Possible Worlds, God exists.
I was talking to @Bartricks in another thread about the notion of possibility. It led to something interesting.
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.
If I now say, it's possible that God is (exists), by the same logic above, there is a world in which God really is (exists)
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.
QED
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.
If I now say, it's possible that God is (exists), by the same logic above, there is a world in which God really is (exists)
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.
QED
Comments (108)
How do you know?
Also I disagree with premise 2.
Quoting TheMadFool
“Possible” means can exist in a possible world. Not actually exists in some world.
I disagree.
Quoting 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.
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?
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.
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.
Quoting 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.
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.
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.
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...
@TheMadFool, the actual world is, after all, possible.
I don't think anyone said this. What was said was: If world X is possible, that doesn't imply it's actual.
Quoting 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"
:up:
"God" is undefined, therefore the argument is invalid.
It really is that simply (or complex).
I'm not happy to say I am god but I am aware of its truth nevertheless.
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.
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.
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.
: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?)
So P does not lead to A.
Quoting TheMadFool
X is P
Quoting 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.
Quoting 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.
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!]
Quoting 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.
But we're not talking about points in space are we?
Of course, it's an analogy. You got it, right?
In logic, A can imply B without B implying A right? Now replace "A" with "Actual" and "B" with "Possible"
Conversely, that B does not imply A doesn't mean A does not imply B. That's why a "gap" is not analogous. Because it's possible to be able to move from A to B without it being possible to move from B to A.
There is a gap in mutual understanding here. All gaps can be logical, while at the same time being being realty-detached. Which logic is. A gap can exists litterally in spacetime, as a hole in a black.Though a gap in the common physicists mind is due to this gap. There can be gaps between all possible worlds of knowledge, as is surely the case in this case. There simply is no universal gap, and to pretend there is to deny the gaps of fellow people turning the discussion into a battle between the gaps.Which is very interesting, articulating the various gaps we have as human beings. The articulation of the gap seems, in my humble mind, a nice philosophical discussion, savely remote from standard lexicon like that standard dictionaries of Stanford and related institutions. Ah yes, the gap. How many of them I still have jump over, before reaching Nirvana? How many bridges I try to build, they always seem to crumble right after. Poor me. Luckily I have the power of the word, imagination, and sense of relativity, a God-given present, which came packed inside the God-given gift of life and existence. I rejoyce in the mad fool having found a logical proof of the obvious! Though I'm not sure what Quantum ElectroDynamics have to do with it.
Quoting 180 Proof
such that
Quoting 180 Proof
and so a purported "gap between possible and actual" is conceptually incoherent in actualist terms. You're only chasing "possibilist" shadows, Fool, deeper and deeper into Meinong's Jungle. :chin:
I'm not sure if there's a philosophy centered around what philosophers mean when they say "possible." One only needs to know that God is possible to prove God exists, IMO.
The only things that can't possibly be known to be false are truths, as it's possible God exists and knows all things, true and false, and God can't possibly know Itself to be false.
Theism is not true, "God" is imaginary; therefore your problem is (dis)solved. And if you're a theistic anti-realist (i.e. theological noncognitivist), then "the real God" makes no more sense than "the real Middle Earth".
Lots of imaginary things are true. Unicorns, for example.
Statements, not objects, can be true. :roll:
There are more things in Heaven and Earth, Horatio.
The God that kills the Christian God possibly exists, his name is Will Hoff.
Therefore Will Hoff exists.
God is dead and Will Hoff killed him.
It is also possible that you're not Christian and are actually lying about being Christian. Therefore it is actually the case that you're not Christian and are actually lying about being Christian.
You could be wrong about the possible being actual. Therefore you're wrong about the possible being actual. You could also be right about the possible being actual. Therefore you're right about the possible being actual. So you're right and wrong about the possible being actual.
And a whole lot of other messes happen when what's possible is what's actual.
I couldn't possibly be wrong if I'm right. I'm gonna go now and let you atheists try to solve the mystery of your anal retention.
Great comment! I am sure there are gods. No one can prove me wrong how well they try scientifically (on which grounds I usually am the better).
But also, it's possible for you to be wrong, but only think you're right. And since if something is possible it is factual, you are in fact wrong.
