Would the logical axioms be true in all possible worlds?

No, I'm saying nothing can be reasonably said about god.

Would the logical axioms be true in all possible worlds? — Tom Storm

How could they not be? Where does the expression 'true in all possible worlds' come from? I think it is a reference to a priori truths. How could a world exist where A was not equal to A? Isn't it a necessary truth?

This is not my area but I am fairly sure I have heard people like Sean Carroll argue that the laws of physics would not necessarily apply in other worlds so why should the logical axioms? Or is that a whole separate line of thought?[/quote]

Logic is needed in order to have the discussion, not as a consequence of the discussion. The laws of physics are a result of the discussion. So they are not on a par with the laws of logic.

So introducing the notion of a priori and a posteriori truths will only serve to muddy the clarity of possible world interpretations.

This is not my area but I am fairly sure I have heard people like Sean Carroll and argue that the laws of physics would not necessarily apply in other worlds so why should the logical axioms — Tom Storm

Yeah, they do say that, but I think it's bullshit. They're simply figments of the mathematical imagination, they're not 'possible' in any real sense.

So introducing the notion of a priori and a posteriori truths will only serve to muddy the clarity of possible world interpretations. — Banno

I don't think so. I think the notion of the necessity of a first cause is a logical notion, not a postulation about 'something that may or may not exist'. Anyway, can't get bogged down in this, work to do elsewhere.

A being that necessarily exists cannot coherently be thought not to exist. And so God, as the unsurpassably perfect being, must have necessary existence—and therefore must exist. — Tom Storm

Many "proofs" are not presented this way. Anselm, for instance, presents the matter of what one could come up with on their own. The idea that there is a power beyond what we can imagine is said to be a factor. The argument has drawn many objections but the role of "necessity" is more of a question than an answer.

I think the notion of the necessity of a first cause is a logical notion, — Wayfarer

SO were is it located - in propositional logic? Predicate calculus? What could it mean to claim causation is a logical notion - that it is a variant on implication? DO you want to interpret p⊃q as "p causes q"?

Logic always starts with some axioms, like for instance the law of identity etc. What guarantees those principles? Why is it that A=A? Dumb question, it's like asking why 2 + 2 is 4. Simply is the case. Science itself doesn't explain why it has the laws it has, it simply discovers those laws as principles and works out how to exploit them. All of that order is assumed in speech and sought in the order of the cosmos. So the traditionalist understanding is that this order is grounded in the 'causal realm', which is where the idea of 'first cause' comes from.

I suspect that you're thinking of 'God' as 'some existing being', like a cosmic director or design engineer. If you think that such a God doesn't exist, then I definitely agree.

Ya I’m not really understanding why necessity entails all possible worlds. I dont see why we couldn't talk about possibilities of just the one we know about.
Ok, so this is about defining “necessity” as used by the religious folk as an argument for gods existence? And you are unsatisfied because you cannot quite articulate whats wrong with the arguments from necessity? Is that right?

Logic always starts with some axioms... — Wayfarer

Well, no, as those who began their training with Lemmon's Beginning logic will understand intuitively. A=A is assumed, because assuming A=~A leads to anything; and so is useless.

But yes, in order to be the subject to modal logic, I am taking god to be an individual. IF oyu have an alternative, set it out.

But yes, in order to be the subject to modal logic, I am taking god to be an individual. IF oyu have an alternative, set it out. — Banno

It's too big an issue to try and explain here. The very short version is, that you're denying what classical theologians would describe as 'theistic personalism', which is the idea of God as being a super-person. Terry Eagleton's review of The God Delusion, which got me interested in philosophy forums the first place, might be a useful primer.

