Not in this world necessarily though so who cares?

Not in this world necessarily though so who cares? — khaled

How do you know?

your argument isn’t world specific. So you haven’t said anything about the existence of God in this world which is what people care about. That’s how I know that he doesn’t exist necessarily in this world, from your argument at least.

Also I disagree with premise 2.

2. If something is possible then there is a world in which that something is real. — TheMadFool

“Possible” means can exist in a possible world. Not actually exists in some world.

“Possible” means can exist in a possible world. Not actually exists in some world. — khaled

I disagree.

If I say an argument is invalid it means there's a world in which all the premises are true and the conclusion is false. — TheMadFool

1. It is possible that God exists.

2. If something is possible then there is a world in which that something is real.

Ergo,

3. God exists. — TheMadFool

(1) reads "there is a possible world in which god exists"

SO yes, god exists in some possible world; but that possible world need not be the actual world.

The argument does not show that god exists in our world.

Moreover, god is usual take as necessarily existing - that it is not possible that god not exist; or that god exists in all possible worlds.

You don’t need to agree with that one. The first critique doesn’t talk about any of the premises but the scope of the argument. The “God exists” that you came up with isn’t the “God exists” that people care about.

If I say an argument is invalid it means there's a world in which all the premises are true and the conclusion is false. — TheMadFool

Eh? Invalid: illicit major, illicit minor, negative premise, negative premises, undistributed middle, four terms. Maybe I forgot some - or not. Anyway, validity has to do with the form of the argument, not whether premises or conclusion are true or false. If the form is good (valid) and premises and conclusion true, then the argument is sound.

As to a world in which an invalid argument may have true premises and a false conclusion, this one right here is as far as you have to look.

Top marks for total inconsistency.

If Bartricks says it, it's false.

But elsewhere, Banno may say it and there it is true.

Are you being thick, or do you not care about consistency?

There's a possible world in which a contradiction is true. Doesn't mean any are true in the actual world, does it?

There's a possible world in which a contradiction is true. — Bartricks

Possible worlds that include contradictions are called impossible worlds.

But what is really delightful is that you say both that you care about contradiction and that there are possible worlds with contradictions in them.

I don't see how that the idea of possibility in itself makes something 'real', because all it suggests is some remote chance rather than something definite. I am not sure how the concept of such a logical possibility would be of any use to anyone because those who adopt a belief in God are mainly interested in a being who they can relate to on a personal level rather than as a remote possibility.

Update

To all the above posters:

If a world x is possible but world x is not actual is acceptable then there's something not possible about an actual world.

1. World x is possible & World x is not actual (true according to all the posters above)

Ergo,

World x is actual can't be consistent with world x is possible. After all, world x is actual is the negation of world x is not actual.

A way out:

All possible worlds are actual worlds.

, something's a bit off. By "the actual world" we normally just mean our world.

All possible worlds are actual worlds. — TheMadFool

With this (I think) you're moving towards modal realism, which means that all possible worlds are real, like our's is real.

A possible world need not be real, just possible, or let's say a self-consistent whole, if you will, even if hypothetical/imaginary/fictional.

What's bothering me is the claim that the following statement is true:

1. X is a possible world & X is not an actual world.

If 1 is true then the following statement should be false:

2. X is a possible world & X is an actual world.

and even this should be false:

3. X is an impossible world & X is not an actual world.

Possible worlds that include contradictions are called impossible worlds. — Banno

Question begging. Nothing is impossible.
Anyway, call them what you like - I have no idea what a possible world is anyway - my point is that it is not necessarily true that there are no true contradictions, it is just true. Around and around we go.

, instead of "an actual world", I'd use "the actual world", but maybe that's just me?

1. X is a possible world ∧ X is not the actual world = X is a possible world but not our's

Say, one where Napoleon drowned by suicide. At least that seems possible.

2. X is a possible world ∧ X is the actual world = X is our world

Or, instead of "an actual world", we could use "a real world", i.e. not fictional or merely imagined, despite being unknown to us.

1. X is a possible world ∧ X is not real = a possible world but imaginary/fictional

2. X is a possible world ∧ X is real = our world or another real world (unknown to us)

(Technically, there's a presumption that our world is a self-consistent whole, but that doesn't seem controversial; either way, the possible world semantics, I think, is intended to allow reasoning that includes our world, the actual world.)

If that makes any sense...

Yep.

@TheMadFool, the actual world is, after all, possible.

1. World x is possible & World x is not actual (true according to all the posters above) — TheMadFool

I don't think anyone said this. What was said was: If world X is possible, that doesn't imply it's actual.

Ergo,

World x is actual can't be consistent with world x is possible. After all, world x is actual is the negation of world x is not actual. — TheMadFool

But this doesn't follow from either "world X is possible and not actual" or "If world X is possible, that doesn't imply it's actual"

A possible world need not be real, just possible, or let's say a self-consistent whole, if you will, even if hypothetical/imaginary/fictional. — jorndoe

:up:

"God" is undefined, therefore the argument is invalid.

