I think I might be able to answer my own questions:
Is the real mountain more perfect than the imagined one simply because it is real?
And, is the God that exists necessary simply because it literally cannot not exist? For a second, I thought everyone was saying it was necessary for life to go on, but maybe they mean it is necessary simply for life to be as we know it…
Am I correct here? If so, then I don’t really find a whole lot wrong with this statement, mainly because the definition of God means as perfect as physcially and logically possible.
Although, I can think of a better God… one that can change the rules of laws and physics in order to make that circular square. So, how does that fit into this statement? Because, I am a Christian and since Jehovah made this world, it’s safe to assume he could alter it. So, essentially, not only could Jehovah do everything possible, but he can simply do everything imaginable, plus infinite more things. That sounds like a better, more perfect God to me…
Regarding the RN, you can conclude ~A if and only if ~A follows from a truth that is itself necessary. It might be easy to misread (because they wrote it a bit poorly perhaps) the link you provide where they say:
If (the conditional) if p then q is necessary, then if it is necessary that p, then it is necessary that q.
On first glance, it might look like that says p -> q but it doesn’t. It says (p -> q) -> (p -> q).
I agree. This proof shows both more, and less, than what most people mean when they say “God”.
Heck, even in this thread some people have made references to this “being” which has NE committing suicide, or other sorts of things. Whereas this proof does not even show that the “being” is a being insofar as it can take actions such as this, or any actions at all, for that matter.
These recurring threads would be fine if they existed on their own. But what urks me, to a degree that any philosophical debate can urk me, is when people bring this proof up in an irrelevant context.
For instance, in a debate about the supernatural, this proof is brought up as proof of the supernatural. If there is anything that this is not, it is a proof of the supernatural.
It would be sort of like if I were engaging in a debate about the prevalence of sex discrimination, and someone came in and said “you know, no prominent academician disagrees that all men are still sexist.” Then when pressed they reveal that by “sexist” they mean “passively partakes in the benefits of a sexist system” rather than “discriminates or believes in discrimination against or superiority of people on the basis of sex”.
In both cases, some academicians and the general public are using terms that have little to do with each other.
OK, I misundertood what you were calling the rule of necessitation. I was using the rule of inference given on my link, which is equivalent to the axiom A -> A.
This is not a logically possible god and so remains outside the context of this proof.
I agree, which is why I am a Discordian. Eris solves some of the problems with this proof, such as the not-ruled-out possibility of contradictory or otherwise exclusive properties in different possible worlds. I might adopt it for my own nefarious purposes.
It’s really an unconvincing proof. Especially since you have to deny at the outset the possibility of God not existing to show that the counter example (which proves that God doesn’t exist) is flawed. I don’t know how to call this, but it looks like question begging to me. Or the method itself is actually flawed.
See the section titled “Metatheorems and Derived Rules”.
The notation |- means “is provable from” and is read backwards. So, A |- a means that a is provable from A. Or put another way, if A |- a, then there must be some set of inferences, f1, f2, f3… such that the last inference, fn, is a. But it does not mean A → A.
Every premise of every argument in every bivalent system denies the possibility of its opposite being true. For example, by declaring that the argument must be flawed, you are denying that it may be valid. Why does your own criticism not apply to your own argument?
We are restricting our consideration to things that possibly exist. Why is this really so unsound? Even very general proofs restrict the domain of items considered. They usually begin with words like, “Consider the set of…” or “We will begin with a general [object]”, etc. In proving that being G encapsulates exists in actuality we restrict our attentions to only those things not logically forbidden.
OK, so if A is derivable from necessary truths, then whenever we see A, we may infer A. From that, it should be simple to prove that if A is derivable from necessary truths, then A -> A. Yes?
I always try to think simply about things first, so that’s where I still am in this topic… is it even possible to be able to do all things logically and physically possible?
First off, I am doubting that a being could exist in only one form in which it could alter the universe in any way possible. Since the being is under the constraints of logic and physics, what form could it possibly be in in order to do all the possible things? A big wave of energy? A black hole? A ball of light? A large dinosaur-looking creature? Can any of these physical formations pet a dog, have sex and remove all the clouds in the sky all in one afternoon? Of course not…
Therefore, I am assuming that in order for one being to be able to do all things possible, it MUST be able to toggle between many many different physical forms in order to acheive these things.
I guess you are thinking, “Yeah, so what? I’ve seen those shape shifters on Star Trek before…”. I guess it’s theoretically possible to assume different physical forms, but it is quite an outlandish idea this statement is implying, isn’t it?
Furthermore, not only is this shape shifting outlandish, but the amount of technology that would need to be available to this being would need to FAR exceed our known technologies. So, basically, the statement also says that our current technology is barely scratching the surface of what is possible.
Does anybody have any comments on this? These simplistic thoughts are certainly not proving the statement wrong, but it is putting it into perspective… I already know now what this statement says, but I am trying to figure out now how substantial its message is, the ramifications and implications that accompany this being.
Actually, there is no mention of physically possible, hauss, just logically possible. That is my mistake. The definition is simply, “The greatest possible being.” I would imagine a strict reading would require that we only mean logically possible in a modal sense… else why use a modal logic proof?
The contrast of form (or existence) and essence has a long history of discussion from Plato to Aquinas to Sartre and beyond. The being need not shift in any way to be perceived differently in different worlds. The perceptions are contingencies of the worlds, not of the being. Consider, for example, how you might be perceived by someone who is deaf. The fact that you cannot be heard is because he is deaf, not because your mouth emits no sound when you speak to him.
Why is “It is possible that God does not exist” logically forbidden, when the very existence of God is what you’re intending to prove? If you’re trying to prove God’s existence, isn’t it only proper that both possibilities (God exists, God does not exist) be given equal weight (as premises)? If you’re saying that we cannot even posit the possibility that God does not exist, why even go through the entire process. There’s your answer right there.
I think you’re looking at the conclusion first and then thinking the premises are somehow specious because of it. Try and look at it like this.
Define a being, G, such that it is the greatest possible being that can exist.
Assumption one: “The being that can exist”; <>G
Assumption two: “The greatest possible being”; G -> []G
Proof: [ommitted].
We then come to the question: what is this being? There are those who would have us believe that “The greatest possible being that can exist” is God. That is, there is historically, traditionally, etc, only one being which fits that same definition, and that being is God.
It is not that “God might not exist” isn’t otherwise an assumption one might make in a valid proof. It is that we are constructing a logical entity as the conjunction of two statements in all possible worlds:
( (G->[]G) & (<>G) ).
This being is logically the case. This being, to some, is the logical representation of God. To those, it is a proof of God.
You can posit it. It just leads to a contradiction. In fact, positing that God does not exist is a part of one famous version of the proof by Hartshorne himself. It’s called “reductio ad absurdum” and is a commonplace method of proof. Assume the opposite of what you wish to prove and then show that your assumption is contradicted by the conclusion.
Even if that were the case, circular arguments are definitively valid.
