Modal ontological argument revised
Posted on: April 24, 2010 - 7:58pm
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Modal ontological argument revised
Cx = x is logically conceivable
g = God
(1) g <--> ~g
(2) g-->~<>~g
(3) ~g-->~<>g
(4) (x)(Cx == <>x)
(5) ~(~Cg)
(6) Cg AP
(7) Cg--><>g 4; UI,Equiv,Simp
(
<>g 6,7; MP
(9) ~(~<>g) 8; DN
(10) ~(~g) 3,9; MT
(11) g 10; DN
(12) Cg-->g 6-11; CP
(13) C~g AP
(14) C~g--><>~g 4; UI,Equiv,Simp
(15) <>~g 13,14; MP
(16) ~(~<>~g) 15; DN
(17) ~g 2,16; MT
(18) C~g-->~g 13-17; CP
(19) g-->~C~g 18; Contra
(20) ~g-->~Cg 12; Contra
(21) ~Cg <--> ~C~g 1,19,20; CD
(22) ~C~g 5,21; DS
(23) <>~g-->C~g 4; UI,Equiv,Simp
(24) ~(<>~g) 22,23; MT
(25) []g 24; Modal Equiv
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x=you copied this crap from some other source.
y=you admit the truth of the matter.
z=you are not so cool that you can do what the smartest men in the world have not managed after a few thousand years of trying.
x+y=z
qedb
=
#1 doesn't make any sense: "God if and only if not God"?
That sounds false to me.
It's not "God if and only if not God".
It's "Either God exists or God does not exist and it is not the case that God exists and does not exist".
I've only pasted it from a text file that I wrote and saved.
The truth is that this is my own personal formalization of Charles Hartshorne's modal ontological argument.
God's existence has been proven. It just has not been universally accepted. People have known since antiquity that God existed.
Well the logical connective you used means "if and only if". To say what you mean, you would either have to make two lines, or group the two parts off as conjuncts and connect them with a conjunction.
g = God
Ex = x exists
1) Eg v ~Eg
2) ~(Eg & ~Eg)
or
1) ~((Eg v ~Eg) & (~(Eg & ~Eg)))
But it is absolutely pointless for you to say #2 (or the second conjunct of the second #1): "it is not the case that God exists and God doesn't exist". You actually think there is someone who doesn't know that already? That is a tautology. Why would you express a tautology?
(or you could do away with the "Ex" part if you make "g" represent the entire sentence "God exists".)
No it does not. You have it confused with "<==>" or " == ".
Existence should never be treated as a predicate. All you have to do is use "g" as an atomic sentence.
No, that's just complicating things. To signify an exclusive disjunction, you simply have to use "<-->"
"g v ~g" is the symbolization for an inclusive disjunction, which means "either God exists or does not exist, or both." Insofar that it is a disjunction, it is still true even if one of the disjuncts is false, which, in this case, would apply to "g & ~g". But an exclusive disjunction will make it far more simple.
I've already done that.
Actually, you wrote out quite plainly that "g" equalled "God". But I know what you mean.
Thank you for teaching me about the exclusive disjunction. I did not know that.
Now my only problem with your argument is that in order for the existence of God to be necessary it must also be possible.
If you say that it is either the case that the existence of God is necessary or it is the case that it is possible, you still cannot derive that "if it is not possible then it is necessary" because it must be possible in order for it to be necessary.
I figured out what was throwing me in 1..
XOR is this symbol >--<.
You used <--> which is equivalence (bidirectional implication).
"I do this real moron thing, and it's called thinking. And apparently I'm not a very good American because I like to form my own opinions."
— George Carlin
That makes more sense.
Funny how the Nobel committee seems to have overlooked this.
Nobody I know was brainwashed into being an atheist.
Why Believe?
So that is a basic confusion there.
In modal logic, 'possible' and 'necessary' refer to two distinct 'modes', where the label 'possible' is used for propositions which cannot be shown to be 'necessary', IOW, as used formally within modal logic, something cannot be both 'necessary' and merely 'possible'.
This kind of argument always runs the risk of conflating the formal and 'normal' usage of the word 'possible'. Which is why they use the separate term 'logically conceivable' to describe something which is 'possible' in the normal usage of that word.
So the statement "if it is not possible then it is necessary" simply means that "if something is logically conceivable, and it cannot be shown that it is conceivable that it not exist, then it must be necessary". Again, it really still amounts to a tautology, but all logic amounts to a tautology, in that its cannot conclude anything not already implied in the axioms. It is useful in that many implications of a set of axioms are not obvious.
The underlined section is what needs to be demonstrated. and unfortunately for the argument, Science has provided logically plausible arguments for a Universe, a 'World', which is not dependent on anything that we could meaningfully label 'God'. So while it once would have been intuitively obvious that it is 'inconceivable' that God not exist, that is no longer the case.
