I appreciate your response, but the post you responded to is rather old, and I have since discovered the meaning of the word “possible” in the definition. At that time I was asking if it meant possible as in “possibly exists” or possible as in “attributes are as perfect as possible.” I now know that it means the latter, but that the latter implies the former. your reasoning is somewhere along the lines of this:
You are saying that god is contingent on possible worlds. In fact this is obvious because if god is not contingent, then possible worlds would have no relevance to him. “God exists in at least one possible world” would become “God exists” if possible worlds were irrelevent to god.
Also, you reject the axiom that it is possible for god not to exist because it leads to the conclusion that god does not exist in any possible world. I agree that you are not assuming god’s existence. What you are assuming is that god is contingent. However, if god is not contingent, then, as Anselm said, god not existing in any possible world is NOT contradictory. Again, you must be speaking of god as a contingent being.
Here is the problem. Wouldn’t a god who was NOT contingent be greater than a god who is? I do not believe that it is counterintuitive to believe that god is not contingent. Indeed, it seems counterintuitive to me to believe that even if god does not exist, there was some way reality could have been like to make him exist. To do so is to make reality more powerful than god, and this cannot be because god must have the greatest power: perfect power.
God either exists or does not exist. No circumstances or possible worlds can be relevent to his existence, because he is greater than those circumstances and possible worlds. Therefore it makes no sense to say that god exists in at least one possible world.
The fatal flaw in the proof is that it must make reality greater than god. It must make circumstances greater than god. Because for the proof to work, god must be contingent.
>>Which one is right on what I said? Well, both.
>>Note that <>~G obviously includes what G
>>means (and therefore its definition). So if <>~G
>>is self-contradictory it will have contradicted its
>>definition, which is what self-contradictions of
>>statements are often all about.
>
>I appreciate your response, but the post you responded to
>is rather old, and I have since discovered the meaning of
>the word “possible” in the definition.
Ah.
>At that time I was asking if it meant possible as in “possibly
>exists” or possible as in “attributes are as perfect as possible.”
>I now know that it means the latter, but that the latter implies
>the former. your reasoning is somewhere along the lines of this:
>>To some people (including me), God not being contingent
>>is counterintuitive. That is, the ideas of God existing and
>>God not existing both seem conceivable. Anselm would
>>have us believe that God (perfection) is not contingent,
>>and that He either exists in all possible worlds or none of them.
>You are saying that god is contingent on possible worlds. In fact
>this is obvious because if god is not contingent, then possible worlds
>would have no relevance to him. “God exists in at least one possible
>world” would become “God exists” if possible worlds were irrelevent
>to god.
I’m not sure what you mean by possible worlds being relevant to God. If God is not contingent then he would exist in all possible worlds or he would exist in none of them.
>Also, you reject the axiom that it is possible for god not to exist
>because it leads to the conclusion that god does not exist in any
>possible world.
I rejected the premise of “it is possible for God not to exist” because it lead to a contradiction, as I explained earlier. If a premise leads to something like breaking the law of noncontradiction, the premise can’t be true.
It doesn’t make much sense to say that God cannot possibly exist because of how God is defined in this case: the greatest possible being. For instance, God is said to have perfect power: omnipotence. But can God create a round square? Can he defy such basic rules of logic? The theist under this definition of God could reply that God is only omnipotent to the greatest possible extent. Thus, this theist could respond by claiming that God cannot do what is logically impossible, but He can do anything that can be done. If a certain level of one of God’s traditional qualities is proved “impossible,” this theist could then lower the bar on that aspect of God down to where that quality is possible, such as from, “God is omnipotent and can do literally anything,” to “God is omnipotent to the greatest possible extent.”
Using <>~G in the argument the statement ~G is obtained, which can be translated to mean, “The greatest possible being cannot possibly exist.” Such a statement is absurd because of its self-contradictory nature given the coherent, meaningful definition of God. If a being is possible (e.g. the greatest possible being) it can’t be impossible. Consequently, the greatest possible being would by definition exist in at least one possible world, whether he is contingent or not.
>I agree that you are not assuming god’s existence. What you are
>assuming is that god is contingent. However, if god is not contingent,
>then, as Anselm said, god not existing in any possible world is
>NOT contradictory. Again, you must be speaking of god as a contingent being.
