Ontological arguments are arguments, for the conclusion that Godexists, from premises which are supposed to derive from some sourceother than observation of the world—e.g., from reason alone. Inother words, ontological arguments are arguments from what aretypically alleged to be none but analytic,a priori andnecessary premises to the conclusion that God exists.

The first, and best-known, ontological argument was proposed by Anselmof Canterbury in the eleventh century CE. In hisProslogion,Anselm claims to derive the existence of that than which no greatercan be conceived from the concept ofthat than which no greatercan be conceived. Anselm reasoned that, if such a being fails toexist, then a greater being—namely, abeing than which nogreater can be conceived, and which exists—can beconceived. But this would be absurd: nothing can be greater than abeing than which no greater can be conceived. So a being than which nogreater can be conceived exists. And, very plausibly, if that thanwhich no greater can be conceived exists, then it is God and so Godexists.

In the seventeenth century, René Descartes defended a family ofsimilar arguments. For instance, in theFifth Meditation,Descartes claims to provide a proof demonstrating the existence of asupremely perfect being from the idea of a supremely perfect being.Descartes argues that there is no less contradiction in conceiving asupremely perfect being who lacks existence than there is inconceiving a triangle whose interior angles do not sum to 180 degrees.Hence, he supposes, since we do conceive a supremely perfectbeing—we do have the idea of a supremely perfect being—wemust conclude that a supremely perfect being exists. And, veryplausibly, if a supremely perfect being exists, then God exists.

In the early eighteenth century, Gottfried Leibniz attempted to fillwhat he took to be a shortcoming in Descartes’ view. Accordingto Leibniz, Descartes’ arguments fail unless one first showsthat the idea of a supremely perfect being is coherent, or that it ispossible for there to be a supremely perfect being. Leibniz arguedthat, since perfections are unanalyzable, it is impossible todemonstrate that perfections are incompatible—and he concludedfrom this that all perfections can co-exist together in a singleentity.

In more recent times, Kurt Gödel, Charles Hartshorne, NormanMalcolm, and Alvin Plantinga have all presented much-discussedontological arguments which bear interesting connections to theearlier arguments of Anselm, Descartes, and Leibniz. Of these, themost interesting are those of Gödel and Plantinga; in thesecases, however, it is unclear whether we should really say that theseauthors claim that the arguments areproofs of the existenceof God.

Critiques of ontological arguments begin with Gaunilo, a contemporaryof Anselm. Perhaps the best known criticisms of ontological argumentsare due to Immanuel Kant, in hisCritique of Pure Reason.Most famously, Kant claims that ontological arguments are vitiated bytheir reliance upon the implicit assumption that“existence” is a real predicate. However, as BertrandRussell (1946: 586) observed, it is much easier to be persuaded thatontological arguments are no good than it is to say exactly what iswrong with them. This helps to explain why ontological arguments havefascinated philosophers for almost a thousand years.

• 1. Timeline
• 2. Taxonomy
• 3. Characterisation
• 4. Uses and Goals
• 5. Descartes
• 6.Proslogion II
• 7. Meinong
• 8. Modal
• 9. Gödel
• 10. Hegel
• 11. Parodies
• 12. General Objections
• 13. Concluding Observations
• Bibliography
  • Primary Texts
  • Other Texts
• Academic Tools
• Other Internet Resources
• Related Entries

1. Timeline

1078

Anselm of Canterbury,Proslogion. Followed soon after byGaunilo’s critiqueOn Behalf of the Fool.

1264

Thomas Aquinas,Summa. Criticises an argument whichsomehow descends from Anselm.

1637

Descartes,Discourse on Method. The argument of Discourse4 is further elaborated in theMeditations. TheObjections—particularly those of Caterus andGassendi—and theReplies contain much valuablediscussion of the Cartesian arguments.

c1680

Spinoza,Ethics. Intimations of a potentially defensibleontological 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 byshowing that the Cartesian conception of God is not inconsistent.

1776

Hume,Dialogues Concerning Natural Religion. Part IX is ageneral attack ona priori arguments (both analytic andsynthetic). Includes a purported demonstration that no such argumentscan be any good.

1787

Kant,Critique of Pure Reason. Contains much discussedattacks on traditional theistic arguments. Three objections to“the ontological argument”, including the famous objectionbased on the dictum that existence is not a predicate.

1831

Hegel,Lectures of 1831. In these lectures, Hegel saysthat “the ontological argument” succeeds. However, he doesnot make it clear what he takes the premises of “the ontologicalargument” to be; and nor does he make it clear what it would befor “the ontological argument” to succeed. Some scholarshave claimed that the entire Hegelian corpus constitutes anontological argument.

1884

Frege,Foundations of Arithmetic. Existence is asecond-order predicate. First-order existence claims are meaningless.So ontological arguments—whose conclusions are first-orderexistence claims—are doomed.

1941

Hartshorne,Man’s Vision of God. Defence of modalontological arguments, allegedly derived fromProslogion3.

1970

Lewis, “Anselm and Actuality”. Critique of ontologicalarguments. All ontological arguments are either invalid orquestion-begging; moreover, in many cases, they have two closelyrelated readings, one of which falls into each of the abovecategories.

Godel, “Ontological Proof”. Presentation of ahigher-order modal ontological argument, inspired by the argument thatLeibniz devised in the early eighteenth century, with the conclusionthat God exists. Published in hisCollected Works(1995).

1974

Plantinga,The Nature of Necessity. Plantinga’s“victorious” modal Ontological argument.

For a useful discussion of the history of ontological arguments in themodern period, see Harrelson 2009. For recent attempts to defend oneor more ontological arguments, see Dombrowski 2006, Lowe 2007,Matthews & Baker 2010, Nagasawa 2017, Campbell 2018, and Leftow2022. For detailed critical discussion of ontological arguments, seeSobel 2004 and Oppy 1996.

2. Taxonomy

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

1. Definitional ontological arguments;
2. Conceptual (or hyperintensional) ontological arguments;
3. Modal ontological arguments;
4. Meinongian ontological arguments;
5. Higher-order ontological arguments; and
6. ‘Hegelian’ ontological arguments.

Examples of all but the last follow. These are mostly toy examples,but they serve to highlight features of more complex ontologicalarguments.

First, a (toy) definitional ontological argument:

1. God is a being which has every perfection. (Premise,true by definition.)
2. Existence is a perfection. (Premise)
3. Hence God exists. (Fromi,ii)

Second, a (toy) conceptual ontological argument:

1. I conceive of a being than which no greater can beconceived. (Premise)
2. If a being than which no greater can be conceived doesnot exist, then I can conceive of a being greater than a being thanwhich no greater can be conceived—namely, a being than which nogreater can be conceived that exists. (Premise)
3. I cannot conceive of a being greater than a being thanwhich no greater can be conceived. (Premise)
4. Hence, a being than which no greater can be conceivedexists. (Fromi,ii, andiii)

Third, a (toy) modal ontological argument:

1. It is possible that God exists. (Premise)
2. God is not a contingent being, i.e., either it is notpossible that God exists, or it is necessary that God exists.(Premise)
3. Hence, it is necessary that God exists. (Fromi andii)
4. Hence, God exists. (Fromiii. See Malcolm 1960, Hartshorne 1965, and Plantinga 1974 for closelyrelated arguments.)

