If it only exists in the mind, then an even greater being must be possible — one which exists both in the mind and in reality. Therefore, this greatest possible being must exist in reality.
Other arguments have been categorised as ontological, including those made by Islamic philosopher Mulla Sadra. Since its proposal, few philosophical ideas have generated as much interest and discussion as the ontological argument. Nearly all of the great minds of Western philosophy have found the argument worthy of their attention and criticism.
The general consensus is that the argument is erroneous. He used the analogy of a perfect island, suggesting that the ontological argument could be used to prove the existence of anything. This was the first of many parodies, all of which attempted to show that the argument has absurd consequences. Anselm tried to put forward any proofs of the existence of God.
Even among commentators who agree that St. Anselm intended to prove the existence of God, there is disagreement about where the proof is located.
Some commentators claim that the main proof is in Proslogion II , and that the rest of the work draws out corollaries of that proof see, e. Other commentators claim that the main proof is in Prologion III , and that the proof in Proslogion II is merely an inferior first attempt see, e. In what follows, we ignore this aspect of the controversy about the Proslogion. Instead, we focus just on the question of the analysis of the material in Proslogion II on the assumption that there is an independent argument for the existence of God which is given therein.
Here is one translation of the crucial part of Proslogion II due to William Mann , —1 ; alternative translations can be found in Barnes , Campbell , Charlesworth , and elsewhere :. There have been many ingenious attempts to find an argument which can be expressed in modern logical formalism, which is logically valid, and which might plausibly be claimed to be the argument which is expressed in this passage.
To take a few prime examples, Adams , Barnes and Oppenheimer and Zalta have all produced formally valid analyses of the argument in this passage. We begin with a brief presentation of each of these analyses, preceded by a presentation of the formulation of the argument given by Plantinga , and including a presentation of some of the formulations of Lewis Chambers works with the analysis of Adams From 1 and 2.
It is false that a being greater than God can be conceived. Hence, it is false that God exists in the understanding but not in reality. Each thing which exists in reality is greater than any thing which exists only in the understanding. If a person can conceive of something, and that thing entails something else, then the person can also conceive of that other thing. If a person can conceive that a specified object has a given property, then that person can conceive that something or other has that property.
Hence the being than which no greater can be conceived exists in reality. From 1 - 6 , by a complex series of steps here omitted. From 1, 2, 3. For any understandable being x , there is a world w such that x exists in w. For any understandable being x , and for any worlds w and v , if x exists in w , but x does not exist in v , then the greatness of x in w exceeds the greatness of x in v.
There is an understandable being x such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world.
Hence There is a being x existing in the actual world such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world. From 1 - 3. Hence There is in the understanding a unique thing than which there is no greater. Hence There is in the understanding something which is the thing than which there is no greater. From 2 , by a theorem about descriptions. Hence There is in the understanding nothing which is greater than the thing than which there is no greater.
From 3 , by another theorem about descriptions. If that thing than which there is no greater does not exist in reality , then there is in the understanding something which is greater than that thing than which there is no greater.
Since they also provide a clear reason for thinking that this new version of the argument is not persuasive, it won't be considered further here. Considered as interpretations of the argument presented in the Proslogion , these formulations are subject to various kinds of criticisms. And that is surely a bad result. Second , the Meinongian interpretations of Barnes , Adams and Oppenheimer and Zalta produce arguments which, given the principles involved, could easily be much simplified, and which are obviously vulnerable to Gaunilo-type objections.
Consider, for example, the case of Oppenheimer and Zalta. It would surely be absurd to claim that Anselm is only committed to the less general principles: what could possibly have justified the restrictions to the special cases? But, then, mark the consequences. So, by the first claim, there is at least one existent perfect being in the understanding.
And, by the second claim, any existent perfect being is existent. So, from these two claims combined, there is—in reality—at least one existent perfect being. This argument gives Anselm everything that he wants, and very much more briefly. The Proslogion goes on and on, trying to establish the properties of that than which no greater can be conceived. After all, when it is set out in this way, it is obvious that the argument proves far too much. Third , some of the arguments have Anselm committed to claims about greatness which do not seem to correspond with what he actually says.
