceived except that it only ever creates *n* universes
exists.



(3) It is possible that God does not exist. 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 not possible that God exists.
Hence God does not exist.



(4) It is analytic, necessary, and a priori that the *F G* is
*F*. Hence, the existent perfect being who creates exactly
*n* universes is existent. Hence the perfect being who creates
exactly *n* universes exists.



There are many kinds of parodies of Ontological Arguments. The aim is
to construct arguments which non-theists can reasonably claim to have
no more reason to accept than the original Ontological Arguments
themselves. Of course, theists may well be able to hold that the
originals are sound, and the parodies not--but that is an
entirely unrelated issue. (All theists--and no
non-theists--should grant that the following argument is sound,
given that the connectives are to be interpreted classically:
"Either 2+2=5, or God exists. Not 2+2=5. Hence God
exists." This argument contributes nothing positive to any case
for theism, just as the argument "Either 2+2=5, or God does not
exist. Not 2+2=5. Hence God does not exist." contributes nothing
positive to the case for non-theism.)



There are many parodic discussions of Ontological Arguments in the
literature. See, for example, the parody provided by Raymond Smullyan
(1984), in which the argument is attributed to "the unknown
Dutch theologian van Dollard". A relatively recent addition to
the genre is described in Grey 2000, though the date of its
construction is uncertain. It is the work of Douglas Gasking, one-time
Professor of Philosophy at the University of Melbourne (with
emendations by William Grey and Denis Robinson):


1. The creation of the world is the most marvellous achievement
imaginable.
2. The merit of an achievement is the product of (a) its intrinsic
quality, and (b) the ability of its creator.
3. The greater the disability or handicap of the creator, the more
impressive the achievement.
4. The most formidable handicap for a creator would be
non-existence.
5. Therefore, if we suppose that the universe is the product of an
existent creator, we can conceive a greater being--namely, one
who created everything while not existing.
6. An existing God, therefore, would not be a being than which a
greater cannot be conceived, because an even more formidable and
incredible creator would be a God which did not exist.
7. (Hence) God does not exist.



This parody--at least in its current state--is inferior to
other parodies in the literature, including the early parodies of
Gaunilo and Caterus. To mention but one difficulty, while we
*might* suppose that it would be a greater achievement to
create something if one did not exist than if one did exist, it
doesn't follow from this that a non-existent creator is greater
(*qua* being) than an existent creator. Perhaps it might be
replied that this objection fails to take the first premise into
account: if the creation of the world really is "the most
marvellous achievement imaginable", then surely there is some
plausibility to the claim that the creator must have been non-existent
(since that would make the achievement more marvellous than it would
otherwise have been). But what reason is there to believe that the
creation of the world is "the most marvellous achievement
imaginable", in the sense which is required for this argument?
Surely it is quite easy to imagine even more marvellous
achievements--e.g., the creation of many worlds at least as good
as this one! (Of course, one might also want to say that, in fact, one
cannot conceive of a non-existent being's actually creating
something: that is literally inconceivable. Etc.) 



Chambers 2000 and Siegwart 2014 provide interesting recent discussions
of Gaunilo's parody of the *Proslogion II* argument.


## 7. Godel's Ontological Argument



There is a small, but steadily growing, literature on the ontological
arguments which Godel developed in his notebooks, but which did
not appear in print until well after his death. These arguments have
been discussed, annotated and amended by various leading logicians:
the upshot is a family of arguments with impeccable *logical*
credentials. (Interested readers are referred to Sobel 1987, Anderson
1990, Adams 1995b, and Hazen 1999 for the history of these arguments,
and for the scholarly annotations and emendations.) Here, we give
a brief presentation of the version of the argument which is developed
by Anderson, and then make some comments on *that* version.
This discussion follows the presentation and discussion in Oppy 1996,
2000. 



