The Ontological Argument

INTRODUCTION

The ontological argument is a philosophical argument which claims that by reason alone, one can determine the existence of God to be true. It is a priori (depends on no debatable empirical conditions), formally valid, deductive, and is metaphysically superlative: that there must be an existent God. There are many forms of the argument, of which two of them are the most prominent and convincing. These are the Classical approach and the Modal Logic approach.

Note: Deductive arguments like this may be proved wrong in two ways. One, is that the argument is formally invalid. This is that the argument does not logically follow from one premise to the next. The other reason is that one of the premises is incorrect.

DEFINITIONS

God: God is defined as the Maximally Great Being, that which nothing greater can be conceived of or is possible. (1)

This is to say that God is maximally perfect and therefore possesses every great-making property that it is better to have than to lack, and who possesses this array of compossible properties to their intrinsic maximum value (to their utmost degree - a qualitative infinite). By this definition, there is nothing greater than the Maximally Great Being. (2, 3)

A maximally great being would have great-making properties such as omnipotence, omniscience, omnibenevolence, and necessary existence. This last property attributed is true as nothing that exists contingently can be maximally great. This is not to say that something with maximal greatness must exist, but instead that if it does exist, then it exists necessarily.

Note 1: This definition may be criticized that this is not what they mean by the term God. This however is irrelevant. If the argument is sound, it proves that such a being exists, regardless of what we wish to call it. Furthermore, it is unclear why a rational person would be reluctant to call such a being God, or why God wouldn’t be the Maximally Great Being. 

Note 2: Each of these desirable attributes are possessed in harmony with all of His other attributes. One cannot be both a good bachelor and a good married man, as these contradict. This logically consistent collection of properties is said to be compossible.

Note 3: This qualitative concept of infinity should not be confused with a quantitative concept of infinity, and further clarification is useful. The latter concept is that which has no upper bound (a number, x, can always become 1 bigger: x+1). However, for a qualitative concept, there exists an upper limit or “intrinsic maximum”. For example, it is impossible to score higher than 300 in bowling. Though this example involves a numerical quantity, they indicate qualitative perfection because of its upper limit. In the same way, God’s perfections have upper limit. He is perfectly powerful (omnipotent); perfectly knowledgeable (omniscient); and so on. The result of this is that if one of God’s attributes is proved impossible, the relative bar for this aspect can be toned down to where it becomes possible. For example, “God is omnipotent and can do literally anything,” to “God is omnipotent to the greatest possible extent.”

Possible World: A possible world is a hypothetical situation which describes a way in which the world could have been. It is a description of modal claims – of what is necessary, contingent and impossible. If something is logically possible, it exists in some possible world; likewise, if something is logically necessary, it exists in all possible worlds. The actual world is a possible world.

Possibility: In this argument unless stated otherwise, the term "possible" means "logically possible". If something is logically possible, it exists in some possible world. As long as there are no contradictions in a thing or idea, then it is logically possible, even if not true in the actual world.

The difference between epistemic and logical possibility must be made in order to properly understand the modal logic approach to this argument, which may be shown most clearly through the use of an example. Picture an extraordinarily difficult mathematical equation on a blackboard. If it's beyond our ability to grasp, we may say that it is possibly true or possibly false. This is what is known as an epistemic possibility. As a piece of mathematics however, this equation must be necessarily true or necessarily false (we just don't know which). This is termed a logical possibility. To say that it is possible that it is true, and possible that it is false is correct in an epistemic sense. But in a logical sense, it cannot be false if it is true, and it cannot be true if it is false.

The same applies for the existence of God. To say that it is possible that God exists and it is possible that he doesn't exist is only true epistemically. But if a maximally great being exists, He exists necessarily in the logical sense. Therefore God's existence is either possible, or impossible. (1)

Note 1: An atheist has to maintain that God’s existence is impossible in order to avoid this argument (that is, that the concept of God is incoherent), whereas the defender of this argument thinks that God’s existence is not merely epistemically possible, rather he thinks that God is metaphysically possible as well.

Note 2: It may sometimes be important to note the difference between logical possibility and metaphysical possibility, but in this discussion I shall treat them as synonymous, as I cannot see any useful ontological distinctions being made between them. For further information, see the philosophy dissertation by Alexander Robert Pruss, POSSIBLE WORLDS: WHAT THEY ARE GOOD FOR AND WHAT THEY ARE (particularly section 2: Metaphysical versus logical possibility?).

Necessary: Logically necessary. "No bachelors are married" is a necessary truth. It cannot logically be false. If something is necessary, it cannot not exist, so it exists in all possible worlds. Logical and mathematical truths are one example.

Impossible: Logically impossible. If something is impossible, it cannot exist, so it exists in no possible worlds. It is logically impossible that there are circular squares. It is not logically impossible that a human can live without a head, even though such a thing is physically impossible.

Contingent: It is possible, but not certain to occur or exist. It is neither logically necessary nor logically impossible, so that its truth or falsity can be established only by sensory observation. If something is contingent, it exists in some possible worlds but not in others.It is logically possible that unicorns could exist. There are no apparent contradictions in the idea, and if someone claimed that there were, the burden of proof would be on them. Therefore the proposition, "unicorns exist" is false, but still possible. That is to say, unicorns exist in some possible worlds, but not in all of them, for their existence is possible but not necessary.