Dawkins holds that the existence or non-existence of God is a scientific hypothesis which is open to rational demonstration. Christianity teaches that to claim that there is a God must be reasonable, but that this is not at all the same thing as faith. Believing in God, whatever Dawkins might think, is not like concluding that aliens or the tooth fairy exist. God is not a celestial super-object or divine UFO, about whose existence we must remain agnostic until all the evidence is in. Theologians do not believe that he is either inside or outside the universe, as Dawkins thinks they do. His transcendence and invisibility are part of what he is, which is not the case with the Loch Ness monster. This is not to say that religious people believe in a black hole, because they also consider that God has revealed himself: not, as Dawkins thinks, in the guise of a cosmic manufacturer even smarter than Dawkins himself (the New Testament has next to nothing to say about God as Creator), but for Christians at least, in the form of a reviled and murdered political criminal. The Jews of the so-called Old Testament had faith in God, but this does not mean that after debating the matter at a number of international conferences they decided to endorse the scientific hypothesis that there existed a supreme architect of the universe – even though, as Genesis reveals, they were of this opinion. They had faith in God in the sense that I have faith in you. They may well have been mistaken in their view; but they were not mistaken because their scientific hypothesis was unsound.

Dawkins speaks scoffingly of a personal God, as though it were entirely obvious exactly what this might mean. He seems to imagine God, if not exactly with a white beard, then at least as some kind of chap, however supersized. He asks how this chap can speak to billions of people simultaneously, which is rather like wondering why, if Tony Blair is an octopus, he has only two arms. For Judeo-Christianity, God is not a person in the sense that Al Gore arguably is. Nor is he a principle, an entity, or ‘existent’: in one sense of that word it would be perfectly coherent for religious types to claim that God does not in fact exist. He is, rather, the condition of possibility of any entity whatsoever, including ourselves. He is the answer to why there is something rather than nothing. God and the universe do not add up to two, any more than my envy and my left foot constitute a pair of objects. — Terry Eagleton, Lunging, Flailing, Mispunching

I’m not really understanding why necessity entails all possible worlds. — DingoJones

I can see that. Try "necessarily true" is defined as "true in all possible worlds". You are welcome to provide an alternate definition, but the logical systems that ensue form Kripke's account are particularly powerful, so it would be no small task if you would compete with them.

Put it this way: in possible world semantics it is possible to invoke a world that does not include a given individual. Hence there are no necessary individuals. (@Amalac - does that seem right to you? )

I haven't got time for all that reading. I'm just saying that if god can be represented as an individual, an "a", in a modal system, then he does not exist in all possible worlds.

But if he cannot be represented as an individual, then where does he fit?

Of course some theologian will argue that he is in some way special, but that's just special pleading - When logic shows the notion of god to be problematic, they claim that logic does not apply to god.

If there was a salient point in your quote, set it out.

The thread is here because I have the gut feeling that there must be something wrong with the argument in the OP; it's just too obvious. But I don't see what the eror is. — Banno

Necessity relates to possibility. Something is necessary if its negation is impossible, an a priori axiomatic logical truth, which needs no account of empirical domain.

Something is necessary if it is true in every possible world. — Banno

The proposition should read...it is true a thing is necessary if its negation is impossible. It follows that a god is necessary iff the non-existence of a god is impossible. If true the non-existence of god is possible, then the necessity of god is false. If true or false, where it is true or false, is irrelevant.

Piecea cake.

Did you think you added something to the conversation here? 'cause looks like what you did was re-state it without the possible worlds stuff.

. I'm just saying that if god can be represented as an individual, an "a", in a modal system, then he does not exist in all possible worlds.

But if he cannot be represented as an individual, then where does he fit? — Banno

Doesn't 'fit in' anywhere. You have a faulty idea of what you're criticizing, but explaining why is difficult in twitter posts.

explaining why is difficult in twitter posts. — Wayfarer

...or without quoting someone else, it seems.

If your point that, if there is a god, then he doesn't fit into our logic, then I'll agree with you; to be clear, I do not think that anything of much coherence can be said about god. That's rather the point of this thread - to see if there is a logic into which god might be forced.

I think the putative theist and I needsmust agree that god is beyond logic. While the theist will think this leads to worship, I think it leads only to silence.

That's quite different from @Bartricks view that god can contradict himself, which leads to everything and nothing.

Did you think you added something to the conversation here? — Banno

Don’t know, don’t care. I commented on the subject matter, which is enough.

Ill try that

I like Eagleton, even if he is a Marxist and a Christian. But Dawkins is attacking the literalists version of God. So that is exactly how they do conceive of God. There is a quote from Dawkins somewhere along the lines of - I am not a philosopher criticizing sophisticated forms of theology, I'm criticizing versions of God that cause the most harm and are most plentiful. I have Christian friends who think Dawkins is great at what he does.