The difference in the formal modal usage of the term 'possible' and the ordinary usage makes these arguments hard to follow, at least at first, and very susceptible to unnoticed slip-ups.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
I've taken predicate logic, years ago, and gotten an "A". But I've never taken modal logic, so I had to look it up. I did not realize that possible and necessary were supposed to be mutually exclusive. In fact, I still don't understand. If something is impossible (i.e. not possible) it cannot be the case. If it is necessary then it must be the case. So if it is necessary it must be possible. It doesn't make sense to me that something can be necessary without being possible. It certainly can't be impossible and necessary, right?
LOL. You probably just Google searched that a minute ago. But you get points for effort in making it look like you actually know something.
For what it's worth, "<-->" is not equivalence. It is an exclusive disjunction. Don't take my word for it, ask Mr. Kurt Godel (see "Ax. 2" of the proof):
http://en.wikipedia.org/wiki/G%C3%B6del%27s_ontological_proof
That is certainly the case outside of the usage in modal logic. I see three 'modes' in modal logic.
1. (logically) inconceivable => impossible.
2. Possible => not 1, but not 'necessarily' true, , it 'possibly' may not exist or be true.
3. Necessary. Absolutely must be true.
All 'conceivable' propositions or states are assumed to be either (2) or (3), but not both.
The more I think about it, the more I think that 'necessity' doesn't really work. The only things that can absolutely be said to be 'necessarily' true are definitional or strictly deductive statements, which is already understood. I think treating 'necessity' as some attribute of a proposition, something that is not strictly definitional or deductive, yet still 'necessary', is incoherent, a leftover from outmoded approaches to understanding.
Can anyone suggest any proposition or statement that is not an axiom, a definition, or a logical deduction from either an axiom (a presupposition) or a definitional statement, yet is 'necessarily' true??
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
Lolwut?
The link you provided supports jcgadfly's interpretation of the symbol, not yours.
I don't understand why the Christians I meet find it so confusing that I care about the fact that they are wasting huge amounts of time and resources playing with their imaginary friend. Even non-confrontational religion hurts atheists because we live in a society which is constantly wasting resources and rejecting rational thinking.
jcgadfly is correct.
<--> is equivalence.
>--< is disjunction, exclusive or, ie one side or the other must be true, but not both simultaneously.
BTW, Goedel's proof is as invalid as St Anselm's. it simply assumes the same crucial proposition, that actual existence makes something 'greater' than an imagined entity of otherwise identical attributes, in exactly the same sense that one imagined entity is 'greater' than another imagined entity.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
I admit that I had to look up the XOR symbol as I haven't used it in a while. However, I recognized your confusion with the equivalence symbol immediately.
See, when something bothers me and I'm not sure why, I do research. When something bothers you and you're not sure why, you dismiss it with a "praise God".
Thank you for finally admitting where you took the bulk of your "work" from.
"I do this real moron thing, and it's called thinking. And apparently I'm not a very good American because I like to form my own opinions."
— George Carlin
Any pretense that FS might claim to be an expert in logic has now been thoroughly demolished. So much for those walls of logic symbols.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
ButterBattle: On further investigation, I was wrong.
Religion is a virus.
Fight the infection.
OP, you should just invent your own system of symbolizing logic, and use it for every argument. No one else will be able to analyze it and point out how the argument is invalid or which premises are false. You can feel really superior that way.
Our revels now are ended. These our actors, | As I foretold you, were all spirits, and | Are melted into air, into thin air; | And, like the baseless fabric of this vision, | The cloud-capped towers, the gorgeous palaces, | The solemn temples, the great globe itself, - Yea, all which it inherit, shall dissolve, | And, like this insubstantial pageant faded, | Leave not a rack behind. We are such stuff | As dreams are made on, and our little life | Is rounded with a sleep. - Shakespeare
Okay.
One more time:
http://www.pseudopolymath.com/images/2009/10/godel_proof.png
Look closely at Axiom 2, which says "P(~q) <--> ~P(q)".
Are you suggesting that Kurt Godel, a brilliant mathematician, was honestly saying that ~q is a positive property if and only if q is not a positive property?
Why would Godel use "<-->" to mean "if and only if" when he is already using "<==>" to signify that?
Newsflash: Formal logic uses multiple symbols to signify the same thing. For example, the connective "AND" can be symbolized using a dot, ampersand, or upside down "v".
"<-->" signifies exclusive disjunction. You all have it confused with "<==>".
Please do not continue defending your errors.
Those two forms are equivalent at a basic level, but some treat them as distinct:
The 'stronger' version would be used to imply that the equivalence is 'deeper', I presume.
That expression is still basically asserting iff.
That statement is saying that the truth value of "not having some property' is equivalent to 'having the negation of that property'. Since something cannot simultaneously have some property and have the opposite of that property' that makes sense. 'Not being colored red' is logically equivalent to 'being colored anything but red'.
You apparently have no comprehension of logic, merely a superficial and sometimes erroneous familiarity with the symbols.
From http://en.wikipedia.org/wiki/Exclusive_or
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
You mean the way you're defending yours?
Godel is saying in axiom 2 that "if the property P applies to things that are not q then the negation of the property P applies to q (or P does not apply to q) and vice versa.
What you claim is that if g is god, god's existence implies god's non existence and vice versa.
Your theft would be more convincing if you got it right.
