It seems to me that in the end, this is very similar to those solutions in algebra’s quadratic equations, were one gets both a positive and a negative value: in that world, both values are valid solutions!
Now, to apply those values in the real world, one then uses the value that is pertinent or useful, lets say that after the resolution of an algebraic equation one gets –7 and 7 , to find out how many cubic feet of sand were needed for a sand box for example.
Remember: this is the real world now, one has to choose the value that you can see, not the value that can not be seen, in this case, the negative value is only used here for the purpose that, in the real world, it is invisible! The mistake you are doing is that you think the –7 (god) is valid in the real world. Algebraically speaking, the negative proof is right! Well, bad for the kids when we go to the real world! Or, we use (the also correct) positive value and get the right quantity of sand, making the kids happy! Likewise, modally speaking, counter values to god are right! The problem here is that you think that only you are right! You are happily ignoring that unbelievers are also right! Modally speaking that is.
Unfortunately, for you in our real world, that invisible proof is irrelevant. To get something relevant, I see that it is possible to plug other forces that we can later use and experiment, don’t forget: after all the modal shenanigans are made one gets something concrete (computer software) or something irrelevant (a semi-supreme being as George Carlin once said). As for me and the majority of thinkers out there, I go for the value we can use and see: the amazing but impersonal forces of nature, and not an invisible being that it is unlikely to have modeled anything with sand even.
I have already established that your conclusions are themselves based on faith since even theistic philosophers are not fond of this argument. But, is that a valid proof of The God? No, once again: it is proof of a valid equation, and just that, Of course: if you still want to press the issue you are forced to deal with the other values everybody else is getting from that equation, I am sure you will not bother with them, so who is most dishonest in the end?
This is either extremely deep, or completely nonsensical. You have suggested an entity. An objectively true entity. Now you’re saying that interaction with this entity and the ramifications of this entity’s existance are dependant on how an individual feels about it?
I apologize if I have missed anything. I have re-read all your responses since Ludovic’s post as of 01-21-2004 08:41 AM and I see nothing which addresses his objection. I will admit that I have not kept up with symbolic logic to parse all the discussion in this thread however. I still don’t see a clear, concise definition of the concept you are referring to as “God”. The big-G usage implies a contextual definition as the Judeo-Christian “God”, but you also disclaim that meaning while continuing to use the jargon. You need to pick a less loaded noun if you wish to discuss the matter without ambiguitity.
Firstly, I am not an Athiest. I do not claim there is no god. I have much bigger problems with big-G “God” because it carries the context of things which are not only unproven, but pretty much impossible(sun standing still, mountains re-locating, etc). I am saying that a being which is possible in S5 can still be impossible in reality. There may be some overlap between the worlds, and I am not actively saying it is impossible for god to exist in the overlap between S5 and in reality. What I’m saying is it is still reasonable to look askance at a claim that not only is it possible, but that it is TRUE.
Basically my premises are that something which is possible is not necessarily applicable in a certain framework. Proving it exists in a theoretical model does not translate into reality unless that model is inerrant and I have seen no proof that S5 is an inerrant model of reality. Crossover may exist between things that are true in S5 and actuality. Saying this concept of “god” is one of them seems to require a lot of proof. Something that MUST be possible IN S5 can still be impossible in reality. The “something” that you claim to have proved to exist(after assuming its nature, which by the way looks like a bit of illegitimitate ledgerdomain. How does one seperate G from G? How does one seperate God from his Essence? And if God is contingent on his essence, as you said in the OP, how can he fit the role of NE?) is based on the interactions of many assumed “truths”. All the Axioms of the S5 system and your own givens and definitions. That is without the further complication of the questions of the validity of ontological arguements and modal logic. You’re still a very long way from having a worldview which can compete with existentialism.
