Possibility != Existence

[Liberal]

Just a friendly reminder that the argument’s first premise is not to be taken as a general modal principle that p -> p. (I wouldn’t blame anyone for balking if it were.)

Rather, it is stating that the subject of the (Tisthammer) proof, G, where G = G, will be found to exist necessarily if it is found to exist in actuality. But at this stage of the proof, it has not yet been determined that G qua G exists at all, either actually or necessarily. There is no proof before the first premise that necessary existence itself even exists, and that’s why the first premise is necessary and is found in every version.

The first premise is nothing more than a compaction or restatement of the conclusion from the proof of necessary existence itself, where p = p in any arbitrary world, and where p -> p is the S4-Axiom. In other words, G -> G is a reduction of G -> G. To quote Stanford, “In S4, a string of operators of the same kind can be replaced for that operator…”. And that applies to S5 as well, of course.

Throughout the argument, until the conclusion, you could substitute G for G, since G is what G represents. There are some versions that show Brouwer’s Axiom, p -> <>p, in order to make the notion more obvious. (B added to S4 yields S5.) But Brouwer is really redundant in this case because this version invokes Becker (modal status, except for actuality, is always necessary) in the third premise, which should make it fairly plain what is going on with premise 1. Usually, versions that don’t use Becker do use Brouwer, and vice-versa.

It’s possible that that’s why some people have said that the proof “defines God into existence”. It isn’t always made plain what is meant by saying that premise 1 follows from the definition. It follows from the definition because, and only because, G -> G reduces to G -> G when G = G either by Brouwer or by Becker.

Regarding DJ’s point, I agree with him. This proof says nothing about the nature of God beyond the mere nature of His existence, i.e., that it is necessary. It assigns to God, as existence, a predicate that is also existence of a particular kind. Any consideration about God being Jehovah, of the divinity of Jesus, or that sort of thing is entirely outside the scope of the proof.

All that can be taken from the proof is that IF He is sentient, then He is perfectly sentient. And so on. Sorry for the interruption. Please carry on.

[MEBuckner]

*Originally posted by Libertarian *
Regarding DJ’s point, I agree with him. This proof says nothing about the nature of God beyond the mere nature of His existence, i.e., that it is necessary. It assigns to God, as existence, a predicate that is also existence of a particular kind. Any consideration about God being Jehovah, of the divinity of Jesus, or that sort of thing is entirely outside the scope of the proof.

All that can be taken from the proof is that IF He is sentient, then He is perfectly sentient. And so on. Sorry for the interruption. Please carry on.

Or “He” may not be sentient–I assume that this would include willful, conscious, and so forth–in which case a personal pronoun, let alone a capitalized one, is inappropriate. And I’m really not clear on this point: Can anyone say if this “Necessary Existence” created anything or designed anything or caused anything to be, or is that “outside the scope of the proof” as well?

Is something which is not sentient, which has no will and no consciousness, and which may or may not have caused anything to happen, in any meaningful sense of the word, God?

So it isn’t really a Proof of the Existence of God at all. It’s a Proof of the Existence of Something, Which May or May Not Be God.

Is there any way to connect any of this to “the everlasting Father, the Prince of Peace”, “the Word made flesh”,“the way, the truth, and the life”; “the Father, the Son, and the Holy Ghost”; the “All-Compassionate”, the “All-Merciful”, and “the Protecting Friend”; “the Creator”, “the Great Architect”, “Divine Providence”, or the One who “endows” us with “certain unalienable Rights”?

[Liberal]

I’m used to refering to God as He. Forgive me.

All that can be said about necessary existence ontologically is that it exists in every possible world. The proof attaches a predicate to God — God is defined, and then predicated, i.e., God exists as necessary existence. It speaks to the nature of his being in that it predicates Him to exist in every possible world, including the actual world, which is the final inference.

As with any proof, the final inference may then be taken forward as an axiom into other proofs, just as this proof began with an axiom that incorporated the final inference of the proof that necessary existence exists. But such a proof would no longer be ontological, but rather would be more broadly metaphysical since ontology deals only with the nature of existence.

Naturally, for those of us who already have an epistemic foundation for the Word made flesh, the ontological proof is merely one more piece of the body of evidence that convinces us intellectually of what we already know by faith. The materialist may take an entirely different direction with the conclusion, and many have done just that.

