God, and existence as a predicate

Great Debates
81

It seems like it’s been a couple of years or more since the first modal ontological argument thread.

I confess I didn’t read all of this one so far, but I’ll just try to give a dozen good reasons to reject this argument; and I’ll try not to repeat myself too much.

First, as you say, the argument is valid (in some logics). That’s another way of saying that you’ve assumed your conclusion. So, did you assume your conclusion so egregiously as to be guilty of begging the question? The fallacy of question begging is not that the argument is invalid, but that it lacks the ability to convince. Have you convinced?

Let’s make sure that you have made all your assumptions perfectly explicit. Here is a bevy of reasons to question the arguement.

One. Definition: G. Huh? Why go to so much rigmarole, since your third premise is G -> G. I honestly don’t understand the point of premises 1 and 2, and inferences 4-9. Just go ahead and say it: “I assume that God’s existence is necessary, and I assume that if God’s existence is necessary then God exists; therefore God exists”. Valid? Sure. Compelling? No.

Two. 1. G -> G. This is wrong. Or at least, misleading. This is not the plain old material implication that we are used to. If it were, the argument would be invalid.

A counter model is an interpretation with two possible worlds, W0 and W1. W1 is accessible to W0. ~G is true at W0, G is true at W1. Both G -> G and ~~G are true at W0, but G is not.

The implication in your first assumption is strict implication. Strict implication is (G -> G). This is not “from the definition”, as you claim. A skeptic is free to reject that it is necessary that “if G then necessarily G”, based on the “definition” “necessarily G”

Three. 2. ~~G as an axiom. OK, a skeptic might grant you that it is possible that God exists. What about granting that it might be possible that he doesn’t? Errrt, wrong answer. ~G leads immediately to ~G, via modus tollens and your first assumption G -> G. A nice, short, two step proof that God doesn’t exist.

That is, at the same time you insist as an axiom that it is possible that God exists, your definition already doesn’t allow it to be possible that he doesn’t. See how you’ve begged the question?

Four. 3. G -> G. Do we accept this modal axiom? It requires that we believe that the accessibility relation on possible worlds is reflexive. I for one will believe that, but a skeptic is free to deny it. Not too controversial, though.

Five. 4. G V ~G. Can we reject the law of the excluded middle? You betcha. I do, I’m a constructivist. :slight_smile: Like Spiritus, I’m wary of reasoning classically in modal logic. Perhaps that’s because in my work, modal logics always have some computational content; and things like G V ~G do not always hold.

Six. 5. ~G -> ~G (Becker’s Postulate). This is not an inference. This is an assumption (or rather, you are assuming that Becker’s postulate is valid to apply it here). Becker’s postulate holds for possible worlds whose accessibility relation is symmetric.

That is, if some other world is relevant to this world, then this world is relevant to that other world. Is that true? Imagine a world exactly like our world, except that pigs have wings and the denizens of that world are fundamentally unable to conceive that pigs might not have wings in some world. Then, that world is relevant to this world (when arguing the possibility that pigs have wings); but this world is not relevant to that one.

This is, by the way, equivalent to insisting that A -> <>A; if something is true, then it is necessarily possible. This doesn’t really seem all that controversial; but it is equivalent to <>A -> A, that is if something is possibly necessary, then it is true. Do we accept that? I’m not sure if I do.

Seven. General confusion about possible worlds. What are they? You can’t really ignore them and be doing modal logic. The whole argument is an attempted demonstration that something is true in “this world” by an appeal to what is true in “possible worlds”; but the conclusion rests on the trick of shifting the sort of possible world you’re talking about midway through.

The first assumption (that it is necessary that if God exists, then he necessarily exists) suggests that you mean possible worlds that have similar realities to our own, in some sense. You are not talking about all the worlds we can imagine. One can imagine that God doesn’t exist all they want; but if he does exist anywhere, then he is absolutely necessarily and he exists everywhere—he does not exist anywhere accidentally. And that fact itself is necessary.

