I think that, given modal logic, it is not out of the question to use existence as a predicate (not that you, Voyager, had said it was.) However, I wouldn’t agree that ontological greatness can be measured across possible worlds: in other words, I consider the entity with the same qualities existing in another possible world to be a different entity from the one in this world.
The other assumption, of course, is that God is NE. Which, given my natural language outlook on philosophy, is actually sort of humorous. But, like I have said before, the rest of the proof is logically unimpeachable, if a bit trivial.
I think I have a disproof. I’ve repeated the proof below.
x=x (Identity Axiom)
Ay(y≠x) -> x≠x (Quantifier Axiom)
x=x -> ~Ay(y≠x) (Contrapositive of 2)
x=x -> Ey(y=x) (Definition of E)
Ey(y=x) (Modus Ponens 1 and 4)
Now if x actually exists, of course this is trivially true. But we cannot assume x exists, or this proof is pointless. What happens if x does not exist?
1 is an axiom, so let’s accept it for a while.
is also an axiom, but it seems to be trivially true. This is fine.
is fine as long as x=x is true, so it depends on 1.
is where we have a problem. It states that if x=x Ey(y=x), and by 5, Ey(y=x) But this contradicts our assumption that x is nonexistent - since we have demonstrated that there exists a y that is equal to a non-existent x. Thus one of the axioms 1 and 2 must be incorrect. 2. seems correct even for non-existent objects, and seems to imply that x ne x for nonexistent x.
In other words, the proof only demonstrates existence of existing things, and is useless unless you can demonstrate the existence of something by other means. And Ludovic is quite correct in calling it trivial.
Even if that weren’t the case, I think he would still fail to convince most of those whom he was trying to convince, if he were indeed trying to convince some.
Just from speculation, I imagine that if we could poll all attempts to convince someone of a theological position the speaker wishes the audience to adopt, that have ever happened and will ever happen, a very, very small percentage of them would even be remotely successful.
Jeez, this thread has been going on since before God was born!
First of all: Which God? (Or if you prefer, what god?) So many different cultures have created concepts of god throughout Earth time (Even in Earth Prime, pre-crisis) that are so different that you gotta narrow it down somewhat first.
So which god?
The Creator?
The Destroyer?
The Sustainer?
The Judge?
The One?
The All?
The Nothingness?
The Hunter? The Lover? The Procreator? The Infinite?
or The Experience???
What you’re doing is akin to asking, “What is a thought?”
A waste of four good pages.
And if you don’t mind, I think it’s pretty arrogant to say:
Sorry, but in the absence of proof, both belief in a god and disbelief in the existance of god are both just opinions. QED. One cannot, therefore, hold a “superior position” to the other.
Now if you want to reference the Jewish God, he/she/it was asked, “Who shall I say sent me?” and the answer was, “I am what is.”
If you go by god’s own definition then if god doesn’t exist, then there is nothing.
Supreme is an adjective modifying being, just as necessary is an adjective modifying existence. And in fact, the two phrases have interchangeable terms. Supremacy and necessity are biconditional, as are being and existence. So one could say, “Supreme Being”, “Necessary Being”, “Supreme Existence”, or “Necessary Existence”. Supreme <-> Necessary. Being <-> Existence.
I’ve long suspected that you and I see the world in exactly the same way. We just use different words. Your universe is my God, and my God is your universe. As far as I’m concerned, we are soulmates.
No, you’re correct. There is nothing about any creation. In fact, speaking once again outside an ontological context, it really ought to make no difference to a Christian whether God created the universe or not. It serves His purpose all the same — a mis-en-scene for our moral play.
But you’re putting the cart ahead of the horse. Remember, we cannot assume our conclusion in our premises. We are trying to prove existence, and so cannot invoke existence until there is some rule of logic that will allow us to do so. Since we are setting out to prove that necessary existence is true (in S5), we must wait until an inference can be drawn to do that. You can’t prove that a cat is feral by starting with an axiom that the cat is wild. You can defined “feral” to mean “wild” so that people will know the meaning of your words, but you cannot use that definition as a premise in your chain of inferences. Same same for G in the MOP. Just because God is defined as G doesn’t mean that G is true.
But this proof isn’t even about God. It’s about existence. Just because necessary existence is true does not mean that it exists in actuality. The actual world is chock full of false statements. All of man’s epistemologies — from science to logic — are at work trying to uncover them. Without deductive proof that G exists in actuality, G -> G is just an inductive assumption. No proof will stand if it consists solely of axiomatic premises. It won’t even be valid, let alone sound.
