Author:
Wade A. Tisthammer
|
[
Next Thread |
Previous Thread |
Next Message |
Previous Message
]
Date Posted: 04/15/02 2:15pm
In reply to:
Damoclese
's message, "Still a potential pitfall looms" on 04/ 1/02 10:45pm
>>All the line says is that it is possible for the
>>greatest possible being to exist, a.k.a. statement G
>>is possibly true. Remember, God (in this argument) is
>>defined as “the greatest possible being.” The
>>existence of a “greatest possible being” is by
>>definition possible. Another way to look at it is
>>that either <>G or ~<>G is true by the law of excluded
>>middle. Since it hardly makes any logical sense to
>>say that the greatest possible being cannot possibly
>>exist (and thus ~<>G cannot be true), <>G (a.k.a.
>>~[]~G) is true.
>
>
>Okay, I'll take your word on it being definitionally
>possible, and I'll also take your word on what that
>line actually says since I seem to be missing the
>correct typeset to interpret all the symbols.
The codes I used are standard html. Try getting a more up to date web browser. (I recommend the latest Internet Explorer version.)
>I suppose you could underscore it with the assumption
>that you have the "greatest possible being" although
>the logic itself doesn't really rely on that
>assumption. If I change the underlying assumption to
>"Can God possibly exist?" rather than the greatest
>possible being existing being my underlying
>assumption, then the conclusion that God doesn't exist
>would be perfectly valid.
Where was the underlying assumption that I had “the greatest possible being”? And what exactly did you mean by me “having” the greatest possible being? And why do you think that “the greatest possible being existing” was an underlying assumption at all? Even if I did assume that, the argument did not in any of its premises.
The sentence “Can God possibly exist?” is not an assumption, it’s a question. And would you mind showing me any justification that the conclusion “God doesn’t exist” would be a valid one? For that matter, can you show me the premises at all that allegedly arrive to that conclusion?
>I suppose then, to really
>have a thorough logical argument the underlying
>assumption of a greatest possible being would have to
>be subjected to the rigors of some logical system, for
>as I see it now, it seems the logic itself deals with
>possibility and necessity which in and of itself is
>only as good as the underlying premise or condition it
>is testing.
The actual existence of “the greatest possible being” is not assumed anywhere in first two premises. If it is, please tell me in which premise and exactly why it presupposes it.
>>It seems you do not understand the argument. Yes,
>>premise #1 is a conditional statement. Normally, we
>>can’t prove anything with a conditional argument
>>per se. That’s why premise #2 is added. The
>>purpose of using symbolic logic was to have a formal
>>proof of the validity of the argument. That is, I
>>proved that if premise #1 and premise #2 is true, then
>>the conclusion ([]G) must be true also. And this is
>>indeed the case. The argument is still valid. The
>>mere fact that I used a conditional is irrelevant.
>
>I'm not arguing whether or not your argument is valid.
>(though I do have some problems with your underlying
>assumption that I will discuss later) This particular
>point I'm arguing is that the argument really doesn't
>matter given the nature of the conditional that is in
>effect. It isn't definitive proof of the existance of
>God. It is conditional proof that assumes he exists in
>the first place. (I'll address why it assumes he
>exists in the first place below).
Okay.
>>You are confusing the conclusion with the first
>>premise. The first premise says, “If God exists, then
>>he exists necessarily.” The conclusion is “God
>>necessarily exists.” In the sentence that you quoted
>>me, I was referring to the conclusion.
>
>But the conclusion is dependant on the conditional. It
>isn't true that God necessarily exists except for the
>conditional if that begins the whole thing off. The
>first line must evaluate to true, if it doesn't, the
>conclusion is useless.
True, but all the first line says is, “If God exists, then he exists necessarily.” That does not presuppose the existence of God. Is the premise false? If you think it is, I would like to know exactly why it is false.
>>>That's what it says, it
>>>all rests on your first conditional premise, which is
>>>what is being questioned in the first place.
>>
>>All the first premise says is that, “If God
>>exists, then he exists necessarily.” This is because
>>the greatest possible being would by definition have
>>the greatest possible form of existence: necessary
>>existence. So, If God exists, he necessarily
>>exists; that’s the only thing that the first premise
>>says. I don’t see how you are questioning this. The
>>first premise does not presuppose the existence
>>of God.
>
>This is where we disagree. The first premise does
>presuppose the existance of God. (God defined here as
>some entity that is powerful) You yourself said it
>wouldn't make logical sense to say that the greatest
>possible entity cannot exist.
I said it wouldn’t make any sense to say that the greatest possible being couldn’t possibly exist. That is, ~~<>G. The claim “the greatest possible being cannot possibly exist,” is a claim (I argued) that doesn’t make much sense, because the greatest possible being is by definition possible, given its coherent meaning.
>It wouldn't make logical
>sense to say If God exists, he doesn't exist
>necessarily because you would deny the first part of
>your premise.
I don’t see how it doesn’t make any logical sense simply because it contradicts the first premise. However, it might not make any logical sense given the definition of God as the greatest possible being. The greatest possible being (if the being existed) would have the greatest possible form of existence: necessary existence. Thus, some would argue that the statement, “If God exists, he doesn’t exist necessarily” does not make logical sense.
>Hence the statement If God exists
>automatically rules out the negative case namely if
>God exists he doesn't exist necessarily, or If god
>doesn't exist he exists necessarily because it
>generates a blatant contradiction.
Well, I suppose that’s true. But so what? As the argument stated earlier, the first premise is true by definition. The greatest possible being (if the being exists) would have the greatest possible form of existence: necessary existence. So it logically follows that if God (the greatest possible being) exists, then he exists necessarily. Yes, a consequence of this premise (if the premise is true) is that the statement, “If God exists, he doesn’t exist necessarily” is false. But that does still does not presuppose the existence of God.
