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Author | Topic: Plantinga's ontological argument | |||||||||||||||||||||||
Chiroptera Inactive Member |
quote: 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: 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.)
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DominionSeraph Member (Idle past 4783 days) Posts: 365 From: on High Joined: |
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|xxxxxxxxxxxxxxxxxxxxDoesn't say anything about the rest. This message has been edited by DominionSeraph, 08-24-2005 12:17 AM
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Sylas Member (Idle past 5289 days) Posts: 766 From: Newcastle, Australia Joined: |
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
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.
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
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: 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
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PaulK Member Posts: 17828 Joined: Member Rating: 2.3 |
quote: 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.
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DominionSeraph Member (Idle past 4783 days) Posts: 365 From: on High Joined: |
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
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