Surely, you recognize the contradiction of saying that a nonexistent X can be anything at all. To be is to exist.
No, they aren’t different meanings. “Superlative” is a grammatical description of the term, not its definition. You can call it an adjective. You can call it a 7-letter-word. In so doing, you are not defining it.
What trap? How can two things both be the -est? We might say that Jupiter and Saturn are the largest planets, but the fact remains that Jupiter is larger than Saturn and therefore the largest. Anywhere there is one part of two, there are nine parts of eighteen. But 9/18 is not some quantity other than 1/2.
Supremacy is coherently defined as necessity. Taking note of its part of speech is not redefining it. You should know this since you brought up the Nietzschean notion of labels versus the things they label.
To be necessary, a statement must be true in every possible interpretation. If you pick out stars, then you are disregarding a massive portion of the universe. If you are looking for a physical analogy to metaphysical necessity, I would suggest “energy”. It is everywhere, including so-called empty space.
This is back to the MOP now? Surely you do not disagree with the axioms in the proof of NE because they form the backbone of basic Kripke logic. You yourself are depending on them for every argument you’re making here. And if it is indeed the MOP, and you disagree with both premises, then you must accept that their opposites are true. That is, you accept ~(~~G) and ~((G -> G)). I would be happy to engage you in debate over those, as they seem completely untenable to me for reasons stated previously.
Why are you making assumptions that are not wiffs in the body of your proof (“our assumption that x is nonexistent”)? Let’s try another approach. Let’s set the symbols aside once again, and formulate a narrative proof, or “proof sketch”.
We know that in every possible world, x is x. Otherwise, our words are changing meaning even as we type them, and we’re just talking nonsense. To prove NE, we must show that in every possible world (or for every possible interpretation) where x is x, there exists y such that y is x — that is, y is necessary. In other words, we must show that the domain of y and the domain of x are the same. To be necessarily true, a formula must be true for every possible assignment function, f. So what we have to prove is that “y = x” is true for every possible interpretation in every possible world (set of statements). To begin, pick any arbitrary world. Call it w1. We must show that for every assignment to the variables in f, the assertion that there exists a y identical to x for every interpretation of f at w1. So pick any arbitrary assignment function. Call it f1. We now must show that the assertion is true for f1 at w1. Let’s call the individual that f1 assigns to x i1. Note that there has to be at least one i1 since the domain is not empty. To show that our assertion is a true interpretation for f1 at w1, we need only show that there is some function, f2, that differs from f1 AT MOST in what it assigns to y AND “y = x” is a true interpretation for f2 at w1. Now, assume an assignment function f1 that is identical to f1, except that it assigns to y our i1. Such an assignment function must exist, given the definition of assignment function. Obviously, then, “y = x” is true for any interpretation of f1 at w1 since f1(x) = f1(y). Since our selections of interpretations, worlds, and assignment functions was arbitrary, it holds that for every possible interpretation of every possible assignment function in every possible world that the domain of x equals the domain of y.
Therefore, “x = y” is true for every possible interpretation in every possible world.
You’re not listening. I was covering all the cases. If x is existent, as I said in the beginning, then the proof works. I fully understand it. However, then we must consider whether the proof makes sense if x is nonexistent, and showed that it led to a contradiction, which can only be resolved by noting that the identity axiom is invalid for nonexistent Xs - Thus saying x=x for x being the invisible pink unicorn is meaningless.
Could you point me to a reference saying that the identity axiom holds for nonexistent objects?
As for supremacy, I think you are beating around the bush. I fail to see how necessity is singular. You wisely do not make your definition of supreme based on anything but necessity, but then seem to be infatuated with monotheism, so as to reject the possibility of multiple gods by using a definition of supreme which you have already rejected.
The real weakness of the use of logic is that incorrect results seem correct through misdirection - the writer invites the reader to concentrate on a long, complex, and correct proof and not on the spotty premises. There is an ancient history of this. Diogenes refuted a proof that motion was impossible by walking away.
That’s backwards. If the proof works, then x exists. (Actually, y, but still…)
Sure. Two abstract objects are identical if and only if it is necessary that they encode the same properties; i.e., x = y <-> AF(xF <-> yF). See Meinong’s and Mally’s Theory of Abstract Objects.