Then you should re-write your proof towards a layman. The whole thing seems to revolve around axioms which are assumed to be true for the “S” worlds. In reality we can’t assume much of anything to be true. Even the physical “laws” such as the law of gravity are still barely understood. It was recently discovered that gravity travels at the speed of light instead of being an instantaneous phenomenon, or having its own speed, or other explinations as previously theorized Even if your proof is valid across the two worlds, if you want to claim you’ve proved anything at all about reality which has any kind of implications for existentialism(as you claimed in the OP) then you better get cracking with actual evidence. Your premise G sure as heck looked like assuming there was a god from the get-go.
When I spoke of my own personal experience, you made the point that it was outside the scope of the current discussion.
As I said before, I really don’t mind that — so long as you are consistent about it. I would be more amenable to your point of view, however, it I heard you say that the predicate calculus in general cannot model the real world.
To prove anything about the quality of art, you would need a calculus that measures quality, just as trigonometry is a calculus that measures angles, and modal logic is a calculus that measures modality.
And why should I question your belief? Funny thing is, when I say what you say, my belief is ridiculed.
I believe that intellectual peers can hold opposing opinions and both be honest. But that’s just me. You haven’t established what relevance visibility has either to existence or to modality. You believe that lots of invisible things actually exist that logic says must be there. And you know that many things you see with your own eyes are illusions.
Well, certainly. Mount Everest is real, but the interactions with it and the ramifications of its existence vary greatly among people. Some people make it their life’s mission to climb it. Some people think romantically and fondly of it. Some people don’t like it. And some don’t think of it at all.
I have already said that I am willing to call it XJ-14 or something if that’s what you prefer. The definition is coherent. It is ontological perfection — existing in every world where there is any truth, including this one. Even with that, I don’t understand that fetish over Judeo-Christendom. Religions (and don’t forget Islam, Hinduism, Wicca, etc) are merely interpretations of God. A is A, but I1(A) is not necessarily I2(A).
Wow. That’s pretty much all over the place. You ought to reject that Euclidean geometry models reality for the same reason, namely that you cannot prove that it does, and that certain of its conclusions are impossible in reality. There exist no circles whose ratio of circumference to diameter is pi, and there exist no parallel lines. There are, however, geometries that can model actual circles and lines. It is no different with modal logics. There are accessibility relations expressed by axioms in many kinds of frames. S5 is an appropriate frame here because, like the higher geometries, it models the real world where, if something is necessary it is actual. I never said that God is contingent on His essence; I said that his essence precedes His existence. Existence is a manifestation of essence. Were there no God, nothing at all would exist. Therefore, all of existence is contingent on Him. As far as “competing” with existentialism, as Hartshorne himself has pointed out, the possibility of God’s existence is not something that competes with other possibilities.
Once again, there was no premise “G”. G was the ninth inference, and was established by valid rules of logic. Discoveries about the speed of gravity do not reflect on the inaccuracy of the calculus. The same rules of math that measured gravity before measure it now. All that changed is the values of the constants and free variables. The implications for existentialism are obvious. It is a philosophy which states that existence precedes essence. The onus is upon you to show that essence (G) preceding existence (G) is not the opposite of that.
I’m also waiting for Libertarian’s answer to Pochaco. I don’t see how MOP amounts to anything if, by it, one can arrive at an equally valid but dimetrically opposed conclusion. Why is <>G okay and not <>~G? Aside from labelling <>~G “prima facie absurd”, you’ve not given any compelling reason why it’s wrong.
I’m not sure precisely what you mean by that statement. The predicate calculus (and I admit that I’m not at all certain I understand what, precisely, is meant by “the predicate calculus” as opposed to just “logic”) is the basis for math, which is the basis for science. And there is plenty of evidence that science models the real world well, with the mars rovers being nice topical examples.
Or are you talking about using the predicate calculus to directly model the real world? Or are you talking about using the predicate calculus to discuss, but not directly model, the real world? In any case, in general, some aspects of the real world can be modelled well in certain ways, others can’t. There’s nothing contradictory in wanting to use modal logic to discuss certain quesions in computer science, other forms of logic to argue about politics, and none of the above to discuss art.
