Define God

Great Debates
401

[QUOTE=Indistinguishable]
Liberal, you gave earlier a proof in your modal logic of the statement AxEy(y = x) (I.e., for all x, x exists necessarily), this statement apparently being of some importance to you and your thinking on God.
[/quote]
No, actually, that was in response to Voyager’s assertion that necessary existence is impossible. It was a tangent. In fact, this whole thread, practically, has been off-topic from the OP, which simply solicited definitions of God.

But only in the actual world. I don’t think we are compelled to reject the converse Barcan formula’s application to AxEy(y = x) just because it pisses off actualists hell bent on eliminating NE.

I don’t think so. Possible existence implies necessarily possible existence (the S5 axiom: <>A -> <>A). But <>A -> A is a unique frame (unique in the sense of an accessibility relation of x and y identity), which would be a CD system.

No, I don’t. But the conclusion that you reached applies if and only if Santa Claus is defined as the supreme being, which does nothing but make Santa Claus a synonym for God, just like Dieux or Dios or Gott. We could also use the term Vegemite. Or cat breath. Or XJ-618Z. Or anything else we define the same way we define God. But that would introduce obfuscation.

I left out a part of that paragraph because the complexity of unravelling it and responding would exceed the time I have, but as to your direct question, Plantinga argues that S5 is the appropriate system because of the nature of S5 agents in epistemic logic. If we are to prove something about the ontological nature of a supreme being, then it is reasonable to employ a system in which that being is capable of mapping every implication of its existence. It is certainly unusual for an ordinary ontological agent to exist where it doesn’t exist, but such an ontological demand is called for in examining an agent that cannot not exist.

(Note that we could use the same system to argue epistemically for God’s omniscience as a knowledge agent Who knows what He does not know.)

Well, there are versions of the MOP which do not use Becker’s postulate. For example, a five-step proof can be constructed using the theorem (G -> G) -> (<>G -> G) as a third premise, which seems reasonable to me but weakens the form (weak in the strictly formal sense of adding more axioms).

  1. (G -> G) -> (<>G -> G)

  2. G -> G

  3. <>G

  4. <>G -> G (modus ponens on 1 and 2)

  5. G (modus ponens on 3 and 4)

I would like to add, for your edification, that although I’m flattered by your reference to me as a logician, I’m not. In fact, I’m barely formally educated beyond high school (one semester of college on two textile science scholarships). What I say carries no weight of authority whatsoever aside from the facts themselves. I am self-taught, having studied philosophy for almost forty years. What I’ve learned, I’ve learned by reading and by speaking with other knowledgable people. I am very aware of the shortcomings and pitfalls of autodidacticism. I have always disclaimed myself this way, and make no pretense about any qualifications.

402

[QUOTE=the PC apeman]
From what I’ve read, the reason this works with God but not other possible things is because the object of the proof must be maximally perfect. Nothing else can be maximum possible perfection or it would be God. This seems to open up a problem of competing criteria (and Voyager’s objection). If it cannot be determined what within the realm of the possible constitutes maximum perfection, then the proof will not apply to anything.
[/QUOTE]
That’s right. One must decide in his own mind whether there is an existence greater than existence in every possible world. One might attempt to argue that existence in all possible worlds plus existence in all impossible worlds would be greater, but since existence in an impossible world is undefined, such an argument is meaningless.

403

[QUOTE=Liberal]
That’s right. One must decide in his own mind whether there is an existence greater than existence in every possible world. One might attempt to argue that existence in all possible worlds plus existence in all impossible worlds would be greater, but since existence in an impossible world is undefined, such an argument is meaningless.
[/QUOTE]
Agreed. And that only strengthens Voyager’s objection. One example of the objection is the problem of omniscience versus omnipotence: Consider a possible god that can alter events in any way he chooses. He is maximally perfect except he cannot know ahead of time what will choose. Next, consider a god who knows how all future events will turn out. He too is maximally perfect except he cannot alter what he has foreseen. Finally, consider a god who is maximally perfect, can alter any event, and knows in advance how all events will turn out. Clearly the third god is the most maximally perfect. However, his existence is impossible. He cannot both know what will happen and cause it to be otherwise. Of the two remaining candidates, it cannot be determined which is the more maximally perfect.