"I do this real moron thing, and it's called thinking. And apparently I'm not a very good American because I like to form my own opinions."
— George Carlin
No!
That is not what the premise is stating. You have no idea about Godel's argument, especially when you accuse me of stealing from it when I admitted that my argument is my own personal formalization of Hartshorne's argument. Again, why would Godel use that symbol to signify if and only if when he explicitly uses a completely different symbol to signify the same thing and does so more than once?
"Axiom 2: For all properties Z, either Z is positive or not-Z is positive, but not both."
http://skepticsplay.blogspot.com/2009/06/godels-ontological-argument-step-by.html
It's an *exclusive disjunction*. I'm done arguing this with you, you clearly will not stop defending your error.
Wikipedia is not a generally reliable source of information. Anybody at any time could have edited it. In fact, you could have simply interpolated the symbol yourself.
I've never seen anyone use "<-->" to signify "if and only if". Maybe some people have, I don't know. But I've only seen it used in Godel's argument and he does not use it to signify an equivalence.
What expression? Are you talking about Godel's axiom? No, it is not asserting an equivalence. Please stop trying to defend this error.
Axiom 2: For all properties Z, either Z is positive or not-Z is positive, but not both.
http://skepticsplay.blogspot.com/2009/06/godels-ontological-argument-step-by.html
You don't even know the argument!
"P" refers to "positive property", the expression is saying that either a property is positive or the lack of that property is positive, but not both. It is not saying that a property is positive if and only if the lack of that property is positive. That would make no sense.
No. Superficial understandings come from cursory sources such as Wikipedia. I've actually studied logic and have an genuine interest in the subject matter. You've simply assumed that your knowledge in physics somehow maps itself over to every other area of discourse, yet I've revealed quite nicely that you are philosophically incompetent. A few weeks ago, I formalized an argument for you and employed the rule "add" (a valid inference in propositional logic) and you didn't even realize that the rule existed. When I pointed it out to you, you retreated from the entire forum for a few weeks before coming out of your self-imposed exile to continue spouting the same drivel that you've been spouting for the past couple of years (quantum scales, infinites series, etc.) Now you follow me around like a snippy littel chihuahua trying to get revenge, since I've exposed you for the philosophical amateur that you are.
Why do you even post here? Why not post at a physics forum? Why does the topic of God dominate your life so much?
I will stop defending my position as soon as you acknowledge that what Godel is saying in his proof is not what you're saying in yours. In case you haven't figured it out yet, that's the position I'm arguing.
As you are an arrogant liar I guess that means never.
"I do this real moron thing, and it's called thinking. And apparently I'm not a very good American because I like to form my own opinions."
— George Carlin
I've already said that I'm not using Godel's proof. In Godel's ontological argument, he argues that the positivity of the God-like property necessitates that something must have the property of Godlikeness.
Charles Harthshorne argues that the logical conceivability of God necessitates his existence in some possible world, which thereby necessitates that he exists in every possible world by virtue of his eternity.
Godel argues from positive properties, Hartshorne argues from logical conceivability. Both make the same inference to possibility.
Do you understand the difference?
I've only cited Godel's argument to show that "<-->" is used to signify an exclusive disjunction, as Godel uses a completely different symbol to signify a biconditional.
It reads as though Hartshorne had to posit the thing he was proving before he could start.
Does that really help you?
"I do this real moron thing, and it's called thinking. And apparently I'm not a very good American because I like to form my own opinions."
— George Carlin
Of course we know that something has god-like properties. It is the Flying Spaghetti Monster.
According to this guy,
Goedel's version of the ontological argument seems to hinge on the assumption that the strong form of the term omniscience is coherent, that it literally means knowledge of everything, including knowledge of His own existential status.
So for that form of omniscience to be 'valid', ie logically 'conceivable', an omniscient being must necessarily exist, otherwise it could not know its own state of existence...
It is effectively another example of the logical problems that arise from various versions of the omni-attributes.
The message is that logic cannot be relied upon to make clear conclusions about literally any proposition. The simplest example of this the 'This sentence is false' category, which is literally undecidable, ie neither true or false.
Goedel's work went further into formally analysing this problem, leading to his incompleteness theorems.
The key danger flag is any statement which is in some sense self-referential, that makes some assertion or implication about its own logical status, as that classic example clearly is.
Goedel's version of the OA clearly relies on assuming the possibility of a being having absolute knowledge of its own ontological and/or existential status, so is treading on very dangerous territory.
So basically all ontological arguments rely on the assumption that literally any statement or assertion or assumption can be input to a logical argument and produce a clear and valid conclusion.
Which Goedel's own work formally disproved - essentially that not all statements that are of valid form in a given formal system can be 'decided', ie their 'truth status' determined.
When you use stuff like absolute assertions of infinite or at least maximal knowledge or power or 'greatness' (as per Anselm), you are asking for trouble, and such arguments cannot be accepted at face value without analysing the assumptions in some detail, and we all know the endless debates about the omni crap. So until come up with a logically coherent and water-tight version of the attributes that any particular OA is going to rely on, it cannot be assumed to generate a valid conclusion, even if it is formally valid.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology