Plantiga's ontological argument.

[Mystic]

This is from Wikipedia:

Alvin Plantinga has presented another version of the argument. The conclusion he provides logically follows from the premises, assuming axiom S5 of modal logic - if possibly p, then necessarily possible p and if possibly necessarily p, then necessarily p. A version of his argument is as follows[43]:

A being has maximal excellence in a given possible world W if and only if it is omnipotent, omniscient and wholly good in W; and
A being has maximal greatness if it has maximal excellence in every possible world.
It is possible that there is a being that has maximal greatness. (Premise)
Therefore, possibly it is necessarily true that an omniscient, omnipotent and perfectly good being exists.
Therefore (by axiom S5) it is necessarily true that an omniscient, omnipotent and perfectly good being exists.
Therefore, an omniscient, omnipotent and perfectly good being exists.

This argument has two controversial premises: The axiom S5 and the "possibility premise" that a maximally great being is possible.

S5 is widely but far from universally accepted. For instance, Paul Almond strongly disagrees with the argument based on the "incoherence, incorrectness and triviality" of axiom S5.[44]

The more controversial premise is the "possibility premise". One objection by Richard M. Gale, professor emeritus of philosophy at University of Pittsburgh, is that the "possibility premise" begs the question, because one only has the epistemic right to accept it if one understands the nested modal operators, and if one understands them within the system S5 (without which the argument fails) then one understands that "possibly necessarily" is basically the same as "necessarily"



Now axiom S5 can be derived from the proposition "Possibly P, implies necessarily possibly P".

The argument that it's circular doesn't seem that convincing because it's arguing that if it's possible, then it's necessarily based on this axiom, but it's not simply stating it's necessarily.

Now the controversial axiom seems to be if God is possible in a possible world P. But I don't see how this is a disputed premise, how can it be that God is not possible in any possible world?

However the premise " A being has maximal greatness if it has maximal excellence in every possible world." Does not mean a Being has maximal greatness only if has maximal greatness in every possible world. Rather it seems if there is no possible world with a being with more possible greatness, then it's the maximal greatness.

The conclusion doesn't seem to follow then. However it can be argued a necessary being is possible in a world p. What is meant by necessary is not simply necessary for that world, but necessary in all worlds. But to argue that as possibly true, you have to know that God is necessary in this world and necessary for all possible worlds. So it seems rather circular to do so.

[toro]

Now axiom S5 can be derived from the proposition "Possibly P, implies necessarily possibly P".

The argument that it's circular doesn't seem that convincing because it's arguing that if it's possible, then it's necessarily based on this axiom, but it's not simply stating it's necessarily.

Now the controversial axiom seems to be if God is possible in a possible world P. But I don't see how this is a disputed premise, how can it be that God is not possible in any possible world?

The premise is disputed because it is an assumption with no validity that affects the direction of the argument. One can equally presuppose God doesn't exist in some possible world. This leads to two premises one can make:

1. God exists in a possible world P1.
or...
2. God doesn't exist in a possible world P2.

There is no reason one should presuppose one or the other.

If we follow the logic of premise 1 (Prem:1), we have the above

1. A being is defined as one that if it exists, exists necessarily. (Premise)
2. It is possible that there is a being that exists necessarily. (Prem:1)
3. Therefore, there is a world P1 in which this being exists. (from 2)
4. Therefore, there is a world P1 in which it is necessarily true that this being exists (from 2, 3)
5. Therefore, it is necessarily true that this being exists. (from S5 and 4)
6. Therefore, since necessarily true propositions are true, this being exists (from 5)

However, we have no reason that has yet been stated to choose between the initial proposal that God exists in one world or God doesn't exist in another before we follow the logic.

If we propose premise 2 (Prem:2), we get:

1. A being is defined as one that if it exists, exists necessarily. (Premise)
2. It is possible that there is not a being that exists necessarily. (Prem:2)
3. Therefore, there is a world P2 in which this being (that must exists necessarily) doesn't exists. (from 2)
4. For this being to exist in another world P3, its existence must be necessary in P3. (from 1).
5. This being cannot exist necessarily in P3, as its non-existence in P2 precludes it from existing necessarily in all other worlds. (from 4, 3)
6. Therefore, it is necessarily true that this being does not exist. (from s5 and 5)
7. Therefore, since necessarily true propositions are true, this being does not exist. (from 5)

What we see is that our initial assumption of possibility determines the outcome of the argument. So either we are left not knowing the possibility, and therefore not being able to say anything further. Or, we are left with defining a priori what the outcome is going to be by defining our assumption.

If we do the former, we learn nothing: "God either possibly exists, or possibly doesn't exist."

If we do the latter, we are answering our own question: "God exists. Therefore, God exists." "God doesn't exist. Therefore, God doesn't exist."

... to try and put it sucinctly anyway.

There are a number of other issues with the argument, but I think this one is the most obvious and it is one which explains the uncertainty both theological sides have about its validity. (I don't mean to be appealing to authority here, just pointing out an observation I've had.)