Perfection:
Perfection - A property that it is better to have than to lack (A great-making property)
Imperfection - A property that it is better to lack than to have

THE CLASSICAL OR REDUCTIO AD ABSURDUM APPROACH

This is the original version of the ontological argument, through reductio ad absurdum (“reduction to absurdity”). This is where the opposite of the conclusion is assumed then demonstrated that this leads to an absurdity. The premises are laid out as follows:

1. God is defined as the Maximally Great Being, that which nothing greater can be conceived of or is possible.
2. A thing exists either in (a) the understanding only or (b) in both understanding and reality.
3. It is "greater" to exist in reality than to exist merely in the understanding.
4. If God exists merely in the understanding, then God is not the Maximally Great Being, since a being that existed in reality would be greater than a being that existed only in the understanding.
5. But God is by definition the Maximally Great Being.
6. Therefore, God exists in reality.

THE MODAL LOGIC APPROACH

The following is a more modern version of the ontological argument, where the idea of necessary existence and the possible worlds scenario are employed.

P1: It is possible that a MGB exists.

1a. An MGB is one who possesses all great-making properties.
1b. A great-making property is one that is better to have than to lack, for any being.
1c. The great-making property must be taken in a maximal way (i.e., knowledge of all propositions, or omniscience).
1d. One can affirm this possibility if he has at least one great-making property taken in a maximal way that it seems at least possibly exemplified, or if there is no incoherence in such a concept.

P2: If it is possible that a MGB exists, then a MGB exists in some possible world.

2a. A possible world is a maximal description of the way reality could be, encompassing all propositions or their negations in a consistent way.
2b. Anything that is possible, then, exists in a possible world.
2c.?That is, God’s existence is not impossible (logically contradictory), so we can conceive of a world in which God does exist.

P3: If a MGB exists in some possible world, then it exists in every possible world.

3a. If any P is a great-making property, then MGB possesses it (from 1a).
3b. Necessary existence is a great-making property.
3c. Therefore, MGB possesses it.
3d. Necessary existence entails existence across all possible worlds.

P4: If a MGB exists in every possible world, then it exists in the actual world.

4a. The actual world is a possible world, else it would be impossible.

P5: If a MGB exists in the actual world, then a MGB exists.

5a. Whatever is actual exists in reality.

P6: Therefore, a MGB exists.

MODAL PERFECTION ARGUMENT
This argument is a defense for the soundness of the first premise, P1. That is, is it possible that a Maximally Great Being exists? A common objection is that it is equally reasonable to say that "It is not possible that a MGB exists." The following is a deductive argument that shows that this is not the case.

M1: If a property is a perfection, then its negation is an imperfection

M1 is true because it is better to have a property than not only if it is not better to not have that property than not.

M2: If a property is a perfection and it entails another property, then that entailed property is not an imperfection

M2 is true because it is always better to have that which is a necessary condition for whatever it is better to have than not.

M3: Maximal greatness, M, is a perfection

M3 is true because it is reasonable to assume that a thing is supreme if and only if it is necessarily greater than everything else solely by virtue of having some set of perfections, making the extension of the property of being supreme identical with the intersection of the extensions of those perfections.

M4: Therefore, M cannot entail ~M

This means that if a property is a perfection, it cannot entail an imperfection. A perfection's negation is an imperfection, therefore no perfection can entail its own negation.

Let us propose that P1 is false, that is, "It is not possible that a MGB exists". From this we would come to this deduction:

A1: It is not possible that something with M exists (inverse of P1).
A2: If A1, then necessarily, all things which exist have ~M
A3: If A2, then all properties entail ~M
A4: Therefore, M entails ~M

This is a contradiction with M4, therefore A1 is false, therefore P1 is true.

REVERSE ONTOLOGICAL ARGUMENT

This critique can be used to furthermore show the soundness of the modal logic approach.

P1': It is possible that a MGB does not exist.
P2': If it is possible that a MGB does not exist, then a MGB does not exist in some possible world. (different to W1. Reversing possible/not possible and does not exist/does exist)
P3': If a MGB does not exist in some possible world, then it is impossible. (because it does not exist in every possible world. this being must be necessary - exists in all worlds or none)
P4': If a MGB is impossible, then it does not exist in the actual world.
P5': If a MGB does not exist in the actual world, then a MGB does not exist.
P6': Therefore, a MGB does not exist.

Therefore, either God necessarily exists, or is impossible. But we know that it is possible that God exists from the MPA, therefore God isn't impossible. Therefore God necessarily exists.

The possible worlds argument then becomes this:

1. God is defined as the Maximally Great Being, that which nothing greater can be conceived of or is possible.
2. The existence of God is either impossible or necessary (since He cannot be contingent).
3. The existence of a God is not impossible (since it is neither nonsensical nor self-contradictory - and because MPA shows God is possible).
4. Therefore God is necessary.
5. Therefore God exists.

The second premise claims that if God exists, He must exist necessarily in all possible worlds. God doesn't simply happen to exist as a being than which nothing greater can be conceived to exist. Rather, God exists as a matter of logical necessity. He does not exist as a contingent state of affairs, for example the guitar (we can conceive of a world where guitars were never invented). But since a necessary being must exist, its existence is not a matter of contingent fact (such as the guitar). Therefore God is either impossible or necessary. Furthermore, his necessary existence (if He exists) is justified by His definition. The Maximally Great Being would have the greatest possible form of existence. This is true by definition, and so holds true in all possible worlds. Necessary existence is the greatest form of existence because by definition it is existence in all possible worlds. Therefore, in every possible world it is true to say that if God (the Maximally Great Being) exists, He would have the greatest possible form of existence (necessary existence).

The only way to deny the existence of a necessary being is to demonstrate that its existence is nonsensical or self-contradictory. Premise three claims that God is neither nonsensical nor self-contradictory, therefore God is not impossible. Again by using the definition we gave, this is true. God is defined as the greatest possible being. If a being is possible, it cannot be impossible. For any being that was perfect to an extent that it is not possible, then it would not be the greatest possible being. Given its coherence, it would be irrational to claim that the Maximally Great Being cannot possibly exist.

