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Author Topic:   Plantinga's ontological argument
Chiroptera
Inactive Member


Message 16 of 20 (235915)
08-23-2005 10:05 AM
Reply to: Message 15 by DominionSeraph
08-23-2005 12:58 AM


Re: a thought
quote:
'possibly necessary' = 'necessarily necessary.
I don't think that this part is a fault of Platinga -- I think it is an accepted axiom in some systems of modal logic accepted by legitimate logicians.
-
quote:
He's starting with the assumption that this being exists in all possible worlds, and concludes that this being exists in all possible worlds.
Yes, I think that this is where the circularity comes in, but I think it comes about through his flawed definition of maximally great being.
From Chiroptepedia:
1. By definition an invisible pink unicorn is a being that exists necessarily and necessarily is invisible, pink, and a unicorn. (Premise)
2. Possibly an invisible pink unicorn exists. (Premise)
3. Therefore, possibly it is necessarily true that a being exists that is invisible, pink, and a unicorn. (By 1 and 2)
4. Therefore, it is necessarily true that a being exists that is invisible, pink, and a unicorn. (By 3 and S5)
5. Therefore, a being exists that is invisible, pink, and a unicorn. (By 4 and since necessarily true propositions are true.)

This message is a reply to:
 Message 15 by DominionSeraph, posted 08-23-2005 12:58 AM DominionSeraph has replied

Replies to this message:
 Message 17 by DominionSeraph, posted 08-24-2005 12:05 AM Chiroptera has not replied
 Message 18 by Sylas, posted 08-24-2005 3:37 AM Chiroptera has not replied

  
DominionSeraph
Member (Idle past 4744 days)
Posts: 365
From: on High
Joined: 01-26-2005


Message 17 of 20 (236304)
08-24-2005 12:05 AM
Reply to: Message 16 by Chiroptera
08-23-2005 10:05 AM


Chiroptera writes:
I don't think that this part is a fault of Platinga -- I think it is an accepted axiom in some systems of modal logic accepted by legitimate logicians.
Yes, it's obviously true.
Proposition: "X is true in all possible worlds."
If that proposition is true in one world, it's true in all worlds, as the proposition covers all worlds. It's like:
________________________________________
||||||||||||||||||||||||| 4;||||||||||||||
Where the horozontal line is the proposition, and the vertical ones are the worlds (the proposition covers all worlds). If it is true in one world that the horozontal line covers all the worlds, the horozontal line does cover all the worlds; so it's true in all worlds that it covers all worlds... as it does.
And that looks like:
___________________________________
___________________________________
||||||||||||||||||||||||| 4;|||||||||
"It is true in all possible worlds that X is true in all possible worlds."
Which leads us to:
___________________________________
___________________________________
___________________________________
||||||||||||||||||||||||| 4;|||||||||
"It is true in all possible worlds that it is true in all possible worlds that X is true in all possible worlds."
Which continues ad infinitum.
Both premises are problematic, but I was wrong in that it's circular. The graphical form would be:
'x' represents a world in which the truth value of the proposition hasn't been determined.
'0' represents a world in which the proposition is false.
'|' represents a world in which the proposition is true.
'_' represents the proposition.
Premise 1:
____________________________________
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
(The premise just says the proposition covers all worlds -- it says nothing about whether it's true in any.)
Premise 2:
____________________________________
xxxxx|xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
(The proposition is true in one world}
Therefore:
____________________________________
||||||||||||||||||||||||| 4;||||||||||
{the proposition is true in all worlds.)
ie:
____________________________________
____________________________________
||||||||||||||||||||||||| 4;||||||||||
(It is true in all worlds that the proposition is true in all worlds.)
Premise 1 only gives us 2 possible outcomes:
___________________________________
||||||||||||||||||||||||| 4;|||||||||
or:
___________________________________
00000000000000000000000000000000000
...and premise 2, by presuming an '|', presumes the former.
And yes, there's nothing to say that premise 1 is right -- that we couldn't instead have:
___        _________        _______
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
(The proposition "X exists" does NOT cover all worlds.)
Wherein it being true in one world:
___        _________        _______
xxxxxxxxxxxxxx|xxxxxxxxxxxxxxxxxxxx
Doesn't say anything about the rest.
This message has been edited by DominionSeraph, 08-24-2005 12:17 AM

