It is, like subtle humor, an exercise for the reader.
(For context, look above, where I said I recognized that this proof was problematic, and quit biting my heels!)
Daniel
I do not find the “rock so heavy he can’t lift it” argument very appealing, myself.
Obviously. But that’s like saying logic will never be perfect because it doesn’t prove all false things true.
Almost. It’s saying that logic will never be perfect because it can’t go beyond what’s true and false.
But the point is that you don’t maximize opposites simultaneously… indeed, they wouldn’t be opposites if you could.
Almost. It’s saying that logic will never be perfect because it can’t go beyond what’s true and false.
No, logic can never be perfect, mainly because words have no absolute meaning.
Our words have only an evolutionary function, and so therefore, ( smile) logic has function only within a local frame. So it follows (smile) that the abstract “Reality” can only exist as a semantical construction.
But alas, to our unhappy end, the exercise of all forms of mathematics serves us even worse.
Post-modernists. [sigh]
You don’t think it’s possible that there can be an actual reality, and that words can reflect this reality well or poorly?
And what makes you think that mathematics serves us poorly? Mathematics works.
Post-modernists. [sigh] * ~ Vorlon’s Aide*
You lose Aide, you first resorted to name-calling.
Math is for parlor tricks. Choose your set of calculations and you can build an atomic bomb. Big deal.
But although the human mind cannot conceptualize the absence of everything without the existence of something to provide contrast, through words we can imagine this state, while the best of mathematical calculations cannot.
0 + 0 = 0 is a true statement.
“From nothing came something” is truer.
Most everyone agrees there is a reality. It’s the niggling specifics that bother us. 
Of course, emphasizing “works” does not itself belie the criteria for such a standard.
What makes you think I was referring to you with a derogatory term? “Post-modernist” is descriptive.
Check.
Your words are mathematical calculations. Do you think your brain pulls them out of thin air?
Checkmate.
Such as the definition?
I understand your unwillingness to commit to what you see as an arbitrary definition of a very important concept. At the same time, any small child could easily give me an intelligible and meaningful answer to the question, “What does it mean if something isn’t real?” Why can’t you?
No, working is the standard.
“Your words are mathematical calculations. Do you think your brain pulls them out of thin air?_____Checkmate.”
Now dagumit Aide, stop and think.
“Words”. " Math". Two words. Two semantic entities. Two distinct definitions. Determinism is physical not mathematical.
All mathematical exercises are nothing but the amusements of coincidenties found when adding and subtracting abstract numbers.
Now move your dadgum knight and get my king out of check.
[sigh] They’re interchangable.
** All language is nothing but the manipulation of concepts. English is a language. So is calculus. Both can describe. Both can describe well. Both can describe poorly.**
[/QUOTE]
Finally caught up on this thread again, and I see something that I didn’t really expect:
This being the a priori answer, and being false if post priori. I’m glad to see you finally lay it out finally, even though it took a good 8 or so pages from when I first posted the “possibly does not exist” question untill this comment finally came out.
However, this seems to make your whole logical proof of god’s existance also only true a priori, and false post priori (In relation to the “it’s possible god does not exist” bit).
It seems this whole thing comes down to which we accept first; “it is possible god exists,” or “it is possible god does not exist.” Both seem equally valid, yet result in completely contradictory results (Assuming we define god as “necessary existance,” of course).
How are we supposed to determine which gets used first? Just pick one randomly? Use both, which contradict eachother? Or what? Can you explain?
Methinks you left out a step in making that a standard. What “works”? How do you know when something “works”? I get the nagging suspicion that you feel we can isolate mathematics from our entire worldview and test it and say, “Yep, it works!”
By observation.
The world we observe is all we need to explain or anticipate. If we can’t observe (read: interact with) it, it’s not real and we don’t need to have explanations, theories, or concepts that deal with it. If we can observe it, we can determine the correctness of our models by determining what the models predict and then determining what the reality does.
Mathematics allows us to create models that can answer our questions meaningfully. That’s all it needs to do.
That is the basic idea behind empirical philosophy. (Please see Empirical Philosophy II: The Vengeance for references.)
Well, this seems that it is quickly going to dissolve into another science debate, I won’t have a part in that.
Well, okay. [sigh] It’s been a privilege debating with you, erislover.
Hi everyone,
I admit that i have not taken the time to read through all the posts so chances are someone has already posted this. From the Stanford Encyclopedia of Philosophy overview of Ontological arguments, here http://setis.library.usyd.edu.au/stanford/entries/ontological-arguments/
(3) Modal arguments: These are arguments with premises which concern modal claims about God, i.e., claims about the possibility or necessity of God’s attributes and existence. Suppose that we agree to think about possibility and necessity in terms of possible worlds: a claim is possibly true just in case it is true in at least one possible world; a claim is necessarily true just in case it is true in every possible world; and a claim is contingent just in case it is true in some possible worlds and false in others. Some theists hold that God is a necessarily existent being, i.e., that God exists in every possible world. Non-theists do not accept the claim that God exists in the actual world. Plainly enough, non-theists and necessitarian theists disagree about the layout of logical space, i.e., the space of possible worlds. The sample argument consists, in effect, of two premises: one which says that God exists in at least one possible world; and one which says that God exists in all possible worlds if God exists in any. It is perfectly obvious that no non-theist can accept this pair of premises. Of course, a non-theist can allow – if they wish – that there are possible worlds in which there are contingent Gods. However, it is quite clear that no rational, reflective, etc. non-theist will accept the pair of premises in the sample argument.
So believers - believe,
doubters - doubt!
I think erl has done a fine job of discussing some the most straightforward objection(s) to this proof. At the risk of adding nothing new, I think I would like to stress a couple of points that he made.
G=[]G
Is this a good definition for God? As others have noted, it specifies nothing other than necessary existence. Beyond that, though, why is necessary a predicate which we must set forth for God’s existence? As erl has noted, to do so appears to implicitely accept the ontological argument, which renders the proof moot.
<>G
Is this an acceptable axiom? Lib has argued that the obvious alternatives are invalid:[ul]
[li]~<>G because it denies an ontological possibility a priori.[/li][li]<>~G because <>~G implies contigency and thus implies <>G.[/li][/ul]
Now, there are times when denying an ontological possibility a priori is not a logical fallacy (in fact, logic is determined by such denials), but I agree with Lib that ~<>G is a poor proposition to accept axiomatically. <>~G, however, is a different matter. As erl pointed out several pages back the <>G <-> <>~G relationship breaks down in the case of ~[]G (or []G, as the proof in question demonstrates). Thus, if we accept the proferred definition of G (or accept the axiom G->[]G absent the definition) it is by no means trivial to accept either <>G or <>~G as a “second axiom”.
“Let us accept axiomatically that a being which exists in all possible worlds if it exists in any possible worlds exists in some possible world.” No, I don’t think I will.