> 
> Definition 1: *x* is God-like if and only if *x* has as
> essential properties those and only those properties which are
> positive
> 
> 
> Definition 2: *A* is an essence of *x* if and only if
> for every property *B*, *x* has *B* necessarily
> if and only if *A* entails *B*
> 
> 
> 
> Definition 3: *x* necessarily exists if and only if every
> essence of *x* is necessarily exemplified
> 
> 
> 
> Axiom 1: If a property is positive, then its negation is not
> positive.
> 
> 
> 
> Axiom 2: Any property entailed by--i.e., strictly implied
> by--a positive property is positive
> 
> 
> 
> Axiom 3: The property of being God-like is positive
> 
> 
> 
> Axiom 4: If a property is positive, then it is necessarily
> positive
> 
> 
> 
> Axiom 5: Necessary existence is positive
> 
> 
> 
> Axiom 6: For any property *P*, if *P* is positive, then
> being necessarily P is positive.
> 
> 
> 
> Theorem 1: If a property is positive, then it is consistent, i.e.,
> possibly exemplified.
> 
> 
> 
> Corollary 1: The property of being God-like is consistent.
> 
> 
> 
> Theorem 2: If something is God-like, then the property of being
> God-like is an essence of that thing.
> 
> 
> 
> Theorem 3: Necessarily, the property of being God-like is
> exemplified.
> 
> 
> 



Given a sufficiently generous conception of properties, and granted
the acceptability of the underlying modal logic, the listed theorems
do follow from the axioms. (This point was argued in detail by Dana
Scott, in lecture notes which circulated for many years and which were
transcribed in Sobel 1987 and published in Sobel 2004. It is also made
by Sobel, Anderson, and Adams.) So, criticisms of the argument are
bound to focus on the axioms, or on the other assumptions which are
required in order to construct the proof.



Some philosophers have denied the acceptability of the underlying
modal logic. And some philosophers have rejected generous conceptions
of properties in favour of sparse conceptions according to which only
some predicates express properties. But suppose that we adopt neither
of these avenues of potential criticism of the proof. What else might
we say against it?



One important point to note is that no *definition* of the
notion of "positive property" is supplied with the proof.
At most, the various axioms which involve this concept can be taken to
provide a *partial* implicit definition. If we suppose that the
"positive properties" form a set, then the axioms provide
us with the following information about this set:


1. If a property belongs to the set, then its negation does not
belong to the set.
2. The set is closed under entailment.
3. The property of having as essential properties just those
properties which are in the set is itself a member of the set.
4. The set has exactly the same members in all possible worlds.
5. The property of necessary existence is in the set.
6. If a property is in the set, then the property of having that
property necessarily is also in the set.



On Godel's theoretical assumptions, we can show that
*any* set which conforms to (1)-(6) is such that the
property of having as essential properties just those properties which
are in *that* set is exemplified. Godel wants us to
conclude that there is just one intuitive, theologically interesting
set of properties which is such that the property of having as
essential properties just the properties in that set is exemplified.
But, on the one hand, what reason do we have to think that there is
*any* theologically interesting set of properties which
conforms to the Godelian specification? And, on the other hand,
what reason do we have to deny that, if there is one set of
theologically interesting set of properties which conforms to the
Godelian specification, then there are many theologically
threatening sets of properties which also conform to that
specification?



In particular, there is some reason to think that the Godelian
ontological argument goes through just as well--or just as
badly--with respect to other sets of properties (and in ways
which are damaging to the original argument). Suppose that there is
some set of independent properties {*I*,
*G*1, *G*2, ...} which can be
used to generate the set of positive properties by closure under
entailment and "necessitation".
("Independence" means: no one of the properties in the set
is entailed by all the rest. "Necessitation" means: if
*P* is in the set, then so is necessarily having *P*.
*I* is the property of having as essential properties just
those properties which are in the set. *G*1,
*G*2, ... are further properties, of which we
require at least two.) Consider any proper subset of the set
{*G*1, *G*2,
...}--{*H*1, *H*2,
...}, say--and define a new generating set {*I*\*,
*H*1, *H*2, ...}, where
*I*\* is the property of having as essential properties just
those properties which are in the newly generated set. A
"proof" parallel to that offered by Godel
"establishes" that there is a being which has as essential
properties just those properties in this new set. If there are as few
as 7 independent properties in the original generating set, then we
shall be able to establish the existence of 720
distinct"God-like" creatures by the kind of argument which
Godel offers. (The creatures are distinct because each has a
different set of essential properties.)