Fourth, a (toy) Meinongian ontological argument:

1. [It is analytic, necessary anda priori that]Each instance of the schema “TheF G isF” expresses a truth. (Premise)
2. Hence the sentence “The existent perfect being isexistent” expresses a truth. (Fromi)
3. Hence, the existent perfect being is existent. (Fromii)
4. Hence, God is existent, i.e., God exists. (Fromiii. The last step is justified by the observation that, as a matter ofdefinition, if there is exactly one existent perfect being, then thatbeing is God.)

Fifth, a (toy) higher-order ontological argument:

1. A God-property is a property that is possessed by God inall and only those worlds in which God exists. (Definition)
2. Not all properties are God properties. (Premise)
3. Any property entailed by a collection of God-properties isitself a God-property. (Premise)
4. The God-properties include necessary existence, necessaryomnipotence, necessary omniscience, and necessary perfect goodness.(Premise)
5. Hence, there is a necessarily existent, necessarilyomnipotent, necessarily omniscient, and necessarily perfectly goodbeing (namely, God). (Fromi–iv.)

Of course, this taxonomy is not exclusive: an argument can belong toseveral categories at once. Moreover, an argument can be ambiguousbetween a range of readings, each of which belongs to differentcategories. This latter fact may help to explain part of the curiousfascination of ontological arguments. Finally, the taxonomy can befurther specialised: there are, for example, at least four importantlydifferent kinds of modal ontological arguments which should bedistinguished. (See, e.g., Ross 1969 for a rather different kind ofmodal ontological argument.)

Other (in our viewminor) categories of ontological argumentsthat might be added to this taxonomy include:

1. mereological (or Spinozistic) ontological arguments and
2. experiential ontological arguments.

The former category might be exemplified in something like thefollowing (toy) argument:

1. I exist.
2. Therefore something exists.
3. Whenever a bunch of things exist, their mereological sum alsoexists.
4. Therefore the sum of all things exists.
5. Therefore God—the sum of all things—exists.

And the latter might be exemplified in the following (toy) argument(and see Rescher 1959):

1. The word ‘God’ has a meaning that is revealed inreligious experience. (Premise)
2. The word ‘God’ has a meaning only if God exists.(Premise)
3. Hence, God exists.

3. Characterisation

It is not easy to give a good characterisation of ontologicalarguments. The traditional characterisation involves the use ofcontroversial notions—analyticity, necessity, andapriority—and also fails to apply to many arguments to whichdefenders have affixed the label “ontological”. (Consider,for example, the claim that I conceive of a being than which nogreater can be conceived. This claim is clearly not analytic (itstruth doesn’t follow immediately from the meanings of the wordsused to express it), nor necessary (I might never have entertained theconcept), nora priori (except perhaps in my own case, thougheven this is unclear—perhaps even I don’t knowindependently of experience that I have this concept.)) However, it isunclear how that traditional characterisation should be improvedupon.

Perhaps one might resolve to use the label “ontologicalargument” for any argument which gets classified as “anontological argument” by its proponent(s). This procedure wouldmake good sense if one thought that there is a naturalkind—ontological arguments—which our practice carves out,but for which it is hard to specify defining conditions. Moreover,this procedure can be adapted as apro tem stop gap: whenthere is a better definition to hand, that definition will be adoptedinstead. On the other hand, it seems worthwhile to attempt a moreinformative definition.

Focus on the case of ontological arguments for the conclusion that Godexists. One characteristic feature of these arguments is the use whichthey make of “referential vocabulary”—names,definite descriptions, indefinite descriptions, quantified nounphrases, etc.—whose ontological commitments—foroccurrences of this vocabulary in “referentialposition”—non-theists do not accept.

Theists and non-theists alike (can) agree that there isspatio-temporal, or causal, or nomic, or modal structure to the world(the basis for cosmological arguments); and that there are certainkinds of complexity of organisation, structure and function in theworld (the basis for teleological arguments); and so on. But theistsand 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 theindirectsubject matter of the premises of ontological arguments.

Of course, the premises of ontological arguments often do not dealdirectly with perfect beings, beings than which no greater can beconceived, 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 theuse of vocabulary which non-theists should certainly find problematicwhen it is used in ontologically committing contexts.

Note that this characterisation does not beg the question against thepossibility of the construction of a successful ontologicalargument—i.e., it does not lead immediately to the conclusionthat all ontological arguments are question-begging (in virtue of theontologically committing vocabulary which they employ). For it may bethat the vocabulary in question only gets used in premises in waysthat carry no ontological commitment. Of course, there will then bequestions about whether the resulting arguments can possibly bevalid—how could the commitments turn up in the conclusion ifthey are not there in the premises?—but those are furtherquestions, which would remain to be addressed.

4. Uses and Goals

Before we turn to assessment of ontological arguments, we need to getclear about what the proper intended goals of ontological argumentscan be. Suppose we think of arguments as having advocates and targets:when an advocate presents an argument to a target, the goal of theadvocate is to bring about some change in the target. What might bethe targets of ontological arguments, and what might be the changesthat advocates of these arguments aim to bring about in thosetargets?

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

• The targets might be atheists, and the goal might be to turn theminto theists.
• The targets might be agnostics, and the goal might be to turn theminto theists.
• The targets might be theists, and the goal might be to improve thedoxastic position of theists.
• The targets might be professional philosophers, and the goal mightbe to advance understanding of the consequences of adopting particularlogical rules, or treating existence as a real predicate, or allowingdefinitions to have existential import, or the like.
• The targets might be undergraduate philosophy students, and thegoal might be to give them some sufficiently frustrating examples onwhich to cut their critical teeth.

In the coming discussion, it will be supposed that the targets areatheists and agnostics, and that the goal is to turn them intotheists. Suppose that an advocate presents an ontological argument toa target. What conditions must that argument satisfy if it is fit forits intended purpose? A plausible suggestion is that, minimally, itshould make the targets recognise that they have good reason to acceptthe conclusion of the argument that they did not recognise that theyhave prior to the presentation of the argument. Adopting thisplausible suggestion provides the following criterion: a successfulontological argument is one that should make atheists and agnosticsrecognise that they have good reason to believe that God exists thatthey did not recognise that they have prior to the presentation of theargument. Note that this criterion has a normative dimension: itadverts to what atheists and agnosticsshould do whenpresented with the argument.

There is an important discussion to be had about whether we shouldsuppose that the targets of ontological arguments are atheists andagnostics and that the goal is to turn them into theists. It is simplybeyond the scope of this entry to fully pursue that discussion here.We conclude this section by mentioning just one straw in the wind.

