We can summarize the argument:
A ontological necessary being is ontologically possible.
What is ontologically possibly necessarily, is necessarily.
Therefore an ontological necessary being exists.
What is meant by being ontologically necessary is it must be true in all possible worlds.
Now I use to dismiss this proof, because it was so counter intuitive.
But just as we discover things that are counter intuitive in physics (like two falling objects with different weights), it maybe that reality is that language proves something in logic, we find counter intuitive.
The reason we find in counter intuitive, is because we are use to experience with ontological possible things.
Somethings are ontologically necessary. For example, it cannot be 1 + 1 = 3 in a possible world, and 1 + 1 = 2 in another possible world.
But all the things that fall under necessarily so, are not objects. They maybe statements about what objects have to be or cannot be, but they aren't objects.
The same is not true of the concept of a necessary existence.
This is what makes it so controversial. But it maybe we don't have a firm grasp of the fact possibilities necessitate necessary existence.
It maybe that all possible worlds, it in fact, is true that necessary being is required in all that, and it's one that is same through out all possible worlds.
This may also then prove, not everything we imagine to be an ontologically possible, maybe in fact possible.
And it maybe, by definition, since the real world is a possible world, it too requires a neccessary being.
But a necessary being is so tied into all possible worlds, that, it is implied by the definition.
But how would we know that? Well here is from a very intelligent member of shiachat that analytically proved "what is possibly necessarily, is necessarily" (And it's agreed upon by overwhelming majority of logicians)
Now this seems counter intuitive at first, but when you go the core of it, all it's saying is what is ontologically possible, is ontologically necessarily possible. It's trivial right? Yes, but that trivial statement goes on to prove the counter intuitive premise "What is possibly necessarily, is necessarily".
The thing is, perhaps, it's the case a necessary being is so intertwined with existence, that we can't even say, it's ontologically possible without really acknowledging in reality that it's ontologically necessarily so.
I would say however this is far from a definitive proof. The reason because to acknowledge the necessary being as possible, you must know that it's part of this reality. The reason being is because it cannot be that it's not part of this reality, and that it's possibly necessarily so in all possible worlds.
But when we think of a necessary being, it seems ontologically possible. So intuition with the analysis, seems to point to an ontological necessary being.
But at the same time, we can always claim ignorance. But if it was so that a necessary being so, is it farfetch to say we couldn't know that it was even possible?
This proof really makes me think.
And what makes me think, is there even more reasons we aren't aware of, that a necessary being, if possible, must exist?
We are almost cheated by language and logical rules to this proof, but it seems both valid and sound to me, even though it relies on a counter-intuitive premise.
I'm thinking this is not a concrete proof of a necessary being, but is one that strongly indicates it's likelihood of it existing.
The reason being is that everything that exists is ontologically possible. And fairies, and unicorns, are ontologically possible.
As long as there is no contradiction in it's definition, it's ontologically possible.
Now the big "G" can be contradicting itself in attributes that people give to it.
But this says nothing about a necessary being without contradicting attributes.
Sure we can dismiss the Christian Trinity for example, as possible, since it contradicts itself, but is the same true of a Necessary being in general.
Yes for all we know, a necessary being can be a contradiction, and hence impossible...but it seems this is not the case.
As such I state this argument at least strengthen's the case of likelihood of a Necessary being existing.
A ontological necessary being is ontologically possible.
What is ontologically possibly necessarily, is necessarily.
Therefore an ontological necessary being exists.
What is meant by being ontologically necessary is it must be true in all possible worlds.
Now I use to dismiss this proof, because it was so counter intuitive.
But just as we discover things that are counter intuitive in physics (like two falling objects with different weights), it maybe that reality is that language proves something in logic, we find counter intuitive.
The reason we find in counter intuitive, is because we are use to experience with ontological possible things.
Somethings are ontologically necessary. For example, it cannot be 1 + 1 = 3 in a possible world, and 1 + 1 = 2 in another possible world.
But all the things that fall under necessarily so, are not objects. They maybe statements about what objects have to be or cannot be, but they aren't objects.
The same is not true of the concept of a necessary existence.
This is what makes it so controversial. But it maybe we don't have a firm grasp of the fact possibilities necessitate necessary existence.
It maybe that all possible worlds, it in fact, is true that necessary being is required in all that, and it's one that is same through out all possible worlds.
This may also then prove, not everything we imagine to be an ontologically possible, maybe in fact possible.
And it maybe, by definition, since the real world is a possible world, it too requires a neccessary being.
