Pochacco’s proof looks valid to me.
So far we have that G -> G, and ~G -> ~G. From this, we can conclude that G v ~G, or ~<>~G v ~<>G, which goes to ~(<>G & <>~G). That’s an interesting conclusion.
Is the argument circular?
consider who is greater, Stephen Hawking or God.
well maybe God is greater, but by the argument’s own premise, something that exists is greater than something that doesnt exist. we know Hawking exists, so God is only greater than hawking IF god exists. So this requires God to exist in order to prove that god exists.
Ah, the board is back up!
With respect to Elpool’s question, the argument is not circular. To be circulus in demonstrando, and argument must conclude with its premise.
With respect to the counterargument by Pochacco, the second premise — it is not necessary that necessary existence exists — is prima facie absurd. But more importantly, it leads to a contradiction in 9 ~G. The inference violates the law of noncontradiciton, which applies in S5, and states that the greatest possible being cannot possibly exist. The object of the proof cannot be both possible and impossible.
With respect to Olanv’s assertion that the shortest ontological proof is to define God as existing, definitions prove nothing. Otherwise, I could prove that pigs fly by defining fly to mean “wallow in mud”.
With respect to the purple unicorn argument (evidently a paraphrase of Gaunilo’s objection), a label is not the thing that it identifies. You may call G any arbitrary name — God, purple unicorn, or x5-1297 — the fact remains that whatever label is applied, the thing is still G. It is merely a slightly more subtle attempt to use a definition of make a proof.
With respect to MrBlue92’s objection that the argument is an exercise in semantics, I really don’t think it’s necessary at this point to be that desperate. I recommend that you wait until you have first exhausted ordinary tactics for arguing against a deduction, such as finding logical fallacies (as I did with Pochacco’s argument) or rejecting on or more premises on reasonable grounds.
With respect to Diogenes’ question about the definition of greatness, keep in mind that the context here is ontological modality. Your choices are existence and non-existence qualified by necessity, possibility, and actuality. When it is said that the greatest OM is necessary existence, what is meant is that all other forms of existence are contingent upon it. Although Kant was a critic of Anselm’s argument, he thoroughly understood what it meant. He described the relation between necessary existence and supreme being this way:
— Critique of Pure Reason
With respect to Apos’s analogy of the cube in Flatland, I have used a similar analogy myself, and if I understand what you’re saying, Apos, then you and I agree. Not all worlds need be the same so that, for example, in the actual world, where a circle whose circumference and diameter are a ration of pi is impossible, there would be no part of the cube representing such a figure here. It would be possible only in a world where space is not curved. The analogy that I’ve used is of the SB having “legs of existence”, such that each leg standing in each possible world, even though existing necessarily, might likely be perceived differently in the frame of reference of that world.
With respect to Larry Borgia’s objection that the MOP is summoning God into existence, logical proofs do not cause things to exist. Bob wears a red shirt only on Sunday. Today is not Sunday; therefore, Bod is not wearing a red shirt. The modus tollens does not cause Bob to wear a shirt that is not red.
Finally, with respect to Sentient’s pantheistic interpretation of the proof, I am reminded once again of the breathtaking mysticism of materialist philosophy. A universe without energy. An unobserved multiverse with a fantastical topology entailing unobserved dimensions. And so on. Not being a physicist, I need to ask the question — can there be a universe without spacetime? I know Einstein’s answer, but maybe it has been disproved.
The opposite of necessary existence is not necessary non-existence.
(my emphasis) Your boolean algebra exercise in no way shows the existence of the above linked Supreme Being. For instance, it does not imply omniscience nor omnipotence. Is the MOPoG you cite below the “trivial proof” of the Supreme Being you are claiming exists? If so, it does not show what you think it shows.
Furthermore, as others have pointed out, if you take X as a premise, where X is anything you want, it is simple to prove X. An inherent outcome of the modal system you are using, and one that should not require 9 steps to show.
Where would the nails go?
Sorry, you can’t just get rid of this problem with handwaving.
Your sentence above translates to:
~(~G) … “The proposition ‘It’s not necessary that God exist.’ is necessarily false.”
