This is a continuation of a hijack debate in What to say to people who pray for you.
Yes, I know this has happened before, but I think we’re actually getting somewhere 
DOH! I copied and pasted from your S5 website and didn’t notice the necessarily symbol was an image which disappeared. The original quote was “If A is a theorem of K, then so is A” as you suggest.
- IIRC |->| (hereafter abbreviated T) is a theorem of prop. logic. (It is, isn’t it?)
- Hence T is also a theorem of K, as K is an extension of prop. logic, so all theorems of prop. logic are also theorems of K.
- Hence T, by the Necessitation Rule quoted above.
You said “G is a symbol representing a supreme being.” I don’t think we’re yet agreed that those are the same.
That’s not the impression I got earlier. Anyway:
So you don’t use G to mean supreme at all initially, just “a being Who exists necessarily if He exists in actuality”? And make no other assumptions or definitions on G?
Then at the end we deduce G is supreme? Just from the fact that G is necessary, or is more needed?
Keep in mind that Libertarian is very inconsistent as to what G represents. Sometimes G is being, and sometimes G is statement. Sometimes G is a mathematical object, sometimes G is a physcial object. Sometimes G is defined in terms of axioms, and sometimes axioms are defined in terms of G. In fact, G is pretty much whatever Libertarian wants G to be.
After skimming the linked thread, I see that Libertarian was refuing a statement that, if taken literally, is ridiculously easy to refute namely “Now prove to me that your God – or any other – exists. Can’t be done.” If I claim that God is the number two, then it is quite easy to prove that God exists. Libertarian has presented an only slight more sophisticated version, but it still misses the intent of the statement, as Libertarian’s conception of God is hardly what a normal person would call God.
I also see that Libertarian either is completely lacking in understanding of his proof, or is deliberately lying. He says
In fact, the premises of his proof are:
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~~ G
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G -> G
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G -> G (Modal Axiom)
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G v ~G (Law of Excluded Middle)
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~G -> ~G (Becker’s Postulate)
He has five different postulates, and if he wishes to claim that they are equivalent to “It is possible that God exists and If God exists, then He is the Supreme Being”, that’s going to take a few more postulates. I find it rather dishonest that he claims that he has only two postulates, when in fact he drops postulates into his posts whenever he needs them (and he needs them a lot), and he repeatedly sweeps redefinitions under the rug. His justification seems to be “well, that’s what I originally meant”. Sorry, but if by “Supreme Being”, you mean “something which satisfies my five postulates”, then you should say “something which satisfies my five postulates”. That would be the honest thing to do. He creates new definitions for words, then expects to be able to use the new definitions when convenient, and switch back to the common meanings when that is convenient.
Necessary existence is true. We all agree this. There is something in every possible, actual world with the property of necessary existence.
I’d be happy to say that the Universe is this thing.
Lib is happy to say that G is this thing. He is also happy to say that a pantheistic (ie. Gos is the universe) is an entirely valid interpretation of the MOPGE (Modal Ontological Proof of God’s Existence).
I do not understand why a being, a thing which Jesus/Mohammed/Homer talked about, a loving entity, a creator should be considered synonymous with the concept of Necessary Existence. Lib has tried and tried, and I love him for it, but again and again I see the pea under the cup, the cups move around, and the pea disappears.
He did say he was using S5 logic which I think (correct me if I’m wrong) includes 3, 4 and 5. Given that it seems fair to me to say the proof has two premises. He didn’t define modus ponens either
Hmm… I have had that impression, but then, I don’t understand modal logic yet. I’ll let Lib respond to this one if he wants, but thanks for the warning.
Possible and actual worlds are not the same thing, silly me.
You’re wasting your time.
I’ve been in more arguments with the Lib than I want to remember. Believe me, it’s hopeless. He’s either deliberately lying to provoke a philosophical debate, or he has a psychological blind spot that prevents him from comprehending the pointlessness of his position, or he’s a highly educated idiot with pretensions to competence. I’ve never been able to determine which of the three possibilities is valid.
Lib’s equation simply says “The greatest possible existence exists,” which isn’t that big of a deal. As far as we know, “the greatest possible existence” could (And seems to be) the natural universe. Meaning, Lib just proved that the universe does, in fact, exist. Thanks, but I don’t think it’s news to anyone here…
OK, Lib says he’s not joining us here, so there’s even less point
Looks like this thread will vanish now.
What you say is true may be true, but I am unable not to find out for myself… Lib, bring it on
I, personally, have never seen the point of G->G. We’re talking about friggin modal logic here; the point is to consider possible alternate worlds. Given x->x, proof of its existence using modal logic is trivial.
The idea is that there is only one being that can have this quality. Clearly the proof is trivial. It is how we interpret it that leads to the crazy debates. Apart from that, there are some other arguments surrounding Becker’s Postulate and so on, but still, the cincher seems to be accepting that G is really “God”. Lots of wiggle room there, I think.
It’s also wrong. There might be multiple beings with equal “greatness”. If we’re considering an infinite set, there might not actually be a “greatest being” at all, even if for every being in the set there is a greater being also in the set.
I have a question.
Does there exist a mapping function F, such that each statement of modal logic can be mapped to English (or perhaps a precise subset of)?
That’s trivially easy – just examine the definitions of the symbols used.
Thanks.
Under what circumstances should modal logic instead of English be used to express arguments?
What I was trying to say was, Lib’s modal logic argument seems to be just a recasting of Anselm’s Ontological Argument. Since that is widely held to be refuted, it seems to me that doing so does little actual good. On the other hand, it would appear that Lib’s attempt was to restrict the number of people arguing against him.
Urban Ranger: When the English equivalents contain a level of ambiguity that interferes with their ability to derive conclusions precisely.
Of course, when speaking to large numbers of people who aren’t familiar with it, modal logic is grossly inappropriate. Its use is often associated with a desire, implicit or explicit, to prevent reasoned examination of the claims presented. In those cases, English is better.
Please also note – Anselm’s Argument doesn’t just seem to be refuted, it has been refuted.
This is not simply limited to modal logic, but all logics. And I disagree that English is strictly or even could be any better at it since logics are really subsets of spoken languages. I think modal logic does capture a specific use of the words “necessary” and “possible”. They do not mirror all use of “necessary” and “possible”, though. Whether or not, in absence of logic, something can be estimated as being “better” is a subject for another thread. Oh hey, can you guess which one it was? 