404

[QUOTE=the PC apeman]
Agreed. And that only strengthens Voyager’s objection. One example of the objection is the problem of omniscience versus omnipotence: Consider a possible god that can alter events in any way he chooses. He is maximally perfect except he cannot know ahead of time what will choose. Next, consider a god who knows how all future events will turn out. He too is maximally perfect except he cannot alter what he has foreseen. Finally, consider a god who is maximally perfect, can alter any event, and knows in advance how all events will turn out. Clearly the third god is the most maximally perfect. However, his existence is impossible. He cannot both know what will happen and cause it to be otherwise. Of the two remaining candidates, it cannot be determined which is the more maximally perfect.
[/QUOTE]
I’m afraid that I lack the mental capacity to wrap my brain around such phrases as “maximally perfect except” and “more maximally perfect”. God’s epistemic bounds are the same as His ontological bounds. He knows every truth. A statement that is not a truth, He does not know, just as He does not exist in a world that is not possible. And for potency, same same. When we say that God can do anything, the modality is intrinsic. That is, we do not mean that God can do impossible things, because impossible things are not things.

405

[QUOTE=the PC apeman]
Agreed. And that only strengthens Voyager’s objection. One example of the objection is the problem of omniscience versus omnipotence: Consider a possible god that can alter events in any way he chooses. He is maximally perfect except he cannot know ahead of time what will choose. Next, consider a god who knows how all future events will turn out. He too is maximally perfect except he cannot alter what he has foreseen. Finally, consider a god who is maximally perfect, can alter any event, and knows in advance how all events will turn out. Clearly the third god is the most maximally perfect. However, his existence is impossible. He cannot both know what will happen and cause it to be otherwise. Of the two remaining candidates, it cannot be determined which is the more maximally perfect.
[/QUOTE]
Indeed, one could argue that worlds are possible which would fall under an ordinary English definition of the word “evil.” If God existed in those worlds it would be a lesser, not greater, entity.

If one disagrees that such worlds are possible, we are in disagreement with the logic model used.

If, however, one disagrees that the “greatness” of an entity is diminished by appearance in evil worlds, then that shoots down any additional properties of God one might have been given through revelation, as you’ve pretty much accepted that the maximally-present God allows evil to exist.

406

[QUOTE=Liberal]
I’m afraid that I lack the mental capacity to wrap my brain around such phrases as “maximally perfect except” and “more maximally perfect”. …
[/quote]
I see your point. I guess just “maximally perfect” is a similar problem. But, if perfection is not a continuum, then it must be an ultimate objective state unto itself. There is nothing to say such a state is possible.

407

[QUOTE=the PC apeman]
I see your point. I guess just “maximally perfect” is a similar problem. But, if perfection is not a continuum, then it must be an ultimate objective state unto itself.
[/quote]
Which is what I was illustrating with the hub and spokes metaphor.

And thus the premise. There are four non-actual states that are not, in and of themselves, contradictions or redundancies and thus are likely premises:

(1) <>G It is possible that God exists.

(2) <>~G It is possible that God does not exist.

(3) ~<>G God cannot possibly exist.

(4) ~<>~G God must exist..
(The diamond signifies possibility, just as the block signifies necessity.)

Taking (1), we inescapably reach (4), which implies G — God actually exists. Taking (2), we inescapably reach (3), which implies ~G — God does not actually exist. Incidentally, that’s why you will hear some people say that in S5, possibility implies necessity, but that’s not accurate. Without our second premise, G -> G, we could not go from <>G to G. And so, <>A -> A is not an axiom in S5. If it were, we could indeed say that anything possible is also necessary.

So, the question becomes whether to accept (1) or (2). Rejecting both, of course, is untenable unless we also reject the law of excluded middle, which some systems do, but not this one (and not most ordinary systems). In other words, rejecting both would mean that (A Or Not A) is not true. Try programming a computer with that rule.

