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Ontological is derived from ontos, the greek word being. The name is intended to convey the intent of the argument to prove God's existence by virtue of his existence being necessary. It was first proposed by the medieval philosopher [[Anselm of Canterbury]] in his ''[[Proslogion]]'', and important variations have been developed by philosophers such as [[René Descartes]], [[Gottfried Leibniz]], [[Norman Malcolm]], [[Charles Hartshorne]], and [[Alvin Plantinga]].  A [[modal logic]] version of the argument was devised by mathematician [[Kurt Gödel]]. The ontological argument has been controversial in philosophy and many philosophers have famously criticized or opposed it, including Anselm's contemporary [[Gaunilo of Marmoutiers]], as well as [[David Hume]], [[Immanuel Kant]], and [[Gottlob Frege]]. Some of these opponents have preferred to rely on [[cosmological argument]]s for the existence of God instead. It continues to garner discussion to the present.
#REDIRECT [[ontological argument for the existence of God]]
 
== Anselm's argument ==
 
The ontological argument was first proposed by [[Anselm of Canterbury]] ([[1033]]–[[1109]]) in Chapter 2 of the ''Proslogion''.  While Anselm did not propose an [[Ontology|ontological]] system, he was very much concerned with the nature of being. He argued that there are necessary beings – things that cannot ''not'' exist – and contingent beings – things that may or may not exist, but whose existence is not necessary.
 
Anselm presents the ontological argument as part of a prayer directed to God. He starts with a definition of God, or a necessary assumption about the nature of God, or perhaps both.
 
:"Now we believe that [the Lord] is '''something than which nothing greater can be imagined'''."
 
Then Anselm asks: does God exist?
 
:"Then is there no such nature, since the fool has said in his heart: God is not?"
 
To answer this, first he tries to show that God exists 'in the understanding':
 
:"But certainly this same fool, when he hears this very thing that I am saying – something than which nothing greater can be imagined – understands what he hears; and what he understands is in his understanding, even if he does not understand that it is. For it is one thing for a thing to be in the understanding and another to understand that a thing is."
 
Anselm goes on to justify his assumption, using the analogy of a painter:
 
:"For when a painter imagines beforehand what he is going to make, he has in his understanding what he has not yet made but he does not yet understand that it is. But when he has already painted it, he both has in his understanding what he has already painted and understands that it is.
:"Therefore even the fool is bound to agree that there is at least in the understanding something than which nothing greater can be imagined, because when he hears this he understands it, and whatever is understood is in the understanding."
 
Now Anselm introduces another assumption:
 
:"And certainly that than which a greater cannot be imagined cannot be in the understanding alone. For if it is at least in the understanding alone, it can be imagined to be in reality too, which is greater."
 
(For example, most people would prefer a real £100 rather than an imaginary £100.)
 
:"Therefore if that than which a greater cannot be imagined is in the understanding alone, that very thing than which a greater cannot be imagined is something than which a greater can be imagined. But certainly this cannot be."
 
Anselm has thus found a contradiction, and from that contradiction, he draws his conclusion:
 
:"There exists, therefore, beyond doubt '''something than which a greater cannot be imagined''', both in the understanding and in reality."
 
==Philosophical assumptions underlying the argument==
 
In order to understand the place this argument has in the history of philosophy, it is important to understand the essence of the argument in the context of the [[Influence of Hellenic philosophy on Christianity]]. 
 
First, it is important to realize that Anselm's argument stemmed from the philosophical school of [[Realism]]. [[Realism]] was the dominant philosophical school of Anselm's day. According to Realism, and in contrast to Nominalism, things such as "greenness" and "bigness" were known as [[universals]], which had a real existence outside the human imagination, in an abstract realm, as described by [[Plato]].  Accordingly, if a concept could be formed in the human mind (as was his concept of God), then it had a real existence in the abstract realm of the universals, apart from his imagination.  In essence, if he could imagine God, God existed.
 