Towards the end of his presentation of his modal ontological argument,Plantinga writes:

Our verdict on these reformulated versions of St. Anselm’sargument must be as follows. They cannot, perhaps, be said toprove orestablish their conclusion. But since it isrational to accept their central premise, they do show that it isrational to accept that conclusion. (1974: 221)

Here, it seems, Plantinga is supposing that the targets of ontologicalarguments are those who think that it is not rationally permissible tobelieve in God. Moreover, it seems reasonable to think that hisambition is to bring them to think that it is rationally permissibleto believe in God. But the difficulty here is that the reasons that wehave for supposing that his arguments are insufficient to bringatheist and agnostics to belief in God carry over quitestraightforwardly to reasons for supposing that his arguments areinsufficient to bring those who think that it is not rationallypermissible to believe in God to belief that it is rationallypermissible to believe in God. Atheists think that at least onepremise in his argument is false. Agnostics are undecided about atleast one premise in his argument. And those who think that it is notrationally permissible to believe in God think that there is at leastone premise in his argument in which it is not rationally permissibleto believe.

Perhaps it might be objected that Plantinga supposes, instead, thatthe targets of ontological arguments are theists.However—setting aside the point that it is not at all clear whatsuch arguments could do for theists—it is unclear why Plantingasupposes that the status of the claim that it is rationallypermissible to believe that God exists is importantly different fromthe status of the claim that God existsfor theists. Afterall, theists for whom Plantinga thinks that the argument might do someuseful work believe all of the premisesand believe that allof the premises are such that it is rationally permissible to believethem. What could be the source of the asymmetry which brings it aboutthat, while the argument fails to show to these theists that Godexists, it succeeds in showing to these theists that it is rationallypermissible to believe in God?

For discussion of Plantinga’s argument, seeSection 8 below.

5. Descartes

Descartes presents what have come to be called ‘Cartesianontological arguments’ in various places:Meditation V,many of theReplies (including theFirst (Caterus),theSecond (mostly Mersenne), and theFifth(Gassendi)),Discourse IV, andPrinciples XIV.Although there is little that is uncontroversial in the discussion ofCartesian ontological arguments, even the most casual reading of thetexts reveals that the following argument has some relevance:

1. God has every perfection.
2. Independent existence is a perfection.
3. (So) God exists.

While it is now quite common to claim that Descartes was not advancingany argument in favour of the existence of God in the texts inquestion—see, for example, the entry onDescartes’ ontological argument—it is clear that, insofar as there is a valid argument for the existenceof God that is properly associated with the Cartesian texts, it issomething like the argument just given.

A natural objection to this argument is that the conclusion followstrivially from the first premise alone. While the argument isvalid—albeit possessed of a redundant premise—it isobvious that it can play no role in persuading informed atheists andagnostics to change their views. After all, informed atheists denythat God has every perfection on the ground that God does not exist,i.e., on the ground that there is no God that has so much as oneperfection, let alone all of them. Equally, informed agnostics do notaccept that God has every perfection by dint of not accepting that Godexists, i.e., by dint of not accepting that there is a God that has somuch as one perfection, let alone all of them.

One response to this objection is to reject the claim that it followsfrom the non-existence of God that there are no true sentences of theform ‘God has [such and such perfection]’. To go this wayis to suppose that there are non-existent beings that nonetheless canbe truly claimed to have properties. That is the way of Meinong. Weshall return to consider it below.

Another response to this objection is to claim that the first premisereally doesn’t do justice to the argument that is properlyassociated with the Cartesian texts. On this kind of view, theargument is better represented like this:

1. By definition, God has every perfection
2. Independent existence is a perfection.
3. (So) God exists.

This won’t do. The argument is now clearly invalid. The mostthat we can conclude, from the premise set is: (By definition) God hasindependent existence. And it simply does not follow from this thatGod exists. No informed agnostic or atheist, when presented with anargument that begins with the claim that, by definition, God is thebeing that has every perfection, will reach any conclusion other thanthat there is no being that has every perfection (on the grounds thatthere is no God).

There are other fixes to which one might turn. Perhaps we might followrecent discussion which claims that all that Descartes wants to commithimself to, initially, is that it is obvious to intuition that God hasevery perfection.

1. Intuitively, God has every perfection.
2. Independent existence is a perfection.
3. (So) God exists.

On the most natural reading of this argument, it suffers from the sameliability as the very first argument that we associated with theCartesian text: given that we accept thatp follows fromintuitivelyp, it is clear that informed agnostics andatheists reject that claim that intuitively, God has every perfection.And, on what seems a less natural reading of the argument, which takesit to be saying something like the following:

1. It seems intuitive to me (Descartes) that God has everyperfection.
2. Independent existence is a perfection.
3. (So) God exists.

the argument is obviously invalid. Why should informed agnostics oratheists be in the least bit impressed by what seems intuitive toDescartes on the question whether God has everyperfection?

There is a general lesson that we can extract at this point. If werepresent our Cartesian argument in the following way:

1. [Operator] God has every perfection.
2. Independent existence is a perfection.
3. (So) God exists.

then we can raise the following question: what could possibly go infor[Operator] that would both (a) yield a claim that isacceptable to informed agnostics and atheists, and (b) deliver a validargument? It is tempting to suggest that, at least setting Meinongianconsiderations to one side, it is obvious that there isn’tanything that can fit this bill.

There is a very large and complicated literature on Cartesianontological arguments. Apart from the discussion in the SEP entry onDescartes’ ontological argument, readers might like to consider: Nolan (2018).

6.Proslogion II

There is an enormous literature on the material inProslogionII–IV. Some commentators deny that Anselm tried to putforward any proofs of the existence of God. Even among commentatorswho agree that Anselm intended to prove the existence of God, there isdisagreement about where the proof is located. Some commentators claimthat the main proof is inProslogion II, and that the rest ofthe work draws out corollaries of that proof (see, e.g., Charlesworth1965). Other commentators claim that the main proof is inProslogion III, and that the proof inProslogion IIis merely an inferior first attempt (see, e.g., Malcolm 1960). Yetother commentators claim that there is a single proof which spans atleastProslogion II–III (see, e.g., Campbell 1976 andTapp & Siegwart 2022) and, perhaps, the entire work (see, e.g., LaCroix 1972). In what follows, we ignore this aspect of the controversyabout theProslogion. Instead, we focus just on the questionof the analysis of the material inProslogion II on theassumption that there is an independent argument, for the existence(in reality) of that than which no greater can be conceived, that isgiven therein.

Here is one translation of the crucial part ofProslogion II(due to William Mann [1972: 260–1]; alternative translations canbe found in Barnes 1972, Campbell 1976, Charlesworth 1965, andelsewhere):

Thus even the fool is convinced that something than which nothinggreater can be conceived is in the understanding, since when he hearsthis, he understands it; and whatever is understood is in theunderstanding. And certainly that than which a greater cannot beconceived cannot be in the understanding alone. For if it is even inthe understanding alone, it can be conceived to exist in reality also,which is greater. Thus if that than which a greater cannot beconceived is in the understanding alone, then that than which agreater cannot be conceived is itself that than which a greater can beconceived. But surely this cannot be. Thus without doubt somethingthan which a greater cannot be conceived exists, both in theunderstanding and in reality.