In deciding which we well accept, it would behoove us to keep sight of what we are talking about. Luckily, we have our definition, and that is what definitions are for — to clarify what we are talking about. And so, substituting our definition for our term, then it becomes a matter of defending one of two positions: (1) it is possible that that which would exist in every possible world would exist in the actual world; versus (2) it is possible that that which would exist in every possible world would not exist in the actual world. And this, of course, is where immovable materialists cry “Foul!”. Things circle back to rehash the matter of proof by definition, and we begin anew explaining the nature of definitions versus the nature of propositions, only to arrive back here again. At some point, we must stop retracing our steps and accede to what is sensible and reasonable. We should never have to revisit the business about definitions.

Number (1) obviously is easier to hold. It is Ockhamly simple, and bears no inherent contradiction. It is an affirmation, rather than a negation, and thus lacks a particular entity — “not”. And so the question is, Ockhamly speaking, is “not” a necessary entity. (Recall that the parssimony principle states that we ought not to multiply entities beyond necessity. It is a side issue whether Ockham in fact conceived it or invoked it.) Number (2) adds the entity, “not”. It is possible that God does not exist. Is there any compelling reason to add the entity?

One must ask oneself in adding the entity whether one is doing so simply because it would contradict one’s default position that God does not exist, because epistemically, if one does not know whether God exists, one does not have reasonable cause to add the entity.

The above is a simplified version of the thought processes that I went through in deciding between possible G and possible not G. And I decided that I would default to the position that I don’t know whether G is true or not. I decided to let the rules of inference tell me one way or the other. Therefore, I chose the simplest expression of modality.

If you think there is a better reason to accept (2) than (1), I am open to hearing it.

408

[QUOTE=Liberal]
… God’s epistemic bounds are the same as His ontological bounds. He knows every truth. A statement that is not a truth, He does not know, just as He does not exist in a world that is not possible. And for potency, same same. When we say that God can do anything, the modality is intrinsic. That is, we do not mean that God can do impossible things, because impossible things are not things.
[/QUOTE]
Let me try it again. A perfect being would be maximally capable of doing all doable things and maximally capable of knowing all knowable things. Any intersection where both are possible falls short of the full extent of either. Perfect capacity in one regard precludes perfect capacity in the other. There might be multiple possible beings each with a narrow perfect capability. There cannot be a single being that is the better of all of them. Of the individuals, which by itself is perfect?

On preview, I see you’ve aleady addressed my first point. Put this on hold if you wish.

409

Okely dokely. :slight_smile:

410

[QUOTE=Liberal]
Which is what I was illustrating with the hub and spokes metaphor.
…
[/quote]
Please flesh that out for me. It sounds like you are saying that we with our logic in our spoke cannot see the whole wheel. And further that other logic exists in other spokes and also applies to the whole. That would be saying the God and/or the supernatural isn’t defined by (our) logic. And that would make the proof meaningless.

Note my added colors:

Hmmm. Does (2) inescapably lead to (3)? That sounds like one of the parodies mentioned in the SEP article as an attempt to counter ontological arguments. Is (2) leading to (3) valid in all of the major forms of the argument? I wasn’t aware there was a modal ontological proof of the nonexistence of God. Do you find it equally valid once the starting premise is selected?

Well, yes, you may have predicted me here. This isn’t the substitution I was expecting. Are you sure you worded that right? If the choice is (1) it is possible that perfection exists; versus (2) it is not possible that perfection exists; then I’ve already concluded that (2) is my choice. (See post #408).

In general, adding “not” is not adding an entity. Not adding “not” is adding an entity. “Not” is the default. In the case presented, the question is premature until my following confusion is resolved.

I’ve add the colors above because it’s not clear which (2) and (1) you are referring to here. The blue and the green sets don’t strike me as the same. Does my choice in red shed any light?

Let’s try this: Let’s say there isn’t anything supernatural. For this question the material world (and, if you like, other possible material worlds) is all that can exist. Is it possible for there to be a supreme being - a being to which there is no one superior in the material world? Would this being be perfect, or the greatest existence, or have whatever quality that is needed for the proof to establish him as necessary? I suspect your answer is no to at least the latter. Adding the supernatural seems to be the ultimate wildcard.