Next, we must admit that God is possible. Waitaminnit! If possible worlds are those that share similar realities with our own, why must we admit the possibility of God in any world?

The only way out is to insist that there is a fundamental asymmetry. God’s existence will necessarily imply that he necessarily exists. But his possible non-existence doesn’t compel us to reject his possibility.

OK. So the accessibility relation on possible worlds is not symmetric. No biggie. But—we insist that it is when we assert Becker’s postulate. Ooops.

That is, a skeptic might grant any two of 1 (amended to be strict implication), 2, and 5; but not all three.

Eight. 7. ~G -> ~G. This, again is not constructive. It relies on double negation elimination, which is not valid in an intuitionistically. I’m in an intuitionistic phase, so I would reject this step.

Nine. 9. G. Hmm, this step isn’t constructive, either (it relies on excluded middle). But, it’s the same as the “definition”. Why not just assert this as step zero, G -> G as step 1, and the conclusion immediately? And don’t say that you are trying to avoid begging the question, since the justification for the first premise is “from the definition”.

Ten. One man’s question begging is another’s convincing logical argument. I don’t find this argument convincing, and I doubt many others will. However, there is another purpose for informal logical discourse: to explain. That is, even if this argument didn’t convince me of God’s existence, but explained why you believe, then it would be useful. I find it hard to buy that these symbols and definitions are the reasons you believe. Please understand that I do not intend to impugn you or your honesty. I’m just not buyin’ it.

OK, I can only come up with ten, not a dozen. I’m a scientist, not a philosopher, so I’m not inclined to endlessly argue definitions.

To me, the serious objections (besides that you have assumed your conclusion immediately) is the assumption that we have some symmetric possible world relation (I don’t buy that, I think the real world is more like S4 than S5), and the non-constructive-ness. Oh yeah, and it’s disturbing that you play fast and loose with the modal quantifiers, by not stating right up front what sort of “possible worlds” you are talking about and justifying why.

82

Lib:

As I argued before, and demonstrated in the first thread, there are three assumptions that one can reject: (G -> G), ~~G, or the use of Becker’s postulate to conclude ~G -> ~G.

So don’t just focus on rejections of ~~G; reasonable people can also reject Becker’s postulate.

83

Oh, sure, Newton, I agree. Reasonable people can also reject the Induction Axiom. But I think that modal status is always necessary and every natural number has a successor are equally reasonable premises.

I think that’s an extremely poor and amphibolous paraphrase of validity. Even misleading. An argument is valid if the truth of its premises forces the truth of its conclusion. That has nothing to do with begging the question because the reason the truth of the premises forces the truth of the conclusion is that all the steps in between are logically formed.

Surely, you understand the difference. You’ve stated G as a premise. Hartshorne’s proof *infers * G. You’ve left God undefined, and therefore it is not at all clear why you should be allowed to posit that the existence of your undefined entity is necessary.

That doesn’t make any sense here, since our frame is S5. Our accessibility relation is Euclidean since <>G -> <>G (the 5 Axiom). To put it another way, (wRv&wRu) -> vRu where v and u range over w.

But your ~G premise is untenable given your G -> G premise. ~G translates to <>~G (~~<>~G). What you are saying is that it is possible that a possible being is not possible. And that’s impossible.

A skeptic, of course, is free to deny the validity of logic altogether if it suits his purpose.

Of course we can. We can reject the axiom of identity as well. We can accept these things whenever they please us, such as when we are arguing against creationists, and we can reject them whenever they get in our way. But since this is not 3-value logic, the LEM seems reasonable.

It’s not at all unprecedented to use a postulate as a tool to form an inference. Cf Russell and Whitehead’s “primitive propositions”.

Oy. Becker’s postulate is essentially a statement about equivalence of interpretations of <>. All that is required to satisfy B in the discussion about pigs is that the two worlds can agree on which *contingencies * are possible. There are, as you likely know, both a metaphysical and an epistemic interpretation of possibility. Since this is an ontological argument, it is the metaphysical interpretation that applies. It isn’t a matter of whether it is possible *for * pigs to have wings, but whether it is possible *that * pigs have wings.