But this is logically equivalent to:
G … “It is necessary that God exists.”
(I don’t need to walk you through the steps, do I?)
Establishing that G is actually true is the penultimate step in your proof. You can’t just take it as a given.
(That’s actually the real problem with your proof, by the way. You’re taking as a given what you’re trying to prove. It’s just masked by all the symbol manipulation.)
There is no contradiction in step 9 of my proof. I never assert G. Again, you are taking as an axiom the object of your proof.
Your proof boils down to:
Axiom: G
Proof: G
Forgive me for being unconvinced.
I really think you’re dead in the water here.
Grrr … in my last post replace “axiom” with “premise” …
“Proving” any god is a joke, since gods are a joke.
Can you “prove” Thor or Mercury?
Like asking to prove 2+2=5.
You can’t prove a false statement.
Wasn’t 344 responses enough for you to mull over in the first coming of the logic God
or the 300 responses in further clouds of the logic God?
Ok, I just want to back up to the OP for a minute. I admit that I don’t follow the vocabulary and notation for the logic proofs, but I don’t understand something in the OP.
You talk about a thing’s existance being defined by the amalgamation of all the things that make it it (the paragraph beginning with "Some modern philosophers).
Are you then making the assertation that defining Socrates (for example) as “Ancient Greek philosopher, teacher of Plato, blah blah blah,” <i>means</i> that Socrates must exist?
But that’s the problem I have. In each world, we have a leg, not the entire being, and the world’s themselves don’t seem to have the scope to define something like G = G. Premise two seems to specify legs, Premise 1 the entire being, and the proof uses these two different things interchangably. Is this interchangability legitimate?
I don’t see how this is in any way illicit given that the question of interpretation is inherently speculative, and in this context is working against an argument of necessity. Pointing out alternative interpretations and possibilities is entirely appropriate without the need for scoffing.
Maybe what scientists mean by “the (known) universe” and what is meant by “all-that-exists” are not the same thing. Once you leave the known universe, the context for all empirical observation, all bets are off just as surely for theists as for those with non-theistic interpretation.
If a name is just a shorthand for a list of qualities, then we coulc interpret a statement like “X does not exist” as “we cannot find anything that fits the defined specifications of the concept X”
Well… actually, it is about defining. To take it a step further, I could define God as “existing as a loaf of bread” or some other uncontroversial existent.
But, I do conceed to earlier mentions of how you define “greatest” or “supreme”, because there are different scales of greatness. The principle of incompleteness allows for any of these ambiguous terms of judgement to be inverted. In terms of God, I we can reference “greatest” from what we have available. As I stated earlier, God is generally defined as possessing all the properties of inequitability that humans seek. This isn’t a democratic greatness though, this isn’t an existential greatness in terms if “you have an inherent purpose for being here” greatness. If God simply gave everyone a “kill God switch” when they were born, which we aren’t even given chuckle, then you can actually falsify his greatness in the democratic sense. What is so great about a being that just has technology so good that interacts with beings so comperably incomperable that they cannot even get to it without God being able to know and kill them instantly. Having better technology is not the sole definition of greatness. There are also definitions of intrinsic worth, that rely upon handicapping yourself and still being selected over and over again; like giving everyone else guns but yourself, giving everyone else intelligence but yourself… etc…
It certainly is critical how you define greatness, because making a proof with an undefined term will seem quite sensical if you want it to be.
Well, the argument uses ‘God is the greatest being’ as a premise. Because you also assume that things that exist are greater than things that dont exist, that premise only holds true when ‘God exists’ is true. You assume as a premise the conclusion which you wish to reach.
Here’s another to address the problems with not defining greatness… leaving it ambiguous.
Let’s take your statement “it’s better to exist than to not exist” as an axiom.
We can replicate and give things that we possess. Therefore “We can replicate and pass on things that we possess” exists.
God possesses “being the greatest being”, therefor God is not as great as we are unless God can replicate and pass on things that God possesses. Or rather, if God cannot do this, then there is a greater being than the God being spoken of.