The conclusion doesn't seem to follow then. However it can be argued a necessary being is possible in a world p. What is meant by necessary is not simply necessary for that world, but necessary in all worlds. But to argue that as possibly true, you have to know that God is necessary in this world and necessary for all possible worlds. So it seems rather circular to do so.

I don't see the definition as particularly problematic. I mean, the definition does nothing more than define what you're talking about. The problem is that the circularity of the argument comes from the assumption of possible existence over possible non-existence.

[Justtristo]

I can apply simply to Mr Plantinga's arguments that it can be used for anything you can imagine like say the most delicious pizza you can convince of.

mmm Ontological Pizza :p

[fr0d0]

@ toro : proposing nothing accomplishes just that. You need to include propositions capable of becoming viable, that God satisfies.

[toro]

@ toro : proposing nothing accomplishes just that. You need to include propositions capable of becoming viable, that God satisfies.

One isn't proposing 'nothing'. That would be the following:

1. (Premise)

One is proposing a truth: that a specific individual does not exist in a possible world. This is a perfectly valid proposition. Indeed, that is why the definition of 'necessarily existent' is so important, because one can propose non-existance.

The point made is that the ontological argument is circular, and therefore completely arbitrary for all propositions.


Furthermore, claiming that it is nonsensical to suppose any truth is invalid in any possible world means that every truth is valid in every world. Otherwise, we would be able to propose a possible world where the truth is invalid (which you claim is nonsensical). This actually then makes the term 'necessary' pointless as all truths are always true. It also allows us everything to always be true.

Ahem...

1. There is a possible world where an invisible dragon lives in Carl Sagan's garage. (Premise)
2. We cannot suppose there is any possible world in which such a dragon does not exist. (fr0d0's axiom)
3. Therefore, an invisible dragon lives in Carl Sagan's garage in all possible worlds. (from 1,2)
4. Therefore, an invisible dragon lives in Carl Sagan's garage. (from 3)

We even get contradictions...

1. There is a possible world where toro rules the world. (Premise)
2. We cannot suppose there is any possible world in which toro does not rule the world. (fr0d0's axiom)
3. Therefore, toro rules the world in all possible worlds. (from 1,2)
4. Therefore, toro rules the world. (from 3)
5. However, toro doesn't rule the world. (fact)
6. Yes he does, you can't assume that. That means nothing. (fr0d0's axiom)
7. But, he doesn't rule the world. (fact)
8. Nuh uh! (fr0d0's axiom)
...
and so on.

You see the fault in your claim I hope.

[fr0d0]

I don't think you're addressing the problem in full toro. It's what underpins the point that makes it valid. Neither in Sagans Dragon nor toros world are there any coherant propositions, unless you substitute the Xtian God for those words.

[Mystic]

God is possible -> God necessarily exists.
Means if it's possible God doesn't exist, then God is impossible. I understand that.

But if we say God is not an impossible thing for sure, then the argument states God exists.

I think God being possible is obvious, while God possibly not existing is not obvious. Therefore this argument is still good argument, if you accept that God being possible is obvious, while God possibly not existing is not obvious (it maybe he is a necessary existence).

[frankiej]

But if we say God is not an impossible thing for sure, then the argument states God exists.

And that is why it is bullshit. It is a bollocks argument.

[The Grand Nudger]

What a wonderful way to say the same thing twice in one sentences without actually repeating yourself. Appealing to probability is a troubling thing. It's a claim to the material. A probability is the measure of the likeliness that an event will occur. See all the troubling words in that sentence for the immaterial argument? We've entered the territory of appealing to immaterial "likliness", a difficult metric to define. Immaterial "events", "occurrences". The immaterial is getting awfully crowded. Words like possible or probable don't have much meaning divorced from the material world. They are words that describe very specific metrics, made from demonstrable observations, or they are invalid (by definition no less, to borrow someone's favorite line).

[toro]

I don't think you're addressing the problem in full toro. It's what underpins the point that makes it valid. Neither in Sagans Dragon nor toros world are there any coherant propositions, unless you substitute the Xtian God for those words.

Please explain what was logically incoherent and why.

But if we say God is not an impossible thing for sure, then the argument states God exists.

I think God being possible is obvious, while God possibly not existing is not obvious. Therefore this argument is still good argument, if you accept that God being possible is obvious, while God possibly not existing is not obvious (it maybe he is a necessary existence).

You need to remember, these two statements are premises of the argument. So you cannot say that we can't premise God possibly does not exist because the argument states he exists. That's a fallacy:

You are assuming the outcome of the argument under one premise as a premise for why one can't make a different premise at the beginning of the argument.

This is where the term 'possible' in modal logic becomes misleading. You keep assuming one premise is valid but another isn't because the other is valid. That makes no sense. Both are valid premises unless you are assuming the outcome to the statement at question.

You cannot say "it is impossible for God to not-exist" and still pretend you are leaving the question open. If God's non-existence is presupposed to be impossible, that means you have presupposed God exists. You can't have it both ways. Either you assume God exists/doesn't exist, or you have no answer.

One might actually argue you can premise both propositions. This however leads to the outcome that God is contradictory and therefore doesn't exist.