It does seem to trade on an ambiguous interpretation of the phrase "necessary". Modality is tricky. When I say that it is possible that it will rain tomorrow, I'm not simply saying that there is some possible world (e.g. parallel world) where it will rain tomorrow, but rather saying that the actual world might be such a world.

Is there a form of modal logic that can make this distinction?

Is there a form of modal logic that can make this distinction? — Michael

No idea. SEP has a related article.

Although actually, I'm not sure this response is even warranted. Even if our "ordinary" concept of God is one that isn't to be interpreted as being modally necessary, the modal ontological argument does posit such a God, and their argument should be addressed on that premise.

Does it show that a modally necessary God exists? Is ◊◻∃xGx true and does ◊◻∃xGx entail ◻∃xGx?

Does it show that a modally necessary God exists? Is ◊◻∃xGx true and does ◊◻∃xGx entail ◻∃xGx? — Michael

First quibble: it isn't demonstrated to be any particular god, just an entity which satisfies G. The only thing which makes it god-ish is that G is associated with god. It would need to be argued that any given god has the property G, which is established independently (and is a theological thing, right). Moreover, it would need to be argued that an entity could, in principle, have that property.

Second quibble: possibly there exists x such that Gx is unsupported. Modal logics do lots of different things. You can say that 1 is possible for 2 under the accessibility relation "less than or equal to" in the integers. Whether the relevant sense of modality in the logic models an appropriate notion of metaphysical necessity is still something that you can quibble with. Why would you need something like an equivalence accessibility relation between worlds?

An example of that quibble: it was possibly physically necessary that the luminiferous aether existed, therefore it was physically necessary that the luminiferous aether existed, therefore the luminiferous aether existed. A sense of metaphysical necessity which lets you do this conjuring trick is... well, it needs a good argument to support.

Third quibble: you can always deny that it's possible that any particular god exists. And in that case the entity in question would not exist in any world.

Nevertheless, it might be the case that the underlying metaphysics that facilitates the argument is the correct one. It just still would have relatively little to do with a god. Or, as with other ontological arguments, you can perform the same conjuring trick where you posit an entity with G and then it suddenly exists. Like the aether example.

Nevertheless, it might be the case that the underlying metaphysics that facilitates the argument is the correct one. It just still would have relatively little to do with a god. Or, as with other ontological arguments, you can perform the same conjuring trick where you posit an entity with G and then it suddenly exists. Like the aether example. — fdrake

I did offer a more substantial notion of God here. The argument attempts to show that there exists something which necessarily created the world.

But you are right that we can posit any entity. So if anything it's a reductio ad absurdum against the assumption that ◇∃x□Fx is true for every logically consistent Fx.

Second quibble: possibly there exists x such that Gx is unsupported. Modal logics do lots of different things. You can say that 1 is possible for 2 under the accessibility relation "less than or equal to" in the integers. Whether the relevant sense of modality in the logic models an appropriate notion of metaphysical necessity is still something that you can quibble with. Why would you need something like an equivalence accessibility relation between worlds? — fdrake

The argument does depend on S5 where the accessibility relation is universal. From my reading there are good reasons to accept S5 so it would be shortsighted to deny it simply to dismiss the modal ontological argument, and special pleading to deny it only for the modal ontological argument.

So if anything it's a reductio ad absurdum against the assumption that ◇∃x□Fx is true for every logically consistent Fx. — Michael

On this point, consider this:

1. ∃xFx → ∃x∀y(Fy ↔ (x = y))
2. ◇∃x□(Fx ∧ Ax) ∴ ∃x□(Fx ∧ Ax)
3. ◇∃x□(Fx ∧ ¬Ax) ∴ ∃x□(Fx ∧ ¬Ax)

The first premise asserts that if there is an x such that Fx then there is exactly one x such that Fx. The second asserts that there is an x such that it is necessary that both Fx and Ax. The third asserts that there is an x such that it is necessary that both Fx and ¬Ax. Obviously this is a contradiction.

If we take Fx to mean something like "x is the sole creator of the world" then 1 is true, and as both 2 and 3 are valid under S5 it must be that one or both antecedents are false, and so one or both of these is true:

4. ¬◇∃x□(Fx ∧ Ax)
5. ¬◇∃x□(Fx ∧ ¬Ax)

Therefore we cannot assume that ◇∃x□Px is true for any logically consistent Px, and so cannot assume that it is possible that something necessarily created the world.

Or we have to reject S5, but if we reject S5 then the modal ontological argument is invalid as “possibly necessary” wouldn’t entail “necessary”.

The argument does depend on S5 where the accessibility relation is universal. From my reading there are good reasons to accept S5 so it would be shortsighted to deny it simply to dismiss the modal ontological argument, and special pleading to deny it only for the modal ontological argument. — Michael

Eh, possibly necessary => necessary is reasonably easy to argue against. I don't like it for the above stated reasons. That lets you conjure up the luminiferous aether, assuming the "true logic of metaphysics" lets you do possibly necessary implies necessary. In that regard, either we'd have to rejected that the luminiferous aether isn't possibly physically necessary, or the law of logic which leads to the inference. I'm inclined to reject the latter, since I intuit that things like physical laws are "physically necessary" (whatever that means).