Even if the above considerations are sufficient to cast doubt on the
credentials of Godel's "proof", they do not
pinpoint where the "proof" goes wrong. If we accept that
the role of Axioms 1, 2, 4, and 6 is really just to constrain the
notion of "positive property" in the right way--or,
in other words, if we suppose that Axioms 1, 2, 4, and 6 are
"analytic truths" about "positive
properties"--then there is good reason for opponents of the
"proof" to be sceptical about Axioms 3 and 5. Kant would
not have been happy with Axiom 5; and there is at least some reason to
think that whether the property of being God-like is
"positive" ought to depend upon whether or not there is a
God-like being.



For detailed recent discussion of Godel's argument, see
Kovac (2003), Pruss (2009) (2018), and Swietorzecka (2016).


## 8. A Victorious Ontological Argument?



The "victorious" modal ontological argument of Plantinga
1974 goes roughly as follows: Say that an entity possesses
"maximal excellence" if and only if it is omnipotent,
omniscient, and morally perfect. Say, further, that an entity possesses
"maximal greatness" if and only if it possesses maximal
excellence in every possible world--that is, if and only if it is
necessarily existent and necessarily maximally excellent. Then
consider the following argument: 


1. There is a possible world in which there is an entity which
possesses maximal greatness.
2. (Hence) There is an entity which possesses maximal greatness.



Under suitable assumptions about the nature of accessibility relations
between possible worlds, this argument is valid: from it is possible
that it is necessary that *p*, one can infer that it is
necessary that *p*. Setting aside the possibility that one
might challenge this widely accepted modal principle, it seems that
opponents of the argument are bound to challenge the acceptability of
the premise.



And, of course, they do. Let's just run the argument in
reverse.


1. There is no entity which possesses maximal greatness.
2. (Hence) There is no possible world in which there is an entity
which possesses maximal greatness.



Plainly enough, if you do not already accept the claim that there is
an entity which possesses maximal greatness, then you won't
agree that the first of these arguments is more acceptable than the
second. So, as a proof of the existence of a being which possesses
maximal greatness, Plantinga's argument seems to be a
non-starter.



Perhaps somewhat surprisingly, Plantinga himself agrees: the
"victorious" modal ontological argument is not a proof of
the existence of a being which possesses maximal greatness. But how,
then, is it "victorious"? Plantinga writes: "Our
verdict on these reformulated versions of St. Anselm's argument
must be as follows. They cannot, perhaps, be said to *prove* or
*establish* their conclusion. But since it is rational to
accept their central premise, they do show that it is rational to
accept that conclusion" (Plantinga 1974, 221).



It is clear that Plantinga's argument does not show what he
claims that it shows. Consider, again, the argument: "Either God
exists, or 2+2=5. It is not the case that 2+2=5. So God exists."
It is a mistake for a theist to say: "Since the premise is
*true* (and the argument is valid), this argument
*shows* that the conclusion of the argument is
*true*", just as it is a mistake for a non-theist to say
that the argument "Either God does not exist, or 2+2=5. It is
not the case that 2+2=5. So God does not exist." shows that God
does not exist. Similarly, it is a mistake for a theist to say:
"Since it is *rational* to accept the premises (and the
argument is valid), this argument *shows* that it is
*rational* to accept the claim that God exists", just as
it is a mistake for the non-theist to say: "Since it is
*rational* to accept the premises of the non-theistic argument
(and that argument is valid), the non-theistic argument *shows*
that it is *rational* to accept the claim that God does not
exist". While there is room for dispute about exactly why all of
this is so, it is plausible to say that, in each case, any even
minimally rational person who has doubts about the claimed status of
the conclusion of the argument will have exactly the same doubts about
the claimed status of the premise. If, for example, I doubt that it is
rational to accept the claim that God exists, then you can be quite
sure that I will doubt that it is rational to accept the claim that
either 2+2=5 or God exists. But the very same point can be made about
Plantinga's argument: anyone with even minimal rationality who
understands the premise and the conclusion of the argument, and who
has doubts about the claim that it is rationally permissible to
believe that there is an entity which possesses maximal greatness,
will have exactly the same doubts about the claim that it is
rationally permissible to believe that there is a possible world in
which there is an entity which possesses maximal greatness.