411

[QUOTE=Liberal]
No, actually, that was in response to Voyager’s assertion that necessary existence is impossible. It was a tangent. In fact, this whole thread, practically, has been off-topic from the OP, which simply solicited definitions of God.
[/QUOTE]

Ah, my confusion. Sorry for continuing this hijack, then; perhaps you would prefer to discuss your modal arguments outside this thread, or in private correspondence?

[QUOTE=Indistinguishable]
But as this asserts that all objects exist necessarily, if we accept it, we must conclude that, for example, the Eiffel Tower exists necessarily; it is not possible for the Eiffel Tower to not exist.
[/QUOTE]

[QUOTE=Liberal]
But only in the actual world. I don’t think we are compelled to reject the converse Barcan formula’s application to AxEy(y = x) just because it pisses off actualists hell bent on eliminating NE.
[/QUOTE]

Well, it just seems to me an odd thing to believe, that the Eiffel Tower must exist necessarily, that there are no possible worlds without the Eiffel Tower, but apparently you don’t find it so bizarre. (I have my own problems with the concept of transworld identity, anyway, though, so I particularly find it hard to swallow).

[QUOTE=Indistinguishable]
And, indeed, in your modal logic, possible existence implies necessary existence.
[/QUOTE]

[QUOTE=Liberal]
I don’t think so. Possible existence implies necessarily possible existence (the S5 axiom: <>A -> <>A). But <>A -> A is a unique frame (unique in the sense of an accessibility relation of x and y identity), which would be a CD system.
[/QUOTE]

Well, necessary possible existence should imply necessary existence in your logic. Here, starting from your conclusion of AxEy(y = x), I will prove that possible existence implies necessary existence.

Proof:

  1. AxEy(y = x) [Proved by Liberal in #287]
  2. <>Ey(y = z) [Hypothesis that z has possible existence; to be discharged later]
  3. Ey(y = z) [From 1 by universal instantiation with z; if you like, refer to the quantifier axioms in the PDF file linked to in #287]
  4. <>Ey(y = z) -> Ey(y = z) [From 3, discharging the hypothesis on line 2]

Ta-da! Possible existence implies necessary existence. Is this not condoned by your particular modal first-order logic?

I’m afraid I don’t know what a CD system is. But as I said, my quibble is not with your use of S5, but there’s more than one way to set S5 up to deal with first-order logic (universal and existential quantifiers). Your particular way seems to be set up to require that the domain of individuals at each possible world in the Kripke frame must be the same. (Is this not the case? If not, what do you take to be the allowable Kripke frames?). And my quibble is, why not use a different logic with looser conditions than that? [Specifically, if you used Kripke’s Quantified Modal Logic, it is line 6 of your argument in #287 which would be invalid, the closest valid conclusion being instead AxEy(y = x)]

[QUOTE=Indistinguishable]

We must conclude that if it’s possible for Santa Claus to exist, then it’s necessary for Santa Claus to exist (and thus, if it’s at all possible for Santa Claus to exist, then Santa Claus really does exist). This strikes me as a ludicrous way to set things up. Do you really buy this?
[/QUOTE]

[QUOTE=Liberal]
No, I don’t. But the conclusion that you reached applies if and only if Santa Claus is defined as the supreme being, which does nothing but make Santa Claus a synonym for God, just like Dieux or Dios or Gott. We could also use the term Vegemite. Or cat breath. Or XJ-618Z. Or anything else we define the same way we define God. But that would introduce obfuscation.
[/QUOTE]

I’m afraid my mentioning Santa Claus may have been misleading here; I wasn’t intending to discuss God in this paragraph, but just your particular modal logic, which is set up to have possible existence imply necessary existence, and which I think is a silly way to set things up.

[QUOTE=Liberal]
I left out a part of that paragraph because the complexity of unravelling it and responding would exceed the time I have, but as to your direct question, Plantinga argues that S5 is the appropriate system because of the nature of S5 agents in epistemic logic. If we are to prove something about the ontological nature of a supreme being, then it is reasonable to employ a system in which that being is capable of mapping every implication of its existence. It is certainly unusual for an ordinary ontological agent to exist where it doesn’t exist, but such an ontological demand is called for in examining an agent that cannot not exist.