It is also possible for you to be right while thinking you're right. So you are indeed right.
You're right and wrong.
First things first, what we agree on.
1. If X is an actual world then X is a possible world.
Now, the sticking point,
2. If X is a possible world then X is an actual world.
Statement 2, all of you say is false.
Consider now the following statement (contrapositive of 2)
3. If X is not an actual world then X is not a possible world (contrapositive of 2)
Invoking the principle of sufficient reason, if X is not an actual world, it follows that there are reasons why X is not an actual world. These reasons show why X can't be an actual world. In other words, there's an argument that proves X is not a possible world.
That is to say, it's true that,
3. If X is not an actual world then X is not a possible world.
Undoing what we did, we get
4. If X is a possible world then X is an actual world (contrapositive of 3). This statement is true.
QED.
Therefore possible worlds are needed as a way for us to make sense of what is NOT. It has no value when it comes to proving something that may exist in our world.
1. If X is an actual world then X is a possible world.
2. If X is a possible world then X is an actual world.
I can also say:
1. If is apple then it is a fruit
2. If is fruit then it is an apple
Possible world has a greater scope that contains all actual worlds
Therefore you can't say that a possible world is an actual world because possible worlds do not completely contain actual worlds in its set- there are some worlds that are just potential. Otherwise it would be not be a set of potential worlds but actual worlds.
In a possible world we could be ants in the playground of a little kid. In another possible world there is a massive horse that rules the universe.
Therefore being ants in a playground and being subject to the whims of a horse are real. But if these words have no causal influence on ours at all, does it matter?
In other words, if God exists in another possible world what meaningful difference does that entail for us here? I can think of nothing, but perhaps you can tell me what I currently not seeing.
Suppose a world Y is not actual. Why? There has to be a reason why that is. That reason becomes an argument the conclusion of which is Y is not actual. A conclusion is necessarily true i.e. Y is not actual implies Y is necessarily not actual. If Y is necessarily not actual then Y is not possible. Therefore, Y is not actual implies Y is not possible. That means Y is possible entails Y is actual. QED.
Read my reply to tim wood
I'll repeat myself at the risk of boring you but it's quite exciting to say the least.
If a possible world X is not actual, there's got to be a reason why. That reason, in an argument, proves X is not actual. In an argument, the conclusion (here X is not actual) is necessarily true.
Therefore,
1. X is not actual implies X is necessarily not actual.
2. X is necessarily not actual implies X is not possible.
3. X is not actual implies X is not possible (1, 2 HS)
Ergo,
4. X is possible implies X is actual (3 Contra)
QED
I have no idea what you're trying to say here.
My argument is rather simple.
Suppose X is not an actual world.
There has to be an reason why it's not actual (the principle of sufficient reason).
What does having a reason for X is not actual mean?
It simply means that we have an argument that proves X is not actual. If there's a proof for X is not actual, it implies X is necessarily not actual.
In other words,
1. If X is not actual then X is necessarily not actual.
2. If X is necessarily not actual then X is not possible.
Ergo,
3. If X is not actual then X is not possible (1, 2 HS)
Ergo,
4. If X is possible then X is actual (3 Contra)
QED
There is a possible world in which my cat is ginger.
In the actual world, he is black.
Now the reason, if you need one, that the possible world in which my cat is ginger is not the actual world is that my cat is black.
World X is not actual.
Why?
Reason R
Argument A1:
1. R
Therefore,
2. World X is not actual
However, given argument A1,
3. Necessary that world X is not actual.
4. If world X is not actual then necessary that world X is not actual. [from 2, 3]
Argument A2:
5. If necessary that world X is not actual then world X is impossible.
Argument A3:
6. If world X is not actual then world X is impossible [4, 5 HS]
Ergo,
7. If world X is possible then world X is actual [6 Contra]
QED.
Nuh. "Actual" is an indexical. Like left and right. The folk in each possible world think they are in the actual world.
Add that "Necessarily" is just "In all possible worlds", and hopefully you will see why your proposition is ill-formed.
There is randomness, not only technicality; not every world ends up being made depending on supply and demand.
The thought of possible worlds is the thought of a paradox, an illusionary phenomenon.
Are there any actual worlds where God exists?