For further discussion of Plantinga's argument, see--for
example--Adams 1988, Chandler 1993, Oppy 1995 (70-78,
248-259), Rasmussen (2018), Tooley 1981, and van Inwagen
1977).


## 9. St. Anselm's Ontological Argument



There is an enormous literature on the material in *Proslogion
II-III*. Some commentators deny that St. Anselm tried to put
forward any proofs of the existence of God. Even among commentators
who agree that St. Anselm intended to prove the existence of God,
there is disagreement about where the proof is located. Some
commentators claim that the main proof is in *Proslogion II*,
and that the rest of the work draws out corollaries of that proof
(see, e.g., Charlesworth 1965). Other commentators claim that the main
proof is in *Prologion III*, and that the proof in
*Proslogion II* is merely an inferior first attempt (see, e.g.,
Malcolm 1960). Yet other commentators claim that there is a single
proof which spans at least *Proslogion II-III*--see, e.g.,
Campbell 1976 and, perhaps, the entire work--see, e.g., La Croix
1972. In what follows, we ignore this aspect of the controversy about the
*Proslogion*. Instead, we focus just on the question of the
analysis of the material in *Proslogion II* on the assumption
that there is an independent argument for the existence of God which
is given therein. 



Here is one translation of the crucial part of *Proslogion II*
(due to William Mann (1972, 260-1); alternative translations can
be found in Barnes 1972, Campbell 1976, Charlesworth 1965, and
elsewhere):



> 
> Thus even the fool is convinced that something than which nothing
> greater can be conceived is in the understanding, since when he hears
> this, he understands it; and whatever is understood is in the
> understanding. And certainly that than which a greater cannot be
> conceived cannot be in the understanding alone. For if it is even in
> the understanding alone, it can be conceived to exist in reality also,
> which is greater. Thus if that than which a greater cannot be
> conceived is in the understanding alone, then that than which a
> greater cannot be conceived is itself that than which a greater can be
> conceived. But surely this cannot be. Thus without doubt something
> than which a greater cannot be conceived exists, both in the
> understanding and in reality.
> 



There have been many ingenious attempts to find an argument which can
be expressed in modern logical formalism, which is logically valid,
and which might plausibly be claimed to be *the* argument which
is expressed in this passage. To take a few prime examples, Adams
1971, Barnes 1972 and Oppenheimer and Zalta 1991 have all produced
formally valid analyses of the argument in this passage. We begin with
a brief presentation of each of these analyses, preceded by a
presentation of the formulation of the argument given by Plantinga
1967, and including a presentation of some of the formulations of
Lewis 1970. (Chambers 2000 works with the analysis of Adams 1971.)


### 9.1 Formulation 1


1. God exists in the understanding but not in reality. (Assumption for
*reductio*)
2. Existence in reality is greater than existence in the understanding
alone. (Premise)
3. A being having all of God's properties plus existence in reality
can be conceived. (Premise)
4. A being having all of God's properties plus existence in reality
is greater than God. (From (1) and (2).)
5. A being greater than God can be conceived. (From (3) and
(4).)
6. It is false that a being greater than God can be conceived. (From
definition of "God".)
7. Hence, it is false that God exists in the understanding but not in
reality. (From (1), (5), (6).)
8. God exists in the understanding. (Premise, to which even the Fool
agrees.)
9. Hence God exists in reality. (From (7), (8).)



See Plantinga 1967.