From these first three premises it follows that God necessarily exists in all possible worlds, and because reality is itself a possible world, God therefore exists.

Note: Premise 2 does not presuppose the existence of God. This is true because the claim that God has necessary existence only holds if He exists. 

THE ONTOLOGICAL ARGUMENT IN SYMBOLIC LOGIC

G is the claim that God, the Maximally Great Being, exists. This existence as explained earlier would be necessary existence. If this is true (that He would have a necessary existence if He existed), then it logically follows that:

  1. ◻(G ⊃ ◻G)   
If God exists, He exists necessarily in all possible worlds
The following statement holds true in all possible worlds: If God (on the definition above) exists, He exists necessarily.
  2.  ~◻~G
“The Maximally Great Being is possible”
This states that G is not impossible, or ⟡G.
  3.  ~◻G ⊃ ◻~◻G   
If God does not necessarily exist, He does not necessarily exist in all possible worlds
Becker’s postulate applied to ~◻G
  4. ◻G ⊃ G
If God necessarily exists then God exists
If God necessarily exists, then he exists.
  5. ◻G ⋁ ~◻G
God necessarily exists or God does not necessarily exist
Law of Excluded Middle
  6. ◻G ⋁ ◻~◻G
God necessarily exists or He does not necessarily exist in all possible worlds
3,5 substitution
  7. ◻~◻G ⊃ ◻~G   
If God does not necessarily exist in all possible worlds, then He is impossible
1, modal modus tollens
  8. ◻G ⋁ ◻~G
God necessarily exists or God is impossible
6,7 substitution
  9. ◻G
God necessarily exists
8,2 disjunctive syllogism
∴ G
God exists
9, 4 modus ponens

Note 1: The third premise can be read as “If it is not the case that G is true in every possible world, then ~G is true in all possible worlds.” This is true as if G is not true in all possible worlds, then in each possible world the statement “G is not true in all possible worlds” would in fact be correct.

Note 2: This reasoning does not prove any possible proposition. This is unique due to the nature of the proposition G, which is that the Maximally Great Being exists. For example: Unicorns exist in one possible world. But as unicorns are contingent, they do not necessarily exist in all possible worlds.

OBJECTIONS 
WE ARE UNABLE TO FORM A COMPLETE CONCEPT OF GOD

Critique 1: Given God's unsurpassable greatness, we cannot fully comprehend or understand Him. God is being severely limited if He is only as great as one can conceive.

Response: This claim falters as it does not directly involve itself with the argument given. We do not need to understand everything about this superlative being to have a proper apprehension of it; one just needs to understand the definition given for the maximally great being.

THE CONCEPT OF GOD LACKS AN INTRINSIC MAXIMUM
Critique: This critique claims that the concept of God lacks any intrinsic maximums, therefore is logically impossible. The analogy of "the greatest possible integer" could be used here. There is always an integer one greater. God would thereby be an incoherent concept because there are no intrinsic maximums. When God's possibility was justified, it was presupposed that He has these intrinsic maximums. If this objection is correct, then premise 1 is unsound.

Response: But, there are indeed intrinsic maximums for the qualities of God (see definition of God). For example, God's omniscience can be defined as belief that all true propositions are true (and that false propositions are false), and similarly for God's omnipotence being defined as the ability to do anything that can be done. There aren't any greater possible conditions for these as they are intrinsic maximums.

NOTHING EXISTS NECESSARILY

Critique: This claim goes against the premise that if God exists, He necessarily exists. Nothing exists necessarily, therefore God must exist contingently. From this it follows that it is possible He does not exist in some worlds, therefore does not exist in all worlds.

Response: Many metaphysical problems arise very quickly from this objection however. This would entail an ontological disproof of numbers, sets, propositions, properties and so on - which we know are indeed necessary.

A QUASI-MAXIMALLY GREAT BEING 

Critique: This is a parody objection in which the objection is made that the argument would also prove the existence of a quasi-maximally great being. This being would have all perfections bar at least one. Such as a great being that does not exist in all possible worlds, or a necessary being that isn't omniscient or omnipotent.

Response: Some of the great-making attributes cannot be possessed by more than one being in any given possible world, for example, omnipotence. If two or more beings all have the property of being omnipotent, then a logical contradiction would occur. If they attempt to actualize opposing state of affairs, then there would exist a possible world in which a contradiction has occurred. But this is illogical, and therefore a maximum of one being can be omnipotent.

Furthermore, if it was metaphysically impossible for their wills to conflict, then we are talking about only one will but described as two concepts. And so only one being is actually described.

Now in the case that this quasi-maximally great being was not omnipotent, but has necessary existence, a logical contradiction again follows. If an omnipotent being exists, then nothing else can exist unless caused by it's will. And so this maximally great being could refrain from creating any quasi-maximally great beings, so there would be possible worlds in which only the maximally great being existed. Therefore quasi-maximally great beings cannot exist necessarily.

As a result of the above two objections, two conclusions are brought about which are consistent with Christian doctrine. One, God is omnipotent whilst the Devil is not. The other is that polytheism is false. This is because the properties of omnipotence and necessary existence can be held only by one being. The other gods, which by their very definition must exist necessarily to be gods, cannot exist.

A PERFECT DEVIL

Critique: Like the objection above, this claim argues that the ontological argument would prove the existence of a maximally wicked being. That is, a being which has all of the great-making properties like that of a maximally great being, with the exception that it is omnimalevolent, rather than omnibenevolent.