There have been many ingenious attempts to find an argument which canbe expressed in modern logical formalism, which is logically valid,and which might plausibly be claimed to bethe argument whichis expressed in this passage. As a first effort, we might suppose thatthe argument might be represented as follows:

1. When the fool hears the words ‘that than which nogreater can be conceived’ he understands those words.(Premise)
2. Whatever is understood exists in the understanding.(Premise)
3. (So) That than which no greater can be conceived existsin the understanding. (Fromi,ii)
4. If that than which no greater can be conceived exists inthe understanding, it can be conceived to exist in reality.(Premise)
5. That than which no greater can be conceived is greaterif it exists in reality than if it exists only in the understanding.(Premise)
6. It is impossible to conceive of something greater thanthat than which no greater can be conceived. (Premise)
7. (So) That than which no greater can be conceived existsin reality. (Fromiii,iv,v, andvi.)

The obvious difficulty with this representation is that it is notexactly clear how we are meant to get to(vii) from(iii),(iv),(v), and(vi). We might hope to confront this difficulty by‘translating’ Anselm’s argument into a differentidiom. However, attempts to recast Anselm’s argument in modalterms or Meinongian terms seem not to do justice both toAnselm’s argumentative ambitions and to other sections of theProslogion.

If we stick with a formulation that stays close to the original text,then there are many other questions of interpretation that remain tobe addressed. In particular, the key vocabulary that is used inframing this argument raises many issues. What is it for one thing tobe ‘greater’ than another? What is required for it to betrue that something ‘can be conceived’? What is meant by‘the understanding’? What is it for something to‘exist in the understanding’? How is ‘existence inthe understanding’ related to being something that ‘can beconceived’? Can the very same thing ‘exist in theunderstanding’ and ‘exist in reality’? If so, doesit have the very same properties ‘in the understanding’and ‘in reality’? Since we certainly appear to understandthe expression ‘the really existent tallest inhabitant of theplanet Mars’, does Anselm think that the really existent tallestinhabitant of the planet Mars exists in the understanding? If so, doeshe think that, in the understanding, the really existent tallestinhabitant of the planet Mars has the property of really existing? Ifso, does he think that it follows that the really existent tallestinhabitant of the planet Mars has the property of really existing?Would Anselm be uncomfortable witha priori commitment to thereal existence of Martians? Would he deny that we understandthe expression ‘the really existent tallest inhabitant of theplanet Mars’? Would he say that, even though, in theunderstanding, the really existent tallest inhabitant of the planetMars has the property of really existing, nonetheless it does notfollow that that the really existent tallest inhabitant of the planetMars has the property of really existing? And so on.

The important point here is that, until we are given answers to thequestions raised in the previous paragraph, we have no way ofdetermining whether anyone can safely accept Anselm’stheoretical framework. It is not true that the only important questionis whether Anselm’s conclusion follows from his premises.Another equally important question is what else follows from the(perhaps tacit) theory that informs Anselm’s construction of theargument. If that theory has absurd consequences, then the validity ofthe argument is inconsequential.

The literature onProslogion II–IV is so vast that itcould easily have an entry devoted solely to it. Important recentcontributions to the literature include: Campbell (2018); Holopainen(2020); Leftow (2022); Speaks (2018); and Tapp & Siegwart (2022).Finally, see Smith (2014) for an Anselmian causal-cum-ontologicalargument.

7. Meinong

It is very natural to affirm both of the following things:

(1)

Santa Claus has a white beard.

(2)

Santa Claus does not exist.

However, if we affirm both(1) and(2), then it seems that we are committed to the claim that there arenon-existent beings. What makes (1) true is that there is a being,Santa Claus, that has a white beard. What makes (2) true is that thatbeing is non-existent.

As Russell noted, naive theories about non-existent beings are apt toend in contradiction. Perhaps we can happily accept that the tallMartian is tall (for a Martian) while also accepting that the tallMartian is non-existent. But we contradict ourselves if we say thatthe existent Martian is existent while also maintaining that theexistent Martian is non-existent.

The general point here is that, when we think about which assignmentsof properties to beings could receive oura prioriendorsement, we have to put limitations on the class of propertiesthat figure in those assignments. While we might be happy with theidea that we knowa priori that the tall Martian is tall (fora Martian), we know that we cannot be happy with the idea that we knowa priori that the existent Martian is existent. Of course, itshould not be thought that existence is the only problematic property:we can no more givea priori endorsement to any of thefollowing:

(3)

The possible round square is possible.

(4)

The necessary round square is necessary.

(5)

The actual round square is actual.

The upshot for ontological arguments is clear. If your theory commitsyou to a distinction between being and existence, then, while thattheory alone may give you that it is true that Santa Claus has a whitebeard, that theory alone does not give you that God is a perfect being(if, for example, perfection requires existence, or necessaryexistence, or the like). A proponent of the simple Cartesian argumentthat we considered earlier cannot properly claim that the truth of thefirst premise—‘God has everyperfection’—simply falls out of the general (Meinongian)theory of being and existence while also insisting that the secondpremise is true.

Moreover, it should be noted that we cannot avoid this conclusion bypreferring a theoretical framework in which, because essence is priorto existence, claims like ‘Santa Claus has a white beard’are made true by essences. While it might be true that it falls out ofthis kind of theory that ‘The tallest Martian is tall (for aMartian)’ is made true by the essence of the tallest Martian, itcannot be true that ‘The necessary tallest Martian isnecessary’ is made true by the essence of the necessary tallestMartian. Of course, it is open to theists to claim,on othergrounds, that there is a divine essence; but while that canentitle them to suppose that our Cartesian ontological argument issound, it is plainly insufficient to entitle them to suppose that ourCartesian ontological argument is such as ought to persuade agnosticsand atheists to accept its conclusion.

The point that we have just made extends to other ontologicalarguments. In particular, it extends to Meinongian interpretations ofAnselm’s argument. While, as we noted above, it is not entirelyclear how to understand talk about ‘the understanding’,etc., it is tempting to interpret it in a Meinongian light. However,if we do that, then the formulation of the argument requiresassumptions—rejected by atheists and agnostics—that do notsimply fall out of the general Meinongian theoretical framework.

For further discussion of Meinongian ontological arguments, see, forexample: Dummett (1983 [1993]); Oppenheimer & Zalta (1991); Oppy(1996); Priest (2018); and Salmon (1987). And, for Meinongianismitself, see the entry onnon-existent objects and the literature cited therein.

8. Modal

The modal ontological argument (MOA) proceeds from God’spossible existence to God’sactual existence.While different variations of the argument exist (e.g., Malcolm 1960,Hartshorne 1965, Plantinga 1974), they typically share four parts:

• The first part is acharacterisation of the being to beargued for. Some MOAs focus on amaximally great being, wherea being is maximally great if and only if it exists necessarily and isessentially omnipotent, omniscient, and morally perfect (Plantinga1974). Other MOAs focus on aperfect being, where a being isperfect if and only if it essentially possesses every perfection andessentially lacks every imperfection (Bernstein 2014). Still otherMOAs focus simply onGod (McIntosh 2021). The precisecharacterisation at play will influence the justification of thesecond and third parts.
• The second part is thepossibility premise, which assertsthat the characterised being is metaphysically possible.(Metaphysical possibility is here understood minimally as thebroadest kind of objective, non-epistemic possibility.)
• The third part is thenecessity premise, which assertsthat the characterised being would be ametaphysically necessarybeing—in any possible world in which the being exists, itis necessary that said being exists.
• The fourth part is a modal logic that (a) accurately capturesmetaphysical modality and (b) is strong enough to validate aninference from thepossible necessary existence of \(x\) tothenecessary existence of \(x\) (or, minimally, to theexistence of \(x\)). Typically used is S5, whosecharacteristic axiom is \(\Diamond p \rightarrow \Box\Diamond p\),which in turn entails \(\Diamond\Box p \rightarrow \Box p\) (Rasmussen2018: 180). But a weaker system like B validates \(\Diamond\Box p\rightarrow p\) and could therefore be used instead (Leftow2005).

Thus, with God as our characterised being and S5 as our modal logic, astandard formulation of the MOA runs:

i.

Possibly, God exists. (Possibility premise)

ii.

Necessarily, if God exists, then it is necessary that God exists.(Necessity premise)

iii.

(Hence) It is necessary that God exists. (Fromi,ii)

According to(ii), it’s true in any possible world in which God exists that it isnecessary that God exists. According to(i), there’s some possible world in which God exists. From(i) and(ii) it follows that there’s some possible world in which it isnecessary that God exists—i.e., it’s possibly necessarythat God exists. By S5, \(\Diamond\Box p \rightarrow \Box p\). Hence,it’s necessary that God exists. By axiom M (\(\Box p \rightarrowp\)), it follows that God exists.

Naturally, there are three ways to challenge the MOA so construed,each corresponding to the final three parts articulated earlier.First, one can challenge the inference from(i) and(ii) to(iii) by challenging whether the modal logic underlying the argumentaccurately captures metaphysical modality. (For some such challenges,see Chandler 1976 and Salmon 1989. For defences of S5’smetaphysical adequacy, see Pruss & Rasmussen 2018: 14–29,Williamson 2016, Hale 2013, and Leftow 1991: 6–14). Second, onecan challenge the necessity premise. While some characterisations(e.g.,maximally great being as defined above) render thepremise definitionally true, others require substantive argumentation.For example, if the characterisation at play isperfectbeing, then the MOA proponent must argue thatnecessaryexistence is a perfection. Similarly, if the characterisation atplay isGod, then the MOA proponent must justify the claimthat God would be a necessary being. (Against this claim, seeSwinburne 2012. Against Swinburne and for God’s necessity, seeRasmussen 2016.) Third, one can challenge the possibility premise byarguing either that the characterised being is metaphysicallyimpossible or that its metaphysical possibility hasn’t beenadequately justified. Falling into this third category is perhaps themost important objection to the MOA: the symmetry problem.

To draw out this problem, consider the followingReverse MOA(RMOA):

i*.

Possibly, God doesn’t exist.

ii.

Necessarily, if God exists, then it is necessary that Godexists.

iii*.

(Hence) It is necessary that God doesn’t exist. (i*,ii)

Like the MOA, the RMOA is valid in S5. To see this, notice that(i*) is the negation of(iii) and that(iii) follows from(i) and(ii) in S5. Hence,(i*) and(ii) together entail the negation of(i)—i.e., they entail that it isimpossible that God exists. Thisimpossibility, in turn, is logically equivalent to(iii*).

But(iii*) is incompatible with(iii), and(ii) is the same in both arguments. Thus, assuming(ii) and S5,(i) and(i*) are incompatible. And yet(i) and(i*) seem epistemically on par—it seems intolerably arbitrary toprivilege one over the other absent further considerations.What’s needed is some principled reason favouring one over theother, i.e., a consideration thatbreaks symmetry betweenthem.Absent such a symmetry breaker, however, the MOA isdialectically toothless—quite clearly, if you don’talready accept the claim that God exists, you won’t agree that(i) is more acceptable than(i*) absent some symmetry breaker. Thus, without a symmetry breaker, theMOA makes no headway in the dispute between theists andnon-theists.

The natural solution to the symmetry problem, of course, is to offer asymmetry breaker favouring(i) over(i*). Categorisation problems loom on the horizon here—for example,many such symmetry breakers appeal to premises that aren’tapriori, and so they threaten MOA’s status as a properlyontological argument. Furthermore, even if they only appealtoa priori premises, symmetry breakers may representdistinct ontological argumentsin their ownright—distinct, that is, from the MOA. Notwithstandingthese concerns, the MOA debate has centred around symmetry breaking,and hence symmetry breakers merit consideration here.

For further discussion of the most influentialMOA—Plantinga’s MOA—see (e.g.) Adams (1988),Chandler (1993), Oppy (1995: 70–78, 248–259), Tooley(1981), van Inwagen (1977), and Rasmussen (2018). For a recentre-casting of the modal ontological argument using only a standardextension of system K, see Hausmann (2022).

9. Gödel

We begin with a representative Gödelian ontological argument.This argument—like all Gödelian ontologicalarguments—is couched in terms of the notion of a positiveproperty. The conclusion of the argument is that there is a beingwhose essential properties are all and only the positive properties.The argument has the following premises:

1. A property \(A\) is positive only if its negation \(\negA\) is not positive.
2. If \(A\) is positive and \(A\) entails \(B\) then \(B\)is positive.
3. Having as essential properties all and only the positiveproperties is positive.
4. Necessary existence is positive.

From(i) and(ii), we can infer that any collection of positive properties is possiblyjointly instantiated. Given(iii), we can then infer that having as essential properties all and onlythe positive properties is possibly instantiated. Given(iv), we can then infer that having as essential properties all and onlythe positive properties is possibly necessarily instantiated. Andthen, assuming that the modal logic is S5, we infer that there is anecessarily existent being that has all and only the positiveproperties. (See Pruss 2018a for discussion of ways in which thisrepresentative argument can be improved. These improvements have nobearing on the subsequent discussion in this section.)

Perhaps the most important point to note, for discussion of thisargument, is the following: no property that is necessarilyuninstantiated is positive. Suppose that \(A\) is necessarilyuninstantiated but positive. Since \(A\) is necessarilyuninstantiated, for any \(B\), \(A\) entails \(B\) and \(A\) entails\(\neg B\). But by2—since any property entailed by a positive property is itselfpositive—\(B\) is positive and \(\neg B\) is positive. But, by1, if \(B\) is positive, then \(\neg B\) is not positive. Contradiction.Hence, if \(A\) is necessarily uninstantiated, then \(A\) is notpositive.