I would agree with you that in the world of metaphysical speculation and higher consciousness posits, this version of God does not appear.

Oh, I see you've mentioned me. And gotten it all wrong, as ever. Do move aside, amateur!

First, let's crucify your opening argument:

God is supposed to be a necessary being. Something is necessary if it is true in every possible world.

There is a possible world in which god does not exist.

Hence, god is not a necessary being. — Banno

Well, the conclusion is true, but the argument is shit (it is circular). God is not a necessary being. I believe in God, but I'm not stupid. So I recognize that God, being all powerful, can destroy himself if he wishes. Thus he does not exist of necessity.

Some idiots - you know, the kind of people who confuse the metaphysical possibility of the law of non-contradiction being false with it actually being false - confuse existing with necessity with existing. God exists. But God does not exist of necessity as reflection on the concept reveals.

Your opening line - God is supposed to be a necessary being - is also false. God is an omnipotent, omniscient, omnibenevolent being. Some theists - idiot ones - think he exists of necessity and some - clever ones - think he doesn't. To make existing with necessity a defining feature is just to attack a straw man.

Now for your next line: There is a possible world in which god does not exist. That's no different from saying that God does not exist with necessity. That is, you are not inferring from it that God does not exist with necessity. You are just stating it in other words. To say that God does not exist in a possible world is one and the same as saying that God does not exist with necessity. And that's also your conclusion. Thus your argument is circular. You've said "God does not exist with necessity.....therefore God does not exist with necessity'.

To remedy matters you need to conclude that there is a possible world in which God does not exist. Presumably you'd have to go via some kind of conceivability claim - that it is conceivable that God does not exist, and as what's conceivable is a fairly reliable guide to what's metaphysically possible, there is a possible world in which God does not exist.

But that argument is relatively weak as the relationship between conceivability and metaphysical possibility is contested somewhat. Plus you'd no doubt reject similar arguments offered for, say, the immateriality of the mind (I can conceive of my mind existing apart from my body, thus it is metaphysically possible for it to....that would not be metaphysically possible if my mind was part of my body, thus my mind is not part of my body). (Note, I don't reject such arguments, I just don't think they're all that powerful, precisely because of the dubious nature of the relationship between conceivability and metaphysical possibility).

Anyway, your argument is circular as it stands.

But its conclusion is correct. Here's my much better argument, that is simple and decisive: God can do anything. Thus God can destroy himself. Thus God does not exist of necessity. Indeed, nothing does. If God exists, nothing exists of necessity. For God can destroy anything and everything at any time. Thus all things exist contingently.

And that also means that......the law of non-contradiction is contingently true (look - 'true'....it's 'true', not false), not necessarily true. It's 'true'. But it is not 'necessarily' true. True, but not necessarily true.

That's one you have difficulty with, isn't it. Ironically, if you think God exists and the law of non-contradiction is necessarily true, then you're involved in a contradiction (for you would be committed to affirming that God can do anything and not some things). To avoid a contradiction, one needs to conclude that if God exists, then all truths are contingent and thus the law of non-contradiction is contingently true.

Anyway, consider yourself lessoned.

Put it this way: in possible world semantics it is possible to invoke a world that does not include a given individual. Hence there are no necessary individuals. (@Amalac - does that seem right to you? ) — Banno

First of all, apologies for quoting philosophers here (since you said to Wayfarer that you haven't the time to read too much) but I thought I should give a somewhat detailed reply to this, and because the work of Kolakowski that I quote here (“If There is No God...”) deserves far more attention than it receives at present.

I take Leibniz's definition of a possible world, according to which a world is impossible if it contradicts the laws of logic, and possible otherwise.

So long as the states of affairs in which some individual does not exist do not involve a contradiction, then yes: nothing exists necessarily.