There’s no shift. There is a direct correspondence among frames whenever their axioms are of the form (<>[sup]h[/sup][sup]i[/sup]A -> [sup]j[/sup]<>[sup]k[/sup]A). That is to say that a Euclidean frame may contain symmetry and reflexivity. Cf Lemmon and Scott, and also Sahlqvist.

I feel like I’m reading Kuhn about those evil scientists. I have no idea what you mean about double negation elimination. G -> G, therefore ~G -> ~G is just a modus tollens. Of course, you’re free to reject modus ponens and modus tollens as well.

Because definitions don’t imply anything. You might define Triangle A as a right triangle, but until you inspect its properties, you may not declare that it is in fact a right triangle. Euclid’s Definition #3 is “The ends of a line are points”. His Postulate #1 is “To draw a straight line from any point to any point”, which is a paraphrase of his definition. But he couldn’t draw inferences from his definition, and so he constructed a wff. That’s what we did here.

Nonsense. An argument begs the question if its conclusion is the same as one of its premises. That is not the case here. An argument is convincing if it is sound. And I believe that this argument is sound.

Fast and loose is as fast and loose does, I reckon. S4 is transitive, and S5 is Euclidean. B is symmetric. And the conclusion, G, was never assumed.

84

It’s frustrating how all this discussion seems to be about Gm (modally omnipresent), whereas…ahem, some people here are trying to prove Go3i*. To put it simply, any statement that is true across all possible worlds is G. The premises of the proof in no way imply O3I status.

Furthermore, I would like to reiterate my stance that modal extent is not a great-making predicate. I have re-read some of the other threads, and it appears that Libertarian implies that, in other possible worlds, not only does a being having exactly the properties of G, such that it satisfies the definition of G, exist, but it the EXACT SAME G. In other words, the same being G exists over multiple worlds simultaneously. Now, if this were true, it would indeed make existence a great-making predicate (in this instance,) but I don’t consider myself to exist over multiple worlds, and neither does any entity. Copies of myself, and G exist, but they cannot be considered inherently the same entity. Now, Lib, if this is not your stance, existence cannot be considered a great-making predicate. However, if it is your stance, I disagree with the logically unique treatment of God.

*Omnipotent, Omniscient, Omnibenevolent, Intelligent

85

No, you are right. My previous response was overzealous, and as a result rather unfocused. And one of my technical objections was incorrect (embarassingly so). Please allow me to start over.

I’m not criticizing your argument, merely trying to reveal its essential structure. Given a valid argument, if a reader agrees with the assumptions (and all the assumptions are made explicit), then he is compelled to agree with the conclusion or admit contradictions. And a reader who does not agree with the conclusion of a valid argument knows that he must find at least one of the assumptions that he rejects.

So what are we left with? You have three assumptions: (1) G -> G (not (G -> G) as I asserted before; I am very sorry for that), (2) ~~G, and (3) that the accessibility relation on possible worlds is symmetric.

My contention is that you will likely get your opponent to accept any two of those three axioms, but not the third. And obviously, we see why: acceptance of all three compels the conclusion that God exists. To reject that, your opponent must reject at least one of your assumptions. All I’m claiming is that I find it reasonable to reject any one of your three assumptions.

Presume that I disagree with your conclusion, but that I come to your argument with an open mind (open enough to consider all of your assumptions individually and truly find if there is any that I can disagree with).

Your first assumption is that if God exists at a world, then God exists at every world accessible to that world. OK. I’ll give you that. You claim it follows directly from the definition of God, and it’s your God in question.

Now, your second assumption is that God exists in some world accessible to this world. That he’s possible. Sure, I’ll buy that. As you suggest, if I deny the very possibility of God in an argument about God’s existence, then certainly I am guilty of the fallacy.

Now, I’ve already formed a picture of what we mean when we are talking about “possible worlds”. Based on your first assumption, that I have allowed you to assert because it follows from the definition, worlds accessible to a “God world” are God worlds. And based on your second assumption, which I have likewise accepted, there is a world accessible to this one that is a God world.

