Necessary existence is existence in all possible worlds. To say that God exists necessarily is to say that God cannot not exist.
Thanks for your kind mercy. 
What’s the utility or purpose of the definition, then?
‘God’ and "Supreme Being’.
Why must ‘God’ be ‘Supreme Being’ unless it is already a tautology by definition?
Yes, I got the difference in form of the argument, but they say the same thing. If not this, then that.
The reason that (7) still seems fallacious is because only by definition, it holds. Coming to your definition, God = Supreme Being = Ontological Perfection = Existence in all possible worlds. Are we talking about Everett-style worlds? What’s all “possible” worlds, and why do we need to talk about more than one i.e. ours?
Now talking outside the proof, since you admit that the universe could be God, I fail to see just what new information does this proof provide?
The same as for any definition — to contextualize or give meaning to the terms under discussion. Suppose, for example, that we want to talk about “force”. Without a definition, I won’t know whether you’re talking about legal validity (as in the force of law), coercion (as in political philosophy), capacity to do work (as in mass times acceleration), baseball (as in forced play), and so on. It is always good practice to preceed proofs with coherent definitions, although necessarily (for obvious reasons) some terms must be left undefined.
A tautology is a vacuous statement that, owing to its construction, cannot be false. I don’t understand your usage of the term in this context. There is nothing suspect or strange about God qua Supreme Being.
Again, they do not say the same thing. One is an implication; the other is not. To progress, it would behoove you to get beyond that hurdle.
No, 7 doesn’t hold by definition. It holds by modus ponens, as I explained in quite some detail. I do not mind covering these basics even in detail, but *repeatedly * covering them and, of all things, defending them as though they were something new or strange — well, I’m just not going to do that. The rules of logic are available on the Internet for you to peruse if you do not trust what I tell you. But we cannot proceed if you intend to deny that a modus ponens is a modus ponens or that an implication is the same as a disjunction.
Because our argument would be a petitio principii if we assumed God’s existence in the actual world before it emerged by wiff. That’s a no-no. A “world” is any truth or set of truths.
You have mischaracterized what I said. Perhaps I was mistaken that you value precision. The universe is God if and only if the universe is eternal; otherwise, there is truth outside it. But if the universe is God (i.e., exists necessarily), then science is an inadequate epistemology with which to study it.
Your statement says: It must be the case that if God exists, then He is the Supreme Being. Isn’t this statement inherent from the definition, or is the definition imported only at this stage? In which case, the ‘God’ in statement 1 is not the supreme being.
What I meant was the MP applies only because your definition is defined as it is.
Well, science can’t get rid of uncertainty, so that’s a fair conclusion.
just for kicks, disjunctions and implications can say the same thing. for example:
p -> q <-> ~p v q
so, if we define P and Q such that:
P = ~G
Q = ~G
we have:
- P -> Q
- ~P v Q
so, in fact, they do say the same thing. unless i’ve made some sort of transcription error.
To be precise, what I meant was that 3 and 6 leave me with the same alternatives.
I’m disregarding the process or its validity.
It is possible there is just a terminology problem here.
"Material implication is easily confused with the meta-concept of semantic consequence; when material implication is used, semantic consequence is often what is intended. To avoid this confusion, use the logically equivalent ¬A∨B instead of A→B, and if ¬A∨B does not seem right, consider using the meta-operation of semantic consequence instead. "
Either we need to use the term “logically equivalent” from propositional logic rules instead of “they say the same thing”, or in modal logic those two statements are not logically equivalent.
Liberal?
It’s the necessity of the entire proposition that is pertinent. “It must be the case that…”. If we said simply G -> G, then our accessibility relation would be quasi-symmetric. Since our accessibility relation is reflexive and Euclidean, we have to modalize the entire proposition.
The MP has nothing to do with the definition. It has to do with the two cited propositions.
Agreed. Science doesn’t prove anything true. It only proves things false. That’s why it’s useless as an epistemology for analytic systems (such as an eternal universe).
Oy. What a semantic consequence is depends on what system of logic you’re using. For propositional logic, q is a semantic consequence of p if and only if there is no interpretation in which q is true and p is false — in other words whatever models p models q. But in predicate logic, q is a semantic consequence of p if and only if p is always satisfied when q is satisfied. (Satisfied as in true for some sequence in some domain.) Modal logic is a Kripke system, and therefore propositional. With respect to material implication, in modal logic you must be careful about how your modalities are associated with what. The problem is that negation is a unary operator, and a modal statement is complex. (There is the modality, the proposition, and the whole: e.g., does ~G mean (~)G or ~(G)?) The former means that it is not necessary that God exists in actuality, whereas the latter means that it is not the case that God exists necessarily. Likewise, there is a difference between ~G (it is not necessary that God exists) and ~G (it is necessary that God does not exist). The negation of ~G qua ~(G) is G. The negation of ~G qua is <>G. In premise 3, the negation is of the modality, not of the proposition. Failure to derive the disjunction via the excluded middle would create ambiguity, and we would be here arguing about whether we had negated or G. Hence, statement 5. All that said, a disjunction is still not an implication anymore than an implication is its contrapositive, despite that both are true and form a tautology when combined.
The sleight of hand, I believe, is in steps 1 and 2. There is a claim that God has the possibility of existence by induction. However, if the definition of God includes a paradox of necessity, then it might be the case that it is not possible for God to exist, and the proof fails.
How can we say that the definition of god involves a contradiction? Let’s look at the concept of Supreme Being. There is an assumption here that there is an ordering of properties such that you can always tell if an entity with one set is greater than an entity with another set. If this is true, it is meaningful to describe a Supreme Being, and the proof works. However if there are properties where supremacy in one implies non-supremacy in another, then there is no such thing as a Supreme Being. Graphically, consider two strands rising up, with a vertex on each that is greater than anything below it, but no vertex greater than both, a partial ordering in other words.