Response 1: Firstly, this being does not have all the qualities possessed by a Maximally Great Being. This maximally wicked being fails by definition, as it has both omnipotence, and omnibenevolence - making this being an incoherent concept. A being who is fully powerful, by nature, must also be omnibenevolent. Any power held by a non-omnibenevolent being is offset by it's own inferiority in moral worth. A being would be greater if He is morally good even if He can't perform immoral deeds. Furthermore, one could argue that the ability to do immoral deeds is actually a weakness, rather than power. This revolves around the definition of omnipotence and that it does not mean the power to do just anything. Just like omnipotence cannot make logical contradictions, it cannot make immoral actions. But, can an omnipotent being perform only amoral deeds? That is, it is a morally neutral being?

Response 2: In similar fashion to the first response, the property of being omnimalevolent entails other properties which are imperfect. For example, evil would lead to injustice.

Response 3: In terms of the classical approach, what would it mean to say that a devil is greater to exist in reality than in the understanding? It would be worse for the devil to actually exist in reality, and so this version of the ontological argument is not compatible with this concept.

Does the argument fail because a quasi-deity/devil lack maximal greatness by definition?

If these two above arguments are sound, they wouldn't prove God doesn't exist - only that other 'supernatural' beings exist also.

GREATEST POSSIBLE HANDICAP

Critique: If God is the Maximally Great Being, then would it not it be greater for God to not exist and still bring the universe into being? But far from undermining the Ontological Argument, it shows its coherence.
"The creation of the Universe is the greatese real achievement, because it encompasses all other real achievements. An achievement is greater, the greater the handicap of the achiever. The greatest possible handicap is not to exist. Therefore a God who created the Universe and does not exist is greater than one which created the Universe and which does exist. Therefore God does not exist."

Response: Greater? Maybe. But for any being with any great-making properties would only be great if it existed - so likely no, the being would not be greater as it would be logically incoherent. Possible? No. For in what possible world does a non-existent being exist?

THE GREATEST POSSIBLE ISLAND

Critique: This argument states that the ontological argument can be applied to many things. The most famous of these examples is the "greatest conceivable island" is proved to exist (this will be referred to as the greatest possible island, which though is a slightly modified definition, will come to the same conclusion). By replacing God with this island, the ontological argument becomes the following:

1. It is possible that a greatest possible island exists.
2. If it is possible that a greatest possible island exists, then it exists in some possible world.
3. If a greatest possible island exists in some possible world, then it exists in every possible world.
4. If a greatest possible island exists in every possible world, then it exists in the real world.
5. But it is absurd that a greatest possible island exists in this world, since every extant island is less than perfect.
6. Therefore, this refutes the ontological argument, since it substitutes similar terms and uses the identical argument form, by reductio ad absurdum.

This argument is deductive in form, and is valid. Symbolic logic can also be used to prove this. The same reasoning for the justification for God can be used here. That is, if the greatest possible island exists, then it exists necessarily. And also similarly, it is at least possible for the greatest possible island to exist.

Something therefore must be wrong with the ontological argument. If this refutation is sound, then it proves that the ontological argument cannot prove anything to exist. Unfortunately, it does not tell us what is wrong with the argument, be it that one of the premises is false, or that the argument is invalid. Using the symbolic logic approach, we know that the argument is valid. Therefore the problem would lie with one of the premises. Since the objection does not explain why something is wrong, it should be viewed warily.

Response: The argument's first premise is unsound. There can be no greatest possible island for at least two independent reasons.

Firstly, a maximal thing reaches the upper limit of greatness, that is to say it would possess an intrinsic maximum value to all of its attributes. Because of this, the concept of a maximal island is incoherent. The island could always have more sand or palm trees or beaches - furthermore, its greatness would be relative to each person. For example one may like more shade, whilst the other may like more sun (no objective standard of greatness exists for this concept). Another example may be useful here - such as the idea of the greatest possible integer. Neither this integer or island could possibly exist, as neither has an intrinsic maximum, and therefore the greatest possible island is not a coherent concept.

The second problem is that this island (or most other examples we may think of - excluding sets/numbers etc.) is by definition not a necessary being (or thing/entity). Its existence is contingent. For example, it is contingent on matter. The island could be destroyed with a large bomb. The island no longer exists, and therefore is not a necessary entity. We can easily conceived of a possible world in which there are no islands. The ontological argument works because of the ontology of God as a necessary being. Anything that is less than God necessarily lacks this ontology (set of properties) and so cannot be the subject of the ontological argument. Therefore this parallel/parody argument fails.

One response is that Anselm’s ontological argument only applies to the greatest possible thing. It’s not absurd to believe that something greater than the greatest possible island exists (e.g. an intelligent person) but that would not be the case for God, a being that is the epitome of maximum possible perfection. God is that which nothing (and no being) greater is possible. So, unlike the island, it would be absurd to think that something is greater than the greatest possible thing.

There is nothing inherent in the definition of “island” and “chicken” that entails such perfection that was used when the argument described God. Thus, it isn’t so much as possible that there really be a greatest possible island. The concept of an island (sock, crap etc.) does not inherently include the notion of supreme perfection, instead the vague aspect of “perfection” is artificially pasted on to the core concept, while the concept of God (maximal perfection, “that which nothing greater is possible”) cannot be separated from its hardcore intrinsic meaning: maximal perfection. With God there is only one clear and coherent concept of maximal perfection, and so the argument that flows forth from this can’t be used to support any other concept. What about God? Aren’t his attributes of greatness subjective? Not at all. One way the theist could justify defining God as maximal perfection is to look at the summary property of God’s attributes. God is perfectly powerful, perfectly good, perfectly wise, perfectly knowledgeable, and so forth. Being perfectly powerful (omnipotence) for instance, is an objective quality. Or one can put this in terms of questions asked on the aspects of God. For instance, how much power does God have? Perfect power: omnipotence (to the greatest possible extent). How much knowledge does God have? Perfect knowledge: omniscience (to the greatest possible extent) etc. These questions have legitimate and objective answers and thus God (as defined here) is a legitimate concept, unlike the greatest possible island/number/chicken etc.