See? I (the generic “I”, the hypothetical opponent) have only accepted those because I’m thinking of possible worlds as asymmetric. Sure, there might be some world accessible to this one where there’s a God (your second assumption), but I surely won’t accpept that this world is accessible to that one.

Where are we? I deny your conclusion, and I can point to which assumption is in error. OK, so you can try to get me to accept that third assumption. We could even have a multi-page :slight_smile: thread on the structure of accessible worlds, and how no reasonable person could insist that it was not symmetric. But, in the process, if you convince me, you will also succeed in convincing me to reject one of your other two axioms. Because certainly, if possible worlds are symmetric, then it may well be the case that there is no world accessible to this one where God exists. That is, I will deny his possibility in this world.

In that case, I’ll accept your first and third assumptions, but I’ll see a fundamental partition of possible worlds. There is a set of worlds all of where God exists (by the first axiom), and there is a set of worlds none of where God exists. And there is no accessibility relation between any world of the first and second set (and vice versa, due to the symmetry that I have accepted).

So there are two kinds of worlds, God-worlds and otherwise. Your argument is about the God worlds, but I refuse to conclude that this world is a God world until I get some other reason (other than this argument). So I now reject ~~G.

But in this very thread you insist that I ought to accept ~~G! OK, I’ll accept it. And I’ll give you the symmetry you need for your argument. But in the process of convincing me that I have no basis to doubt ~~G, you have succeeded in convincing me that G -> G is wrong. Now I’m going to quibble endlessly with your definition of God (didn’t we already have that version of this thread?).

86

Is that all there is to question begging? Consider the following argument: my assumptions are A and A -> B.

  1. A { assumption}
  2. A -> B { assumption }
  3. B { modus ponens; 1,2 }

Have I committed the logical fallacy of begging the question? Consider this example from the Skeptic’s Dictionary.

See, my assumption A is that abortion is murder, that’s just the definition of abortion as the unjustified killing of a human being. And also, A -> B, that if abortion is murder, then abortion should be illegal. This is a simple consequence of the definition of the legal definition of murder. Ergo, abortion should be illegal, right?

Begging the question isn’t really a logical fallacy, it’s a rhetorical fallacy. Is there a test we can apply to recognize the rhetorical fallacy of begging the question?

Does your argument explain? Does it reveal anything about G that was not obvious from the axioms you forced us to accept about G? I don’t think it does. Does your argument convince? Can a non-believer or someone who is undecided read your argument and come to a belief in God through the validity of your logic? Possibly, for sure, but I have trouble imagining it. Does your argument explain? Is this the reason that you believe in God?

By the way: an argument is convincing only if it is sound and your opponent is unwilling to accept contradictions. Since many of us seem willing to accept contradictions in our lives, I think you need something more than just true premises and a valid argument to actually convince anyone. :wink:

87

I think those two paragraphs sum up your point, Newton, and you still have me a little bit confused about a technical point. This particular version of the MOP does not use Brouwer’s theorem, and yet you keep talking about symmetry. That would be an interpretation where G -> ~~G, and that is not a premise of this proof.

~~G follows intuitively from a deontic interpretation of necessity and is stated before the M axiom. Let wRw’ express a relation such that w’ is a condition brought about by some truth in w. By this relation, each possible world must have some variant of w that is accessible over R. In other words, the relation is serial: there exists u, such that wRu. This relation suggests that G -> ~~G, which is in fact the D axiom. But because we are not invoking the D axiom, we are offering ~~G as a premise.

Your beef, apparently, is that a relation cannot be both serial and symmetric, but in fact it can. Let <>[sup]0[/sup][sup]1[/sup]G -> <>[sup]1[/sup][sup]0[/sup]G & <>[sup]0[/sup][sup]0[/sup]G -> <>[sup]1[/sup][sup]1[/sup]G. That is the logical intersection of seriality and symmetry (the D axiom and the B axiom). Then <>[sup]0[/sup][sup]0[/sup]G -> <>[sup]1[/sup][sup]0[/sup]G. Therefore, G -> <>G, or G -> ~~G, which is eminently reasonable (at least to me).