Secondly, it is important to understand Anselm's concept of "perfections" (and that of later writers, up to about the late seventeenth century).  A perfection is a property that has been completed; thus, power is a property, but complete (absolute, unlimited) power is a perfection.  The term later came to be used almost completely evaluatively, to mean something like the absolute best, the best possible ([[Baruch Spinoza]] complains about this change in his ''Ethics''), and it has thus become an error to talk about one thing being ''more perfect'' than another.  For writers like Anselm and Descartes, however, "more perfect" simply meant 'more complete', so that perfections come in degrees.  The old meaning of 'perfect' survives in music (e.g., "[[Cadence (music)|perfect cadence]]"), grammar (the [[Perfect aspect|perfect tense]]s),  and in phrases such as "a perfect stranger".
 
Thirdly, it is important to understand Anselm's concept of "necessary existence". Anselm held that there were two types of existence: necessary existence and contingent existence.  Contingent existence is a state of existence which depends on something else — that is, if something else were not the case, the object in question would not exist. Necessary existence, by contrast, depends on nothing.  Something that necessarily exists will exist no matter what. It can't not exist.
 
==A modern description of the argument==
 
Here's a short, and very general description of the ontological argument:
 
# God is the greatest possible being and thus possesses all perfections.
# Existence is a perfection.
# God exists.
 
This is a shorter modern version of the argument.  Anselm framed the argument as a [[reductio ad absurdum]] wherein he tried to show that the assumption that God does not exist leads to a logical contradiction.  The following steps more closely follow Anselm's line of reasoning:
 
# God is the entity than which no greater entity can be conceived.
# The concept of God exists in human understanding.
# God does not exist in reality (assumed in order to refute).
# The concept of God existing in reality exists in human understanding.
# If an entity exists in reality and in human understanding, this entity is greater than it would have been if it existed only in human understanding (a statement of existence as a perfection).
# from 1, 2, 3, 4, and 5 An entity can be conceived which is greater than God, the entity than which no greater entity can be conceived (logical self-contradiction).
# Assumption 3 is wrong, therefore God exists in reality (assuming 1, 2, 4, and 5 are accepted as true).
 
Anselm in his Proslogon 3 made another a priori argument for God this time based on the idea of necessary existence. He claimed that if God is that than which nothing greater can be conceived, it is better to be necessary than contingent. Therefore God must be necessary, to sum it up:
 
# God is that than which nothing greater can be conceived.
# It is greater to be necessary than not.
# God must be necessary.
# God exists
 
==Criticisms and Objections==
 
===Gaunilo's island===
 
One of the earliest recorded objections to Anselm's argument was raised by one of Anselm's contemporaries, [[Gaunilo]].  Gaunilo invited his readers to think of the greatest, or most perfect, conceivable island.  As a matter of fact, it is likely that no such island ''actually exists''. However, his argument would then say that we aren't thinking of the ''greatest'' conceivable island, because the ''greatest'' conceivable island would ''exist'', as well as having all those other desirable properties.  Since we can conceive of this greatest or most perfect conceivable island, then it must exist. While this argument seems absurd, Gaunilo claims that it is no more so than Anselm's. 
 
Such objections are known as "Overload Objections"; they don't claim to show where or how the ontological argument goes wrong, they simply argue that if it is sound, then so are many other arguments of the same logical form which we don't want to accept, arguments which would overload the world with an indefinitely large number of things like perfect islands, perfect pizzas, perfect pencils, etc.
 
Such objections always depend upon the accuracy of the analogy.  That is, we must be able to show that the objector's argument is sufficiently like the ontological argument for us to be able to conclude that if one works so must the other.  There are at least two problems with Gaunilo's version, though.  First, what exactly is the concept of the perfect island — the island than which no greater can be conceived?  In any group of people, there will be disagreements as to what makes an island perfect; there will be different preferences concerning size, climate, inhabitants, food-availability, etc.  There ''is'' no single concept of a perfect island, because perfection here can only mean what is perfect for us, rather than perfect in itself.  The notion of the perfect being, however, isn't relativised to any individual; it's the notion of a being that is maximally great — not for me or for you, but great, full stop.
 
It might be objected that "perfection" is also a culturally relative notion, so that Anselm's argument faces exactly the same problem as Gaunilo's.  As we have seen, however, Anselm and Descartes use "perfection" not (primarily) evaluatively, but to refer to God's having ''complete'' or ''total'' properties.  Moreover, it isn't necessary to say what the properties are in order for the argument to go through; we only need to consider the concept of a being that has all perfections (whatever they may be). Then again, some properties might lead to contradictions in the same object. For example, it is not impossible to think of utter malice as evil's perfection, which one would be hard-pressed to combine with superlative goodness. Or consider the case of "sober-minded" and "poetically-minded." Both are presumably good qualities, yet incompatible even outside of superlatives.
 