EXISTENCE IS NOT A PREDICATE

Critique: This argument attacks premise 3 of the classical approach, and the justification for premise 1 of the symbolic logic approach. A predicate is a property we attribute to something. For example, a red door has "red" as one of its predicates. A predicate is used to denote additional information about its subject.

"Being is evidently not a real predicate, that is, a conception of something which is added to the conception of some other thing. It is merely the positing of a thing, or of certain determinations in it. Logically, it is merely the copula [i.e. the verb linking the subject and the predicate] of a judgment. The proposition, God is omnipotent, contains two conceptions, which have a certain object or content; the word is, is no additional predicate—it merely indicates the relation of the predicate to the subject. Now if I take the subject (God) with all its predicates (omnipotence being one), and say, God is, or There is a God, I add no new predicate to the conception of God, I merely posit or affirm the existence of the subject itself, with all its predicates, in relation to my concept, as its object." - Kant, Critique of Pure Reason

This is showing that there is a difference in predicating something (eg. this person is tall) and saying that something exists. Consider the following predicates:

• God is omnipotent
• God is omniscient
• God is omnibenevolent

Existence says "God is". But 'is' is not a predicate itself. Existence doesn't tell us additional information about its subject, only that it exists. Therefore existence even though functions grammatically as a predicate, it is not genuine predicate, and therefore the ontological argument fails.

Response 1: This argument states that existing adds nothing to the concept of God (or the Maximally Great Being). That is, existence is merely a logical predicate and not a genuine predicate. The latter adds significant information regarding the subject, whilst the former adds nothing (eg. a tree's leaves are leaves). Any grammatical statement can function as a logical predicate, but a real predicate "determines" a thing or "enlarges" the idea of the subject in question.

This may be made clearer through the use of an example. Consider this statement: "My future house will be better if it is air conditioned than if it is not." But what does it mean to say that it would be better if the home existed? To say it would be better is bizarre.

Following this, we should grant that it is odd to add the idea of existence to that of a desired home. This oddness occurs because the existence of the home is presupposed in the context of discussion. However, there are situations where it is not odd to use existence as a predicate. For example, a child may ask of any particular animal, "Is that animal real or imaginary?" That is to ask, does the animal described exist in reality, or only in understanding? There is no fallacy here. Existence is legitimately functioning as a predicate in this case and in cases of similar sort (many examples are easily imagined, such as: Does the Loch Ness Monster or Bigfoot exist?). From this, it seems that there is nothing wrong with existence functioning as a predicate for the subject God, since the matter of God's objective existence is a legitimate question (just like that of an animal - real or imaginary). These things are possibly existing things, so existence is an appropriate and meaningful predicate concerning their ontological status.

Example: Suppose an inquiring child who has always believed that Santa Claus existed asks me if this is so. I tell the child that Santa Claus does not exist, and the child believes me. The objection of existence not being a predicate would seem to say that the child has not learned anything new about Santa Claus, but surely that is a bit peculiar. To say that the child has not learned anything new about Santa Claus when the child learns of Santa’s nonexistence seems dreadfully nonsensical. When a mathematician says that there exists prime numbers between 12 and 21, is she not denoting a characteristic of prime numbers? The objection would again seem to say no. But clearly the child has learned something about Santa Claus, and the mathematician has mentioned a characteristic of prime numbers. Thus, existence does seem to be a property one can attribute.

Response 2: It does not matter if existence is a predicate. A similar line of justification is used instead. Necessary existence is certainly a predicate (hence its use as a predicate in predicate logic), even if existence per se is not. If the Maximally Great Being exists, then it exists necessarily (as necessary existence is greater than contingent existence).

Reponse 3: Kant’s justification for existence not being a predicate seems unsound. He claims that existence is merely the copula for the predicate and the subject, such as the word is in “God is omnipotent,” and any other form of “[subject] is [predicate].” Suppose that existence is just the copula. If that were true, then attaching a predicate to a subject with the copula would presuppose the subject’s existence. But we predicate non-existent things all the time. Suppose I say, “Santa Claus is a jolly fat guy.” I really don’t mean to imply that Santa actually exists when I describe him.

Thoughts: The only kind of existence the copula seems to imply is conceptual existence, not real (actual) existence. All predicated subjects have at least conceptual existence (i.e. any predicated subject is a concept). So given that this is already known, one could argue that conceptual existence doesn’t add anything new to a subject. But even if conceptual existence is not a predicate, how useful is this claim in attacking the ontological argument? In the reductio ad absurdum approach, the ontological argument suggests that a God with actual existence is greater than a God with actual non-existence. Actual existence may be required to be a predicate here, but not conceptual existence. The kind of existence the symbolic logic approach uses in the justification for the first premise concerns itself with both actual existence and modal existence, but not conceptual existence (conceptual existence does not imply any sort of actuality or modal status, since even logically impossible statements are conceptual in nature). It would appear that, for Kant’s objection to work, it would have to show that existence other than conceptual existence (e.g. actual existence) is not a predicate. Whether or not such existence is a predicate, it seems clear that Kant’s copula justification for it does not seem to work.