But in any case, the frame used in the MOP is neither serial nor symmetric. It is Euclidean. That is, it adds transitivity (G -> G) and reflexivity (G -> G) to Kripke.

Well, I would say that there is some controversy about that. Consider this argument: Begging the question is a logical fallacy; therefore, begging the question is a logical fallacy. If you accept the premise, then you must reject the conclusion even though the argument is sound. But if the argument is sound, then you must accept the conclusion and reject the premise. Maddeningly, you can neither accept nor reject either the premise or the conclusion.

I do agree with that.

88

A circular argument is where the conclusion is the same as the premise. A begged question is where the premise is at least as questionable as the conclusion. I don’t think that is strictly rhetorical or strictly logical, it is simply a matter of overly-strong assumptions being used to drive questionable conclusions. The premise sidesteps the question of its own foundation, which is too strong to be assumed. A circular argument is a special case of the begged question, which is more general.

This is why some people think it means “raises the question” which is possibly true, but not necessarily so.

Questionable premise to drive a questionable conclusion: begged question.

Premise used to derive itself: circular argument.

Obviously, if a conclusion is the same as the premise, it will be as questionable as the premise.

89

I may be barking up the wrong tree, but it seems to me that Libertarians whole argument is circular, and is something like this.
If a Supreme Being that exists is more Supreme than an imaginary Supreme being, then existence is a predicate, and vice versa.

The ontological argument works if and only if existence is predicate.

The conclusion of the ontological argument: that it is necessary that God exists and God exists, is correct.

Therefore, existence is a predicate.

90

But nothing prevents me from rejecting both the premise and the conclusion, does it? Isn’t that what I did above, when I said “Begging the question is not really a logical fallacy…”.

91

Nicky2

Actually, the way I said it was this: existence is a predicate when it individuates its subject by the bounds of the existence. Thus, the supreme being is individuated by existing necessarily. Were there some other being with identically bounded existence, then one would not be supreme over the other.

Newton

Even after more than two thousand years and countless debates over the controversy, I still like Aristotle’s original delineation best — a logical fallacy is a fallacy from the argument, whereas a rhetorical fallacy is a fallacy from the arguer.

In Analytics, he wrote:

That is a logical fallacy and is about the argument as a syllogism. The conclusion fails as a law of inference, making the argument invalid.

But in Topics, he wrote:

That is about people who beg the question and their rhetoric.

92

I am going to backpedal on my backpedaling earlier (forward pedal?). Your proof is invalid, and my counter-model still stands. I had let you talk me out of it, and I shouldn’t have.

The counter-model contains (at least) two worlds. G -> G and <>G are true at world 0. G is true at world 1, which is accessible to world 0. ~G is true at world 0.

G -> G is true at world 0, because ~G is true at world 0. <>G is true at world 0 because G is true at world 1. There is no contradiction. Pictorially:


  W0:             R         W1:
G -> []G       -------->     G
  <>G
  ~G

The problem with this counter-model (problem from your standpoint) is that there can exist worlds where G -> G is false, and the world that witnesses the possibility of G might just be one of them. You can fix this by requiring (G -> G), which is why I keep harping on material vs. strict implication.

I’ve argued from the semantics that there is a counter-model, yet you provide a syntactic proof that you claim is valid. What went wrong? You use something you call modal modus tollens. That is, you use a rule like this:

(P -> Q) -> ~Q -> ~P

Which is not valid. This rule says that if P implies Q, and Q is necessarily false (is false in all possible worlds), then P is false in all possible worlds.

To see why this isn’t valid, consider that there are two kinds of possible worlds, those where P -> Q is true, and those where it is not true. In the worlds where P -> Q is true, and since ~Q is true at all worlds (by its necessity), then it follows that ~P is true by plain old classical modus tollens.

But in the worlds where P -> Q is not true (and ~Q is true), nothing requires ~P to be true as well. Both P and ~P are consistent in those worlds. Thus, there is nothing inconsistent with a world where P is true (provided P -> Q is not true in that world).