A pantheistic materialist interpretation is not unreasonable. The materialist may reasonably use the conclusion of this proof as an axiom to formulate an argument that the universe is eternal (since NE exists in every possible world, including an eternal one). However, because science is an epistemology that is applicable to the natural world, the materialist would have to consider scientific evidence, if any exists, that the universe is temporal to be in direct contradiction to his interpretation of the conclusion. In that case, he would have to reconsider some other interpretation, such as one that is panentheistic, deistic, theistic, etc.

When S5 logic is combined with KD, two binary relations emerge: reflexivity (for S5) and seriality (for KD). That gives us a sufficient frame to develop a temporal logic, where worlds are coordinates of time. In such a frame, temporal necessity () means “eternity”. A system can be constructed in which the M axiom holds: p -> p, meaning that eternal existence implies existence in the present.

So, basically the proof can be taken wherever you are capable of taking it. But this is the place to start.

[TVAA]

*Originally posted by Libertarian *
**All that can be said about necessary existence ontologically is that it exists in every possible world. The proof attaches a predicate to God — God is defined, and then predicated, i.e., God exists as necessary existence. It speaks to the nature of his being in that it predicates Him to exist in every possible world, including the actual world, which is the final inference.

** [sigh] It’s an error to say that something ‘exists’ in a possible world. You’re also confusing the ability to conceive of a concept and that concept’s possibility.

**The materialist may reasonably use the conclusion of this proof as an axiom to formulate an argument that the universe is eternal (since NE exists in every possible world, including an eternal one).

** Who says that there are any eternal worlds, possible or otherwise?

[Liberal]

As I just finished explaining, I (we, you, anybody) can add a serial frame to the reflexive frame of S5 and develop a temporal logic wherein temporal necessity () can be shown to be true. In fact, Aquinas’ Third Way argument can then be modalized, and presented as a proof of God’s existence (or the existence of eternity) using temporal logic.

[dalovindj]

Is something which is not sentient, which has no will and no consciousness, and which may or may not have caused anything to happen, in any meaningful sense of the word, God?

Perfect. So what we’ve proven isn’t the classic “definition” (aware creator), simply that somthing is necessary for existence.

We still don’t know if there is a God. Now, I’m using the laymans defintion of God. You know, bringing the word back to the meaning of an aware being that willfully creates everything. That is the real mystery. It is, alas, still unsolved. Not nough evidence either way. But stay tuned. I hear the guys at MIT are working on a god detector.

DaLovin’ Dj

[Left_Hand_of_Dorkness]

*Originally posted by Libertarian *
** This proof says nothing about the nature of God beyond the mere nature of His existence, i.e., that it is necessary. **

I disagree with this. There are two problems, as far as I can tell, with the proof:

1. It excludes one of the logical evaluations of modal logic, i.e., that an entity is contingent, in the defintion, thereby making the entity in question unable to be evaluated by modal logic; and
2. It defines “God” in such a way that God’s only characteristics are ones that cannot be evaluated by a logical system (i.e., God has no positive modifiers, and therefore can only be described in “transcendental” terms, terms that have no meaning within a logical system). His God is therefore, within a logical system, indistinguishable from nothingness.

Elsewhere, I’ve addressed #1. Here, I want to expand problem #2.

First, I want to say that I’m arguing specifically against McHugh’s formulation of the ontological argument, available here, for those of you that have not read it yet. To recap, McHugh is trying to modify the ontological argument in order to avoid two objections raised against it (I will assign them letters, rather than numbers, so that I can refer to them below as separate from my objections to McHugh’s reformulations):
a) “God” is a contradictory entity: for example, no entity may both be immutable and omniscient. “God” is therefore logically impossible.
b) “God” may equally be a nefarious being as a good being: the God whose existence is “proved” by the ontological argument could be a being of perfect hatred. He could also be a being of perfect Giraffeness, as far as that’s concerned.

McHugh comes up with a novel way to avoid these two problems: he defines God as " that to which no positive descriptive term can be applied." Then he lists a number of terms that must be applied to God (since these terms signal the absence of positive descriptors): “non-contingent, non-finite, non-spatial, non-temporal, not dependent on anything else, etc.”

Notice that he slipped “non-contingent” in there with the other terms. Notice my first objection to his proof above. But that’s a matter for another post. For now, we’ll grant him his definition.

This brings us back to my quote from Libertarian, above. The God that McHugh defines is non-spatial, non-temporal, etc. I believe that “etc.” MUST include MANY facts about the nature of God, giving us a great deal of information about McHugh’s God.