Now the issue of ethics comes up. We generally assume that God has not given Gods own possessions… this is the inequity that we phenomenally can verify every waking moment. So, God being the greatest being, by definition, means that the greatest ethic is to not give what you possess to others, even though you can. [remember, if God cannot give what God possesses than it cannot be the greatest being by definition – per the “that which exists is better then that which does not exist” axiom].
I don’t know about you, but I certainly wouldn’t think it anything less than absurd to prove this being and thus this ethic, which necessarily follows. In fact, your attempt at communicating with us is an affront to the ethic that the theory espouses, as you are attempting to give something of yourself, or are at least vulnerable to having something recieved of yourself. In a roundabout way, this effectively refutes your ability to have an intent - as you would b e recieving something from yourself - your perception of self awareness.
I forgot to add the critical step here, I suppose I guessed that it was implied.
What this allows us to do is reference
a.) That you are not an intelligent being and thus cannot make the argument (which i submit is false)
or
b.) God is not an intelligent being, which excludes the existence of God through the accepted axiom of existence being greater than non-existence.
In this case it would be “A being who is not intelligent cannot be greater than a being that is intelligent.”. Or however such nonsense is parsed. The point is that “greatness” needs defining.
One of the “greatest” largest animals ever to walk the earth hypothetically died because it couldn’t escape forest fires. The problem with defining greatness without conditions is that these odd scenarios will always pop up self referentially in a manner that refutes the being. To accomidate for this, additional axioms need to be added, which makes the proof that much more difficult to pull off. In the above example, you would have to explain why this “greatness” doesn’t replicate when everyone wants it, and by definition it is able to be replicated and given to anyone. You also have to explain why it STOPS replication just short of everyone, given that this is defined as “the greatest”, and given the condition that you use to describe WHY it is never passed on, by a being that must necessarily be able to pass it on in order to qualify as the greatest being under the “that which exists is better than that which does not” axiom. Defining God is a slippery slope. Once you star moving beyond “I define god as existing” or " I define God as a loaf of bread" (which we already assume exists), you’re going to encounter the difficulties involved in the discovery and presentation of a new verifiable existent to the human race, such as the difficulties encountered through the scientific process over time that seperates the quackery from the tangible.
I do see Modal logic as valid, but it does not follow that God comes from it.
Devastating parodies are entirely valid in that world, and just like Flatland it is a very fascinating place to investigate, if only we could interact with it, we could be gods! But, I think whatever God you can infer from that argument has the same limitations as us regarding Flatland. Modal logic is a Flatland where a God is valid, the obvious lack of interaction, to the real world, in that argument shows to me only the possibility of an irrelevant god.
“Considered by daylight…and without prejudice, this famous Ontological Proof is really a charming joke.” –Schopenhauer.
Non-logician and non-philosopher here. But just a basic stupid question.
(I think this is called argumentum absurdium) Couldn’t the same logic could be applied to the IPU? “The Invisible Pink Unicorn exists … etc.” therefore since that is an absurd statement the argument is an absurd argument.
I think that the absurdity rests on changing meanings. An object exists. A concept exists. Just because the concept of an object exists does not mean the object exists. The argument only proves that the concept of God exists and tautologically at that.
BTW “greater” is a subjective term needing to be defined within a value system and along a particular dimension or else it has no meaning. In this context it is meaningless because there is no salient value system or dimension.
Dseid:
Regarding the pink unicorn: we only have to plug some ultimate powers into it and then we apply modal proof to it (or is a he or a she?). I think the important thing to keep in mind is that using modal logic it is not absurd: we can indeed imagine an ultimate pink unicorn and using this logic, we will prove it. The absurd comes only after we check the results: The IPU is as valid as god! So, does Zeus, Og, etc…
Which precisely shows the weakness of this argument.
Since parodies are valid, it is an argument that only shows that Marx was right, Groucho Marx that is… 
Now that I think about it more, I’m ready to discard modal logic for many purposes. After all, it assumes that all possible worlds follow the laws of logic. We know that scientific laws are not immutable across possible universes: how can we say that the rules of logic are not also artifacts of this universe?
In fact, come to think of it, a world in which G exists, yet there is still much suffering and evil, would come close to violating basic rules of logic.