Gaunilo might have added that he means to refer to an island that is perfect in itself, without reference to us.  Now, what is an island?  It's a body of land surrounded by water.  But every island is a body of land surrounded by water (if it weren't, it wouldn't be an island); so every island is a perfect island (every island is perfectly an island).  Here, the disanalogy arises because whatever example Gaunilo chooses, it will be a being of a particular type – such a pizza, a pencil, or a Prime Minister – and so its perfection will be relative to that type.  In the case of Anselm's premise, though, we're not concerned with a being of this type or that type, but just with a being — a being than which no greater can be conceived.
 
On the other hand, what is a being that has no specific properties? And is it more conceivable than the perfect island? [[Bishop Berkeley]] insisted five centuries later that an abstract triangle, a triangle of no specific proportions and angles is a non-entity, unimaginable, an empty sound. Now "a being" is conceivable, though not picturable, in that we understand the word and its use. But any attempt to endow the concept with content leads to particular properties and particular beings. We may wonder, then, whether "perfect being" is more than a by-product of grammar.
 
<!-- tidied to here; much more needs doing -->
 
===Necessary nonexistence=== 
 
Another rationale is attributed to Melbourne philosopher [[Douglas Gasking]] <ref>''[http://www.uq.edu.au/~pdwgrey/pubs/gasking.pdf W.Grey, "Gasking's Proof", ''Analysis'' 60:4 (2000), pp 368&ndash;70.]''</ref> (1911&ndash;1994), one component of his proof of the nonexistence of God:
#The creation of the world is the most marvelous achievement imaginable.
#The merit of an achievement is the product of (a) its intrinsic quality, and (b) the ability of its creator.
#The greater the disability (or handicap) of the creator, the more impressive the achievement.
#The most formidable handicap for a creator would be non-existence.
#Therefore if we suppose that the universe is the product of an existent creator we can conceive a greater being &mdash; namely, one who created everything while not existing.
#Therefore God does not exist.
 
Gasking was apparently thinking of the "world" or "universe" as the same as "everything."  The proof is strengthened if "everything" is substituted. However, defenders of Anselm would reject the thesis that disability and handicap are things that make a creator greater.
 
===Existence as a property===
 
Another traditional criticism of the argument (first found in [[Gassendi]]'s Objections to [[Descartes]]' [[Meditations on First Philosophy|Meditations]], and later modified by Kant) is that existence is not a perfection, because existence is not a ''property'' as such, and that referring to it as a property confuses the distinction between a concept of something and the thing itself. The argument is that anything which has the property of being non-existent could not possibly have any other properties, being non-existent, and thus not having color, location, or any other property. One cannot, the argument says, speak meaningfully of the non-existent apple that one is holding, saying that it is red, crisp, weighs a certain amount, is in one's right hand, and does not exist. Another way of phrasing this is that, if existence is a property, then there exist a number of things that have the property of not existing.
 
===Miscellaneous===
 
A fourth criticism of Anselm's argument rests on the claim that, even if existence is a property, it is ''still not a perfection'' because existence is either true or false while degree of perfection is a continuous scale.  Defenders of the ontological argument have replied to this objection that its conclusion does not follow from its premise.
 
A fifth criticism is that the choice of "God" as the term for the perfect being is misleading, and invites the reader to substitute a particular culturally-determined deity for the perfect being used in the argument. This criticism does not directly contradict the validity of the argument but instead suggests that using the ontological argument to demonstrate the existence of a particular deity involves a [[Equivocation|fallacy of equivocation]].
 
A sixth criticism is that Anselm's "fool" does ''not'' necessarily understand ''some object'' when he hears the words "a thing greater than which nothing can be imagined". He might understand the meaning of the words, but it does not follow from this that even a single mental object exists, even if purely in his mind, of which these words are true. According to this criticism, "I understand some given description" does not imply "I can imagine something that fits the given description". For example if one were to hear the words "a thing that is at the same time [[Invisible_Pink_Unicorn|pink and invisible]]" it does not follow from understanding the words that one then has a mental concept of such a thing.
 
