Now, suppose an individual is a member of a certain universe, of course that individual is not a member of certain other universes. So, yes, there is no individual that is a member of every universe. — TonesInDeepFreeze
Name one thing in modal logic literature that proved something in philosophy. — Gregory
To build a model, we set up a bunch of possible worlds. — Banno
Within that universe — Banno
"a" refers to some given individual. — Banno
In some possible worlds, "a" exists, in others, "a" does not exist — Banno
First order logic gets its content from non logic — Gregory
In some possible worlds, "a" exists, in others, "a" does not exist
— Banno
No, 'a' is a symbol, not an individual. For a given possible world, 'a' names a member of the universe of that possible world. And for any possible world, some member of the universe of that possible world is named by 'a'. — TonesInDeepFreeze
Now, suppose an individual is a member of a certain universe, of course that individual is not a member of certain other universes. So, yes, there is no individual that is a member of every universe.
— TonesInDeepFreeze
Hmm, but isn't that what the advocates of the modal ontological argument would reject? — Amalac
they argue that God, and God alone, is a member of all “universes” or “possible worlds” without exception. — Amalac
So the member of the universe named by "a" exists in some possible worlds but not others. — Banno
What I see as the problem with modal logic and the way many posters reason on this forum too is trying to use logic to prove something beyond itself. Proper philosophical intuition rarely considers logic as logic — Gregory
That strikes me as being an additional premise. Of course we can't rule out that additional premises have consequences. — TonesInDeepFreeze
The actual world is one among the possible worlds (this again follows in some systems of modal logic). If one admits that god exists in all possible worlds, that would imply that god exists in the actual world.
And so, if one accepts that it is possible that it is necessary that god exists in all possible worlds (meaning: in some possible worlds, necessarily God exists in all possible worlds), then it follows that in all possible worlds, god exists in all possible worlds, and therefore “god exists in all possible worlds” is true in the actual world, which is one of the possible worlds in which that statement is true, and therefore god exists in the actual world.
All this follows if one accepts system B of modal logic, from the corollary of axiom B (if the modal ontological argument is valid):
◇□X → X (If it is possible that it is necessary that X, then X is the case).
Likewise in system S5, the corollary of axiom 5:
◇□X → □X — Amalac
make the form of the syllogism of the understanding the basis and criterion that one might say not a single one of the metaphysical concepts could have arisen or stood on ground, if it had been subjected to the laws of logic. — Gregory
he does not allow the forms of syllogism to govern or encroach on the sphere of speculative philosophy — Gregory
Has modal logic always fail or has it proved something which takes logic to prove? — Gregory
logic is about proof — Gregory
I think they claim that follows from the definition of God, using corollary B or corollary 5. So it's not a premise, but rather something that follows from other premises (they say). — Amalac
...and must there be a number that exists in all universes?
The answer is "no"? — Banno
Now logic is about the forms of itself and can't comment on the inexperienced. — Gregory
You admit this! — Gregory
modal logic is just logic and much closer to programming than philosophy — Gregory
even if one accepted S5, the modal ontological argument would still have major problems, like dealing with the objection that existence is not a predicate or is a second order predicate, since that premise is required — Amalac
The argument would go something like this:
The actual world is one among the possible worlds — Amalac
(this again follows in some systems of modal logic) — Amalac
this again follows in some systems of modal logic — Amalac
you just say that E!(a), let's say, where 'a' refers to that individual, values true relative to every world W in the domain of worlds in your frame. — Snakes Alive
f there is some individual x identical to a in the domain of individuals, then there will be at any world, — Snakes Alive
On the other hand, you can make the domain relative to a world, such that at world w, there is an individual x identical to a, but at world w', there is no (because the domain associated with w includes a, while the domain of individuals associated with w' does not). — Snakes Alive
you are not forced to make existence necessary existence, but you can – you can just include a in the individual-domain of every world in your domain of worlds. — Snakes Alive
If you just have an existence predicate, E! — Snakes Alive
A logic that banned the necessary existence of an individual would have to make some special provision for how existence is interpreted, and why you could never have a domain of worlds such that an individual exists at every world. — Snakes Alive
What systems have that predicate? Is it definable in typical modal systems? What is the definition? — TonesInDeepFreeze
You can define any predicate you like — Snakes Alive
To make a predicate 'P' that is necessary for an individual a at a model, you just posit that the model you're working with is such that for all worlds w in the set of worlds W associated with the frame of the model, P(a) evaluates to true at w. — Snakes Alive
But necessity, on a Kripkean semantics, is not a matter of logical truth that generalizes over models – it's a matter of truth at all accessible worlds to some particular world, and if we have an accessibility relation on which every world is accessible from every other, then this is equivalent to truth at all worlds in that particular model. There is no impediment to supposing such a model. — Snakes Alive
Anyway, what you mentioned is a semantical. How would we express that as a formula in the modal logic itself? — TonesInDeepFreeze
So do the proofs you mention indeed first prove there exists a unique individual with such and such properties that is then named 'God'? — TonesInDeepFreeze
Especially, one can't just assert without proof that there does exist a unique individual having certain properties and then go on to demonstrate that that individual then has other properties for a QED. — TonesInDeepFreeze
But it would mean something like: Necessarily, there exists/is an x (God), such that a (the greatest conceivable being/ subject of all perfections) = x. — Amalac
How does a system of modal logic talk about its own semantics? I'm not saying it can't be done, but I'd like to know how it works. — TonesInDeepFreeze
How does a system of modal logic talk about its own semantics? I'm not saying it can't be done, but I'd like to know how it works.
— TonesInDeepFreeze
The corollary of axiom M states that A→◇A , so systems that have axiom M do consider the actual world as one of the possible worlds, since a possible world is simply a world, real or imagined, that does involve any contradictions, and so the actual world is one of them. — Amalac
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