The natural reading of the text is that, if two beings are identical save that one exists only in the understanding and the other exists in reality as well, then the latter is greater than the former. But Barnes , for example, has Anselm committed to the much stronger claim that any existing thing is greater than every non-existent thing. Given these kinds of considerations, it is natural to wonder whether there are better interpretations of Proslogion II according to which the argument in question turns out NOT to be logically valid.
Here is a modest attempt to provide such an analysis:. Now, entertaining this idea or possessing this concept requires the entertainer or possessor to recognise certain relationships which hold between given properties and the idea or concept in question.
For example, given that you possess the concept of, or entertain the idea of, a smallest really existent Martian, it follows that you must recognise some kind of connection between the properties of being a Martian, really existing, and being smaller than other really existing Martians, and the concept or idea in question.
In other words, we must be able to have the concept of, or entertain the idea of, a smallest really existing Martian without believing that there really are any smallest Martians.
It will be useful to introduce vocabulary to mark the point which is being made here. We could, for instance, distinguish between the properties which are encoded in an idea or concept, and the properties which are attributed in positive atomic beliefs which have that idea or concept as an ingredient. On the other hand, it is perfectly possible to entertain the idea of a being than which no greater can be conceived—and to recognise that this idea encodes the property of real existence—without attributing real existence to a being than which no greater can be conceived, i.
Of course, the argument which Anselm actually presents pays no attention to this distinction between encoding and attributing—i.
And then the reductio argument is produced to establish that that than which no greater can be conceived cannot exist only in the understanding but must also possess the property of existing in reality as well and all mention of the Fool, and what it is that the Fool believes, disappears. As it stands, this is deeply problematic. How are we supposed to regiment the references to the Fool in the argument? Is the reductio argument supposed to tell us something about what even the Fool believes, or ought to believe?
Are the earlier references to the Fool supposed to be inessential and eliminable? How are we so much as to understand the claim that even the Fool believes that that than which no greater can be conceived exists in the understanding? Following the earlier line of thought, it seems that the argument might go something like this:.
Hence Even the Fool believes that that than which no greater can be conceived exists in the understanding. No one who believes that that than which no greater can be conceived exists in the understanding can reasonably believe that that than which no greater can be conceived exists only in the understanding.
Hence Even the Fool cannot reasonably deny that that than which no greater can be conceived exists in reality. While this is not a good argument, it could appear compelling to one who failed to attend to the distinction between entertaining ideas and holding beliefs and who was a bit hazy on the distinction between the vehicles of belief and their contents.
When the Fool entertains the concept of that than which no greater can be conceived he recognises that he is entertaining this concept i. Conflating the concept with its object, this gives us the belief that than which no greater can be conceived possesses the property of existing in the understanding.
Now, suppose as hypothesis for reductio , that we can reasonably believe that that than which no greater can be conceived possesses the property of existing only in the understanding. Ignoring the distinction between entertaining ideas and holding beliefs, this means that we when we entertain the idea of that than which no greater can be conceived, we entertain the idea of a being which exists only in the understanding.
But that is absurd: when we entertain the idea of that than which no greater can be conceived, our idea encodes the property of existing in reality. So there is a contradiction, and we can conclude that, in order to be reasonable, we must believe that that than which no greater can be conceived exists in reality. But if any reasonable person must believe that that than which no greater can be conceived exists in reality, then surely it is the case that that than which no greater can be conceived exists in reality.
And so we are done. However, the point of including it is illustrative rather than dogmatic. In the literature, there has been great resistance to the idea that the argument which Anselm gives is one which modern logicians would not hesitate to pronounce invalid. But it is very hard to see why there should be this resistance. Certainly, it is not something for which there is much argument in the literature. For a more complex analysis of Proslogion II that has it yielding a valid argument, see Hinst Many recent discussions of ontological arguments are in compendiums, companions, encyclopedias, and the like.