In the context of necessary being theism, it is controversial betweentheists and atheists which properties are necessarily uninstantiated.Atheists who suppose—as many do—that omnipotence,omniscience, perfect goodness, and so forth, are necessarilyuninstantiateddeny that omnipotence, omniscience, perfectgoodness, and so forth, are positive (on the assumption that positiveproperties obey both 1 and 2). Moreover, some—though notall—atheists deny that necessary existence is positive (on theassumption that positive properties obey both1 and2). Unless we have an independent, non-question-begging way to discernwhich properties are positive, this looks like game over forGödelian ontological arguments.

A significant part of the recent literature has tried to motivateparticular ways of understanding the notion of a positive property. Wemight take the relevant axioms to provide a partial definition ofpositivity; but those axioms provide no guidance when it comes tosubstantive content. Pruss (2018a) discusses five candidatesubstantive proposals:

• Comparison. A property \(A\) is positive iff for any\(x\), it is better for \(x\) to have \(A\) then for \(x\) to lack\(A\).
• Excellence. A property \(A\) is positive iff for any\(x\), having \(A\) in no way detracts from the excellence of \(x\),but having \(\neg A\) does in some way detract from the excellence of\(x\).
• Anti-Negativity. A property \(A\) is positive iff \(\negA\) is negative.
• Leibniz. A property is positive iff \(A\) is entailed bya (possibly trivial) conjunction of simple, absolute properties,
• No Limitations. A property \(A\) is positive iff \(A\)does not entail being limited and \(\neg A\) does entail beinglimited.

One obvious problem with all of these proposals, in the context of theimportant point noted above, is that they do not give definitiveguidance when it comes to controversial cases in which some hold thata property is necessarily uninstantiated and others do not. Considernecessary omnipotence. If it is impossible for anything to benecessarily omnipotent—and if we are holding onto the assumptionthat positive properties are non-trivially closed underentailment—then:

1. it is clearly not the case that it is better to be necessarilyomnipotent than to be not necessarily omnipotent;
2. it is clearly not the case that being necessarily omnipotent doesnot detract from excellence in any way;
3. it is clearly not the case that not being necessarily omnipotentis negative;
4. it is clearly not the case that being necessarily omnipotent isentailed by a (possibly trivial) conjunction of simple, absoluteproperties; and
5. it is clearly not the case that not being necessarily omnipotententails being limited.

While there are other difficulties that confront all of theseproposals, there is no need to engage in exploration of thosedifficulties here.

Perhaps there is one final point worth making. There is nothing thatwe have said here that suggests that one cannot rationally supposethat

1. the positive properties are non-trivially closed under entailment,and
2. necessary existence, necessary omnipotence, necessary omniscienceand necessary perfect goodness are all positive properties.

Nor does anything in what we have said suggest that one who rationallysupposes these things cannot find the various claims intuitive. Whatmatters here is only that, given the conditions that we have set fordetermining whether or not arguments are successful, what certaintheists find intuitive has no bearing on thesuccess of Gödel’s ontological argument.

The literature on Gödel and Gödel’s ontologicalargument is vast. Notable contributions include: Adams (1995);Anderson (1990); Hazen (1998); Kovač (2003); Pruss (2009, 2018a);Pruss & Rasmussen (2018: ch. 8); Sobel (1987, 2004); andŚwiętorzecka [ed.] (2015).

10. Hegel

There is a large literature on Hegel and ‘the ontologicalargument’. As noted by Redding and Bubbio (2014: 467–8),Hegel was clearly attracted to Anselm’sProslogionargument. However, Hegel thought that Kant had shown thatAnselm’sProslogion argument is fatally flawed. ButHegel also thought that the fatal flaw that Kant had identified couldbe overcome. Assessing this last claim of Hegel’s is not easy.In particular, as many people have noted, Hegel nowhere gives anexplicit formulation of the premises and conclusion of ‘theontological argument’ that he endorses. Given the conception ofargument with which we have been working, it is not clear that thereis any such thing as ‘the ontological argument’ that Hegelendorsed.

Redding and Bubbio attempt to

point a way towards a reconstruction of the [ontological argument]from the framework within which Hegel makes his diagnosis [of theincompleteness of the Proslogion argument]. (2014: 466)

However, they do not give an explicit formulation of the premises andconclusion of ‘the ontological argument’ that Hegel isalleged to endorse. Instead, they outline some important parts ofHegel’s philosophy, and claim that something that might be takento be the conclusion of ‘the ontological argument’ fitscomfortably with that outline.

The interpretation of Hegel’s philosophy is, of course,controversial. As noted in Redding (2020), we can distinguish betweenat least:

1. the traditional metaphysical view of Hegel’s philosophy(Taylor 1975; Rosen 1984);
2. the ‘non-metaphysical’ Kantian view of Hegel’sphilosophy (Pippin 1989; Pinkard 1994; Brandom 2002; McDowell 2006);and
3. the revised metaphysical view of Hegel’s philosophy (Stern2002; Houlgate 2005; Kreines 2006; Yeomans 2012).

Moreover, the interpretation of Hegel’s writings about religionand God are also controversial: perhaps depending upon which of hiswritings we emphasise, we may take him to be Christian, pantheist, oratheist.

According to Redding and Bubbio:

The speech of act of mutual forgiveness, says Hegel, ‘is Godmanifested in the midst of those who know themselves in the form ofpure knowledge’. In the human act of forgiveness, God isfleetingly given corporeal existence, and what looks like human actsprovide the occasion of the self-actualisation of the divine. Indeed,Hegel seems to conceive of the apparently human act of proving theexistence of God in the same way. It is an act in which God passesfrom ‘mere’ concept into existing ‘idea’. Andit is fitting that this happens within the medium proper toHegel’s God—thought. (2014: 482)

What should those who identify as atheists or agnostics make of this?They can clearly acknowledge that there are human acts of mutualforgiveness. But, in the light of the history of religion, theology,etc., they will likely have not the slightest temptation to invoke Godor the divine when we make this acknowledgement. Moreover, andconsequently, they will simply dismiss talk about God’s passingfrom “‘mere’ concept to existing‘idea’”: whatever content you might want toattribute to that talk, it simply does not touch atheists andagnostics. The notion that there is an argument here that ought topersuade atheists and agnostics to revise their worldviews seemsutterly forlorn. This is not to deny that, from within a Hegelianperspective, these claims might be seen to be utterly compelling. Nodoubt there are people who suppose that in human acts of forgiveness,God passes from ‘mere’ concept to existing‘idea’. But those people have a range of controversialtheoretical commitments that are not shared by atheists and agnostics(nor by a great many theists, we might add).

11. Parodies

There is a large literature discussing parodies of ontologicalarguments, beginning with Gaunilo’s ‘perfect island’objection to Anselm’sProslogion II argument. It isimportant to note, at the outset, that particular parodies are tied toparticular formulations of ontological arguments, and are intendedonly to raise questions about the probative value of those particularformulations of ontological arguments.