(Note that we could use the same system to argue epistemically for God’s omniscience as a knowledge agent Who knows what He does not know.)
[/QUOTE]

Again, I have no problems with using S5 (requiring of Kripke frames that the accessibility relation be an equivalence relation). But S5 only completely specifies a propositional modal logic. When you add in the first-order quantifiers, there’s more than one way to do it and still be called S5. Your way of dealing with the first-order quantifiers in S5 seems tenuous to me (puts a condition on Kripke frames that all worlds have the same individuals). And that’s what I’m asking you to justify, not the S5 part.

Just to make it really clear: There’s more than one system of first-order modal logic which can be said to be S5. Some of these will validate necessary existence, etc., and some will not. The particular one you’ve chosen seems implausible to me, and I ask you what is its justification over one of the others? (Here, from the Stanford Encyclopedia of Philosophy again, is an example of an S5 system spelled out in detail which does NOT prove the things I have a problem with)

[QUOTE=Liberal]
Well, there are versions of the MOP which do not use Becker’s postulate. For example, a five-step proof can be constructed using the theorem (G -> G) -> (<>G -> G) as a third premise, which seems reasonable to me but weakens the form (weak in the strictly formal sense of adding more axioms).
[/QUOTE]

I would find that a rather odd premise and would see no reason to grant it, whether for God or Horf, so, yes, the argument would be valid but I wouldn’t consider it sound. Indeed, I’d consider that premise to really be the source of where I think the ontological proofs find themselves based on an unwarranted assumption.

[QUOTE=Liberal]
I would like to add, for your edification, that although I’m flattered by your reference to me as a logician, I’m not. In fact, I’m barely formally educated beyond high school (one semester of college on two textile science scholarships). What I say carries no weight of authority whatsoever aside from the facts themselves. I am self-taught, having studied philosophy for almost forty years. What I’ve learned, I’ve learned by reading and by speaking with other knowledgable people. I am very aware of the shortcomings and pitfalls of autodidacticism. I have always disclaimed myself this way, and make no pretense about any qualifications.
[/QUOTE]

Well, as I must obligatorily note as a new poster, I’m a long-time lurker and have some knowledge of these things. But my reference to you as a logician was meant to be in the sense of your having a hobby of discussing formal logic, and my reference to us having “calm discussion as logicians” was in the sense of us conversing on formal objective logical matters, the way one might describe two people working out a math problem as “mathematicians”, in that situation, even if they have no professional training in the subject.

412

[QUOTE=the PC apeman]
Please flesh that out for me. It sounds like you are saying that we with our logic in our spoke cannot see the whole wheel. And further that other logic exists in other spokes and also applies to the whole. That would be saying the God and/or the supernatural isn’t defined by (our) logic. And that would make the proof meaningless.
[/quote]
Actually, it was in the context of subjective versus objective spirits that it was brought up, but it applies here as well because both are epistemic questions. All modal logics have certain “accessibility relations” by which they may be identified, and in this case our relation is called “Euclidean”. It means that if x has some relation to world W and y has some relation to world W, then x has some relation to y. If God is W, and you and I are x and y, then you and I have accessibility to one another but only through God. Just as an ant may crawl from one spoke to another, but only by transversing some portion of the hub. This is what Jesus was expressing when He said, “I am the way, the truth, and the light. No one comes to the Father except through me.” He was saying that He is the hub. He often used similar metaphors that are equally illustrative, such as “I am the vine, and you are the branches.” Same same.

Yes. It is a valid proof. The negation of the premise ripples throughout the proof and emerges as a negation of the actual existence of God. But there is no paradox. A flat plane geometry, for example, may be developed by holding to the premise that parallel lines do not intersect; but a curved plane geometry may be developed by negating the same premise. Such non-Euclidean geometries are useful for examining things like curved space, where pi does not describe the ratio between a circle’s diameter and its circumference.

Your “not” is misplaced. “It is not possible that perfection exists” is not the same as “it is possible that perfection does not exist”. You are negating the modal (which is premise 3), but premise (2) negates the term. See the difference? <>~G. ~<>G. ~<>G is an extremely daring premise on a footing equal to G (or ~<>~G). And especially given the coherent definition of God, ~<>G is practically gibberish.