So, for example, there are review discussions of ontological arguments in: Leftow , Matthews , Lowe , Oppy , and Maydole While the ambitions of these review discussions vary, many of them are designed to introduce neophytes to the arguments and their history. Given the current explosion of enthusiasm for compendiums, companions, encyclopedias, and the like, in philosophy of religion, it is likely that many more such discussions will appear in the immediate future. Some recent discussions of ontological arguments have been placed in more synoptic treatments of arguments about the existence of God.
So, for example, there are extended discussions of ontological arguments in Everitt , Sobel , and Oppy His analyses are very careful, and make heavy use of the tools of modern philosophical logic. There has been one recent monograph devoted exclusively to the analysis of ontological arguments: Dombrowski Szatkowski is a recent collection of papers on ontological arguments.
A significant proportion of papers in this collection take up technical questions about logics that support ontological derivations. Those interested in technical questions may also be interested in the topic taken up in Oppenheimer and Zalta and Gorbacz The most recent collection is Oppy Finally, there has been some activity in journals.
The most significant of these pieces is Millican , the first article on ontological arguments in recent memory to appear in Mind. Needless to say, both the interpretation and the critique are controversial, but they are also worthy of attention. Among other journal articles, perhaps the most interesting is Pruss , which provides a novel defence of the key possibility premise in modal ontological arguments. There is also a chain of papers in Analysis initiated by Matthews and Baker Relatively recent work on ontological arguments by women includes: Anscombe , Antognazza , Crocker , Diamond , Ferreira , Garcia , [Haight and] Haight , [Matthews and] Baker , Wilson and Zagzebski Oppy monash.
History of Ontological Arguments 2. Taxonomy of Ontological Arguments 3. Characterisation of Ontological Arguments 4. Uses of Ontological Arguments 5. Objections to Ontological Arguments 6. Parodies of Ontological Arguments 7. A Victorious Ontological Argument? History of Ontological Arguments St. Anselm, Proslogion. Thomas Aquinas, Summa. Criticises an argument which somehow descends from St. The argument of Discourse 4 is further elaborated in the Meditations.
The Objections —particularly those of Caterus and Gassendi—and the Replies contain much valuable discussion of the Cartesian arguments. Intimations of a defensible mereological ontological argument, albeit one whose conclusion is not obviously endowed with religious significance.
Part IX is a general attack on a priori arguments both analytic and synthetic. Includes a purported demonstration that no such arguments can be any good. Contains famous attack on traditional theistic arguments. Some scholars have claimed that the entire Hegelian corpus constitutes an ontological argument. Existence is a second-order predicate. First-order existence claims are meaningless.
So ontological arguments—whose conclusions are first-order existence claims—are doomed. Defence of modal ontological arguments, allegedly derived from Proslogion 3.
A key critique of ontological arguments. All ontological arguments are either invalid or question-begging; moreover, in many cases, they have two closely related readings, one of which falls into each of the above categories. Detailed critique of ontological arguments. See, especially, chapters 2—4, pp.
Characterisation of Ontological Arguments It is not easy to give a good characterisation of ontological arguments. Uses of Ontological Arguments Before we turn to assessment of ontological arguments, we need to get clear about what the proper intended goals of ontological arguments can be.
Here are some proposals; no doubt the reader can think of others: The targets might be atheists, and the goal might be to turn them into theists.
The targets might be agnostics, and the goal might be to turn them into theists. The targets might be theists, and the goal might be to improve the doxastic position of theists. The targets might be professional philosophers, and the goal might be to advance understanding of the consequences of adopting particular logical rules, or treating existence as a real predicate, or allowing definitions to have existential import, or the like.
The targets might be undergraduate philosophy students, and the goal might be to give them some sufficiently frustrating examples on which to cut their critical teeth. Objections to Ontological Arguments Objections to ontological arguments take many forms. The sample argument consists, in effect, of two premises: God exists in at least one possible world. God exists in all possible worlds if God exists in any. Given that a minimally rational non-theist says that there is at least one possible world in which God does not exist, such a non-theist can offer a parallel counterargument with the following two premises: God fails to exist in at least one possible world.