But a necessary being is so tied into all possible worlds, that, it is implied by the definition.
But how would we know that? Well here is from a very intelligent member of shiachat that analytically proved "what is possibly necessarily, is necessarily" (And it's agreed upon by overwhelming majority of logicians)
Quote:I dont know enough about ontological arguments to say whether I think they are ultimately successful, but here's one modern version.
1. It's possible that a Necessary being exists.
2. If it's possible that necessarily x, then necessarily x.
3. Therefore a Necessary being exists.
(something like that)
Premise 2 is known as axiom S5 in modal logic, and apparently most logicians accept it as true. It can be derived from the following intuitively true premise:
a. If its possible that x, then its necessarily possible that x.
This basically says that if something is possible, then it has to be possible. Possible things are necessarily possible. Possibility here doesnt refer to mere physical possibility, but is more broad, kind of like logical possibility (but not exactly the same). It's a logical truth that green tables are possible, and logical truths are necessary, so its necessary that green table are possible. On the otherhand, things that arent possible (eg square circles) are also necessarily impossible - nothing could make them possible. So how do you get premise 2 from (a) above? Premise (a) is equivalent to (b ):
b. If its not necessarily possible that x, then its not possible that x
^ This says that if the consequent of (a) is false, then so is its antecedent. Premise (b ) is equivalent to c):
c. If it's not necessarily possible that x, then it's necessarily the case that not x.
^Something is possible means that its not necessarily not the case. So if something is not possible then its not not necessarily not the case. And two 'nots' cancel out making it necessarily not the case that x.
d. If it's possible that it's not possible that x, then it's necessarily the case that not x.
^ If something is not necessary, then its possible that its not the case.
e. If it's possible that it's necessarily not the case that x, then its necessarily not the case that x.
^ If something is possible then it's not impossible.
f. If it's possible that it's necessarily x, then necessarily x
^You can drop the 'nots' on both side because x can be rewritten as a negation so doesnt need the 'not' before it.
And f is the same as 2. Although this looks quite complicated, if you think about each step you'll see that they are logical. There isnt anything controversial about the move from (a) to (f).
Let me rewrite it in symbol form. N = necessary, and p = possible, so Nx means 'its necessary that x' and px means that 'its possible that x'. Finally, > means 'if...then'.
a. px > Npx
b. not Npx > not px
c. not Npx > N not x
d. p not px > N not x
e. pN not x > N not x
f. pNx > Nx
I love this argument for a few reasons. I think that the idea that God can be proved just from His possibility of existing is awesome. And I like it that the argument almost looks like cheating - you just dont expect the conclusion to follow, at least not that quickly.
Now this seems counter intuitive at first, but when you go the core of it, all it's saying is what is ontologically possible, is ontologically necessarily possible. It's trivial right? Yes, but that trivial statement goes on to prove the counter intuitive premise "What is possibly necessarily, is necessarily".
The thing is, perhaps, it's the case a necessary being is so intertwined with existence, that we can't even say, it's ontologically possible without really acknowledging in reality that it's ontologically necessarily so.
I would say however this is far from a definitive proof. The reason because to acknowledge the necessary being as possible, you must know that it's part of this reality. The reason being is because it cannot be that it's not part of this reality, and that it's possibly necessarily so in all possible worlds.
But when we think of a necessary being, it seems ontologically possible. So intuition with the analysis, seems to point to an ontological necessary being.
But at the same time, we can always claim ignorance. But if it was so that a necessary being so, is it farfetch to say we couldn't know that it was even possible?
This proof really makes me think.
And what makes me think, is there even more reasons we aren't aware of, that a necessary being, if possible, must exist?
We are almost cheated by language and logical rules to this proof, but it seems both valid and sound to me, even though it relies on a counter-intuitive premise.
I'm thinking this is not a concrete proof of a necessary being, but is one that strongly indicates it's likelihood of it existing.
The reason being is that everything that exists is ontologically possible. And fairies, and unicorns, are ontologically possible.
As long as there is no contradiction in it's definition, it's ontologically possible.
Now the big "G" can be contradicting itself in attributes that people give to it.
But this says nothing about a necessary being without contradicting attributes.
Sure we can dismiss the Christian Trinity for example, as possible, since it contradicts itself, but is the same true of a Necessary being in general.
Yes for all we know, a necessary being can be a contradiction, and hence impossible...but it seems this is not the case.
As such I state this argument at least strengthen's the case of likelihood of a Necessary being existing.
