Author:
Wade A. Tisthammer
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Date Posted: 04/ 1/02 12:50pm
In reply to:
Damoclese
's message, "Symbolilc Pitfall?" on 03/28/02 12:02pm
>>2. ~[]~G This states that G is not impossible, or <>G
>>
>
>This line looks to me to state that God not existing
>is not possible, or perhaps God's nonexistance isn't
>necessarily true.
>
>That's a pretty big premise especially the first
>interpretation. The first interpretation would be
>blatantly wrong, because it is possible that God
>doesn't exist (but since we are in conditional land I
>can let that slide).
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.
>I realize the conditional I chopped off labors from
>the preconception that if God does exist, he exists
>necessarily, but then, if I were so inclined I could
>formulate the negative of that; if God doesn't exist,
>he doesn't exist necessarily and we could run it
>through the same rules and come out with the same
>conclusion, only on the negative side.
If I am understanding you correctly, you are saying that by switching premise #2 with <>~G (a.k.a. ~[]G). I too once believed that <>~G (which is equivalent to ~[]G) was just as reasonable as <>G (which is equivalent to ~[]~G). So, I figured out I could replace premise #2 with ~[]G (“It is not necessary for God to exist,” or in other words, “It is possible for God not to exist”), get ~[]G together with premise #9 and then use disjunctive syllogism to get []~G (God necessarily does not exist). Because I believed there’s no logical reason to favor ~[]~G over ~[]G, I believed I proved the argument defective since switching ~[]~G (premise #2) could be easily switched with ~[]G to logically prove that God does not exist. To illustrate, I’ll copy the symbolic logic thing again:
| 1. G ⊃[]G | If God (on the definition above) exists, He exists necessarily. | | 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 | | 9. []G | 7,2 disjunctive syllogism | | ——————————— | | ∴ G | 9, 3 modus ponens |
Then I realized (two days later) that premise #9 wouldn’t make any logical sense once premise #2 was switched with ~[]G (because premise #9 would then become []~G). []~G means that God (the greatest possible being) necessarily does not exist, which means that G does not hold true in any possible world. Put another way, []~G can be translated to mean, “The greatest possible being cannot possibly exist,” which is absurd because of its self-contradictory nature. If a being is possible (e.g. the greatest possible being) it can’t be impossible. The greatest possible being would by definition exist in at least some possible worlds. So switching premise #2 with ~[]G doesn’t and can’t prove that God does not exist because of the law of noncontradiction. So one reason <>G is favorable to <>~G in this argument is that <>G doesn’t lead to a contradiction within any of the premises in the argument, unlike <>~G. Another reason is that <>G logically must be true (again, unlike <>~G), because “the greatest possible being” is by definition possible. It would be a contradiction to say that the greatest possible being isn’t possible, whereas it wouldn’t break any rules of logic to say that it’s impossible for <>~G to be true.
>All of this looks good to this point. We have God is
>either possible or necessary (existing) or God
>possibly doesn't exist. ( by the way your horseshoe
>and Vee and triangular dots all appear as squares to
>me, so I'm sort of at a disadvantage.)
Sorry about that. I hope this post does a better job of showing the symbols. The ontological argument relies only on two premises (which then logically follow to the conclusion of []G.):
- If God (defined merely as “the greatest possible being”) exists, he exists necessarily.
- It is possible for God to exist.
The “or God possibly doesn’t exist” wasn’t actually a premise.
>>———————————
>> []G 7,2 disjunctive syllogism
>
>
>This is where it all falls apart in my opinion. Above
>it reads either God exists or doesn't, but you
>implicitly assume perhaps from your conditional that
>the case cannot possibly be that God doesn't exist
>with the application of your disjunctive syllogism.
Again, “either God exists or doesn’t” wasn’t actually a premise, albeit ~G or G is true via the law of excluded middle. I do not simply “assume” that ~G can’t be true, I implicitly prove it using the rules of logic and the first two premises (if the first two premises are correct).
>The thing is is that your first premise is a
>conditional of the if then form. It isn't a definitive
>this is the way it is sort of form. If God doesn't
>exist, we might be able to accomplish a similar line
>of reasoning with the same rather melodramatic
>conclusion. An argument that rests on a conditional is
>only true if it's conditional is true, and that's the
>very thing being debated.
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.
>>And there you have it. Why does God exist? Because
>>he necessarily exists.
>
>That really isn't what it says. It says if God exists,
>then he exists necessarily.
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.
>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. But if the first premise is true, and if G is possible (i.e. it is possible for the greatest possible being to exist), then it logically follows (via the formal proof I gave) that []G is true.
>It would
>be like me doing something like this in an argument:
>
>If I am right you are wrong.
>You are wrong.
>
>Therefore I am right.
>
>
>This is much different from this:
>
>Either I am right, or you are wrong.
>You are wrong.
>Therefore I am right.
>
>The difference is that the first argument [premise] is
>conditional. I may not be right and that other person
>could still be wrong.
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. 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.
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