It isn’t singular; it’s superlative: “Of the highest order, quality, or degree; surpassing or superior to all others.” — American Heritage.
Infatuated with monotheism? I’m on record as saying that the MOP supports any theistic viewpoint from monotheist to pantheist. I am a monotheist, but the two times I’ve expressed my opinions about that in this thread, I’ve clearly disclaimed its association with the MOP.
Not this writer. I said early on in this thread (and in other discussions about it as well) that the most serious objection to the MOP is its first premise.
If that means you’re leaving the discussion, that is regrettable.
perhaps you’re misunderstanding the objection, becuase it seems to me you’re answering two different questions. if G is defined only as “necessary existence”, what is it about that definition that requires it to be singular? why is “necessary existence” ontologically supreme, to the point that “there can be only one”?
another thing that’s occurred to me is if G can have any number of different properties in the various possible worlds, what is it that allows us to say it’s the same entity?
Can I ask a little more about this “Necessary Existance”.
Does it mean The existance that must exist in all possible worlds"? And does it mean anything beyond that?
My apologies for the delay in responding. I was working on getting a paper in, and the formatting was taking longer than the writing did.
I understand that if the proof works x (or a y that is x) exists - but my point is that the proof only works if x does exist. If x is nonexistant, then we should get a contradiction to that premise. (Though I don’t see how if you don’t limit anything.) See below - I think we are converging here.
Here’s the rub. God as an abstract object, in other words the concept of god, certainly does exist. My objection to the use of the identity axiom does not hold in this case, since the moment we think of an abstract object it can be said to exist in some sense. Even if an omniscient, omnipotent god is self-contradictory, and does not exist in either a physical sense of in the sense that it could impact anything in the real world (whatever that is) the concept of an double omni god certainly exists.
I’m sure most of our readers are not thinking of godness as akin to “twoness.” Two itself can have no influence on other, but the concept of twoness certainly can.
Oh good grief - a superlative thing is certainly singular. If the definition was “unsurpassed by any other” then it would not be.
My apologies then. You’re talk of the superlativess of the supreme being fooled me.
Not at all. It has often struck me how the ancient Greek natural philosophers could prove all sorts of incorrect things through the correct application of logic to incorrect premises. I am in the middle of reading Tristram Shandy and this anecdote, which I had not heard before, came up.
In addition, if we define God as EVERYTHING which necessarily exists, we get around that pesky double-existence problem, since everything which is not God doesn’t exist in all possible worlds.
Of course, modal logic doesn’t define accessibility relationships between worlds, except that in G5 there is mutual accessibility. A world is possible from our point of view if it is “accessible” from our world, whatever that means, and in G5, our world is also “possible” in that other imaginary world.
This means that we have to define what is a “possible” world is. Is a world where what appears to be the Christian God is by every definition of the English word an evil sonofabitch possible? There’s nothing in the MOPOG to say it isn’t.
In fact, IIRC the last time I asked Lib what the accessibility relationship was, he stated that the possible worlds are all those that follow the rules of logic.
If that is the case, then the only thing these worlds do have in common are the rules of logic.
Therefore, by MOPOG wherein you assume:
– All that is NE is God.
– G5 modal logic ensues.
– Accessibility relationship is: any world that follows the rules of logic is related to our world.
– The only thing these worlds have in common is they follow the rules of logic.
– Therefore, via this loose pseudo-proof, God is Logic.
I’m not sure that Lib would even object to this, since he says that MOP does not specify the characteristics of a god.
However, we should be able to define an empty possible world, where the rules of logic still hold.
If such a world is possible, then God by definition does not exist. If God exists then such a world is not possible. We might also define a World W’ identical to world W except that God does not exist in it. How is this not possible unless you assume the existence of God as defined as existent in all possible worlds? Then “possible” becomes subsidiary to God. This is at least deeply unsatifying.
Then Number theory shows that 1 and 0 exist in all possible worlds (can’t remember if they are needed for define loops or fields,…, 1 is certainly needed for Integers). And are in fact necessary for the existance of integers, which I would argue are necessary for the existance of things, since things are generally countable. So would this not make 1 and 0 part of God?
It also seems to me likely that at least one spacial and one time like dimension is necessarily existant.
On another track of thoughts, it seems that a possible world could be imagined where there is no love. Would that not lead to asking if God contains love, since love seems not to be necessarily existant.