A seventh criticism comes from analyses, and is related to the idea that existence is not a property. Anselm's argument could be put as "there is x, such that x is all perfections; existence is a perfection, therefore x must exist". We can call this simply C(x) (a proposition in which x is a constituent). But, the fool could ask, for what value of x will C(x) be true?
 
An eighth criticism of Anselm's argument attacks the premise which implies that one must conceive of the greatest conceivable being ([[God]].)  The criticism is that the greatest conceivable being is in fact inconceivable, as it lacks a required property of the GCB, existence outside of the mind.  To give a parallel, if a person could not conceive of [[dragons]], and wanted to conceive of a three-headed dragon, it would not be possible for him to do so as a requirement for conceiving of a three-headed dragon is to be able to conceive of the inconceivable dragon.  Thus, the argument that the greatest conceivable being must exist in order to achieve its greatest potential is defeated in its premise on the fact that this object is not conceivable.  This criticism also concludes that all conceived objects are inconceivable (or at least not at their greatest conceivability) as in [[a priori]] the required property of existence is absent.
 
===Hume===
 
Hume claimed that nothing could ever be proven to exist through an a priori, rational argument by arguing as follows:
 
# The only way to prove anything a priori is through an opposite contradiction. For example, I am a married bachelor.
# The resulting contradiction makes something inconceivable. Obviously it is impossible to have a married bachelor.
# It is possible to comprehend anything not existing. Thus it is not inconceivable to imagine anything not existing.
# Nothing can be proven to exist a priori, including God.
 
==Revisionists==
 
Obviously Anselm thought this argument was valid and persuasive, and it still has occasional defenders, but many, perhaps most, contemporary philosophers believe that the ontological argument, at least as Anselm articulated it, does not stand up to strict logical scrutiny.  Others, like [[Gottfried Leibniz]], [[Norman Malcolm]], [[Charles Hartshorne]], [[Kurt Gödel]] and [[Alvin Plantinga]] have reformulated the argument in an attempt to revive it.
 
==Descartes' ontological arguments==
 
[[René Descartes]] ([[1596]]-[[1650]]) composed a number of ontological arguments which differed from Anselm's formulation in important ways.  Generally speaking, it is less a formal argument than a natural intuition.
 
Descartes wrote in the [[Meditations on First Philosophy|Fifth Meditation]]: <ref>''[http://www.classicallibrary.org/descartes/meditations/8.htm René Descartes. Meditations on First Philosophy: 5th Meditation.]''</ref>
:But if the mere fact that I can produce from my thought the idea of something entails that everything which I clearly and distinctly perceive to belong to that thing really does belong to it, is not this a possible basis for another argument to prove the existence of God? Certainly, the idea of God, or a supremely perfect being, is one that I find within me just as surely as the idea of any shape or number. And my understanding that it belongs to his nature that he always exists is no less clear and distinct than is the case when I prove of any shape or number that some property belongs to its nature (AT 7:65; CSM 2:45).
 
The intuition above can be formally described as follows:
# Whatever I clearly and distinctly perceive to be contained in the idea of something is true of that thing.
# I clearly and distinctly perceive that necessary existence is contained in the idea of God.
# Therefore, God exists.
 
The key premise to the argument is the first premise, which is, in essence, a statement of faith in his intuition.
 
Another formulation of his argument is as follows:
# I exist
# I have an idea of a supremely perfect being, i.e. a being having all perfections.
# As an imperfect being I would be unable to create such a concept.
# The concept must have come from God.
# To be a perfect being God must exist.
# God exists.
 