Does God contain such a contradiction? Omnipotence and Omniscience is a certainly possible one, which has been described over and over again. Now, it has been claimed that it is meaningless to compare these attributes, which is indeed the point. It is possible for an entity to be omnipotent, but not omniscient. It is possible for an entity to be omniscient, but not omnipotent. It is possible for to be one of each - or is it? But it is arguably not possible for one entity to contain both attributes. Since we cannot claim that an omnipotent entity is greater than an omniscient one, and vice versa, there is no supreme being, and the proof fails.
There might be other mutually contradictory attributes also. But unless you can prove that there are none, you can’t sneak in Supreme Being as a possibly existent entity.
And thanks, Lib, for repeating the proof.
You’re welcome, Voyager. As always, I’m glad you’ve joined the discussion. With respect to your comments, the proof deals only with the nature of being. The supremacy here is supremacy of existence only — in other words, there is no greater existence possible than existence in every possible world. Other attributes are not examined by this proof (but may be examined by other means in other ways.) Here is some information about existence. Of particular interest is the notion of existence as an individuator, contrary to Kant’s famous assertion that existence is not a predicate.
I should have said “objections” rather than “comments”. My own problems with the proof is pretty much the same as SentientMeat’s, namely the opinionlike quality of words like “supreme” (in what objective way is something existing more supreme than something that doesn’t?) and that the only thing you really can say about “God” is that it exists and must exist, which leads us neatly back to my first post in this thread.
Yes, but you could get out of having to explain yourself forty ways from Sunday by not using the word “God” to start with. You must see that, at least here and now, it is a barrier to communication, not a facilitator of it.
Yes, my apologies for forgetting that this was what you meant by supremacy. My response, if I remember it, was that a slime mold existing in all possible worlds would have the attributes of godhood by your definition.
I was about to say that this is spurious, since slime molds have finite existence and gods do not. However your link seems to support the idea that slime molds and Socrates have existence not connected to time. I think part of the problem is the confusion of conflating the tag “Socrates” with the person Socrates, which leads some mentioned in the article to claim that saying “Socrates is nonexistent” has problems. There is no problem if you accept the Socrates the tag exists even if Socrates the object does not. Even the strongest atheist agrees that God the tag exists even if God the “object” does not. Quotes used to show I am not assuming God is phyical in any sense.
One thing I was hoping to get from the link, which I did not, was whether God is the same in all possible worlds - that is, can communicate between them. If not, then a string, (if such exists) the basis of all reality is necessarily existent, by definition, in all worlds. Any thoughts on this?
Another problem is that Lib’s use of supreme is nonexclusive. While the traditional supreme being is singular, more than one entity might be existent in all possible worlds. Entity 1 might be able to clean the clock of entity 2, but by this definition of supreme they are both gods.
And of course we have the relevance problem, since I kind of missed the connection between necessary existence and love. A deistic god certainly fits the definition.
I very much respect Sentient’s objections to the proof. I do not agree with them, but due to our ability to communicate well with one another, I understand his position and he understands mine. In fact, I would be completely comfortable with him arguing my case on my behalf because I know that he would argue it honestly and earnestly. He probably would argue it better than I do.
This argument has been presented now for decades. It is not the case that I have pulled a rabbit out of a hat. I am doing my best to answer questions from people unfamiliar with late 20th century advances in philosophy, but some of the complaints are from people who know full well what is going on and what is meant. It is too late for you to put a cork back on the bottle. God qua necessary existence is out there. Kant’s views on existence have been debunked. You must deal with what is before you.
I don’t recall the particular discussion, but if that was your response, then my reply would have been something like this: you’re right.
As Nietzsche said, “I’m afraid we’ll not get rid of God until we get rid of grammar.”
The accessibility relation of the Modal Axiom (invoked in the proof) is reflexive: wRw. The accessibility relation of S5, the system of logic used by the proof, is Euclidean: (wRv&wRu) -> vRu. What that means in plain English is that God is accessible in all worlds and from one world to another. Note that this does not mean that perceptions of God would necessarily be the same in one world as another. Necessary existence, of course, is contingent on nothing. But the perception from each world is contingent on rules of that world. So, for example, in a world in which possible necessity implies necessary possibility, i.e., <>G -> <>G, the perception of God would be convergent, i.e., wRv&wRx -> Eu(vRu&xRu).
Not so. Refer to the proof that necessary existence is true, and consider the Identity Axiom: x=x. There cannot be a y such that y=x and y≠x. Put another way, if A is A, then there cannot be some other A such that A is not the same as A. In an ontological context, only one existence is necessary. In a modal context, A -> A — and in fact, that is the S4 Axiom.
Can I try and put Lib’s proof into my own words, just so Lib et al can tell me if I’m getting the idea right.
1 ~~G = <>G : it is possible that G exists : There is a possible world where G exists
2 (G -> G) : Given G is defined as supreme being, if G exists in any possible world, then that G is supreme being of all possible worlds
So
1 says G exists in a possible world
2 says if G exists in a possible world, then G is the supremem being of all possible worlds, hence including this possible world in which we exist.
So G is the supremem being in this world, ergo G is God and exists.
Arguments 3 to 9 are all logical verifyable steps, and 1 and 2 are the only arguable statements.
There is no doubt in my mind that the universe exists and we are discovering scientifically and constantly that which has been in existence for billions of years.
My definition of God is that which existed at the very beginning.
I am an atheist only in that I do not see or understand why this creator has to automatically be endowed with loving, caring and the like.
A theist, I believe, believes that love, prayer listening and response are part and parcel of God. I don’t.