### 9.2 Formulation 2


1. The Fool understands the expression "the being than which no
greater can be conceived". (Premise)
2. If a person understands an expression "*b*", then
*b* is in that person's understanding. (Premise)
3. If a thing is in a person's understanding, then the person can
conceive of that thing's existing in reality. (Premise)
4. Each thing which exists in reality is greater than any thing which
exists only in the understanding. (Premise)
5. If a person can conceive of something, and that thing entails
something else, then the person can also conceive of that other thing.
(Premise)
6. If a person can conceive that a specified object has a given property,
then that person can conceive that something or other has that
property. (Premise)
7. Hence the being than which no greater can be conceived exists in
reality. (From (1)-(6), by a complex series of steps here
omitted.)



See Barnes 1972.


### 9.3 Formulation 3


1. There is a thing *x*, and a magnitude *m*, such that
*x* exists in the understanding, *m* is the magnitude of
*x*, and it it not possible that there is a thing *y*
and a magnitude *n* such that *n* is the magnitude of
*y* and *n*>*m*. (Premise)
2. For any thing *x* and magnitude *m*, if *x*
exists in the understanding, *m* is the magnitude of
*x*, and it is not possible that there is a thing *y*
and magnitude *n* such that *n* is the magnitude of
*y* and *n*>*m*, then it is possible that
*x* exists in reality. (Premise)
3. For any thing *x* and magnitude *m*, if *m* is
the magnitude of *x*, and it it not possible that there is a
thing *y* and a magnitude *n* such that *n* is
the magnitude of *y* and *n*>*m*, and
*x* does not exist in reality, then it is not possible that if
*x* exists in reality then there is a magnitude *n* such
that *n* is greater than *m* and *n* is the
magnitude of *x*. (Premise)
4. (Hence) There is a thing *x* and a magnitude *m* such
that *x* exist in the understanding, and *x* exists in
reality, and *m* is the magnitude of *x*, and it it not
possible that there is a thing *y* and a magnitude *n*
such that *n* is the magnitude of *y* and
*n*>*m*. (From 1, 2, 3)



See Adams 1971.


### 9.4 Formulation 4


1. For any understandable being *x*, there is a world *w*
such that *x* exists in *w*. (Premise)
2. For any understandable being *x*, and for any worlds *w*
and *v*, if *x* exists in *w*, but *x*
does not exist in *v*, then the greatness of *x* in
*w* exceeds the greatness of *x* in *v*.
(Premise)
3. There is an understandable being *x* such that for no world
*w* and being *y* does the greatness of *y* in
*w* exceed the greatness of *x* in the actual world.
(Premise)
4. (Hence) There is a being *x* existing in the actual world such
that for no world *w* and being *y* does the greatness
of *y* in *w* exceed the greatness of *x* in the
actual world. (From (1)-(3).)



See Lewis 1970.



Lewis also suggests an alternative to (3) which yields a valid
argument:



> 
> (3') There is an understandable being *x* such that for
> no worlds *v* and *w* and being *y* does the
> greatness of *y* in w exceed the greatness of *x* in
> *v*.
> 



and two alternatives to (3)--not presented here--which yield
invalid arguments. (Of course, these further two alternatives are
crucial to Lewis' overall analysis of the passage: essentially,
Lewis suggests that Anselm equivocates between an invalid argument
with plausible premises and a valid argument with question-begging
premises. In this respect, Lewis' analysis is quite different
from the other analyses currently under discussion.)


### 9.5 Formulation 5


1. There is (in the understanding) something than which there is no
greater. (Premise)
2. (Hence) There is (in the understanding) a unique thing than which
there is no greater. (From (1), assuming that the
"greater-than" relation is connected.)
3. (Hence) There is (in the understanding) something which is the thing
than which there is no greater. (From (2), by a theorem about
descriptions.)
4. (Hence) There is (in the understanding) nothing which is greater than
the thing than which there is no greater. (From (3), by another
theorem about descriptions.)
5. If that thing than which there is no greater does not exist (in
reality), then there is (in the understanding) something which is
greater than that thing than which there is no greater.
(Premise)
6. (Hence) That thing than which there is no greater exists (in reality).
(From (4) and (5).)
7. (Hence) God exists. (From (6).)



See Oppenheimer and Zalta 1991.