In the meantime, I’ll just say that I’m flummoxed by that contradiction. Let’s look at this statement “Not adding ‘not’ is adding an entity”. It is an assignment function (from “is”). And so we have “Not adding ‘not’ = adding an entity”. The entity in question is “not”. And so by substitution, we have “Not adding ‘not’ = adding ‘not’”. Let A = “adding ‘not’”. Then, you are saying that A = Not A. That simply cannot be true.

As explained above, your red (2) does not match the blue (2).

I’m not sure what an “other possible material world” means since a materialist is bound by an empirical epistemology. If he cannot observe another world, then there isn’t one. That said, there are some pantheistic interpretations of the MOP. But they are logically suspect and full of frightful difficulties. Intuitionists rationalizing Platonic forms is among the most bewildering philosophical machinations ever conceived. Even as an atheist, I was struck by how weird it all seemed. And, with all due respect to SentientMeat, one can scarcely imagine a more mystical worldview than physicalism, where physical, it seems to me, means everything conceivable plus everything that isn’t.

413

Yes, sorry. My carelessness is a terrible obstacle. Obviously the substitution I intended to write was:

(1) It is possible that perfection exists.
(2) It is possible that perfection does not exist.

If picking exactly one is the most reasonable, then to me accepting (2) is the more reasonable as I expressed in the earlier post. We’re moving from the premises into the proof now. I’m sure I will not provide any new insight there that the likes of Hume, Kant, and Russell have not.

That you focused on this small throw-away option rather than the main tells me I’ve reached the end of your patience in examining the premises. I do thank you for the generous responses. I will remain an appreciative spectator as you engage the part of the argument that interests you most.

414

[QUOTE=the PC apeman]
I’m sure I will not provide any new insight there that the likes of Hume, Kant, and Russell have not.
[/QUOTE]
“All are lunatics, but he who can analyze his delusion is called a philosopher.” — Ambrose Bierce

415

[QUOTE=Indistinguishable]
Ah, my confusion. Sorry for continuing this hijack, then; perhaps you would prefer to discuss your modal arguments outside this thread, or in private correspondence?
[/quote]
I wasn’t complaining, just informing. You seemed to under the impression that that discussion was somehow pertinent to the discussion of the MOP.

Esse quam videri, I suppose. :slight_smile:

I think it is important at this point to examine our respective takes on the S5 system. We seem to interpret it differently. It caught my eye when you first sort of put aside the issue of what modal reference frame we’re dealing with. And then in your penultimate post, when it appeared that you wanted to foist the CD axiom onto S5 (let alone that you kept refering to it as “your system” as though I invented it or own it), I began to grow concerned. And now you have me in your mind advocating that the Eiffel Tower exists necessarily.

So if you don’t mind, we need to stop here until this is resolved. We can deal later with your proof sketch about possibility implying necessity. (Apparently, one or more steps are missing.) What exactly is your chief complaint or question, worded as clearly (and briefly) as you can?

416

Lib

I have tried to follow the logic for the MOP in this thread, but I find that little of it makes any intuitive sense at all. Perhaps I misunderstand the nature of a “possible” world. I would take that to mean any universe who’s description does not contain logical contradictions. So the empty universe - the universe with nothing in it - ought to be a possible universe since I cannot see how there could be a logical contradiction in it’s description. Since it by definition does not contain God, God must not be necessary, which I take to mean existing in all possible universes. Where do you disagree with this?

417

My understanding is that a possible world is a world with at least one truth bearer. An empty universe would have none.

418

This is new to me. Would an ordinary fallible human qualify as a truth bearer?

419

[QUOTE=Liberal]
My understanding is that a possible world is a world with at least one truth bearer. An empty universe would have none.
[/QUOTE]
Huh? What’s a “truth bearer”? A statement that is true? A conscious entity?

420

A truth bearer is a statement that is either true or false, but not neither and not both. My post to Truthpizza is inaccurate, by the way. A possible world must have at least one true statement, so the truth bearer would have to be true.