>I would be just as guilty of assuming an implied
>premise if I said "If God doesn't exist, he doesn't
>exist necessarily"
Yes you would. But so what? A defender of this ontological argument would happily agree with that premise, since it would be true by definition according to the defender. You could not use that premise to disprove the existence of God.
>because I know that I cannot
>possibly have the statement If God does exist, he
>doesn't exist necessarily for reasons which you have
>already named.
I suppose that’s true. But so what?
>I also cannot have If God doesn't
>exist, he exists necessarily.
That statement would be an outright absurdity. If God doesn’t exist, He can’t possibly exist in all possible worlds (i.e. necessarily existing) because than he would exist in this world (our world is a possible one).
>In fact there is only
>combination that will work that my argument will
>generate that I can keep and not have to throw out and
>that is If God doesn't exist, he doesn't exist
>necessarily.If I wanted to make my argument as valid
>as yours, my underlying premise could be that there
>doesn't exist a greater being.
>
>By uttering the words "If God exists" you've committed
>yourself to the affirmitive case, and you haven't
>dealt with the negative case if that particular value
>isn't true. In computer programming as you've
>indicated you are interested in, it is a rare thing to
>see only one value accounted for in a program unless
>the programmer happens to know that is the only value
>that will come up in a case selection.
This is true. If you wish I could add the premise, “If God doesn’t exist, then he does not necessarily exist.” It’s just that I can’t see how it could possibly be useful the formal proof.
>It ususally takes the form if so and so is true,
>then...
>if not then...
>But you haven't left any room for not in part because
>of your underlying assumption and your first premise
>which as I see it, assumes the existance of God
>allbeit implicitly.
What underlying assumption? If the underlying assumption is, “God exists” then it does not appear in the first premise in the argument. Indeed, the statement, “God doesn’t exist” does not in any way contradict the premise, “If God exists, then he exists necessarily.” If it does, please tell me exactly why.
This just doesn’t logically follow. By saying, “If God exists, then he exists necessarily” you do not automatically rule out the possibility of God not existing simply because you did not include a “If God doesn’t exist…” As an analogy, suppose I say, “If jump off a cliff, I will be dead.” That statement does not in any way imply that I presuppose my own death via jumping off a cliff, regardless of whether or not I include an “If not…” statement.
But if you wish, I can still put the premise, “If God doesn’t exist, then he doesn’t necessarily exist” in the argument.
1. G ⊃ []G | If God (on the definition above) exists, He exists necessarily. |
| 1a. ~G ⊃ ~[]G | Additional premise. |
| 2. ~[]~G | This states that G is not impossible, or <>G |
Those are the premises. The conclusion logically follows as demonstrated:
| 3. []G ⊃ G | If God necessarily exists, then he exists. |
4. []G ∨ ~ []G | Law of Excluded Middle |
5. ~[]G ⊃ []~[]G | Becker’s postulate applied to ~[]G |
6. []G ∨ []~[]G | 4,5 substitution |
7. []~[]G ⊃ []~G | 1, modal modus tollens |
8. []G ∨ []~G | 6,7 substitution |
——————————— |
∴ []G | 7, 2 disjunctive syllogism |
As you can see, the conclusion is still the same. It can only be unsound if premise #1 or premise #2 is wrong. If you think the first premise is wrong or that it somehow presupposes God’s existence, please explain it clearly to me since I would like to know exactly why.
>>You appear to be confused on what the first premise
>>actually says. Again, premise #1 just says,
>>“If God exists, then he exists necessarily.”
>>This is because the greatest possible being would have
>>the greatest possible form of existence: necessary
>>existence. I don’t see why this premise fails.
>
>It fails in part because it implies by contradiction
>that the opposite case cannot be true via the first
>premise. It implies it's own conclusion.
The first premise does not by itself imply the conclusion “God necessarily exists.” That conclusion can only be implied via at least one additional premise, such as “It is possible for God to exist.”
>God not
>existing would clash horribly with the first premise
>of God existing.
Again, the statement “God doesn’t exist” does not contradict the premise, “If God exists, then he necessarily exists.” If does, I would like to know why. What is the “opposite case”? If it is, “If God doesn’t exist, then he doesn’t necessarily exist,” then you cannot use that premise in conjunction with the rest of the argument to read “God doesn’t exist.”
>The conclusion would look monsterous
>if it read If God exists, and the conclusion read God
>doesn't exist.
I’m not sure what you mean by that, since you seemed to have left out the proper consequent of the first premise. There is nothing inherently monstrous about having the first premise be, “If God exists, then he necessarily exists.” And the conclusion read, “God doesn’t exist,” because the statements do not at all contradict each other.
>>The
>>ontological argument is not simply a single syllogism
>>where I immediately affirm the antecedent to utilize
>>modus ponens or immediately state the negation of the
>>converse statement to utilize disjunctive syllogism.
>>Rather, I used a series of steps to obtain a formal
>>proof that if premise #1 and premise #2 are correct,
>>then []G must be true. The only way to deny []G in
>>this argument is to deny either premise #1 or premise
>>#2, (or both). But since both seem to be true by
>>definition, I’m not too sure how you can accomplish
>>that.
>
>Well you left off the underlying assumption of the
>greatest possible being as well.
What underlying assumption? There was no underlying assumption of “God exists” in either of the two premises. If there is, you have yet to provide a clear explanation on why this is the case.
[
Next Thread |
Previous Thread |
Next Message |
Previous Message
]
|
Feedback: 