Oppenheimer and Zalta 2011 provides a "simplified" version
of this argument, in which the number of controversial assumptions is
reduced. Since they also provide a clear reason for thinking that this
new version of the argument is not persuasive, it won't be considered
further here. 


### 9.6 Critical Appraisal



Considered as interpretations of the argument presented in the
*Proslogion*, these formulations are subject to various kinds
of criticisms. 



*First*, the modal interpretations of Lewis 1970 and Adams 1971
don't square very well with the rest of the *Proslogion*:
the claim that "being than which no greater can be
conceived" should be read as "being than which no greater
is possible" would have us render the claim of *Proslogion
15* to be that God is a being greater than any which is possible.
And that is surely a bad result.



*Second*, the Meinongian interpretations of Barnes 1972, Adams
1971 and Oppenheimer and Zalta 1991 produce arguments which, given the
principles involved, could easily be much simplified, and which are
*obviously* vulnerable to Gaunilo-type objections.



Consider, for example, the case of Oppenheimer and Zalta. They have
Anselm committed to the claim that if anyone can understand the phrase
"that than which *F*", then there is something in
the understanding such that *F* (see their footnote 25); and
they also have him committed to the claim that if there is something
which is the *F*-thing, then it--i.e., the
*F*-thing--has the property *F* (see page 7).
Plainly though, if Anselm is really committed to these principles,
then he could hardly fail to be committed to the more general
principles: (1) if anyone can understand the phrase "an
*F*", then there is at least one *F*-thing in the
understanding; and (2) if there are some things which are the
*F*-things, then they--i.e., the
*F*-things--must have the property *F*. (It would
surely be absurd to claim that Anselm is only committed to the less
general principles: what could possibly have justified the
restrictions to the special cases?)



But, then, mark the consequences. We all understand the expression
"an existent perfect being". So, by the first claim, there
is at least one existent perfect being in the understanding. And, by
the second claim, any existent perfect being is existent. So, from
these two claims combined, there is--in reality--at least
one existent perfect being.



This argument gives Anselm everything that he wants, and very much
more briefly. (The *Proslogion* goes on and on, trying to
establish the properties of that than which no greater can be
conceived. How much easier if we can just explicitly build all of the
properties which want to "derive" into the initial
description.) So, if Anselm really were committed to the principles
which Oppenheimer and Zalta appear to attribute to him, it is hard to
understand why he didn't give the simpler argument. And, of
course, it is also hard to understand why he didn't take
Gaunilo's criticism. After all, when it is set out in this way,
it is obvious that the argument proves far too much.



*Third*, some of the arguments have Anselm committed to claims
about greatness which do not seem to correspond with what he actually
says. The natural reading of the text is that, if two beings are
identical save that one exists only in the understanding and the other
exists in reality as well, then the latter is greater than the former.
But Barnes 1971, for example, has Anselm committed to the much
stronger claim that any existing thing is greater than every
non-existent thing.



Given these kinds of considerations, it is natural to wonder whether
there are *better* interpretations of *Proslogion II*
according to which the argument in question turns out *NOT* to
be logically valid. Here is a modest attempt to provide such an
analysis:



We start with the claim that the Fool understands the expression
"being than which no greater can be conceived", i.e., even
the Fool can entertain the idea or possess the concept of a being than
which no greater can be conceived. Now, entertaining this idea or
possessing this concept requires the entertainer or possessor to
recognise certain relationships which hold between given properties
and the idea or concept in question. For example, given that you
possess the concept of, or entertain the idea of, a smallest really
existent Martian, it follows that you must recognise some kind of
connection between the properties of being a Martian, really existing,
and being smaller than other really existing Martians, and the concept
or idea in question.