Parodies of Ontological Arguments Positive ontological arguments—i. Here are some modest examples: 1 By definition, God is a non-existent being who has every other perfection. It is the work of Douglas Gasking, one-time Professor of Philosophy at the University of Melbourne with emendations by William Grey and Denis Robinson : The creation of the world is the most marvellous 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—namely, one who created everything while not existing. An existing God, therefore, would not be a being than which a greater cannot be conceived, because an even more formidable and incredible creator would be a God which did not exist.
Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive Definition 2: A is an essence of x if and only if for every property B , x has B necessarily if and only if A entails B Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified Axiom 1: If a property is positive, then its negation is not positive.
Theorem 1: If a property is positive, then it is consistent, i. Corollary 1: The property of being God-like is consistent. Theorem 3: Necessarily, the property of being God-like is exemplified. The set is closed under entailment. The property of having as essential properties just those properties which are in the set is itself a member of the set.
The set has exactly the same members in all possible worlds. The property of necessary existence is in the set.
If a property is in the set, then the property of having that property necessarily is also in the set. Then consider the following argument: There is a possible world in which there is an entity which possesses maximal greatness. Hence There is an entity which possesses maximal greatness. And, of course, they do. Rather it is a precondition for the instantiation of properties in the following sense: it is not possible for a non-existent thing to instantiate any properties because there is nothing to which, so to speak, a property can stick.
Nothing has no qualities whatsoever. To say that x instantiates a property P is hence to presuppose that x exists. But even if we concede that existence is a property, it does not seem to be the sort of property that makes something better for having it.
Norman Malcolm expresses the argument as follows:. The doctrine that existence is a perfection is remarkably queer. It makes sense and is true to say that my future house will be a better one if it is insulated than if it is not insulated; but what could it mean to say that it will be a better house if it exists than if it does not?
My future child will be a better man if he is honest than if he is not; but who would understand the saying that he will be a better man if he exists than if he does not? Or who understands the saying that if God exists He is more perfect than if he does not exist? One might say, with some intelligibility, that it would be better for oneself or for mankind if God exists than if He does not-but that is a different matter. The idea here is that existence is very different from, say, the property of lovingness.
A being that is loving is, other things being equal, better or greater than a being that is not. As it turns out, there are two different versions of the ontological argument in the Prosologium. The second version does not rely on the highly problematic claim that existence is a property and hence avoids many of the objections to the classic version.
Here is the second version of the ontological argument as Anselm states it:. God is that, than which nothing greater can be conceived. For, it is possible to conceive of a being which cannot be conceived not to exist; and this is greater than one which can be conceived not to exist.
Hence, if that, than which nothing greater can be conceived, can be conceived not to exist, it is not that, than which nothing greater can be conceived. But this is an irreconcilable contradiction.
There is, then, so truly a being than which nothing greater can be conceived to exist, that it cannot even be conceived not to exist; and this being thou art, O Lord, our God. This version of the argument relies on two important claims.
As before, the argument includes a premise asserting that God is a being than which a greater cannot be conceived. But this version of the argument, unlike the first, does not rely on the claim that existence is a perfection; instead it relies on the claim that necessary existence is a perfection.
This latter claim asserts that a being whose existence is necessary is greater than a being whose existence is not necessary. Otherwise put, then, the second key claim is that a being whose non-existence is logically impossible is greater than a being whose non-existence is logically possible.
This second version appears to be less vulnerable to Kantian criticisms than the first. To begin with, necessary existence, unlike mere existence, seems clearly to be a property. Notice, for example, that the claim that x necessarily exists entails a number of claims that attribute particular properties to x. For example, if x necessarily exists, then its existence does not depend on the existence of any being unlike contingent human beings whose existence depends, at the very least, on the existence of their parents.