You can make this into a valid rule of inference, by making it:

(P -> Q) -> ~Q -> ~P

which forces P -> Q (and ~Q) to hold in all possible worlds, thus ~P holds in all possible worlds.

By applying (your version of) this rule, you tacitly (and invalidly) convert G -> G into (G -> G).

Your objection to my countermodel is that my objection doesn’t make any sense, since the accessibility relation is Euclidean. The counter-model is Euclidean (provided you add 0R0, 1R1, and 1R0), and is still a counter-model. G -> G and <>G are true at world 0, ~G is true at world 0, and G is true at world 0. You need to require G -> G at the world 1 that witnesses the possibility of G.

Now, for my nattering on about the symmetric accessibility relation. First, I’ve done a bad job of presenting the objection, if you think that I’m complaining that a relation cannot be serial and symmetric. Every reflexive relation is serial, and I certainly know of reflexive and symmetric relations!

You say “But in any case, the frame used in the MOP is neither serial nor symmetric. It is Euclidean.”. But, it is Euclidean and reflexive (your third premise makes it reflexive), and is thus both serial and symmetric (though I’m not sure why serial is important here). Every reflexive relation is serial. Demonstration: let R be reflexive. Then, for all x, xRx. Since for all x there exists a y such that xRy, then R is serial.

And every Euclidean and reflexive relation is symmetric. Demonstration: let R be reflexive and Euclidean. Presume xRy. Since R is reflexive xRx. Since R is Euclidean, xRy and xRx together imply yRx. Thus, R is symmetric.

It’s true that you don’t use Brouwer’s axiom to obtain symmetry, but your version of Becker’s postulate requires a Euclidean relation, and you’ve already required reflexivity; and you use the two together to get symmetry. If you’re trying to skirt some objection to Brouwer’s axiom, then this end around isn’t going to get you anything.

What I’m claiming is an interesting observation (at least to me): you don’t need a reflexive and Euclidean relation. You’re using that to get symmetry but all the proof requires is the symmetry.

That is, the proof from (G -> G) and <>G to G is valid with a symmetric accessibility relation. I will argue from the semantics. <>G is true at world 0, which means that there is some world 1 accessible to 0 where G is true. Since (G -> G) is true at world 0, G -> G is true at world 1. By modus ponens, G is true at world 1. If the accessibility relation is symmetric, then 1R0 and G is true at world 0.

93

Libertarian: First of all, I respect the passion and vigor with which you pursue this discussion. It’s good to see some truly serious and weighty intellectual topics batted about.

That said, as far as I can tell, you’ve been ignoring what I believe is the most important and meaningful objection to your whole argument, which has been raised at least twice by mtgman, and which, if you’ve addressed at all, you’ve addressed in only a cursory fashion…

You’re attempting to use an abstract intellectual tool (modal logic) to prove something about the real world (the existence of God). You can’t just arbirtarily pick some set of logical rules and axioms, no matter how interesting and self-consistent it is, and no matter how analogous parts of it seem to be to real life phenomena, and claim that a proof in your system proves anything about the real world.

If I had walked up to a very smart and open minded ancient greek mathematician, and first taught him everything there was to know about calculus and geometry, and then applied that math to orbital dynamics and used it, without any intermediate steps or discussions of the real world, to prove something or other about the orbits of the planets, it would be ridiculous for him to believe me.

On the other hand, if I first taught him the math, then we did some experiments to demonstrate how falling objects accelerate, did some observations of planets to verify their orbits, and so on and so forth, I could probably eventually convince him that basic Newtonian physics govern the movements of the planets. And of course, even then, it’s not a proof. Very little outside of pure theoretical mathematics can ever be proven. Can you prove to me that the earth goes around the sun? No. You can argue it very very very persuasively, such that it’s incalculably more likely than any other possible explanation, but something like that can not be, strictly speaking, proven. (And in fact, Newtonian physics don’t accurately describe movements of planets in all cases, what with relativity and all…)
So my challegne to you is to use Modal Logic to prove simpler things, or predict simpler things. Build up some framework of connections between Modal Logic and the universe we live in. Just because Modal Logic can contain terms named “God” and “Universe” doesn’t mean a thing about the actual universe, and an actual God.

