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Maydole's second theorem

Rusty
Posts: 2,109
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10/26/2010 7:27:04 PM
Posted: 6 years ago
So I was reading up on the Modal Perfection Argument for the Existence of a Supreme Being and I ran across the three theorems.

Theorem 1: If it's possible than p and q are true, then p is possible and q is possible
Theorem 2: If it's possible that p is not possible, then p is not possible
Theorem 3: If it's possible that there exists an x that is an F, then there exists an x so that it's possible that x is an F.


From:
http://rfforum.websitetoolbox.com...

Now, although it's true that I have no real education on modal logic, I just can't see how theorem 2 would hold up. If it's possible that something's impossible, then by golly, it is without a doubt impossible. Does not compute to me. I assume I'm missing something here.

Also, I'm not trying to start a forum debate. I'm honestly looking for an answer here, not trying to "attack" the argument or anything of the sort. Thanks.
popculturepooka
Posts: 7,924
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10/26/2010 8:15:45 PM
Posted: 6 years ago
theorem 2 is basically axiom s5 in modal logic. sorry, can't get into much detail right now....
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J.Kenyon
Posts: 4,194
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10/26/2010 8:34:23 PM
Posted: 6 years ago
At 10/26/2010 7:27:04 PM, Denote wrote:
So I was reading up on the Modal Perfection Argument for the Existence of a Supreme Being and I ran across the three theorems.

Theorem 1: If it's possible than p and q are true, then p is possible and q is possible
Theorem 2: If it's possible that p is not possible, then p is not possible
Theorem 3: If it's possible that there exists an x that is an F, then there exists an x so that it's possible that x is an F.


From:
http://rfforum.websitetoolbox.com...

Now, although it's true that I have no real education on modal logic, I just can't see how theorem 2 would hold up. If it's possible that something's impossible, then by golly, it is without a doubt impossible. Does not compute to me. I assume I'm missing something here.

Also, I'm not trying to start a forum debate. I'm honestly looking for an answer here, not trying to "attack" the argument or anything of the sort. Thanks.

It's just the contrapositive of the statement "if p is possible, then it's impossible that p is not possible." Sounds less controversial when you state it that way, but it means the same thing.
Ren
Posts: 7,102
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10/26/2010 8:42:16 PM
Posted: 6 years ago
Reality is absolute. Doubt means that you don't have proof. Without proof, it's all in your head.

It's really a fundamental law to accompany Occam's razor.

These modalities are contingent on knowing all other possible characteristics of an instance, object, or idea. Otherwise, it is impossible to irrevocably determine the possible impossibility of something.

Since humanity is yet to understand everything about anything, those rules are purely theoretical and only apply to arguments rather than the attainment of new knowledge.
Ragnar_Rahl
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10/26/2010 9:56:49 PM
Posted: 6 years ago
Theorem 3: If it's possible that there exists an x that is an F, then there exists an x so that it's possible that x is an F.
It is sufficient that it is possible that there exists an x.

What the heck makes a being supreme anyway?
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J.Kenyon
Posts: 4,194
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10/26/2010 10:31:11 PM
Posted: 6 years ago
At 10/26/2010 9:56:49 PM, Ragnar_Rahl wrote:
What the heck makes a being supreme anyway?

The ability to understand Maydole's ontological argument.
GeoLaureate8
Posts: 12,252
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10/26/2010 10:42:09 PM
Posted: 6 years ago
At 10/26/2010 7:27:04 PM, Denote wrote:
Theorem 2: If it's possible that p is not possible, then p is not possible

Am I missing something here, or is this blatantly and obviously false?
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popculturepooka
Posts: 7,924
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10/26/2010 10:55:17 PM
Posted: 6 years ago
you're miaaing something. basically, the theorem is saying is that if in some possible world p (say 2 +2 = 5) is not possible (impossible or necessarily false) then p is necessarily false in all possible worlds - including the actual one.
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J.Kenyon
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10/26/2010 10:56:29 PM
Posted: 6 years ago
At 10/26/2010 10:42:09 PM, GeoLaureate8 wrote:
At 10/26/2010 7:27:04 PM, Denote wrote:
Theorem 2: If it's possible that p is not possible, then p is not possible

Am I missing something here, or is this blatantly and obviously false?