Consider our earlier formulation of Anselm’sProslogionII argument:

1. When the fool hears the words ‘that than which nogreater can be conceived’ he understands those words.(Premise)
2. Whatever is understood exists in the understanding.(Premise)
3. (So) That than which no greater can be conceived exists inthe understanding. (Fromi,ii)
4. If that than which no greater can be conceived exists inthe understanding, it can be conceived to exist in reality.(Premise)
5. That than which no greater can be conceived is greater ifit exists in reality than if it exists only in the understanding.(Premise)
6. It is impossible to conceive of something greater thanthat than which no greater can be conceived. (Premise)
7. (So) That than which no greater can be conceived exists inreality. (Fromiii,iv,v, andvi.)

We can formulate a perfect island parody as follows:

1. When the fool hears the words ‘that island thanwhich no greater island can be conceived’ he understands thosewords. (Premise)
2. Whatever is understood exists in the understanding.(Premise)
3. (So) That island than which no greater island can beconceived exists in the understanding. (Fromi,ii)
4. If that island than which no greater island can beconceived exists in the understanding, it can be conceived to exist inreality. (Premise)
5. That island than which no greater island can be conceivedis greater if it exists in reality than if it exists only in theunderstanding. (Premise)
6. It is impossible to conceive of some island greater thanthat island than which no greater island can be conceived.(Premise)
7. (So) That island than which no greater island can beconceived exists in reality. (Fromiii,iv,v, andvi.)

Since the arguments have the same logical form, either they are bothvalid or they are both invalid. If they are both invalid, then theProslogion II argument fails. If they are both valid, then,if theProslogion II argument is to succeed, there must be apremise pair concerning which atheists and agnostics suppose that thepremise in the first argument is true but the premise in the secondargument is false. Which premise pair could that be?

Arguably, not the first. Which atheists and agnostics are going tosuppose that, while the words ‘that than which no greater can beconceived’ are understood, the words ‘that island thanwhich no greater island can be conceived’ are not understood?(If you think that islands—unlike beings in general—do notadmit of comparison in terms of greatness, we can change the example.The parody does not need to be formulated in terms of islands. It can,for example, be formulated in terms of scores on a test for whichthere is a maximum possible score: ‘that score on this test thanwhich no greater score on this test can be conceived’.)

Definitely not the second, since it is the same for botharguments.

Arguably, not the third. As noted above, all we need for the purposesof the parody is some category for which we think that existence inreality is great-making compared to mere existence in theunderstanding. It is not clear why atheists and agnostics should thinkthat existence in reality (as compared to existence in theunderstanding) is great-making for that than which no greater can beconceived and yet not great-making for that island than which nogreater island can be conceived. But, in any case, which atheists andagnostics are going to accept that existence in reality (as comparedto existence in the understanding) is great-making for that than whichno greater can be conceived and yet not great-making for that score onthis test for which no greater score on this test can beconceived?

And surely not the fourth. Which atheists or agnostics would acceptthat nothing is greater than that than which no greater can beconceived and yet deny that no island is greater than that island thanwhich no greater can be conceived?

The upshot seems pretty clear: it cannot be that Anselm’sProslogion II argument, as formulated for the purposes ofthis discussion, is a successful argument for its conclusion because(a) it has nothing to recommend it to atheists and agnostics that doesnot equally recommend the conclusion of the island parody argument toatheists and agnostics, and yet (b) weall know that theconclusion of the island parody argument is false (if not absurd).

Perhaps one will object that, in the relevant sense, while we dounderstand the words ‘that than which no greater can beconceived’, we do not understand the words ‘that islandthan which no greater island can be conceived’. Perhaps, forexample, we might suggest, following Plantinga, that, since we knowa priori that there is no intrinsic maximum for the greatnessof islands, we can attach no sense to the words ‘island thanwhich no greater island can be conceived’. According toPlantinga, any island, no matter how great, can be improved by theaddition of more palm trees. While there is an intrinsic maximum forknowledge—knowing everything—there is no intrinsic maximumfor the number of palm trees on an island. There are at least thefollowing three points to make here. First, it seems false that theaddition of palm trees is guaranteed to add to the greatness of anisland. For any island, there comes a point where the addition of morepalm trees overcrowds the island with palm trees, and so detracts fromits greatness. (Of course, the point here generalises to any otherkinds of things that might be taken to conduce to the greatness ofislands. There is nothing that might conduce to the greatness ofislands for which it is guaranteed that, no matter how much you have,more will be better.) Second, the greatness of islands will inevitablyinvolve a trade-off between various things that contribute togreatness of islands. We simply do not knowa priori thatthere is no distribution of these things that is an intrinsic maximumfor the greatness of islands. Third, even if these objections arewaived, until we have a satisfactory detailed theory of existence inthe understanding, conceivability, etc., we have no grounds for movingfrom these points to the claim that we do not understand the words‘that island than which no greater island can beconceived’ when we hear them. (For more on theseresponses—and for other responses—see Oppy 2017:54–56.)

The discussion to this point illustrates the general strategy that ispursued by those who look for parodies of a given ontologicalargument. Such people have been presented with an argument for theexistence of God. What they seek is an argument, with the same logicalform as the argument that has been presented to them, that has at itsconclusion either that something exists whose existence isincompatible with the existence of God or that something exists whoseexistence is recognised by all to be absurd, and yet whose premisesare all no less acceptable to those who frame the parody than thecorresponding premises in the ontological argument that has beenpresented to them. (Of course, the discussion in preceding paragraphsis an instance of the second kind: the conclusion of the argument issomething that is recognised on all hands to be absurd.)

Why might someone offer a parody of an ontological argument ratherthan either a criticism of the logic or premises of that ontologicalargument? If someone can show that an ontological argument is invalid,then their best objection to the ontological argument is todemonstrate its invalidity. And, if someone can show even toproponents of an ontological argument that the argument has one ormore false premises, then their best objection to the ontologicalargument is to show the falsity of one or more of its premises. But,often enough, an opponent of a given ontological argument may not beable to do either of those things. However, if they can provide asuccessful parody of the argument, then they still have an adequateobjection to the argument. For an argument like Anselm’sProslogion II argument, where the background theory and thelogic are greatly underspecified, it may well be that parody offersthe most immediate way to make it clear to proponents of the argumentthat there is nothing in the argument that ought to give pause toatheists and agnostics.

Even in cases where opponents of given ontological arguments supposethat they can demonstrate invalidity or falsity of premises, there maystill be at least academic interest in parodies of those arguments.However, it seems doubtful that there could be more than academicinterest in providing parodies in such cases.

12. General Objections

Objections to ontological arguments take many forms. Some objectionsare intended to apply only to particular ontological arguments, orparticular forms of ontological arguments; other objections areintended to apply to all ontological arguments. It is a controversialquestion whether there are any successful general objections toontological arguments.