Though, I may be wrong, there may be a creative entity that creates all possible worlds [I]for the hell of it[/I].
That whole idea is incoherent. Your cat could not be ginger in any possible world, because it would not be the same cat. All you're saying is that there could be a ginger cat in some possible world, which is trivially true. Modal logic is garbage.
Let me get this straight.
1. Your cat (in the actual world) is black
Therefore,
2. The possible world in which your cat is ginger is not the actual world.
The word "the" is key. Of course any possible world which differs from this (the) actual world is not this world. However that doesn't prove that those possible worlds are not actual. You're assuming that this (the) world is the only actual world.
Quoting Banno
The word "actual" as an indexical is not, I think, important. My argument has little to do with modal realism although we come to the same conclusion.
Nuh. Jack - a rigid designator - might have been ginger. That sentence makes sense. It's exactly the sort of thing modal logic is intended to deal with.
Jack's identity is maintained across possible worlds.
Actually I explicitly said that the folk in each possible world think their world is the actual world.
But yes, there is only one actual world, within the structure of modal logic.
Quoting TheMadFool
If you think that, you've missed the point.
A new universe did not pop into existence when I pointed out that Jack might have been ginger*. It's just a way of talking about such possibilities that clarifies the relations of possibility and necessity. Mad, you are over-egging the ontology.
(*that sort of rubbish is the domain of quantum.)
Your reasoning still lies in the fallacy that I discovered.
This is what you say:
1. If X is an actual world then X is a possible world.
2. If X is a possible world then X is an actual world.
Consider now the following statement (contrapositive of 2)
3. If X is not an actual world then X is not a possible world (contrapositive of 2)
3. If X is not an actual world then X is not a possible world.
Undoing what we did, we get
4. If X is a possible world then X is an actual world (contrapositive of 3). This statement is true.
If X is an actual world (if apple is a fruit) then it is a possible world (a possible fruit) See how this argument is beginning to fall apart? You're stating that something real is a possibility of being real. This is a logical contradiction. Moving on.
If X is a possible world (a possible fruit) then X is an actual world (an actual fruit)
Still this doesn't make sense because as I said, the set of all possible conditions must be greater than the set of all actual objects. This is because a set of possible X should mean there is number of X that is not actual. The set of possible worlds therefore is greater than the set of actual worlds.
Therefore, we cannot say your second point as it is a logical contradiction. If X is a possible world it does not mean that X is an actual world because the set of X as possible worlds is bigger than the latter. Moving on.
You say in point 3 that if X is not an actual world then X is not a possible world. This contradictions everything you've said and been building up to so far. I can imagine a world that is made of gas, and although this planet is not real, it can be a possible world because it contains all the conditions of being real. For example, if something has possible properties then it is possible but not always actual.
Going to point 4 now which is built upon several logical mishaps, we will see that the conclusion must be false or at least doubtable. This can be done simply however.
Fourth point: If X is a possible world then X is an actual world. You just said in point 3 that if X is not an actual world then X is not a possible world. This is a complete contradiction to each other.
According to what you said, the set containing all possible worlds is equivalent to the set of all actual worlds. First of all "possible" means that there is a possibility that the world in question is not actual. This means that the set of possible worlds can never equal the set of actual worlds, because actual worlds are manifestations of conditions whereas possibility itself is a condition to be questioned. Therefore possibility is always superior in its set than actual manifestations of it, otherwise there is no need to use the word "possibility"- merely just call it actual- but before actuality there is always possibility and therefore the two cannot be equated to each other as you have done.
I don't buy that. How can modal logic (about possibilities and necessities) ever even claim there is only one actual world.
Quoting Banno
I believe you're barking up the wrong tree here.
Let's try another route.
1. World X is possible & World X is not actual (you would agree)
2. World X is impossible & World X is not actual (obvious)
I give you world Z which is not actual. That is to say,
3. World Z is not actual.
Question for you: Is world Z impossible or is world Z possible?
How would you be able to tell?
It doesn't. Rather, the folk in each world think their worlds is the actual world. Third time I've said it.
Quoting TheMadFool
Might be either. You haven't yet specified.