I already explained it. If-then statements can always be converted to contrapositive form. If you restate it as "if p is possible, then it's impossible that p is not possible" it makes a lot more sense.
GeoLaureate8
Posts: 12,252
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10/26/2010 11:06:34 PM
Posted: 6 years ago
@pcp and Kenyon

That's not a rewording or restatement of the premise. Those are completely different claims.
"We must raise the standard of the Old, free, decentralized, and strictly limited Republic."
-- Murray Rothbard

"The worst thing that can happen to a good cause is, not to be skillfully attacked, but to be ineptly defended."
-- Frederic Bastiat
J.Kenyon
Posts: 4,194
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10/26/2010 11:15:48 PM
Posted: 6 years ago
At 10/26/2010 11:06:34 PM, GeoLaureate8 wrote:
@pcp and Kenyon

That's not a rewording or restatement of the premise. Those are completely different claims.

If Socrates is a man, then he is a mortal.

Converse: If Socrates is a mortal, then he is a man.
Inverse: If Socrates is not a man, then he is not a mortal.
Contrapositive: If Socrates is not a mortal, then he is not a man.

The inverse and the converse are always logically equivalent to eachother, but can't be inferred from the conditional. The contrapositive is always equivalent and can be inferred from the conditional.
Freeman
Posts: 1,239
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10/26/2010 11:53:42 PM
Posted: 6 years ago
At 10/26/2010 11:06:34 PM, GeoLaureate8 wrote:
@pcp and Kenyon

That's not a rewording or restatement of the premise. Those are completely different claims.

Geo, these two books helped me quite a bit when I started studying logic.

1. Logic and Philosophy: A Modern Introduction (Tenth Edition) - Alan Hausman
2. A Profile of Mathematical Logic - Howard Delong

If I think I've ever made a really dumb argument (or I think someone else has), I go back and consult them. Our intuitive sense of what is logical or logical isn't always accurate, especially when you're dealing with modal logic or quantum logic.
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GeoLaureate8
Posts: 12,252
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10/27/2010 12:05:04 AM
Posted: 6 years ago
At 10/26/2010 11:53:42 PM, Freeman wrote:
At 10/26/2010 11:06:34 PM, GeoLaureate8 wrote:
@pcp and Kenyon

That's not a rewording or restatement of the premise. Those are completely different claims.

Geo, these two books helped me quite a bit when I started studying logic.

1. Logic and Philosophy: A Modern Introduction (Tenth Edition) - Alan Hausman
2. A Profile of Mathematical Logic - Howard Delong

If I think I've ever made a really dumb argument (or I think someone else has), I go back and consult them.

How is this relevant?

Our intuitive sense of what is logical or logical isn't always accurate,

I didn't use intuition. In Theorem 2, the premise presented did not necessitate the conclusion. Just because it's possible for something to be "not possible," does not mean it MUST be "not possible."

Rephrasing, restating, or even JKenyon's explanation of "Converse," "Contrapositive," etc. (which I understand), does not change that fact.

especially when you're dealing with modal logic or quantum logic.

I am familiar with modal logic (even the basic rules of modal logic demonstrate that Theorem 2 is false), not quite familiar with quantum logic.
"We must raise the standard of the Old, free, decentralized, and strictly limited Republic."
-- Murray Rothbard

"The worst thing that can happen to a good cause is, not to be skillfully attacked, but to be ineptly defended."
-- Frederic Bastiat
popculturepooka
Posts: 7,924
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10/27/2010 6:22:18 AM
Posted: 6 years ago
No offense, but if you think the basic rules of modal logic prove theroem 2 false then you don't know modal logic.

Think - "not possibly p" means that p does not obtain in ANY possible world. All possible worlds exhaust every single possibility (naturally) if p does NOT obtain in any possible world then it is not a possibility e.g. impossible. If something is not possible in any possible world then it is not possible in the actual world. Necessity doesn't vary over possible worlds.
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Cerebral_Narcissist
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10/27/2010 6:42:39 AM
Posted: 6 years ago
At 10/26/2010 10:42:09 PM, GeoLaureate8 wrote:
At 10/26/2010 7:27:04 PM, Denote wrote:
Theorem 2: If it's possible that p is not possible, then p is not possible

Am I missing something here, or is this blatantly and obviously false?

I agree.
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badger
Posts: 11,793
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11/1/2010 4:34:59 PM
Posted: 6 years ago
At 10/26/2010 10:55:17 PM, popculturepooka wrote:
you're miaaing something. basically, the theorem is saying is that if in some possible world p (say 2 +2 = 5) is not possible (impossible or necessarily false) then p is necessarily false in all possible worlds - including the actual one.

and do you think that follows?
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