In another, less formal statement of his argument, he draws an analogy between belief in the existence of God and the geometric demonstration:
:Whatever method of proof I use, I am always brought back to the fact that it is only what I clearly and distinctly perceive that completely convinces me. Some of the things I clearly and distinctly perceive are obvious to everyone, while others are discovered only by those who look more closely and investigate more carefully; but once they have been discovered, the latter are judged to be just as certain as the former. In the case of a right-angled triangle, for example, the fact that the square on the hypotenuse is equal to the square on the other two sides is not so readily apparent as the fact that the hypotenuse subtends the largest angle; but once one has seen it, one believes it just as strongly. But as regards God, if I were not overwhelmed by philosophical prejudices, and if the images of things perceived by the senses did not besiege my thought on every side, I would certainly acknowledge him sooner and more easily than anything else. For what is more manifest than the fact that the supreme being exists, or that God, to whose essence alone existence belongs, exists? (AT 7:68-69; CSM 2:47)
 
==Plantinga's modal form and contemporary discussion==
 
[[Alvin Plantinga]] has given us another version of the argument, one where the conclusion follows from the premises, assuming [[axiom S5]] of modal logic.  A version of his argument is as follows:
#By definition a maximally great being is one that exists necessarily and necessarily is omniscient, omnipotent and perfectly good. (Premise)
#Possibly a maximally great being exists. (Premise)
#Therefore, possibly it is necessarily true that an omniscient, omnipotent and perfectly good being exists (By 1 and 2)
#Therefore, it is necessarily true that an omniscient, omnipotent and perfectly good being exists. (By 3 and S5)
#Therefore, an omniscient, omnipotent and perfectly good being exists. (By 4 and since necessarily true propositions are true.)
 
The [[axiom S5]] says that if a proposition is possibly necessarily true, then it is necessarily true. 
 
Plantinga's ontological argument has two controversial premises: The [[axiom S5]] and the "possibility premise" that a maximally great being is possible.  Given these, the conclusion indisputably follows.  The more controversial of these two is the "possibility premise" since S5 is widely (though not universally) accepted.  Some critics (e.g., [[Richard M. Gale]]) have even argued that the "possibility premise" [[begs the question]], because one only has the epistemic right to accept it if one understands the nested modal operators, and if one understands them then one understands that "possibly necessarily" is basically the same as "necessarily".
 
The crucial question is whether the possibility premise can be justified.  The problem is a thorny one, since none of the more reliable of our ways of showing something to be possible appear applicable:
#We might show a proposition to be possible by showing that it is true.  Thus, we know that consciousness is possible because we know that we have consciousness.
#We can show a [[state of affairs]] to be possible by exhibiting how the state of affairs might arise by the laws of nature from other possible states of affairs.  That is how we know that horse-like mammals with one horn are possible, since we can sketch an evolutionary story whereby they physically could evolve.
#We might provide a mathematical or other ''model'' of the situation to be shown to be possible, a model that mirrors all the relevant logical structure of the situation, and show the model to be possible.  This is how we know that it is possible to have three people where there are two fathers and two sons--we construct a model in our minds in which there is a grandfather, his son and his son's son.
 
However, it does not appear that any of these approaches has any hope in the case of the ontological argument's possibility premise.  The first option would be blatant question-begging.  The second is inapplicable since at least as far as we know a maximally great being cannot arise from anything else.  And the third option would require us to have a full grasp of the logical structure of a maximally great being.
 
There are, however, some less reliable ways of showing something to be possible.  We might simply have a modal "intuition" about the possibility of something.  Such intuitions are highly fallible, but may carry some epistemic weight.  The disadvantage of this method is that it may not be possible for someone who shares the intuition to convince another.
 
Or one might do this on a social and not individual level and argue (this follows ideas of Richard M. Gale, though it does not appear likely that he would endorse this application) that when a concept has been in play for centuries in a well-developed [[language game]], such as the concept of a maximally great being in the religious language game, that the concept has some likelihood of being coherent and hence possible.  Again, the weight that such a historical claim carries is not very great since we can make mistakes about it.  Thus, before [[Georg Cantor|Cantor]], people may have thought that the idea of a collection than which a greater collection is impossible was coherent, while [[Cantor's diagonal argument]] suggests otherwise).  Still, the history of a concept's use may provide some evidence in favor of the possibility of that which the concept purports to be of.
 
There are, nonetheless, yet other approaches to the possibility premise.  Leibniz thought that the possibility premise followed from the claim that "positive qualities" could not logically conflict with one another, and hence the notion of a being that had all the positive qualities had to be coherent.  [[Gödel's ontological proof]] uses similar ideas.
 