Quoting TheMadFool
When I said Jack might have been a ginger, I specified the nature of a possible world - one in which Jack was a ginger. SO, go ahead and decide if Z is possible or impossible by specifying what's special about it.
I suppose we might specify a possible world such that the folk therein believe their world is not the actual world.
A world of mad fools?
You had to come up with the solution.
It's what I do.
It's nothing but a fantasy. If it gives you pleasure to imagine you are thinking something coherent when you say that your cat could have been different than he is,. I suppose there's little harm in it.
:chin:
So? Where's your solution?
Stop while you are ahead.
What's the problem?
:up:
One I share with most modal logicians and others since Kripke.
But I think we've had this conversation before? Have you forgotten, again?
Quoting TheMadFool
Quoting Banno
Who you talking too?
Either click on the back arrow at the bottom of a post to reply, or highlight a piece of text in a pst and click on "quote".
Or if all else fails, use a name instead of "You"
Okay I will do that from now on.
You seem to think of possible worlds as things we find and investigate, through a microscope or telescope.
They are just stuff we make up. A way of talking about possibilities.
SO, when you tell us more about world Z, we might decide if it is possible or not.
1. If world X is not actual then there's a proof why world X is not actual.
2. If there's a proof that world X is not actual then necessarily world X is not actual.
3. If necessarily world X is not actual then world X is impossible.
4. If world X is not actual then necessarily world X is not actual. (1, 2 HS)
5. If world X is not actual then world X is impossible. (3, 4 HS)
6. If world X is possible then world X is actual. (5 Contra)
Nuh. The "proof" is just you specifying that X is the actual world or that it isn't.
Quoting TheMadFool
Nuh. The "proof" is just you specifying that X is not the actual world or that it is. But also, the phrase "Necessarily word X is not actual" is ill-formed. It comes out as something like "in all possible worlds world X is not actual"; which presumably is just "World X is impossible".
Try substituting "in all possible worlds" for "necessarily" in your thinking; you may begin to see why the possible world way of talking clears the air. The confusion you are suffering might be because you are mixing two ways of speaking about modality.
But the limits to this cannot be coherently established. It might seem coherent to say I could have been born a woman, but what about the idea that I could have been a stone, a tree or a mountain? I think the inconceivability of this (absent the idea of a unique individual soul or essence or something like that) shows that description plays an ineliminable part in establishing identity, if not in merely stipulating it..
What if Janus had a haircut yesterday? What if Janus had never developed an interest in modality? What if Janus had been born a woman? What if Janus were a rock? What if Janus were not identical with Janus?
Some of these are possible worlds, some impossible worlds, and for different reasons. The semantics helps us sort them out.
Sure we can try to imagine all those things and discover the special conditions we would need to posit to make them coherently imaginable (as opposed to merely saying them). But such things were done long before rigid designation ever became an explicit thing. Think about aboriginal myths, for example.
Rigid designation is just a new term for something we've done all along. It serves to set out what we are doing, and to allow is to differentiate between certain modal problems in a way that allows us to dissipate or explain them.
:up:
Not necessarily. There could be some true statements we can't prove (incompleteness)
Quoting TheMadFool
Wot? Max I'd be willing to say is "If there is valid proof that world X is not actual then we are justified in believing that world X is not actual"
Quoting TheMadFool
But those premises are false.
Why? Sentential logic works fine.
Quoting khaled
You're bending over backwards, going to great lengths as it were, to make a point. You have to prove incompleteness whatever that means in your case.
Here's the deal. I present to you a world Z that is not actual.
The question: Why is world Z not actual?
No I don't. You stated the premise that if something is true, we can prove it. Prove that premise. You think if it is true, there should be a proof for it, so where is the proof for that.
I don't need to definitively state or even prove that there are true, unprovable statements. Because I'm not making a case here. You have a dubious premise in your argument, you need to back it up. It is not at all obvious that every true statement has a proof, not since Godel.
Quoting TheMadFool
Here is the deal. I present to you a red car.
The question: Why is this car red?
Answer that and I'll tell you why Z is not actual.
:lol: I have not time for your silly games khaled
The only worlds where God actually exists are not equalised by an amount of worlds where God doesn't.
So how does God exist, if equally he doesn't?
How is that paradox if there is no certainty nor self-contradiction?