One general criticism of ontological arguments which have appearedhitherto is this: none of them ispersuasive, i.e., none ofthem provides those who do not already accept the conclusion that Godexists—and who are reasonable, reflective, well-informed,etc.—with either apro tanto reason or anall-things-considered reason to accept that conclusion. Any reading ofany ontological argument which has been produced so far which issufficiently clearly stated to admit of evaluation yields a resultwhich is invalid, or possesses a set of premises which it is clear inadvance that no reasonable, reflective, well-informed, etc.non-theists should accept, or has a benign conclusion which has noreligious significance, or else falls prey to more than one of theabove failings.

As we have seen in the discussion that we have given above, for eachof the families of arguments introduced in our initial taxonomy, thereare good reasons for thinking that none of the extant arguments thatbelong to those families are successful.

Even if the forgoing analyses are correct, it is important to notethat no argument has been given for the conclusion that no ontologicalargumentcan be successful. Even if all of the kinds ofarguments produced to date are unsuccessful—i.e., not such asought to give non-theists reason to accept the conclusion that Godexists—it remains an open question whether there is some otherkind of hitherto undiscovered ontological argument which does succeed.(Perhaps it is worth adding here that there is fairly widespreadconsensus, even amongst theists, that no known ontological argumentsfor the existence of God are successful, in the sense in which we arehere understanding what it is for an argument to be successful. Mostcategories of ontological argument have some actual defenders; butnone has a large following.)

Many other objections to (some) ontological arguments have beenproposed. All of the following have been alleged to be the key to theexplanation of the failure of (at least some) ontologicalarguments:

1. existence is not a predicate (see, e.g., Kant; Smart 1955; Alston1960);
2. the concept of god is meaningless/incoherent/inconsistent (see,e.g., Findlay 1948);
3. ontological arguments are ruled out by “the missingexplanation 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 inphilosophy of religion);
6. ontological arguments presuppose a Meinongian approach to ontology(see, e.g., Dummett 1983 [1993]); and
7. ontological arguments are question-begging, i.e., presuppose whatthey set out to prove (see, e.g., Rowe 1989).

There are many things to say about these objections: the mostimportant point is that almost all of them require far morecontroversial assumptions than non-theists require in order to be ableto reject ontological arguments with good conscience. Trying tosupport most of these claims merely in order to beat up on ontologicalarguments is unlikely to be a productive undertaking.

Of course, all of the above discussion is directed only to the claimthat ontological arguments are dialectically inefficacious—i.e.,they give reasonable non-theists no reason to change their views. Itmight be wondered whether there is some other use which ontologicalarguments have—e.g., as Plantinga claims, in establishing thereasonableness of theism. This seems unlikely. After all, at bestthese arguments show that certain sets of sentences (beliefs, etc.)are inconsistent—one cannot reject the conclusions of thesearguments while accepting their premises. But the arguments themselvessay nothing about the reasonableness of accepting the premises. So thearguments themselves say nothing about the (unconditional)reasonableness of accepting the conclusions of these arguments. Thosewho are disposed to think that theism is irrational need find nothingin ontological arguments to make them change their minds (and thosewho are disposed to think that theism is true should take no comfortfrom them either).

13. Concluding Observations

It will be useful to collect together some of the main points thathave been made in the preceding discussion:

• There are many different extant kinds of ontologicalarguments.
• Some ontological arguments display potential entailments betweenthe possibility of God’s existence (or non-existence) and thenecessity of God’s existence (or non-existence). Theseentailments put a spotlight on an open, general question: under whatconditions can one reasonably believe something of the form, ‘itis possible thatF’ without merely deriving thatconclusion from ‘it is actual thatF’?
• There are significant challenges to extant ontological arguments,and they may cast doubt on whether any current arguments provideatheists and agnostics with good or compelling reasons to becometheists.
• It remains an open question whether there are hithertoundiscovered ontological arguments that would provide atheists andagnostics with good or compelling reasons to become theists (just asit remains an open question whether there are hitherto undiscoveredparodies of ontological arguments that would provide theists with goodor compelling reasons to become atheists or agnostics).
• It may well be that theists have—or can have—goodreasons for thinking that there are sound ontological arguments. Thatis: it may well be that there are valid ontological arguments all ofwhose premises are such that theists can reasonably deem themintuitive.
• It remains an open question whether theists can give a plausibleaccount of a way in which arguments can be successful on which itturns out that at least one extant ontological argument is successful.‘Plausibility’ constrains the account inat leastthe following way: it is not plausible that ‘God exists and\(2+2=4\) therefore God exists’ is a successful argument, eventhough all monotheists accept that it is (classically) sound.

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Websites

• Medieval Sourcebook: Philosophers’ Criticisms of Anslem’s Ontological Argument for the Being of God (Paul Halsall, Fordham University)
• Dericioglu, Umit (ed.), 1998, “ Ontological Argument Revisited by Two Ottoman Muslim Scholars”,Anadolu, 8(2).
• Himma, Kenneth, “Anselm: Ontological Argument for God’s Existence”,Internet Encyclopedia of Philosophy
• Lourdes Borges, Marie de, “Hegel and Kant on the Ontological Argument”,Meta religion.

Papers

• Recent paper by Christoph Benzmüller and Bruno WoltzenlogelPaleo on the computational analysis of Gödel’s ontologicalargument:
  • “Formalization, Mechanization and Automation of Gödel’s Proof of God’s Existence”, unpublished manuscript.

Videos

• Majesty of Reason (Joe Schmid) YouTube channel
  • 10-December-2020, “Ontological Arguments” (1:43:21), Tyron Goldschmidt inteviewed by Joe Schmid.
  • 3-July-2022, “11 Ontological Arguments: An Analysis” (1:25:54), presented by Joe Schmid.
  • 17-November-2021, “A User’s Guide to the Modal Ontological Argument” (1:23:11), Than Christopoulos and Joe Schmid.
  • 19-June-2022, “Graham Oppy responds to Josh Rasmussen’s Ontological Argument” (1:43:03).
• The Analytic Christian (Jordan Hampton) YouTube channel
  • 17-March-2020, “Assessing Various Forms of the Ontological Argument” (1:31:39), Tyron Goldschmidt interviewed by Jordan Hampton.
  • 5-August-2020, “A Deeper Analysis of Anselm’s Ontological Argument with Dr. Daniel Rubio (#1)” (12:24), interview with Daniel Rubio.
• Daniel Bonevac YouTube channel
  • 22-March-2020, “Anselm’s Ontological Argument” (24:06).
  • 23-March-2020, “Gaunilo’s Objection to the Ontological Argument” (22:23).
  • 11-March-2022, “Gödel’s Ontological Argument” (27:56).
• 22-April-2021, “Graham Oppy on the modal ontological argument” (2:08).Friction YouTube channel.
• Capturing Christianity (Cameron Bertuzzi) YouTube channel
  • 19-February-2022, “A New Ontological Argument, Dr. Josh Rasmussen // CCv1 Session 5” (1:03:03), Josh Rasmussen and Cameron Bertuzzi.
  • 18-July-2018, “The Ontological Argument—Ben Arbour & Graham Oppy” (2:02:02), Ben Arbour, Graham Oppy, and Cameron Bertuzzi.

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