This message is a reply to:
 Message 16 by Chiroptera, posted 08-23-2005 10:05 AM Chiroptera has not replied

  
Sylas
Member (Idle past 5250 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 18 of 20 (236319)
08-24-2005 3:37 AM
Reply to: Message 16 by Chiroptera
08-23-2005 10:05 AM


Re: a thought
Chiroptera writes:
I don't think that this part is a fault of Platinga -- I think it is an accepted axiom in some systems of modal logic accepted by legitimate logicians.
Well, yes; but that only means the argument is incomplete It requires an additional layer of argument to justify the choice of axioms.
The fact that different axioms systems exist is not a basis for picking one willy-nilly to make your argument work.
Modal logic common uses two modal connections. They are
  • M (possibility) -- often written as a diamond: ◊
  • L (necessity) -- also written as a box:
Depending on what you think these connectives really mean, different axioms may or may not be part of your logic. A common modal for such logics is possible worlds semantics. For every world we have a set of related possible worlds. A formula Lp is true in a world if and only if it is true in every possible world related to that world.
Here are some common axioms.
  • If "p" is a theorem, then "Lp" is a theorem. This is tecnically a rule of inference, not an axiom.
  • L(p => q) => (Lp => Lq)
  • Mp <=> ~L~p
These axioms, and inference rule, apply for any possible worlds semantics. The logical system using these three rules is called K.
Here are some additional axioms
  • Lp => p. That is, if p is necessarily true, then it is true.
  • Lp => LLp. That is, if p is necessarily true, then p is necessarily necessarily true.
  • Mp => LMp. That is, if p is possibly true, then p is necessarily possible.
S5 is the system obtained by adding these three axioms. It is the "strongest" modal logic. Other famous logical systems include M, which adds only the first, and S4, which adds the first two.
You can think of these as restrictions on the "possible worlds" relation. S5 is the system that works simply with a set of possible worlds, each of which is possible for any other. It is, in a sense, the simplest modal structure.
As a minor aside; I did a PhD many years ago in which modal logic was a major aspect. However, my logics tended to be based around S4; because I was looking at temporal logics. I was especially interested in some very expressive operators that cannot be captured just with single monadic connectives like L and M; but which worked in the same underlying possible worlds semantics.
In any case, a good survey of modal logics is available at Modal Logic, from the Stanford Encyclopedia of Philosophy. It explains the possible worlds semantics and the range of different logical systems and applications.
In fairness to Plantinga, he is a serious philosopher who is well published on modal logics; especially concerned with quantification. He knows what he is talking about; although his work was of no relevance to my own thesis since we were using modalities for different purposes, and I did not use quantification -- at least not in the sense that Plantinga has explored.
Plantinga recognizes the problems with his own Ontological argument as a "proof". In his 1978 book "The Nature of Necessity", he considers the "ontological argument", and says this in the abstract:
quote:
In Ch.10, I apply the previous chaptersf account of modality to the Ontological Argument for the existence of God. I begin the chapter by attempting to develop a sound version of the Ontological Argument based on the work of St. Anselm. I conclude that this argument fails, as does a more recent attempt by Charles Hartshorne and Norman Malcolm. I then give a modal version of the Ontological Argument that is sound and is based on the claim that the property of unsurpassable greatness is possibly exemplified. I grant that this premise is not likely to be accepted by those who do not already hold that the property is actually exemplified, but I argue that it is still rational to accept the premise.
-- Alvin Plantinga, Abstract of "God and Necessity"

