3

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.

Firebirdofnercy
  • 61
  • 5
  • 2
    I think the problem is in 1. already. After all, there seems to be no restriction of what the "necessary X that is possible" can be. A necessary unicorn, a necessary . There should be a way to select only things that are truly necessary. You need to add something to justify why X is necessary, or the premise is just arbitrary itself, and the rest of the argument has no value. – Frank Feb 13 '23 at 20:15
  • 3
    This is the same sort of objection that Gaunilo of Marmoutiers raised against Anselm's original argument (he had the perfect island instead of the necessary unicorn). [Anselm's reply](https://plato.stanford.edu/entries/anselm/#ArgPro) is instructive. As for [other necessary beings](https://plato.stanford.edu/entries/god-necessary-being/), the argument *should* go through for them, but they cannot be conceived by merely attaching "necessary" to a noun. There must be something in their conception that *grounds* that necessity, and whatever it might be is missing in the "necessary unicorn". – Conifold Feb 13 '23 at 21:52
  • @Firebirdofnercy for the "maximally great being", it is probably going to end up being circular though. At some point, "necessity" will be assigned to a purely speculative "maximally great being" (by the way, in "maximally great", "great" is not very well defined, IMHO - what does it mean for something to be "greater" than something else?) – Frank Feb 13 '23 at 23:27
  • @Frank From my understanding which I admit isn't great Kurt Gödel was able to have a pretty clear definition, of what a maximally great being is. Now don't quote me because I've done little research but I think Kurt Gödel defined maxim greatness as having qualities that are great making qualities and not having bad qualities. – Firebirdofnercy Feb 14 '23 at 00:21
  • @Conifold Thanks, I knew it was similar to the objection that Gaunilo proposed, Although I felt like it was a bit different in the sense that this was something that was able to be clearly defined although I think that I agree with you that something should have grounds to be necessary, What are the grounds to make things necessary and what makes a Maximally Great Being have these grounds? – Firebirdofnercy Feb 14 '23 at 00:23
  • I doubt that "necessary" is any clearer than "maximally great", so if you are hoping for some general criteria none will be forthcoming (indeed, Anselm's answer to Gaunillo was that he was not working from any general template as Gaunillo presumed). It has to be some *sui generis* reason specific to each candidate for necessity. There are some such intuitive reasons given for God or math objects (we do typically stick them into all possible worlds), while the only thing necessary about the "necessary unicorn" is the adjective in it. – Conifold Feb 14 '23 at 00:38
  • @Conifold Thanks, I am pretty sure I agree although what I don't understand is what is God's sui generis reason for being necessary or does God not have one that you know of? – Firebirdofnercy Feb 14 '23 at 00:57
  • Well, God comes out as a necessary being ("non-contingent cause") in some versions of the cosmological argument, like [Aquinas's](https://plato.stanford.edu/entries/cosmological-argument/#ArguForNonContCaus). There is a clear parallelism to Anselm's inductive argument for the "maximally great being". – Conifold Feb 14 '23 at 01:14
  • @Conifold Thanks, I think I understand now. – Firebirdofnercy Feb 14 '23 at 01:22
  • @Firebirdofnercy god is not necessarily necessary, no. – Frank Feb 14 '23 at 01:37
  • @Frank I'm under the impression that if God does exist then he would be necessary. – Firebirdofnercy Feb 14 '23 at 03:59
  • @Firebirdofnercy. Re. your last comment. That's part of the problem. If you start off with an assumption that if God exists, he would be necessary...where does this assumption come from? Why could a god not have come into existence unnecessarily? Why could there not be many gods? Why might a god not stop being necessary? A god - even if it exists - exists as a human construct. Why would we presume to have drawn any accurate conclusions about it or them? How do we investigate? Through logic? As your question shows, this can easily lead us astray or at least into confusion. – Futilitarian Feb 14 '23 at 10:46
  • @Firebirdofnercy that's a kind of "circularity" I was alluding to in another comment. The fact that god is necessary is used to prove its existence, but then, the existence if posited first. This is not going anywhere :-) – Frank Feb 14 '23 at 14:49
  • 1
    @Futilitarian there are other arguments for God's necessity you might not believe they work and I haven't done much research into how to defend them, Although I do feel like you are sort of right so let me rephrase it this way if the Biblical God exists, then I think that his sovereignty involves him being necessary. So I believe that if the Biblical God exists then he is necessary. I'm not making a claim that God exists here I'm just making a claim that if he does exists then he'd be necessary. – Firebirdofnercy Feb 14 '23 at 15:46