A very different approach has recently been attempted by [http://www.georgetown.edu/faculty/ap85/papers/Samkara.html Pruss] <ref>''[http://www.georgetown.edu/faculty/ap85/papers/Samkara.html A.R.Pruss, "Samkara’s Principle and Two Ontomystical Arguments", International Journal for Philosophy of Religion 49 (2001), 111–120]''</ref> who starts with the 8th-9th century AD Indian philosopher [[Samkara]]'s dictum that if something is impossible, then we cannot have a perception (even a non-veridical one) that it is the case.  Contraposing, it follows that if we have a perception that ''p'', then even though it might not be the case that ''p'', it is at least the case that ''possibly p''.  If mystics in fact perceive the existence of a maximally great being, it follows that the existence of a maximally great being is at least possible.  And that is all that is needed to get the modal ontological argument off the ground.  One difficulty in this argument is that one might misinterpret the content of one's experience, and hence the mystic might be incorrect even in a cautious description of an experience as an experience "''as of'' a maximally great being."
 
Interestingly, Plantinga himself does not think the modal ontological argument is always a good proof of the existence of God.  It depends on what his interlocutor thinks of the possibility premise.  Nonetheless, Plantinga has suggested that because we do not have any evidence against the possibility premise, it might be reasonable to suppose it has probability 1/2.  It follows from this that the existence of God can at the outset be held to have probability 1/2, though further evidence may increase or decrease this.
 
==The Ontological Argument in Mathematical Form==
 
#A is equal to B.
#B is equal to C.
#Therefore, A equals C.
 
This is simply a restatement of a=b=c.
 
An Example of how this works in terms of logic:
                                 
(God) is equal to (a being with all perfections).
                                                               
(A being with all perfections) is equal to (a being that exists[A being that possess existance]).
                                               
Therefore, (God) equals (a being that exists[A being that possess existance]).
 
When the nouns of the Ontological Argument are seen in terms of variables, the argument doesn't make much sense.
 
==Notes==
 
<references />
 
==Bibliography==
 
* Hartshore, Charles, The Logic of Perfection (LaSalle, IL: Open Court, 1962)
* Malcolm, Norman, "Anselm's Ontological Argument," Philosophical Review, vol. 69, no. 1 (1960), 41-62
* Plantinga, Alvin, The Ontological Argument from St. Anselm to Contemporary Philosophers (Garden City, NY: Doubleday, 1965)
* Plantinga, Alvin. God, Freedom and Evil. (Grand Rapids, Michigan: Eerdmans, 1977) pp.85-112
 
==See also==
 
* Overviews: [[Arguments for the existence of God]], [[Arguments against the existence of God]]
* Other major attempted proofs: [[Cosmological argument]], [[Teleological argument]], [[Argument from morality]]
* [[Gödel's ontological proof]] for the existence of [[God]]
* [[Pascal's Wager]]
 
== External links ==
* [http://plato.stanford.edu/entries/ontological-arguments/ Ontological Arguments] &mdash; from the Stanford Encyclopedia of Philosophy
* [http://www.iep.utm.edu/o/ont-arg.htm Kenneth Einar Himma, The Ontological Argument] &mdash; from the Internet Encyclopedia of Philosophy
* [http://www.fordham.edu/halsall/basis/anselm-gaunilo.html Medieval Sourcebook: Gaunilo: In Behalf of the Fool, and Anselm's Reply]
* [http://www.fordham.edu/halsall/basis/anselm-critics.html Medieval Sourcebook: Philosophers' Criticisms of Anselm's Ontological Argument for the Being of God]
* [http://mally.stanford.edu/ontological.pdf Paul E. Oppenheimer & Edward N. Zalta, "On the Logic of the Ontological Argument" from James Tomberlin ed., ''Philosophical Perspectives 5: The Philosophy of Religion'' (Atascadero: Ridgeview, 1991) pp. 509–529]
* [http://www.etext.leeds.ac.uk/peter/papers/2004OntArgMind.pdf Peter Millican, "The one fatal flaw in Anselm's argument" from ''Mind'' Vol.113, pp451ff (2004)]
* [http://www.revneal.org/Writings/anselms.htm Gregory S. Neal: "Anselm's Ontological Argument For the Existence of God" from ''Grace Incarnate'' (1990)]
 
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