I still see the impersonal forces of nature surpassing that God.
Libertarian: You gave up the game when you noticed that there were practical uses for the logic. Indeed they are, it is not just me that many conclude that those practical results do not include “The God”, feel free to go back to argue whether several angels can be at the same time in the same place. Me? I will take the new software that was the positive result of the logic.
In other words: eventually the results have to have relevance in our universe, whatever math or logic is there, when the results obtained do not have uses and/or existence outside the numbers or symbols, it is reasonable to ignore those results, outside the logic’s universe that is.
You and Steven are pretty much echoing each other. Some people find God to be relevant, significant, and useful. Still, I doubt if you will apply your principle of practicality evenly and acknowledge that the result of the MOP, God’s actual existence, extends to the real world and real lives of billions of people. Some people don’t even like God. Some don’t care. And everything in between. Just as with Mount Everest, interactions and ramifications differ. But truth has nothing to do with being practical — what is practical depends on what you’re practicing. I don’t find my wife’s bras to be practical, but she does. Either way, they exist.
But that isn’t all the interaction Everest has with the world. At very least, as a source of mass, it has gravitational influence on people no matter what their feelings about it. You see, this is what I mean when I say that if big-G God exists, then such existance would have ramifications no matter what an individual felt or did. If there is a heaven and man has a dual nature, then this is independent of if a particular man believes in a heaven or believes in dual nature. Everest doesn’t stop existing and it doesn’t stop exerting gravitational pull on a person who doesn’t like it or on people who don’t think of it at all.
Then do so. From now on in this discussion and in others about this proof refer to “God” as “XJ-14” and with the pronoun “it”. The other simply carries too much contextual baggage for your arguement to ever be clear to a layman. The usage is simply too loaded. If you like, you may link “XJ-14” to a concise definition of ontological perfection.
I do reject Euclidian geometry in the areas where the model fails and I am dubious of it in places where it is unproven. It clearly does not apply beyond the event horizon of a singularity. That is exactly where
This makes absolutely no sense. This seems to imply a dualistic metaphysical view. A world of essence and a world of existance. A spirit realm and a material realm. If this is not what you mean, then it would seem to be meaningless as “essence” exists only in conceptual space and there is no known mechanism to directly translate such essence into existance without re-using something that already exists.
This is true of the concept of “Necessary Existance”. Well, I should say this is assumed to be true for the sake of consistency in logical modeling/argumentation. The genesis of the universe, if indeed it had one, has no living witnesses who are willing to speak up. NE is a concept invented to keep people from going nuts if they had to model a world where something could come from nothing. In reality we have no idea if something did indeed come from nothing or not. Still, for the sake of arguement we will assume the concept of NE is an accurate component of an accurate model. If XJ-14 did not exist, then nothing would exist. Therefore all existance is contingent on it.
Now that we’ve stripped away all the contextual baggage the usage “God” brings, I ask you. Who cares? Now that XJ-14 exists, what import does it have? What is its nature? How does one interact with it, assuming one wishes to. Moreover, what are the effects of its existance on us. Anything that has existance must have an effect on other things with existance. Natural laws such as the law of gravity and conservation of energy mandate this.
If you wish to posit this entity is outside the laws of the physical universe, then you should demonstrate it. If this entity does not interact with the physical universe then I fail to see how it could merit NE status. Basically, if the universe is contingent on XJ-14, then how could the universe have come into existence if there was no way in which XJ-14 could have affected it. XJ-14 could wink in and out of existance and it would in no way affect the universe unless there is some relationship between the two existances. XJ-14 has to be detectable by the universe in order for it to be contingent on XJ-14.
Regardless of all that, I’m afraid this debate has grown tiresome to me. As a gnostic at heart I’m afraid one can’t prove the existance, or indeed, non-existance, of some Supreme Being to me with angrily chalked symbolic calculus.