I wouldn't want to deny that S5 has applications, just that demonstrating it as the "true logic of metaphysics" is a project unto itself. That a logic applies to a domain isn't something that can be taken for granted, I think. The above argument regarding physical necessity is a reason to reject the application of any logic which allows the inference pattern (possibly necessary => necessary) to metaphysics in general.

In that regard, either we'd have to rejected that the luminiferous aether isn't possibly physically necessary, or the law of logic which leads to the inference. I'm inclined to reject the latter, since I intuit that things like physical laws are "physically necessary" (whatever that means). — fdrake

Given my previous post that shows that under S5 we cannot assume that ◇∃x□Px is true for any logically consistent Px, the third alternative is that “possibly necessary” under S5 means something different to what it means under other systems (or natural English).

Aye! Nothing tells you the meaning of the two modal operators other than the context they're applied to.

Every form of the ontological argument that I've ever heard of assumes that greatness is a property of some entity rather than a speaker evaluation of that entity.

I admit that whether the abstract property of greatness exists independently of speakers and their evaluations can be debated philosophically.

But this leaves the ontological argument, even if logically valid, only as sound as the notion that greatness exists independently of the evaluation of some rational being, rather than existing only as such an evaluation.

IMO, my evaluation of X is not a property of X.

Existence is not a property of God. Existence IS God. All contingent things are properties of existence. Existence is what is from the beginning. It always is. Creation is when existence/God acquires properties.

Verbal fumbling.

But explaining clearly what is added to an apple by existing...? — Banno

You can't add anything to or subtract anything from an apple that does not exist, except in thought.

It's not difficult to understand an apple that is not sweet, or an apple that is not red - but an apple that does not exist? What is it? — Banno

It is not an existent apple, but is merely the thought of an apple; am imagined or non-existent apple.

I have a regular supply of apples that don't exist, which I will happily on-sell.

To your non-existent friends? So you might think.

To you, if you like: there's a free sample next to you. I can provide as many as you need.

Yes, if I think so, although I don't need your free non-existent apples since I have as many of my own as I want.

Do you understand what existence is? What a positive existence, as opposed to nothingness, means? If you don't you will not understand what I'm saying.
Assume X has the property 'existence'.
Now ask; does X exist distinct from its property 'existence'?

Two answers:
1. X does not exist. Therefore it cannot have properties, let alone 'existence'.
2. X exists. This makes existence as a property superfluous, since X exists anyway, whence X is existence.

This proves existence cannot be a property.

Free logic allows us to talk of things that do not exist, hence treating existence as a property.

But I'm not talking about imaginary existences.

Free logic has wider application than just imaginary objects, addressing the difficulties you mention.

Existence is a scientific state not a property:

A property can be physical or chemical etc, it can describe a change or variable attribute.
A state is an instantaneous observation, such as solid, liquid, gas. A property is variable and can cause movement from one state to another. Existence is a state that can change into a state of non-existence.
'State' and 'property' are not synonymous.
If god has an existent state then can that state change into a non-existent state?
Even cyclical or oscillating universe hypotheses still intuit a 'spark' to start the process that then becomes eternal. The eternal god posit suffers from the same problem, 'what sparked god?' and what sparked the spark. That's why it's called an 'infinite' regression.
An ontological argument for god has no significance at all, to theism as it is at it's best, a very poor argument for the existence of A god or first cause mind with an intent/need to create. It offers nothing to the theist by way of supporting evidence that their god flavour exists. Allah and Yahweh remain as likely, as the spider god or the energy god or any, from an infinity of potential god descriptions/properties.

Love how folk just make shit up.

This ontology stuff is so easy!

Existence IS God. — EnPassant

What does this mean? Are you saying that the words "existence" and "God" are synonyms? As a fluent English speaker I'd have to disagree. At the very least, "God" is proper noun and "existence" an improper noun, so clearly there is at least some distinction between the words.

What's the verb form of "God"? For "existence" it's "exists". So how would you rephrase the sentence "there exists more than one apple"? Maybe "there gods more than one apple"? Doesn't make much sense to me.

Or are you perhaps just asserting pantheism? If so then what evidence or reasoning leads you to believe that the universe is "divine" (or whatever it is that distinguishes a pantheistic universe from a non-pantheistic universe)?

In the 'beginning' existence and God are the same thing. Existence is not a verb, it is a noun. God becomes/creates. Contingent creation is a property of existence. Imagine a lump of bronze representing existence; it is. The bronze can be shaped into a horse, an eagle etc. 'Horse' and 'eagle' are properties.
The verb for God is 'becoming' ie. evolving properties.
More than one apple? There is existence and it can have many apples as properties. Pantheism? No. Existence is eternal. It becomes creation.

This doesn't seem to be saying anything.

Why use the word "God" at all? Why not just say that there was some inanimate, formless chaos that happened (without intention) to form into the space and time and matter and energy that we are familiar with?

Using the word "God" brings in all sorts of additional, religious baggage.

Well you can call it the source of all that is, if you want to avoid the religious. Personally I think the emergence of existence into being (life) is an intelligent evolution.

Obvious hypostatisation, verging on anthropomorphism.