What's to stop you from plugging in something else like a necessary being in the Modal Ontological argument?

Question

I was looking at the Modal Ontological argument and I was wondering what stops the argument from not working when we plug in another necessary being. Such as a necessary unicorn. So the argument looks like:

1. a necessary unicorn is possible.
2. if a necessary unicorn is possible then a necessary unicorn must exist in some possible worlds.
3. if a necessary unicorn exists in some possible worlds then a necessary unicorn exists in all possible worlds.
4. if a necessary unicorn exists in all possible worlds then it exists in the actual world.
5. a necessary unicorn exists in the actual world.
6. a necessary unicorn exists.

To try and solve this problem I made a few arguments such as.

1. unicorns are contingent
2. a necessary contingent unicorn is a contradiction.
3. a necessary unicorn is impossible.

I also tried to solve it by saying that the argument still works.

1. a necessary unicorn does exist.
2. the Modal Ontological argument works.

or

1. a necessary unicorn doesn't exist.
2. you can't not exist and be necessary while also being possible.
3. a nonexistent necessary unicorn is not possible.
4. a necessary unicorn is impossible.
5. the necessary unicorn doesn't pass the possibility test in the Modal Ontological argument.
6. The Modal Ontological argument still works.

Although I don't really know if these work. I think that if there is a way to say that two necessary beings can't coexist then it would solve the problem although I don't know of any ways. So if you have any solutions can you please explain them thanks.

Answer 1

Consider this:

1. ∃xF(x) → ∃x∀y(F(y) ↔ (x = y))

If we take F(x) to mean something like "x is the only unicorn" then (1) is true.

Now consider these:

2. ◇∃x(F(x) ∧ A(x))
3. ◇∃x(F(x) ∧ ¬A(x))

If take A(x) to mean something like "x is male" then both (2) and (3) are true.

Now consider these:

4. ◇□∃x(F(x) ∧ A(x))
5. ◇□∃x(F(x) ∧ ¬A(x))

Under S5, ◇□p ⊢ □p, and so these entail:

6. □∃x(F(x) ∧ A(x))
7. □∃x(F(x) ∧ ¬A(x))

(6) and (7) cannot both be true, and so therefore (2) does not entail (4) and (3) does not entail (5):

8. ◇∃xP(x) ⊬ ◇□∃xP(x).

This is where modal ontological arguments commit a sleight of hand. To claim that it is possible that God₁ exists, where necessary existence is one of God₁'s properties, is to claim that it is possibly necessary that God₂ exists, where necessary existence is not one of God₂'s properties.

The claim that it is possibly necessary that God₂ exists isn't true a priori, and so the claim that it is possible that God₁ exists isn't true a priori. As it stands it begs the question.

Or we have to reject S5, but if we reject S5 then modal ontological arguments are invalid because "possibly necessary" wouldn't entail "necessary".

Answer 2

Modal logic usually work with both:

It is possible that ...

It is neccessary that ...

In standard mathematical modal logic these two operators are inter-definable: that is one is defined in terms of the other. If I recall correctly, through double negation. That is:

It is necessary that := it is not possible that it is not possible.

Or more briefly:

It is neccessary that := it is impossible that it is impossible

Answer 3

The modal ontological argument (MOA) fails because the kind of necessity ascribed to God is equivocally equated with necessity-as-actuality-in-all-possible-worlds. Classically, theists were minded to say that God is not a part of any (created) world, not even ours: moreover, then, that God is not a part of anything whatsoever (except as a trivial improper part of Itself). The way they put it was (this is in Kant's first Critique), "The Creator and the world are not parts of some greater whole."

So firstly, the MOA is impious, attributing to God a property that detracts from Its transcendent glory. Secondly, then, the possibility of God is not on account of God being "in" some possible world (God is outside of all worlds besides Its own eternity). Thirdly, then, the MOA "begs the question" of how we identify a being as necessary in possible-worlds terms. Suppose one said, "There is a possible world where the Continuum Hypothesis is necessarily true." One does not (usually) intend to say, "The Continuum Hypothesis is therefore necessarily true in all possible worlds." Again, the sense of the word "necessity" here is distinct from the more empirically-minded sense of possible-worlds talk.

Consider that if God "exists in all possible worlds," then God at least either has a transworld identity or has Lewisian counterparts. As noted, neither such property (or any such...) can be attributed to God piously.

Or consider a statement like, "It is possible that possible-worlds talk is false," converted into, "There is a possible world where possible-worlds talk is false." Possibly self-defeating, though see about the modal æther for some more complications.

Does the MOA equivocate between logical, metaphysical, epistemic, and nomological possibility, then? Is it sensitive to the minutiae of the accessibility relation in standard modal logic? Probably "yes" to the first question, "no" to the second. Note further that if God is the Creatrix, then no possible world is actual but on Its willing so. So this "other" possible world we start out from, where God supposedly already is, would only be actual on account of God's creating it, and God wouldn't be in that world prior to its creation. Otherwise, there are possible worlds that count as actualized for some alien, subdivine reason, which undermines the portrayal of the "maximally excellent being" as the sole possible author of reality.

EDIT: I guess the main thing is that the sentence, "There is a possible world with a being B such that B exists in all possible worlds," is not much of an admissible sentence in the kind of modal logic that the MOA tries to use, or at least this is not admissible as an substantive axiom. Besides allowing for arbitrarily many and bizarre necessary beings, it amounts to a sort of circular illustration of any supposedly necessary being. Or then consider the issue of iterated modal operators: the MOA relies on ◊☐A → ☐A, which is allowable in the local modal logic on account of the collapsing rules for iterated modal operators here. Take ¬☐☐A; this goes to just ¬☐A normally, but if such a collapse is blocked, then we have to define God as necessarily necessary, and necessarily necessarily necessary, and so on and on. God's "maximal excellence" means that Its necessity runs through all the (presumably absolutely infinite) iterations of pure modality. That's poetic but it becomes quite murky how we could ever say that (with V = absolute infinity) ◊☐^V(God exists) with entire confidence in the meaning of this assertion.

Answer 4

Short answer

There is nothing preventing such an arbitrary substitution of claims, as the initial claim is unsupported. Additional unsupported claims of necessity can also be inserted in place of the original one, resulting in different but equally valid or invalid conclusions in each case.

Longer answer

Philosophers and theologians have gotten into a very bad habit of POSTULATING necessity claims. But assertions that something in necessary, are about as strong a claim as one can make. It is an assertion that it is irrational to deny the claim, as unchallengeable logic compels to its truth.

But if something is clearly necessary, then it should not be difficult to demonstrate that necessity -- basically by the definition of this unquestionable logic. SO -- rather than postulating a necessity claim, then having to get by with this modal argument -- just explicate it, and then its necessity would no longer be in doubt.

I critiqued this habit in another recent answer, linked here: https://philosophy.stackexchange.com/a/114765/29339 In that answer I noted that a bombproof logic argument is actually impossible to provide, because of the plurality of logics. I also cited your point here that the multiplicity of competing postulated necessities serves as a demonstration that none of them are actually "necessary".