Following Anselm, we might say that, since you understand the
expression "smallest really existent Martian", there is,
in your understanding, at least one smallest really existent Martian.
(Or, apparently following Descartes, one might say that real existence
is "part of"--or "contained in"--the
idea of a smallest really existent Martian.) However, in saying this,
it must be understood that we are not actually predicating properties
of anything: we aren't supposing that there is something which
possesses the properties of being a Martian, really existing, and
being no larger than any other Martian. (After all, we can safely
suppose, we don't think that any Martians really exist.) In
other words, we must be able to have the concept of, or entertain the
idea of, a smallest really existing Martian without believing that
there really are any smallest Martians. Indeed, more strongly, we must
be able to entertain the concept of a smallest really existent
Martian--and to recognise that the property of "really
existing" is part of this concept--while nonetheless
maintaining that there are no smallest existent Martians.



It will be useful to introduce vocabulary to mark the point which is
being made here. We could, for instance, distinguish between the
properties which are *encoded* in an idea or concept, and the
properties which are *attributed* in positive atomic beliefs
which have that idea or concept as an ingredient. The idea
"really existent Santa Claus" encodes the property of real
existence; but it is perfectly possible to entertain this idea without
attributing real existence to Santa Claus, i.e., without believing
that Santa Claus really exists.



We can then apply this distinction to Anselm's argument. On the
one hand, the idea "being than which no greater can be
conceived" encodes the property of real existence--this is
what the *reductio* argument establishes (if it establishes
anything at all). On the other hand, it is perfectly possible to
entertain the idea of a being than which no greater can be
conceived--and to recognise that this idea encodes the property
of real existence--without attributing real existence to a being
than which no greater can be conceived, i.e., without believing that a
being than which no greater can be conceived really exists.



Of course, the argument which Anselm actually presents pays no
attention to this distinction between encoding and
attributing--i.e., between entertaining an idea and holding a
belief--and nor does it pay attention to various other niceties.
We begin from the point that the Fool entertains the idea of that than
which no greater can be conceived (because the Fool understands the
words "that than which no greater can be conceived"). From
this, we move quickly to the claim that even the Fool is
"convinced"--i.e., believes--that that than
which no greater can be conceived possesses the property of existing
in the understanding. And then the *reductio* argument is
produced to establish that that than which no greater can be conceived
cannot exist only in the understanding but must also possess the
property of existing in reality as well (and all mention of the Fool,
and what it is that the Fool believes, disappears).



As it stands, this is deeply problematic. How are we supposed to
regiment the references to the Fool in the argument? Is the
*reductio* argument supposed to tell us something about what
even the Fool believes, or ought to believe? Are the earlier
references to the Fool supposed to be inessential and eliminable? How
are we so much as to understand the claim that even the Fool believes
that that than which no greater can be conceived exists in the
understanding? And how do we get from the Fool's
*understanding* the words "that than which no greater can
be conceived" to his *believing* that that than which no
greater can be conceived possesses the property of existing in the
understanding?



Following the earlier line of thought, it *seems* that the
argument might go something like this:


1. (Even) the Fool has the concept of that than which no greater can be
conceived.
2. (Hence) (Even) the Fool believes that that than which no greater can
be conceived exists in the understanding.
3. No one who believes that that than which no greater can be conceived
exists in the understanding can reasonably believe that that than
which no greater can be conceived exists only in the
understanding.
4. (Hence) (Even) the Fool cannot reasonably deny that that than which no
greater can be conceived exists in reality
5. (Hence) That than which no greater can be conceived exists in
reality.



While this is not a good argument, it could appear compelling to one
who failed to attend to the distinction between entertaining ideas and
holding beliefs and who was a bit hazy on the distinction between the
vehicles of belief and their contents. When the Fool entertains the
concept of that than which no greater can be conceived he recognises
that he is entertaining this concept (i.e., he believes that he is
entertaining the concept of that than which no greater can be
conceived--or, as we might say, that the concept is in his
understanding). Conflating the concept with its object, this gives us
the belief that than which no greater can be conceived possesses the
property of existing in the understanding. Now, suppose as hypothesis
for *reductio*, that we can reasonably believe that that than
which no greater can be conceived possesses the property of existing
only in the understanding. Ignoring the distinction between
entertaining ideas and holding beliefs, this means that we when we
entertain the idea of that than which no greater can be conceived, we
entertain the idea of a being which exists only in the understanding.
But that is absurd: when we entertain the idea of that than which no
greater can be conceived, our idea encodes the property of existing in
reality. So there is a contradiction, and we can conclude that, in
order to be reasonable, we must believe that that than which no
greater can be conceived exists in reality. But if any reasonable
person must believe that that than which no greater can be conceived
exists in reality, then surely it is the case that that than which no
greater can be conceived exists in reality. And so we are done.