I apologize for the truncation in the previous post. I apparently missed it on preview.
I do reject Euclidian geometry in the areas where the model fails and I am dubious of it in places where it is unproven. It clearly does not apply beyond the event horizon of a singularity. That is exactly the same grounds on which I base my objection to ontological proofs of God using Modal logic. Modal logic has proven its worth in some applications, but it remains to be seen if it can adequately model reality to the point where it can make valid assertions about such sweeping categories as the origin of existance.
I understand your point, but you’re talking about attributes of Everest. If you want me to talk about attributes of God, that’s fine, but it is outside the scope of ontology. I’ll assume you’ll allow me the same courtesy that you extend to yourself, and so I’ll comment on your point. God’s influence is not natural, but supernatural. As the Facilitator of His most valued aesthetic, goodness, His influence is moral. The universe, including Everest and gravity, is amoral. There is no goodness nor evil in the atoms. His concern is morality. And because the context for morality is free moral agency, it makes sense that He allows man to make his own moral decisions, including the decision as to whether He, as the Facilitator of goodness, matters.
No problem. A rose by any other name, and whatnot.
Actually, Euclidean geometry applies nowhere in the universe because space is curved, and Euclidean geometry deals with flat planes. Nevertheless, it has practical use because in extremely localized areas of space, such as a sheet of paper or a table top, it is accurate enough to construct right triangles and make trick pool shots. But that isn’t the extent of its application. It is applicable, for example, to the game of chess — a world in which pieces move in geometric patterns. Euclidean principles are sufficient to describe the moves. With respect to modal logic modelling reality, you would be hard put to model reality without it. That’s because reality has modal states. If you are sitting in a room without windows, you are in reality capable of making statements about outside. The statement, “it might be raining”, is a modal statement. As is the statement, “it must be raining”. And it might not, it must not, it actually is, and so forth. In fact, most of the statements you are making in your argument against me are modal statements. You do not believe this, you believe that, things can’t be this way or must be that way, or modal logic can model this but not that. You are dubious, big-G is contingent on influence, and laymen do not understand the MOP — all of these are modal assertions.
You say that it makes no sense, and then proceed to explain exactly why it does! If God is supernatural, then Ockhamly speaking, no mechanism is required for Him to exist. Mechanics are a natural phenomenon.
You were actually right before. As you pointed out earlier, necessary existence is not about ontogeny, but rather is about metaphysics. It is purely a logical concept of modal ontology, meaning that whatever exists necessarily cannot not exist. For those who posit that XJ-14 is the universe, they are saddled with the unenviable position of defending the notion that the universe cannot not have existed — not epistemically, but metaphysically. It paints the holder of the view into the corner of determinism, which obviously is the least tenable materialist worldview.
Again, we step outside the bounds of ontology, but that’s fine so long as you don’t accuse me of doing it unilaterally. The significance is quite obvious: since your own existence is dependent on the existence of XJ-14, the effect is that you are here to observe things like gravity and conservation of energy. Its nature is supernatural, atemporal, and moral. One interacts with it through morality. It is silly to expect to interact with the supernatural in the same way you would interact with the natural. Your tautological observations of the universe are not applicable. They are tautological because your senses are themselves a part of the universe, and they are not applicable because the universe is natural, temporal, and amoral. Inasmuch as it facilitates goodness, its effect is to introduce goodness into your life and thereby edify you morally. It doesn’t matter whether you believe in gravity or not, Everest will exert gravitational influence. Same same for XJ-14. It will exert its moral influence even if you deny its existence. It loves you whether or not you love it.
That’s unfortunate on so many levels. It is unfortunate that you’ve tired of a debate that Max rightly identified as truly serious and weighty. It is unfortunate that, as a gnostic at heart, you fail to see the simple beauty of God revealing Himself through the greatest intellectual gift that He has given man — reason. But it is most unfortunate that you project your own anger onto the symbols, which merely say what they say. Dispassionately.