  • One response to the ontological argument is to say it works only conditionally. One may allow Anselm his claim that it is more perfect to exist than to be merely the object of imagination, but that proves only the conditional: If there is a maximally perfect being, then that being exists. But maybe nothing is maximally perfect. Anything I imagine is *ex hypothesi* not maximally perfect unless it also exists, but my imagining it does not guarantee its existence. – Bumble Feb 15 '23 at 02:35
  • @bumble that's an interesting idea is it one of Kant's objections, Anyways I think that objection is more for Anselm's ontological argument and doesn't quite work with the Modal Ontological argument, I may very well be wrong although from my understanding it doesn't much affect the Modal Ontological argument. The reason is that this argument doesn't go from an idea to existence it goes to the possibility of to existence. – Firebirdofnercy Feb 15 '23 at 02:45
  • @Firebirdofnercy I think you are right. But of the modal version we might ask what justifies your sentence 3. It assumes S5 and why should necessary existence follow this assumption? I suspect also some equivocation in the use of the word 'necessary'. Theists do not commonly believe that the existence of God is a *logical necessity* only that it is a kind of metaphysical necessity rooted in God's nature. If God's existence is indeed not logically necessary then there are possible worlds where no god exists, but in those PWs where God does exist, God's existence is guaranteed by God's nature. – Bumble Feb 15 '23 at 02:58
  • @Bumble From my weak understanding there are a few types of necessaries, The Modal Ontological argument is based on the Modal Necessary. Which from my understanding means that it exists in all possible worlds. There are basically three stages of existence Impossible, contingent, and necessary. A maximally great being can not be contingent, the first premise shows that God is not impossible because he can not be impossible and possible at the same time. So he must be necessary. Next, I'd argue that PWs with no God are really impossible unless God is impossible. – Firebirdofnercy Feb 15 '23 at 15:33
  • There are many kinds of necessity, and any could be used with possible worlds semantics. When theists say that God's existence is necessary, they usually mean it is not contingent on other things, whereas by contrast my existence is contingent on the existence of my parents. But it is logically possible that there are no gods, and the actual world might be one where that is true. – Bumble Feb 15 '23 at 20:39
  • @Bumble Here is my line of thinking God is either impossible or necessary, As he's not contingent. If God is necessary then there is no world with no god, that is an impossible world because it doesn't contain a necessary. Although if God is impossible then there are no worlds in which God can exist. So the only way that a possible world can contain no god is if God is impossible. So in the end you need to be able to hold the idea that God is impossible to show that a world without God is possible. – Firebirdofnercy Feb 15 '23 at 23:06
  • **Comments have been [moved to chat](https://chat.stackexchange.com/rooms/142916/discussion-on-question-by-firebirdofnercy-whats-to-stop-you-from-plugging-in-so); please do not continue the discussion here.** Before posting a comment below this one, please review the [purposes of comments](/help/privileges/comment). Comments that do not request clarification or suggest improvements usually belong as an [answer](/help/how-to-answer), on [meta], or in [chat]. Comments continuing discussion may be removed. – Geoffrey Thomas Feb 16 '23 at 09:50
  • How is the step between 2 and 3 justified? – Futilitarian Mar 16 '23 at 04:02
  • 1
    @Futilitarian it's justified because, step one a necessary Unicron, being possible makes it exist in a possible world since it exists in a possible world we can conclude that it exists in all possible worlds, the reason being is that it's necessary. – Firebirdofnercy Mar 16 '23 at 22:56

3 Answers3

0

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

Mozibur Ullah
  • 1
  • 14
  • 88
  • 234
0

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 only unicorn" 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:

  1. ¬◇∃x□(Fx ∧ Ax)
  2. ¬◇∃x□(Fx ∧ ¬Ax)

Therefore we cannot assume that ◇∃x□Px is true for any logically consistent Px.

In other words, we cannot assume that a necessary unicorn (or intelligent designer) is possible.

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”.

Michael
  • 235
  • 1
  • 9
0

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.

Kristian Berry
  • 9,561
  • 1
  • 12
  • 33