And this seems to entail that x has the reason for its existence in its own nature. But these latter claims clearly attribute particular properties to x. And only a claim that attributes a particular property can entail claims that attribute particular properties.
While the claim that x exists clearly entails that x has at least one property, this does not help. We cannot soundly infer any claims that attribute particular properties to x from either the claim that x exists or the claim that x has at least one property; indeed, the claim that x has at least one property no more expresses a particular property than the claim that x exists.
This distinguishes the claim that x exists from the claim that x necessarily exists and hence seems to imply that the latter, and only the latter, expresses a property. Moreover, one can plausibly argue that necessary existence is a great-making property. To say that a being necessarily exists is to say that it exists eternally in every logically possible world; such a being is not just, so to speak, indestructible in this world, but indestructible in every logically possible world — and this does seem, at first blush, to be a great-making property.
As Malcolm puts the point:. If a housewife has a set of extremely fragile dishes, then as dishes, they are inferior to those of another set like them in all respects except that they are not fragile. Those of the first set are dependent for their continued existence on gentle handling; those of the second set are not. There is a definite connection between the notions of dependency and inferiority, and independence and superiority. To say that something which was dependent on nothing whatever was superior to anything that was dependent on any way upon anything is quite in keeping with the everyday use of the terms superior and greater.
Nevertheless, the matter is not so clear as Malcolm believes. It might be the case that, other things being equal, a set of dishes that is indestructible in this world is greater than a set of dishes that is not indestructible in this world. But it is very hard to see how transworld indestructibility adds anything to the greatness of a set of dishes that is indestructible in this world.
From our perspective, there is simply nothing to be gained by adding transworld indestructibility to a set of dishes that is actually indestructible. And the same seems to be true of God. Suppose that an omniscient, omnipotent, omnibenevolent, eternal and hence, so to speak, indestructible , personal God exists in this world but not in some other worlds.
It is very hard to make sense of the claim that such a God is deficient in some relevant respect. It is simply unclear how existence in these other worlds that bear no resemblance to this one would make God greater and hence more worthy of worship. From our perspective, necessary existence adds nothing in value to eternal existence.
There have been several attempts to render the persuasive force of the ontological argument more transparent by recasting it using the logical structures of contemporary modal logic. One influential attempts to ground the ontological argument in the notion of God as an unlimited being.
As Malcolm describes this idea:. God is usually conceived of as an unlimited being. He is conceived of as a being who could not be limited, that is, as an absolutely unlimited being. In this conception it will not make sense to say that He depends on anything for coming into or continuing in existence. Nor, as Spinoza observed, will it make sense to say that something could prevent Him from existing. Lack of moisture can prevent trees from existing in a certain region of the earth.
But it would be contrary to the concept of God as an unlimited being to suppose that anything … could prevent Him from existing. The unlimited character of God, then, entails that his existence is different from ours in this respect: while our existence depends causally on the existence of other beings e.
Here is his argument for this important claim. A very similar argument can be given for the claim that an unlimited being exists in every logically possible world if it exists in some possible world W ; the details are left for the interested reader.
Since there are only two possibilities with respect to W and one entails the impossibility of an unlimited being and the other entails the necessity of an unlimited being, it follows that the existence of an unlimited being is either logically necessary or logically impossible. The existence of an unlimited being is logically impossible only if the concept of an unlimited being is self-contradictory. Rather, as we saw above, Malcolm attempts to argue that there are only two possibilities with respect to the existence of an unlimited being: either it is necessary or it is impossible.
And notice that his argument does not turn in any way on characterizing the property necessary existence as making something that instantiates that property better than it would be without it. In particular, Premise 2 is not obviously correct. To defend this further claim, one needs to give an argument that the notion of a contingent eternal being is self-contradictory. Indeed, there are plenty of beings that will probably never exist in this world that exist in other logically possible worlds, like unicorns.
Plantinga begins by defining two properties, the property of maximal greatness and the property of maximal excellence, as follows:.
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