94

Max

Modal logic finds many of its applications in computer science. That was how Hartshorne stumbled upon Goethe’s ontological argument and, from there, Anselm’s, which he then modalized. See this page for an introduction to some applications and real world expressions. Computer applications include artificial intelligence, natural language translation, reasoning systems dealing with theories of knowledge, belief, and time, database systems, software engineering, and so on. Modalities can be modelled like, “He might be wealthy”, “I doubt this is true”, and “One day, there will be a viable third party candidate”, etc. All you have to keep in mind for it to make sense is the obvious implication of its name: modal. It deals with modalities like possibility, necessity, and actuality. All three of those modalities are used in the MOP.

95

And statistics has applications in just about every field that exists. Doesn’t mean that you can use statistics to prove, say, that Hamlet is the greatest of Shakespeare’s plays. (You might be able to use statistics to argue for that point, but that’s not a proof.)

Seriously, I’m not trying to be flip or dismissive here. But I honestly wonder if you really believe in the relevance of this proof. That is, do you believe that any professed atheist or agnostic of sufficient intelligence and intellectual honesty would have no choice, upon reading this proof, but to immediately become a theist?

96

Max

The most convincing proof for me is my own experience. But my take on the MOP is pretty much the same as Plantinga’s. All that it should convince the atheist of is that theism is not necessarily irrational. Or as he put it: “What I claim for this argument, therefore, is that it establishes, not the truth of theism, but its rational acceptability.” I don’t expect it to change anyone’s mind since the premises may be rejected. But rejection of one or more premises is the only intellectually honest way to reject the argument. I won’t (and I know of no philosopher who will) abide irrelevant shots at the definition of God or desparate attacks on the applicability of the argument by people who are willing to apply logic when it suits them but discard it when it doesn’t. God is defined coherently here, and in a way that corresponds to how He is ordinarily defined. I know of no symbological tableau that is more representative of real world terms and concepts than this one. There can be no existence greater than necessary existence in terms of bounds, and that which is greatest is called supreme. The state or quality of having existence is called being. This argument is all about the modality of the Supreme Being. I have never seen another logical model that was more appropriate or meaningful. Reject it if you wish, but please reject it for the right reason.

97

Libertarian:

However, many others before me also pointed out that the impersonal forces of nature are more impressive or supreme than any god proposed so far, and the forces can be plugged in the formula without problems. If you want to press that this modal logic proves something else than a good mathematical proof in a peculiar universe, feel free to do so. However, it is also dishonest to deny that one can also get proof of no god also from that same logic.

98

If you can prove this is a valid and sound proof then I promise I won’t take shots at the definition of god or the applicability of the arguement in any conversation about S5. If you start talking about the real world then you’re fair game. Because, like it or not, a rational, reasonable person can accept the concept of Necessary Existance in S5(although why you continue to call this concept a “god” I don’t know) and still reject this proof, even if it is sound, as having any implications on the real world. A rational person could still consider belief in god irrational because they do not believe S5 is a realistic model of reality. Belief in god in S5? No problem. Belief in god in the real world? That’s another question entirely.

Still, even if you somehow “prove” that the concept of Necessary Existance fits some definition of “god” that is about as far as the implication goes, even in S5. As Ludovic pointed out, existance is a long way from proving Omniscience, Omnipotence, Omnibenevelonce, and Intelligence. O3I is also a common definition of the being you are referring to when you use the capitalized form “God”. As has been mentioned over and over, you’re starting with a definition of “god” which is so vague that it could encompass a range of entities which in no way resemble any big-G “God” of any Earthly faith. As Diogenes the Cynic noted early in the thread, it seems you’re choosing a definition of “god” which has stripped away all of the things which are assosciated with the big-G “God” concept you say you’re trying to prove. Then you take this stripped down definition, force it into some sort of congruence with the concept of Necessary Existance through the use of some questionable premises which reasonable people can have reasonable objections to. Of course the whole process was aided by the specific axioms and assumptions inherent in S5, and the whole thing is dependent on the validity of Modal Logic in general(which is still under debate). Then, by use of the big-G and rhetoric about implications for existentialism, switch contexts on us and claim this is a proof of big-G “God”.