I don't have the book on hand; the abstract is on-line at intega. He's acknowledging that is not a proof of God, but that it can be "rational to accept the premise". I'm not so sure about that.
Many refutations of Plantinga's argument have been published; it has not been very persuasive amongst philosophers who actually use modal logics.
The most critical problem appears to be in the first premise (quoting DominionSeraph in the initial post)
1. By definition a maximally great being is one that exists necessarily and necessarily is omniscient, omnipotent and perfectly good. (Premise)
This is singled out as a problem in the Wikipedia article, and rightly so. It looks like Plantinga is effectively assuming the conclusion by introducing "exists necessarily" as a part of the definition. In an S5 possible worlds semantics, this boils down to saying "exists in all possible worlds", or "exists in no possible world".
Cheers -- Sylas

This message is a reply to:
 Message 16 by Chiroptera, posted 08-23-2005 10:05 AM Chiroptera has not replied

Replies to this message:
 Message 19 by PaulK, posted 08-24-2005 4:02 AM Sylas has not replied
 Message 20 by DominionSeraph, posted 08-24-2005 6:46 AM Sylas has not replied

  
PaulK
Member
Posts: 17815
Joined: 01-10-2003
Member Rating: 2.1


Message 19 of 20 (236320)
08-24-2005 4:02 AM
Reply to: Message 18 by Sylas
08-24-2005 3:37 AM


Re: a thought
quote:
The most critical problem appears to be in the first premise (quoting DominionSeraph in the initial post)
1. By definition a maximally great being is one that exists necessarily and necessarily is omniscient, omnipotent and perfectly good.(Premise)
This is singled out as a problem in the Wikipedia article, and rightly so. It looks like Plantinga is effectively assuming the conclusion by introducing "exists necessarily" as a part of the definition. In an S5 possible worlds semantics, this boils down to saying "exists in all possible worlds", or "exists in no possible world".
I'd say that it's a combination of that premise and the second:
2. Possibly a maximally great being exists. (Premise)
If we choose this instead:
2' Possible a maximally great being does not exist (Premise)
We are forced to the conclusion that it is necessarily true that there is no maximally great being and the argument falls apart. Therefore without a good reason to reject 2' the argument can't be said to be sound.
My view is that 2 as it stands is really a piece of "smoke and mirrors" to make the premise that a God necessarily exists appear more reasonable than it is. And on that basis the rationality of accepting 2 is brought into question.

This message is a reply to:
 Message 18 by Sylas, posted 08-24-2005 3:37 AM Sylas has not replied

  
DominionSeraph
Member (Idle past 4744 days)
Posts: 365
From: on High
Joined: 01-26-2005


Message 20 of 20 (236327)
08-24-2005 6:46 AM
Reply to: Message 18 by Sylas
08-24-2005 3:37 AM


Re: a thought
Sylas writes:
This is singled out as a problem in the Wikipedia article, and rightly so. It looks like Plantinga is effectively assuming the conclusion by introducing "exists necessarily" as a part of the definition. In an S5 possible worlds semantics, this boils down to saying "exists in all possible worlds", or "exists in no possible world".
Yes, but I think there's an even deeper problem.
Wouldn't said 'maximally great being' have to span the possible worlds? One per world wouldn't be maximally great, as one that spanned all worlds would be greater; and would seem to be a requirement for 'omniscience' and 'omnipotence'.
If that's the case, the 'possibly' in 2 wouldn't fit, as that basically says, "This being exists in at least one world" -- but the being doesn't exist in any one world. In order to use 'possibly', you'd have to be talking about a set of possible sets of possible worlds; ie, go off on a right angle to the first set; which, if the first set contains all possible worlds, you can't do; and even if you could, we'd run into the same problem, as said 'maximally great being' would have to span the set of possible sets of possible worlds.
Did I just break Modal Logic?
This message has been edited by DominionSeraph, 08-24-2005 06:48 AM

This message is a reply to:
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