Point to be made here: I do not claim that the ontological argument is correct. I was referring to God being contingent as a way to attack the ontological argument in one of my “disputable point” sections in the web page, not support it. I think you have unwittingly taken the quote out of context. I’ll revise the web page so that it’s more clear. Here’s an excerpt from the article:
Whether God is contingent or not I’m no longer certain. My own personal intuitive feelings in this case are not evidence, however, and without such evidence against the premise I’m left with what I have.
>Here is the problem. Wouldn’t a god who was NOT contingent
>be greater than a god who is? I do not believe that it is
>counterintuitive to believe that god is not contingent.
You may not find it counterintuitive, but I do. The problem with counterintuitive feelings of this sort is that they are subjective, i.e. not necessarily shared by everybody. But if God is not contingent, this would swing the pendulum in favor of the ontological argument, not against it. You may wish to change your opinion on the contingency of God.
>Indeed,
>it seems counterintuitive to me to believe that even if god does
>not exist, there was some way reality could have been like to
>make him exist.
>God either exists or does not exist. No circumstances or
>possible worlds can be relevent to his existence, because
>he is greater than those circumstances and possible worlds.
>Therefore it makes no sense to say that god exists in at least
>one possible world.
Under the argument, yes he is greater than possible worlds, particularly those that do not exist. But this does not at all preclude them from being relevant in the ontological argument. On the contrary, the whole notion of modal logic is quite crucial for the proof.
>The fatal flaw in the proof is that it must make reality greater
>than god. It must make circumstances greater than god. Because
>for the proof to work, god must be contingent.
The exact opposite is true. For the proof of God to work, God must not be contingent. Nothing in the proof makes “reality” greater than God.
Wade writes:
“The application of Becker’s postulate states ~G -> ~G, which can be translated to read that, “If G is not true in all possible worlds, then ~G is true in all possible worlds.” To me, this makes perfect sense. After all, if G is not true in all possible worlds, then in each possible world the statement “G is not true in all possible worlds,” would in fact hold true.”
I argue that “G is not true in all possible worlds” can only be true or false in a hypothetical meta-world containing the possible worlds. In any one particular possible world, these possible worlds do not exist, and so this statement is neither true or false. It is like asking someone in our world if the statement “Unicorns fly” is true or false.
Thus ~G -> ~G is invalid. For the right hand side to be true, it would have to be true that “In each possible world, it is true that ‘there is a possible world in which God does not exist’”. But ‘there is a possible world in which God does not exist’ is neither true nor false in a given possible world.
I think that maybe you’re mixing up the worlds with the statements that comprise the worlds. A statement in any arbitrary world might be true or false in that world and in all other worlds. A statement that is true in at least one world is called “possible”. A statement that is true in all possible worlds is called “necessary”.
If there is a world containing other worlds (or more precisely, q world that is accessible to other worlds), then it itself is a world. There’s nothing hypothetical about it. That’s why Eris’s bird is God.
Libertarian writes:
“I think that maybe you’re mixing up the worlds with the statements that comprise the worlds.”
I think worlds are comprised of things. In the possible worlds, the things can be plants, animals, rocks, and many more things, but not other possible worlds. In the hypothetical meta-world, the things are the possible worlds.
We can have a statement regarding things in a world, and if the things are consistent with it we say it is true. If not, we say it is false.
For instance IN our world I can say:
“Preguntas Sin Pantalones is sitting at his computer.”
TRUE.
“Preguntas Sin Pantalones is a woman.”
FALSE.
“Unicorns fly.”
NOT A VALID STATEMENT. Unicorns are not things in our world.
“There is a possible world in which God does not exist.”
NOT A VALID STATEMENT. Possible worlds are not things in our world.
In the hypothetical meta-world:
“There is a possible world in which God does not exist.”
A VALID STATEMENT. Possible worlds are things in the hypothetical meta-world.
When you say ~G, in English “In each possible world, it is true that ‘there is a possible world in which God does not exist’”, you require that for a given possible world W, that ‘there is a possible world in which God does not exist’ be a valid statement (and also true) IN W. But as in the example above, it is not a valid statement IN W.