The sentience of McHugh’s God is not indeterminate: because “sentient” is a positive descriptive term, McHugh’s God MUST be non-sentient.

Similarly, we can determine whether McHugh’s God is loving: because loving is a positive descriptive term, we know that McHugh’s God is non-loving.

Knowing, present, powerful, caring – these are all positive descriptive terms. We know that the God defined by McHugh is none of these things.

It is possible, of course, to re-reformulate McHugh’s definition of God in order to allow an all-loving, all-powerful, all-knowing, omnipresent entity. What is unclear, however, is how you would create this definition while excluding an all-hating, all-destroying entity. In other words, how would you define God so as to avoid my criticism B without returning to the Professor Martin’s criticism 2?

Scott, if you’re looking for something to address, I’d love to see this addressed. I think this, my second objection to McHugh, is stronger than my first objection.

Daniel

[erislover]

*Originally posted by Libertarian *
Just a friendly reminder that the argument’s first premise is not to be taken as a general modal principle that p -> p. (I wouldn’t blame anyone for balking if it were.)

I don’t take it as a general modal principle, but it is part of the hypothesis in this particular proof.

[Czarcasm]

You might take it that if That Which We Call God For Want Of A Better Term is sentient, it is perfectly sentient. If, on the other hand, it is non-sentient then it is perfectly non-sentient. Thus we have a formula to determine the stupidest thing in the universe. It would make a box of rocks seem Einsteinian by comparison.

[Left_Hand_of_Dorkness]

Czarcasm, I know that’s a simulpost and all, but McHugh’s TWWCGFWOABT cannot be sentient: by definition, it is that to which no positive descriptive term can be applied. It’s definitely dumber than a box of rocks.

Daniel

[Left_Hand_of_Dorkness]

“Dumber than a box of rocks,” of course, being a negative descriptive term.

[Liberal]

Daniel

Why are you stuck on McHugh? If you don’t like McHugh, then use Suber, or Tisthammer, or Dougherty, or Hartshorne, or… write your own!

Czarcasm, I know that’s a simulpost and all, but McHugh’s TWWCGFWOABT cannot be sentient: by definition, it is that to which no positive descriptive term can be applied. It’s definitely dumber than a box of rocks.

That’s incorrect. The definition simply means that God is not dependent on sentience. It does not mean that He cannot be sentient.

Eris

I don’t take it as a general modal principle, but it is part of the hypothesis in this particular proof.

Rather, it is stating that the subject of the (Tisthammer) proof, G, where G = G, will be found to exist necessarily if it is found to exist in actuality. But at this stage of the proof, it has not yet been determined that G qua G exists at all, either actually or necessarily. There is no proof before the first premise that necessary existence itself even exists, and that’s why the first premise is necessary and is found in every version.

The first premise is nothing more than a compaction or restatement of the conclusion from the proof of necessary existence itself, where p = p in any arbitrary world, and where p → p is the S4-Axiom. In other words, G → G is a reduction of G → G. To quote Stanford, “In S4, a string of operators of the same kind can be replaced for that operator…”. And that applies to S5 as well, of course.

Throughout the argument, until the conclusion, you could substitute G for G, since G is what G represents. There are some versions that show Brouwer’s Axiom, p -> <>p, in order to make the notion more obvious. (B added to S4 yields S5.) But Brouwer is really redundant in this case because this version invokes Becker (modal status, except for actuality, is always necessary) in the third premise, which should make it fairly plain what is going on with premise 1. Usually, versions that don’t use Becker do use Brouwer, and vice-versa.

It’s possible that that’s why some people have said that the proof “defines God into existence”. It isn’t always made plain what is meant by saying that premise 1 follows from the definition. It follows from the definition because, and only because, G -> G reduces to G -> G when G = G either by Brouwer or by Becker.

[Liberal]

In other words, he is not bounded by sentience.

[Left_Hand_of_Dorkness]

*Originally posted by Libertarian *
**Daniel

Why are you stuck on McHugh? If you don’t like McHugh, then use Suber, or Tisthammer, or Dougherty, or Hartshorne, or… write your own!

That’s incorrect. The definition simply means that God is not dependent on sentience. It does not mean that He cannot be sentient.
**

Two points. First, I’m stuck on McHugh because it’s useful to consider one proof, and either accept it or discard it, at a time. I’d like to figure out whether or not McHugh’s answer to the traditional flaws in the ontological argument is valid, before we move onto a different reformulation. If everyone agrees that McHugh’s reformulation doesn’t hold water, then I’m glad to move on.