Establish that god exists in S5. I have no problem with it, although it is essentially uninteresting. So broad and vague that it doesn’t tell us a thing about how we should behave in response to this knowledge. Nothing about a heaven, or a hell. Nothing about communication with humans, even any humans lucky enough to live in S5. Heck, even someone who lived in S5 wouldn’t know how to react to this proof. How should it impact their life? Should they stop eating pork(assuming pigs exist in S5)? Start facing East and praying five times a day? Skip work on Saturdays? Should he feel more safe and secure because there is a god? Why should he feel that? Just because there is a god doesn’t mean the god is benevelant. Maybe he’s working his way though the universe destroying all life he finds. Maybe he’s long dead. Even if neither of those is applicable, why should the average Joe even think the supreme being cares one whit about him? Why should he care one whit about the supreme being?

I ask you again, what are the implications for the man on the street.

Enjoy,
Steven

99

With all due respect, Steven, I think the question is jejune. What are the implications for the man on the street if the president is a Demublican or a Republicrat? I think that each man will interpret the implications differently for God, just as he would for anything else. For some, it will mean nothing. For others, it will mean quite much. For me — and I am a man on the street — it means that God is omniexistent. And that’s all the MOP addresses. That’s what I told Ludovic. You brought up his objection, but you didn’t bring up my response. Same same with Diogenes. Reasonable men can reject these premises, yes. But they can also reject any premises of any proof whatsoever, including those of Godel’s Theorem on Undecidable Propositions. But you’re acting like you’ve uncovered something sinister, that because you can reject premises, you’ve smashed the proof to smithereens. But that’s just a naive understanding of the facts. You should consider what it is that you’re rejecting. You’re saying that a possible being is not possible, that what must exist might not, and that even if it exists in actuality it is something less than it actually is. Those are weird counter-premises. Plus, you’re mixing up something else. God was not proved to exist in S5. Necessary existence was proved to be true in S5. God was proved to exist in actuality.

100

Fair enough, and more power to you. Although that is (obviously) outside the scope of the current discussion.

There may be atheists who believe that believing in god is a sign of mental feebleness, etc. I am not, and have never been, one of them. And needless to say, it’s pointless to try to prove the nonexistence of God. From the evidence that I, personally, have observed, and from the arguments that I, personally, have heard, I have come to the conclusion that either there is no God (more likely), or there is a God who doesn’t interact with the world at all, ever, which is, on a practical level equivalent to there being no God. Which is how I live my life.

But your experiences, values, priorities, and thought processes differ from mine. Doesn’t mean you’re irrational.
People who believe in the literal truth of the Bible and deny evolution, on the other hand… :slight_smile:

I’m not certain if I’m being insulted here… I believe that I’m rejecting one of your premises, namely a very fundamental one, which is that modal logic is capable of proving real-world theological truths.

To return to an art analogy, which I think is particularly apt, I could attempt to use math to prove that Hamlet is the best play ever, and start with a few assumptions like:

“The overall quality of a play is equal to its form rating multiplied by its content rating”

and

“The importance of a protagonist in a play is directly proportional to the amount of time he spends on stage”

or anything else of that sort. Then we could argue about those assumptions. And there might be quite a bit of meaning in that discussion. Knowledge might well be extracted, and new ideas created. But there’s a more fundamental assumption there, which is that it’s possible to use math to prove anything about the quality of art. An assumption which I believe to be entirely false.

As for logic, there are many, many times when logic is appropriate. And others, such as poetry, love, art, etc., where, while logic can still be a useful tool, it can not provide absolute answers.

I believe my position on this matter to be quite logical.