Note: Does the claim of existence being merely a copula give a fully accurate description of what existence really is? If so, then the objection works. If not, and if the last response of the section makes sense, then existence really is a predicate. But do the examples of Santa Claus and prime numbers really adduce existence as a property that one can attribute? If yes, then the objection doesn’t work. If not, then it does not establish existence as a predicate and the first premise will require some other justification.

Does the argument about necessary existence being greater than contingent existence work? If yes, then premise #1 is justified. If no, then premise #1 needs other justification for the premise to be accepted. If such justification is not provided, then a critic can point to the first premise and rightfully claim that the argument is not sufficiently supported for it to be accepted as sound.

EXISTENCE IS NOT A "GREAT-MAKING" PREDICATE
Critique: Is it better to exist than not to exist? This objection claims that existence is not a great-making property. Attack on premise 3 of the classical argument. This criticism reasons that the greatest possible island doesn't work as an argument to prove its existence because existence doesn't make something greater. For example, is it greater for an unstoppable flesh-eating virus to exist or to not exist? It is certainly not, and therefore existence is not a great-making property.

Note: This objection cannot be made against the modal approach.

Response 1: However, the ontological argument specifically addresses a singular Maximally Great Being (Read: a perfect being - a class by itself). An existing Perfect Being is certainly greater than the mere idea of one. This notion of greatness seems to consist of power - the ability to accomplish things in the world. Nietzsche granted than the idea of a nonexistent God was very powerful in the history of Western civilization. But an existing Perfect Being would be far greater-more powerful, able to accomplish things as an existing agent, not merely as an idea in the minds of people. In this sense, the lowliest PI is greater than Batman (as the latter exists only in understanding). Furthermore, whilst ideas both true and false have consequence, the ideas themselves are causally inert. Actual agents must believe or be influenced by the ideas and to act in accord to bring about any state of affairs in the world. Therefore, a false idea has no power in itself. Rather, agents who hold false ideas act in accordance with their false beliefs and produce consequence (and vice versa for true ideas).

Response 2: Existence doesn't make something necessarily great, but it appears that it does make some things great. For example, mountains, beauty, or God. Beauty that exists is greater than beauty that does not exist (arguing for the existence of a property something has). Similarly, an existing God is greater than a non-existing God.

Note: How does the attribute of existence make God greater? Does an existing God have more knowledge or more power? Yes. A non-existing God does not really have omnipotence, omniscience, etc. for the simple reason that this God would not exist. A God who exists in reality, however, would be far greater in every one of such attributes. One could conceivably use this fact to argue in favor of in favor of existence being a great-making property, at least when it is applied to God. Of the two ontological arguments, this response is perhaps most useful in arguing for premise 3 in the reductio ad absurdum approach.

GOD IS IMPOSSIBLE
The only way to deny the existence of a necessary being is to demonstrate that its existence is either nonsensical or contradictory (eg. married bachelor). God's existence must be logically necessary or logically impossible. To reject the argument, one must maintain that the concept of God is self-contradictory or nonsensical. This can be done in two way. Show that one or more attributes of God conflict with one or more of His other divine attributes, or show that one of His attributes is self-contradictory. (this needs to be cleaned up)
 

SELF-CONTRADICTORY ATTRIBUTES

Critique: Omnipotence. The claim that this attribute is self-contradictory comes from the famous paradox of the stone. Can God make a stone so heavy that God cannot lift it? The dilemma is as follows:

1. If God cannot create the unliftable stone, then God is not omnipotent, since he cannot create the stone.
2. If God creates the unliftable stone, then God is not omnipotent, since he cannot lift the stone.
3. Therefore, God is not omnipotent, because the very concept of omnipotence is contradictory.

Response: This argument fails because of confusion concerning the definition of omnipotence and its relation to logic. Omnipotence cannot mean the ability to do anything, irrespective of logical coherence. God's power only pertains to actualizing logically possible states of affairs. God cannot make a square circle, simply because the very idea is contradictory. Likewise, for God to create something he could not life would be a contradiction. “God can do anything that can be done.”

CONFLICTING ATTRIBUTES

Critique 1: Omniscience vs. Immaterial. Claim that omniscience is incompatible with God being immaterial. Since God intrinsically without a body, he cannot possibly know what it feels like to have a body with its attendant pains and pleasures. Since God lacks this knowledge, God cannot be omniscient. Therefore the idea of God is self-contradictory and therefore impossible and therefore does not exist.
 

Response:

The flaw lies in the concept of omniscience and its failure to understand a specifically Christian understanding of God.

The classical theological claim of omniscience is not that God has first-person /experience/ of all that occurs in any sentient being in the universe, but that God has /knowledge/ (justified true belief) of all propositions, both true and false (believing the true to be true and the false to be false). Nevertheless, given God's unlimited power to know, He has access to subjective states of the finite and embodied creatures, human and nonhuman, experiencing what they experience "seeing through their eyes, ears, etc.". So while God is not a finite or embodied being, he He is able to enter the subjectivity of finite embodied beings (omnisubjectivity*). Nevertheless, God cannot experience that kind of existence in a first-person sense. This does not contradict classical omniscience (only that it stipulates who God is qua God and God's relation to creation).
Furthermore, Christianity claims that the second person of the Trinity took on human nature at the incarnation. Therefore God does know something of the embodied human condition in the first person. God knows what it is like to be a human being (this being said, He does not know experimentally what was not experienced by Jesus, eg. being married or committing sin).
Therefore the claim that God is not omniscient fails because he does have knowledge of all things (which is what omniscience is) - (and is not a stranger to first person human experience in Christ).

*Further, God could know counterfactual qualia by considering how an embodied, finite creature would experience a state of affairs that is, in fact, not experienced by any such being. On this account, God knows the scent of a rose that is never smelled by any creature.