As for your second point to me, that McHugh’s defintion simply means that God is not dependent on sentience, I don’t see where you get that from. He clearly states that “no positive descriptive term CAN be applied” to God. Presumably, if he’d meant that “no positive descriptive term NEEDS TO BE applied” to God, he would have said so. As it is, the positive descriptive term “sentient” CANNOT be applied to McHugh’s God.

Of course, one could reformulate McHugh’s definition of God by substituting “needs to be” for “can”. Let me repeat myself, though:

It is possible, of course, to re-reformulate McHugh’s definition of God in order to allow an all-loving, all-powerful, all-knowing, omnipresent entity. What is unclear, however, is how you would create this definition while excluding an all-hating, all-destroying entity. In other words, how would you define God so as to avoid my criticism B without returning to the Professor Martin’s criticism 2?

Daniel

[Czarcasm]

It doesn’t seem as if he(for want of a much -needed vaguer term) is bound by much of anything, does it? Is this really something you’d want to worship?

[Left_Hand_of_Dorkness]

*Originally posted by Libertarian *
**In other words, he is not bounded by sentience. **

Aha! A post that I agree with entirely (in words, if not in spirit).

Inasmuch as McHugh’s God is properly described as non-temproal, non-spatial, non-blue, and non-sentient, it is not bounded by sentience.

Daniel

[Liberal]

Czar

It doesn’t seem as if he(for want of a much -needed vaguer term) is bound by much of anything, does it? Is this really something you’d want to worship?

Not necessarily. The only reason I worship the God that I do is because He values goodness above any other aesthetic. If He didn’t, I wouldn’t worship Him.

Daniel

It is the ordinary meaning negative descriptive term, and McHugh himself spells it out: "Since no positively conceived descriptive term can be applied to God, “He"must be considered to be non-contingent, non-finite, non-spatial, non-temporal, not dependent on anything else, etc.” Not dependent on anything is what not contingent means.

[Left_Hand_of_Dorkness]

A side-note:

It occurred to me that McHugh describes his God as non-hot, and I got to thinking. “Cold” is defined as an absence of temperature, essentially equivalent to non-hot, right? And absolute zero is the absolute absence of heat, right? And I have a vague memory of reading somewhere that absolute zero doesn’t exist in our universe, that if any spot reached absolute zero, theoretical physics suggests that it might cause the universe to collapse upon itself.

You see where I’m going with this.

I was thinking that a God to which no positive modifiers could be applied must be absolutely non-hot – must be, in other words, at absolute zero. Such a God would collapse any universe in which it existed, and therefore the existence of the universe disproves the existence of McHugh’s God.

Cool.

I was wrong, though. Temperature is a concept that can only be applied to being with a material existence, and we know that McHugh’s God is non-material. My disproof of God doesn’t work.

It was a fun idea, though :D.

Daniel

[Left_Hand_of_Dorkness]

*Originally posted by Libertarian *
**Czar

Daniel

It is the ordinary meaning negative descriptive term, and McHugh himself spells it out: "Since no positively conceived descriptive term can be applied to God, “He"must be considered to be non-contingent, non-finite, non-spatial, non-temporal, not dependent on anything else, etc.” Not dependent on anything is what not contingent means. **

I know what not dependent on anything else means: this is my first objection to McHugh’s proof.

If it meant what you suggest it means, then McHugh’s god wouldn’t be dependent on not being omniscient, right? wouldn’t be dependent on being non-temporal, right? Wouldn’t be dependent on being non-changing, right?

But as we know, an entity which is both unchanging and omniscient is logically impossible. Furthermore, a God that is not dependent on being good is also not dependent on being evil. This is why McHugh doesn’t set his God up this way.

It’s not that his God is dependent on being sentient: his God is DEFINED as being non-sentient. These are two different things: sentience and contingency are (according to McHugh) both positive descriptive modifiers (although he mentions the second as a descriptive modfier, I think the first is much more clearly a descriptive modifier).

Daniel

[Liberal]

Respectfully, we just have to disagree here, Daniel. That just isn’t my understanding of what is meant by negative descriptors, and until I see documentation to the contrary, I have to assume that McHugh is merely speaking of a logical frame that is free from contradiction. Saying that God is not dependent on anything is just another way of saying that He is not contingent, and not contingent means necessary.