Again, this depends on what is meant by 'God'. Define it and it is possible. Don't define it and it is meaningless.

It really is that simply (or complex).

I do actually have a definition of god though. I think most other people would call it 'me' though and dismiss themselves as ever inhabiting even an iota of godhood.

I'm not happy to say I am god but I am aware of its truth nevertheless.

To all

Suppose X is a possible world and is not actual.

Ergo, the following statement is true.

1. X is possible & X is not actual

If so, the statement

2. X is possible & X is actual

has to be false because X is not actual (X is actual is false)

But then look at 2. It says something odd: X is possible and actual is false.

If I say an argument is invalid it means there's a world in which all the premises are true and the conclusion is false. — TheMadFool

Already here you make a mistake. There exists a logic for which this doesn't necessarily hold. Even necessity looses it's usual meaning in this logic.

Suppose X is a possible world and is not actual.

Ergo, the following statement is true.

1. X is possible & X is not actual

If so, the statement

2. X is possible & X is actual

has to be false because X is not actual (X is actual is false)

But then look at 2. It says something odd: X is possible and actual is false. — TheMadFool

Obviously it says that because we established from the first line that X is possible and not actual. If we are talking about this world, well it's possible and actual.

The only way I can imagine you thinking this is odd is if you generalize X. As in, given a world, X, the above follows. But it doesn't follow, because if you generalize X you can't say that X is possible and not actual.

instead of "an actual world", I'd use "the actual world", but maybe that's just me?

1. X is a possible world ∧ X is not the actual world = X is a possible world but not our's

Say, one where Napoleon drowned by suicide. At least that seems possible.

2. X is a possible world ∧ X is the actual world = X is our world

Or, instead of "an actual world", we could use "a real world", i.e. not fictional or merely imagined, despite being unknown to us.

1. X is a possible world ∧ X is not real = a possible world but imaginary/fictional

2. X is a possible world ∧ X is real = our world or another real world (unknown to us)

(Technically, there's a presumption that our world is a self-consistent whole, but that doesn't seem controversial; either way, the possible world semantics, I think, is intended to allow reasoning that includes our world, the actual world.)

If that makes any sense... — jorndoe

:ok:

I'm mainly interested in what follows from the claim that a possible world need not be actual.

Suppose X is a possible world and that's all we know.

Then the following is true:

1. X is possible & X is not actual.

I'm working with my intuition here so bear with me.

I conclude from 1 that there's something not actual about possible. In other words, there's a gap between the possible and the actual.

How come then that when the poles are reversed, there's a connectionn the gap I mentioned above is bridged, as in if X is actual then X is possible

Summary:

1. If X is possible then X is actual (False i.e. there's a gap between possible and actual)

2. If X is actual then X is possible (True? What happened to the gap mentioned above?)

a possible world need not be actual. — TheMadFool

So P does not lead to A.

Suppose X is a possible world and that's all we know. — TheMadFool

X is P

1. X is possible & X is not actual. — TheMadFool

Thus X is P and !A? That doesn't follow. I think you're confusing "P does not lead to A" with "P leads to !A". With the latter it makes sense, but no one claimed that.

1. If X is possible then X is actual (False i.e. there's a gap between possible and actual)

2. If X is actual then X is possible (True? What happened to the gap mentioned above?) — TheMadFool

These "gaps" are sometimes not two way.

For example "If X is a butler, X is human", True. "If X is human, X is a butler", False. See?

Because the set of all butlers is a subset of the set of all humans. Similarly, the set of actual worlds, is a subset of the set of possible worlds.

@Banno, @Bartricks, @180 Proof, @I like sushi@DecheleSchilder, @khaled, @jorndoe@Jack Cummins, @tim wood

Possible

1. If X is possible then not necessary that X is actual.

Ergo,

2. There's a gap between possible and actual.

Actual

3. If X is actual then necessary that X is possible.

Ergo,

4. There's no gap between possible and actual

5. There's a gap between possible and actual & There's no gap between possible and actual. [Contradiction!]

"There is a gap" is not a logical statement. I think what you mean to say is: Possible does not imply Actual. And 3 shows that Actual does imply Possible. Nothing wrong with that.

These "gaps" are sometimes not two way.

For example "If X is a butler, X is human", True. "If X is human, X is a butler", False. See?

Because the set of all butlers is a subset of the set of all humans. Similarly, the set of actual worlds, is a subset of the set of possible worlds. — khaled

There is a gap" is not a logical statement. — khaled

How can you say that? What's not logical about it?

Why do you say that it's "...not two way"? If there's a gap between point A and point B, it doesn't matter whether I'm at point A or B, there's a gap.

If there's a gap between point A and point B, it doesn't matter whether I'm at point A or B, there's a gap. — TheMadFool

But we're not talking about points in space are we?

But we're not talking about points in space are we? — khaled

Of course, it's an analogy. You got it, right?