No doubt this suggestion about the interpretation of Anselm's
argument is deficient in various ways. However, the point of including
it is illustrative rather than dogmatic. In the literature, there has
been great resistance to the idea that the argument which Anselm gives
is one which modern logicians would not hesitate to pronounce invalid.
But it is very hard to see why there should be this resistance.
(Certainly, it is not something for which there is much argument in
the literature.) The text of the *Proslogion* is so rough, and
so much in need of polishing, that we should not be too quick to
dismiss the suggestion that Anselm's argument is rather more
like the argument most recently sketched than it is like the logically
valid demonstrations provided by commentators such as Barnes, Adams,
and Oppenheimer and Zalta. (For a more complex analysis of
*Proslogion II* that has it yielding a valid argument, see
Hinst 2014.)


## 10. Ontological Arguments in the 21st Century



Many recent discussions of ontological arguments are in compendiums,
companions, encyclopedias, and the like. So, for example, there are
review discussions of ontological arguments in: Leftow 2005, Matthews
2005, Lowe 2007, Oppy 2007, and Maydole 2009. While the ambitions of
these review discussions vary, many of them are designed to introduce
neophytes to the arguments and their history. Given the current
explosion of enthusiasm for compendiums, companions, encyclopedias, and
the like, in philosophy of religion, it is likely that many more such
discussions will appear in the immediate future.



Some recent discussions of ontological arguments have been placed in
more synoptic treatments of arguments about the existence of God. So,
for example, there are extended discussions of ontological arguments
in Everitt 2004, Sobel 2004, and Oppy 2006. Sobel's examination
of ontological arguments is exemplary. He provides one chapter on
'classical ontological arguments': Anselm, Descartes,
Spinoza, and Kant's critique of ontological arguments; one
chapter on 'modern modal ontological arguments':
Hartshorne, Malcolm and Plantinga; and one chapter on
Godel's ontological argument. His analyses are very
careful, and make heavy use of the tools of modern philosophical
logic.



There has been one recent monograph devoted exclusively to the
analysis of ontological arguments: Dombrowski 2006. Dombrowski is a
fan of Hartshorne: the aim of his book is to defend the claim that
Hartshorne's ontological argument is a success. While
Dombrowski's book is a useful addition to the literature because
of the scope of its discussion of ontological arguments--for
example, it contains a chapter on Rorty on ontological arguments, and
another chapter on John Taylor on ontological arguments--even
reviewers sympathetic to process theism have not been persuaded that
it makes a strong case for its central thesis.



Szatkowski (2012) is a recent collection of papers on ontological
arguments. A significant proportion of papers in this collection take
up technical questions about logics that support ontological
derivations. (Those interested in technical questions may also be
interested in the topic taken up in Oppenheimer and Zalta (2011) and
Gorbacz (2012).) The most recent collection is Oppy (2018). 



Finally, there has been some activity in journals. The most
significant of these pieces is Millican 2004, the first article on
ontological arguments in recent memory to appear in *Mind*.
Millican argues for a novel interpretation of Anselm's argument,
and for a new critique of ontological arguments deriving from this
interpretation. Needless to say, both the interpretation and the
critique are controversial, but they are also worthy of attention.
Among other journal articles, perhaps the most interesting is Pruss
2010, which provides a novel defence of the key possibility premise in
modal ontological arguments. There is also a chain of papers in
*Analysis* initiated by Matthews and Baker (2010)



Relatively recent work on ontological arguments by women includes:
Anscombe (1993), Antognazza (2018), Crocker (1972), Diamond (1977),
Ferreira (1983), Garcia (2008), [Haight and] Haight (1970), [Matthews
and] Baker (2011), Wilson (1978) and Zagzebski (1984).