I think you meant to write “then God does not exist in actuality.”
Let’s try a different hypothesis. Your premise #2 in the OP was:
2. ~~G … it is not necessary that God does not exist
The negation of that premise is:
2b. ~G … it is necessary that God does not exist
It may seem strange to say that it’s not possible that God exists. But I can think of several arguments for this premise.
The Moral Argument
God is good. God is omnipotent. If God existed, evil could not exist. Evil exists, therefore God doesn’t exist.
The Obviousness Argument
If God existed, She would reveal herself so that Her existence was obvious to everyone. Some people are not convinced of Her existence. Therefore God doesn’t exist.
The Ontological Argument
Remember that the God we are talking about is “that which exists necessarily”, i.e. that which exists in all possible worlds. But the range of “possible worlds” is so great that nothing can exist in all of them. Consider for instance the one-point world, that contains nothing but a single mathematical point. Nothing that exists in our world can exist in the one-point world, except, obviously, a mathematical point (if you consider such a concept as “existing”.)
Anyway, I don’t think premise 2b can be ruled out, at least, not without further debate. Indeed, this is the premise you said you wanted to debate in the OP, so I find it strange that you are now declaring it “obvious”.
Right. That’s why I quickly added a second post immediately after it that read as follows:
*Correction:
<>G -> ~G … hypothesis: it is possible that if God exists necessarily, then God does not exist in actuality*
Well, of course the chief argument against it is that it is self-contradictory since ~ means ~<> (~<>~~). As with any contradiction, it proves everything, and it leads to a tautology and a petitio principii fallacy of begging the question:
~G v ~~G
~~G -> ~~G
~G V ~~G
~G -> ~G
~G v ~G
~G
which was your premise.
It strikes me that there is audiateur et altera pars. You haven’t defined evil. Suppose we define evil as the obstruction of goodness by a free moral agent. Just as we cannot say that darkness in a room with no windows proves that light does not exist, neither can we say that an evil heart in a free moral agent who has rejected God’s love proves that God does not exist. Quite obviously, it proves the opposite.
But clearly, you set that aside when you posited ~G.
But that’s hypostatizing. If we are to posit a world, then it must be a metaphysical possibility and not an abstraction. If there is a one point world, then the necessarily existing entity manifests as the point that is in it. In other words, the contingency is upon the world, not upon the existence. It is the world that by its own constraints can perceive Her only as a point. She nevertheless exists there.
Indeed I do want to debate it. Debate means I take one side and you the other. I’m just doing my best to represent my side.
I didn’t assume ~G v ~~G , I only assumed ~G. “It is necessary that God does not exist.” How can that be self-contradictory?
Well, if we’re going to start asking for definitions of everything, how about definitions of “free”, “moral”, “agent”? You can play that game till the cows come home…
No, it’s not. My argument was “A implies B, B is false, therefore A is false.” A= God exists, B= God reveals self. The fallacy you refer to is of the form “A implies B, A is false, therefore B is false.” My argument is valid (I don’t know it’s latin name, I’m sure you do), the second form is not.
Well, this is part of the point I’m trying to make. What sort of “possible worlds” are we talking about? In modal logic, it makes a difference. Who is going to decide which possible worlds are metaphysical possibilities?
Indeed, on looking over the thread again I see you have been doing just that. My apologies.
One more point: I admit I don’t understand “necessary existence”. In an earlier post you implied that someone’s snowblower existed necessarily. Really? My snowblower exists in all metaphysically possible worlds? I find that hard to believe. My snowblower didn’t even exist ten years ago. Is the world of ten years ago not metaphysically possible?
It would help me a lot if you could give some examples of things that exist necessarily.
I didn’t assume ~G v ~~G , I only assumed ~G. “It is necessary that God does not exist.” How can that be self-contradictory?