Libertarian writes:
“If there is a world containing other worlds (or more precisely, q world that is accessible to other worlds), then it itself is a world. There’s nothing hypothetical about it. That’s why Eris’s bird is God.”
It is hypothetical to us. We are imagining a meta-world in which all the possible worlds are laid out for the sake of the argument. That doesn’t mean that somewhere in our universe this meta-world exists.
If Eris’s bird is God, then God lives in the hypothetical meta-world. So proving God exists in our world is equivalent to proving the meta-world exists in our world. (If you know a coin is in a wallett, then that coin is in your pocket if and only if the wallet is.)
Libertarian writes:
“I think that maybe you’re mixing up the worlds with the statements that comprise the worlds.”
I think worlds are comprised of things. In the possible worlds, the things can be plants, animals, rocks, and many more things, but not other possible worlds. In the hypothetical meta-world, the things are the possible worlds.
We can have a statement regarding things in a world, and if the things are consistent with it we say it is true. If not, we say it is false.
For instance IN our world I can say:
“Preguntas Sin Pantalones is sitting at his computer.”
TRUE.
“Preguntas Sin Pantalones is a woman.”
FALSE.
“Unicorns fly.”
NOT A VALID STATEMENT. Unicorns are not things in our world.
“There is a possible world in which God does not exist.”
NOT A VALID STATEMENT. Possible worlds are not things in our world.
In the hypothetical meta-world:
“There is a possible world in which God does not exist.”
A VALID STATEMENT. Possible worlds are things in the hypothetical meta-world.
When you say ~G, in English “In each possible world, it is true that ‘there is a possible world in which God does not exist’”, you require that for a given possible world W, that ‘there is a possible world in which God does not exist’ be a valid statement (and also true) IN W. But as in the example above, it is not a valid statement IN W.
A SIDE ISSUE:
Libertarian writes:
“If there is a world containing other worlds (or more precisely, q world that is accessible to other worlds), then it itself is a world. There’s nothing hypothetical about it. That’s why Eris’s bird is God.”
It is hypothetical to us. We are imagining a meta-world in which all the possible worlds are laid out for the sake of the argument. That doesn’t mean that somewhere in our universe this meta-world exists.
If Eris’s bird is God, then God lives in the hypothetical meta-world. So proving God exists in our world is equivalent to proving the meta-world exists in our world. (If you know a coin is in a wallett, then that coin is in your pocket if and only if the wallet is.)
OK, my chess analogy seems to be causing more problems than it solved.
The layout of chessboards was just that: a layout of all possible board states in chess. On each board there are two kings. This is not surprising, as a property of a “possible chess board” is that it has two kings.
Now we turn to our problem, and where I was led astray previously. All possible worlds could mean a few things, and one of the things I thought it meant was all describable worlds period, but instead I do not think this is the case. Instead we mean, “imagine all worlds exactly like our own, except that every single possible thing that can happen, happens.” Remember the chessboards.
There is no “birds eye view” here other than modal logic itself which seeks to describe the relationships within a world or between all worlds.
Now.
We first wish to create a modal definition of God. Modal logic only allows three things to be described: absolute non-existence, existence in possible worlds (hypotheticals, you might say), and existence in all worlds. These are the only three available options. But this is a serious limitation. here is why.
It is possible that I will go to the bank this evening. What modal logic tries to say is that, because it is possible, we can imagine/describe a world in which it does happen. Fine. Now modal logic wants us to consider this hypothetical world as having relevance to our own.
Um??
If I relive this day an infinite amount of times I may never go to the bank. That doesn’t make it impossible for me to go to the bank. The bank exists. I exist. I can drive, my car works, and so on. Nothing forbids me from going to the bank.
Modal logic wants us to assume that it enumerates all possible worlds, and defines “impossible” then as “never happens in any of these worlds.” Again, I think this is severely limiting the way we think of things when we say that something is possible. And this is why it can be that the greatest possible being doesn’t exist. In any world. That doesn’t make it impossible, except in modal logic, which takes a rather dim view of possibility.
Impossible things will never happen. Possible things may never happen. That’s possibility.