Qualia: Is an unfamiliar term for something that could not be more familiar to each of us: the ways things seem to us (though they may not exist)

NOTHING CAN BE PROVED TO EXIST A PRIORI

Critique: This argument claims that nothing can be demonstrated to exist a priori, therefore no ontological argument for God's existence can be sound.

“I shall begin with observing, that there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by arguments a priori. Nothing is demonstrable, unless the contrary implies a contradiction. Nothing, that is distinctly conceivable, implies a contradiction. Whatever we conceive as existent, we can also conceive as non-existent. There is no Being, whose existence is demonstrable. I propose this argument as entirely decisive, and am willing to rest the whole controversy upon it.” - David Hume, Dialogues Concerning Natural Religion

Formalized:

1. The only way to prove something a priori is if its opposite implies a contradiction.
2. If something implies a contradiction, then it is inconceivable.
3. Everything can be conceived not to exist.
4. Therefore, nothing can be proved to exist a priori.

This argument claims that to determine whether or not a statement can be proved priori, we try to conceive that it is false. If this is possible, then it follows that it cannot be proved a priori. But if we cannot imagine it to be false, then the statement must necessarily be true. Therefore to determine whether or not God necessarily exists, we try to conceive that He does not. We seemingly are able to do so, therefore his non-existence is possible. As His existence is not necessary, no a priori argument is sound. 

Response:

What does it mean by the term 'everything' (Hume states "whatever we conceive")? Does it include all contingent things, necessary things, abstract ideas? Surely necessary truths can be proven a priori. So it seems that (3) should be restated to "Everything contingent can be conceived not to exist". But the ontological argument favors a necessary being, so it seems that Hume's objection falls flat.

Point above is the same as Davis' third dispute. His other two look good as well.

It seems to me the argument (particularly premise 3) is begging the question. Is it?

=-=--=-=-=-

Response: In his book, God, Reason, and Theistic Proofs, Stephen T. Davis discusses Hume's argument:

Hume's argument is altogether unimpressive; the first three statements in his refutation are all either false or misleading. It isn't true that 'Nothing is demonstrable unless the contrary implies a contradiction.' There are several ways in which propositions can be intellectually unacceptable besides being strictly logically contradictory. The statement 'There exists a tallest conceivable human being' is not strictly logically contradictory, but it is necessarily false; its contrary is demonstrable. Some statements are intellectually unacceptable because they are incoherent ('The "Not" negates itself non-negatively') without, so far as we can tell, being contradictory. And in at least some senses of the word 'demonstrable', some statements are demonstrable because their contraries are (not contradictory but) very highly improbable....

"Next, Hume is wrong in saying, 'Nothing that is distinctly conceivable implies a contradiction.' As we have seen, there are several senses of the word 'conceive', and on some of them it is quite possible to conceive of contradictory states of affairs. Even Anselm argued that it is possible to word-conceive a statement that he considers contradictory, namely, 'The GCB does not exist.'

"Finally, Hume misleads us when he says, 'Whatever we conceive as existent, we can also conceive as non-existent.' If what we have called word-conceiving were the only species of mental conceiving, Hume might be within his rights. But it isn't. As we have seen, there is also thing-conceiving. Just as a contradictory thing (for example, a square circle) cannot be thing-conceived as existing, so a necessary being (if there is such a thing) cannot be thing-conceived as not existing."

"GCB" is an acronym for "the greatest conceivable being". To "word-conceive" something is to understanding the meanings of the words by which that thing is referred to. To "thing-conceive" something is to understand the thing itself, its properties and relations. What the ontological argument attempts to show is that although we can word-conceive "God does not exist", we cannot thing-conceive it.

Finally, to claim that an a priori argument cannot prove something's existence is to beg the question against the ontological argument. The argument itself will have to be considered to see if it succeeds or not. 

Arguments to address, and notes to think upon:

Is necessary existence a great making property (Is it better to exist or not to exist)?

               http://rfforum.websitetoolbox.com/post/Is-Necessary-Existence-a-GreatMaking-Property-5697180
 
 Nothing can be proved to exist a priori

                    http://www.philosophyofreligion.info/theistic-proofs/the-ontological-argument/st-anselms-ontological-argument/hume-on-a-priori-existential-proofs/

This assumes there is some objective concept of greatness. 

-Attributes are relative. A knife is powerful because of its use. Therefore a sharp knife is better than a blunt knife. Someone who is good to be is better than someone bad to me. etc. But isn't this all subjective? eg. masochist and a normal person (so what is normal?)

trillionth digit of Pi is 8 argument

"Well, there are at least two different senses of "possibility."  There's subjunctive possibility, which (among other things) involves possibilities insofar as they do not entail a logical contradiction, and there's epistemic possibility, which involves possibilities as far we know.

For example, you might say that it is possible that the trillionth digit of Pi is 8.  However, this is only true under the epistemic interpretation of the word "possibility," because the trillionth digit of Pi, whichever single digit it may be, in terms of subjunctive modality, is necessarily the trillionth digit of Pi. So while the atheist may be charitable with regard to the epistemic possibility of God's existence, s/he can still plead ignorance with respect to God's subjunctive possibility."

Note for above: See WLC http://www.reasonablefaith.org/necessary-existence-and-the-ontological-argument

Can you go from GPB existing in concepts to reality?

Levels of omnibenelovence, or no intrinsic maxima, or..? 

Maximally Great Being would be god? Eastern philosophies might say that the Maximally Great Being is the universe instead. etc. 

Perfectly good = omnibenevolent requires absolute moral code?