Hume summarized the idea that nothing exists necessarily (in all possible worlds) quite nicely:

...there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by any arguments a priori. Nothing is demonstrable, unless the contrary implies a contradiction. Nothing, that is distinctly conceivable, implies a contradiction. Whatever we conceive as existent, we can also conceive as non-existent. There is no being, therefore, whose non-existence implies a contradiction. Consequently there is no being, whose existence is demonstrable.

So those who hold that God is a necessary being/ exists necessarily would have to hold, it seems to me, that God's non-existence implies a logical contradiction.

There are, however, some propositions which could perhaps be both analytic and existential. Leszek Kolakowski gives as an example the proposition “something exists”:

However, we can look for an instantia crucis and ask if there is another example of judgment that combines these two properties — incompatible in terms of the conceptions of Kant and Hume—, that is, one that was analytic and existential in its content. A candidate for this impossible chimera is, I suspect, the judgment "something exists." The reason this judgment can be said to be analytic and therefore "necessary" is that its negation "nothing exists" is not only false, but also unintelligible and absurd: indeed, if there is something absurd, it is that. On that basis, one can argue that "something exists" is equal to "necessarily, something exists."

Wittgenstein made a somewhat similar point: “it is nonsense to say that I wonder at the existence of the world, because I cannot imagine it not existing”.

And so, Kolakowski says elsewhere, those who defend the ontological argument can argue in a similar way:

Thus, this argument (the ontological argument) could be expressed in another way by saying that if God is conceivable at all, he cannot not exist. This is how our contemporary defender of Saint Anselm, Charles Hartshorne, approaches the question; in his opinion, the ontological argument is perfectly reasonable if it is re-stated as a hypothetical judgment: "If God is possible, God is necessary." But is God conceivable under the assumption that to conceive him is to admit that his essence and his existence converge and, therefore, that he is a necessary being not only in the sense that he actually exists, eternally and immutably, but in the sense that it is inevitable that he exists, he is causa sui, so that his non-existence would be, as it were, an ontic contradiction?

Hopefully that helped clarify matters a bit.

A "necessary fact" is only true in (all) impossible worlds.

those who hold that God is a necessary being/ exists necessarily would have to hold, it seems to me, that God's non-existence implies a logical contradiction. — Amalac

Yep.

"If God is possible, God is necessary."

Again, that might be valid, but since there is a possible world in which god does not exist, it would follow that god is not possible.

It seems to me that "A necessary being exists" functions much like (P & ~P), in that if it is a consequence of an argument, then there is a problem with that argument.

I might have to drag out my modal logic texts in an effort to pars this.

I just thought Wayfare's quote was a bit too off-track, and would have preferred had he set out the point himself.

I'll return to this; but for now other duties call.

Anyway, consider yourself lessoned. — Bartricks

All you have shown is your confusion. But don't let me stop you. Pray, proceed.

But if he cannot be represented as an individual, then where does he fit?

Of course some theologian will argue that he is in some way special, but that's just special pleading - When logic shows the notion of god to be problematic, they claim that logic does not apply to god. — Banno

In alluding to your interchange with @Wayfarer so far:

I too find the OP's proposition is relative to what one interprets by the term “God”. If, for example, God is the ground of being, aka being-itself, then in what possible world would the ground of being, or being-itself, not be? (An absolute nonbeing, even if someone claims such a thing imaginable, does not constitute a world.) Again, in this example God is not "a being" but "being-itself" and, as such, is necessary in all possible worlds, and is furthermore beyond the principle of sufficient reason.

As to the common Abrahamic notion of God, where in God is "a being", He is omniscient, omnipotent, etc., and, thereby, was fully knowledgeable of and fully responsible for that serpent incident in the garden which He then got upset about, cursing everyone left and right. That self-contradictory God can well be envisioned absent from some worlds, much including the one we live in.

Do you mean that a necessary god is one that exist in every possible world? — Banno

I do not. I mean the necessary God must be so in any instance, so it cannot be subject to the action of existence to make it true over not. Therefore, the necessary God cannot exist. A necessary God cannot be put there by existing or not.

Ah, Tillich; something a bit new. The wiki article is not very helpful, and I'm not sufficiently intrigued to read systematic theology; can you direct me to something that will give me a better grasp of what it might be to be the ground of being?

But yes, I can see that something radical is needed to counter the criticisms here.