Is there a possible world in which nothing exists? 'Nothing' must be defined. If it means all of space, time, and matter, then yes. But if it means absolutely nothing exists, this is surely wrong. Abstract concepts must always exist by their own necessity, such as numbers and sets. Similarly, everything else necessary must exist in every possible world. If this Maximally Great Being is necessary, then it exists in this world where 'nothing' exists.

Critique on S5/Bacran formula/becker's postulate

Yes, the modal ontological argument relies on a quasi-controversial axiom of modal logic called Axiom S5 which is used to reduce chains of modal operators down to the equivalent of the last operator.

Specifically, in S5:
Possibly Necessarily X -> Necessarily X

Clearly the modal ontological argument relies on this axiom alone. The argument can be posed thusly:

Def. 1) Maximal excellence [ME] is possessing omnipotence, omniscience (etc.) in a given possible world
Def. 2) Maximal greatness [MG] is possessing maximal excellence in all possible worlds

P1): Possibly MG
P2): Possibly Necessarily MG (this is because the definition of necessity is being true in all possible worlds, which is automatically implied by MG's mere possibility)
P3): Necessarily MG (because possibly necessarily MG -> necessarily MG, by axiom S5)
Conclusion: MG [exists]

It's an interesting argument but I'd like to point out that it can be used to "prove" any proposed ontologically necessary thing. Also, this argument has an anti-argument:

P1') Possibly not-MG
P2') Possibly necessarily not-MG
P3) Necessarily not-MG
P4') Not-MG

It should be clear that Axiom S5 is being abused by this argument since we can clearly be led into a paradox. The modal ontological argument therefore fails because it becomes a microcosm of the original question (does a god exist).

Response: Maydole's Modal Perfection Argument proves that P1' causes a contradiction. Therefore S5 axiom is A-OK to use.

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

"I'm still trying to wrap my mind around the Ontological Argument, but something about this parody doesn't strike me as quite right.

1. "God does not exist in all possible worlds" is equivalent to "there is a world in which God does not exist". Did I get that right??

2. If God, by definition, is Maximally Great Being (MGB), can we actually say that there is a world in which "God" does not exist if the very definition of God as MGB requires Maximal Excellence in all possible worlds? I.e. If a given entity does not exist in even one possible world, then it is by definition  no longer MGB. So, the entity we are discussing here as not existing is, in fact, an entity less than MGB anyway - perhaps "AMGB" (almost maximally great being).

3. So, you can say AMGB does not exist in all possible worlds, but you can't say MGB exists in all possible worlds without contradicting your own definition of MGB.

So, when you say "3. A god who does not exist in all possible worlds is not 'God'", you are correct, but then statement 4 is not "God does not exist" but rather "god does not exist".

I'm not saying Plantinga's argument works; I'm just thinking that this particular parody doesn't work because it requires a definition of God that is not the definition of God.

Or am I way off base?"

"I think you're mostly right in your criticism of it. One other criticism to be added to this argument is that it seems to rely on epistemic possibility (i.e., for all we know, God may not exist). Strictly speaking, then, the argument would be invalid. However, if they do mean metaphysical possibility, then (1) in the parody is malformed. It needs to say "It's not possible God exists;" else the objector is guilty of making a necessary truth out of a contingent fact. I do happen to think Plantinga's argument is correct and sound, and Robert Maydole's is excellent as well."

"How can the argument work when it clearly commits an equivocation between epistemic and metaphysical possibility?"

"It doesn't--that's why the parody argument fails! It states "It is possible that God does not exist," which is not the same as the required metaphysical premise in the parody, which would be: "It is not possible that God exists." It was that criticism which I would add to the parody, which, strictly speaking, does not afflict the MOA."

See: http://rfforum.websitetoolbox.com/post/Why-the-Ontological-Argument-Fails-5648885?trail=30

"I see it like this: What makes omnibenevolence or omnimalevolence (or anywhere in between) great or not? Either one of the extreme's is great-making, or any 'level' is equally great or ungreat. Omnibenevolence weighs heavily on it being a moral property - which I believe at least every theist would agree with. So if is a moral property, then it appears to us that it would be morally better (read: greater) to be all loving rather all hating (or anywhere in between).

Now, for someone to claim that it has no moral value seems rather odd. Is love not a moral virtue? If objective moral values are rejected, then this would lead to this conclusion, that love is not a moral virtue, and omnibenevolence is not a great-making property - so this concept of God we have formed is incoherent. But if we do agree that love is a moral virtue, we would come to the opposite conclusion. So the question here is, does objective morality exist? That is the only way we can say whether or not omnibenevolence is a great-making property.

I have a problem with this though, as I believe the only way for objective morality to exist is for it to come from God. So then it becomes question begging to say omnibenevolence is great-making. I'd be most interested in thoughts on this position. Perhaps one would have to argue that objective morality exists from our 'god-given' sense or perception of what is morally good and evil - but as far as I'm aware, this would only prove subjective morality.

A second situation is where someone may agree that omnibenevolence is a moral property, but not great-making as it would conflict with omnipotence. But any power held by a non-omnibenvolent being is offset by it's own inferiority in moral worth. A being would be greater if He is morally good even if He can't perform immoral deeds.
Furthermore, one could argue that the ability to do immoral deeds is actually a weakness, rather than power. This revolves around the definition of omnipotence and that it does not mean the power to do just anything. Just like omnipotence cannot make logical contradicitions, it cannot make immoral actions. Anselm held this position, but I don't know any further details about the argument.

These arguments would show omnibenevolence to not contradict with omnipotence. So, omnibenevolence is indeed a great-making property if, and only if, we accept that objective morality exists."