Why Plantinga's modal ontological argument fails

An attempt to demolish the ontological argument

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Re: Why Plantinga's modal ontological argument fails

#61  Postby Paul Almond » Apr 05, 2011 5:39 pm

The modal ontological argument deserves to be taken seriously in one respect: it is an ingenious and contorted piece of dishonesty to cause confusion in the gullible and philosophically naive. It works on multiple levels. First, there is the basic “proof” which tries to suck you into a detailed discussion about modal logic. After that there is a whole meta-argument, containing the original argument, about intuition and how all this is supposed to establish the rationality of what the argument just failed to show.

One thing I want to clarify - when I talk of an intuition about modal possibility being justified, that may seem strange. Isn't the whole point of intuition that it isn't justified - that there is no formal argument behind it? Really, by "justified" I mean "explainable by some kind of process that produces the intuition" or "having characteristics similar to other kinds of intuition" or "there is a plausible source of the information" involved in the intuition. The point here is that the possible worlds in Plantinga's possibility premise don't seem to give anyone anything more than that which a single world - this world, or the actual world - gives. The idea that we sometimes have intuitions about possibility is misleading.

Mick, if I claimed to have intuitive knowledge that it is modally possible that the Goldbach conjecture is true, do you think this could be a plausible claim - and how would you differentiate it from the claim of someone else who simply claims to know, intuitively, that the Goldbach conjecture is true? In each case, the person having the intuition is claiming to know something about mathematics. In the first case, someone (I) is claiming to know something about the disposition of mathematics in all possible worlds - and it is identical mathematics in each possible world. Saying that I somehow, intuitively, work out that something is the case in one possible world, and then extend this to all of them via S5 is just a distraction: I would actually know from the start that anything that I say is necessary in one possible world is possible in all of them. (Of course, you can attempt to refute this by raising the idea of possible worlds which are mathematically inconsistent with each other - but you really don't want to go there as a Plantinga advocate.) It should be apparent here that any mathematical intuition I have is not about "the existence of a possible world" in which some mathematical truth applies - it is about the disposition of the entire set of possible worlds. If I claim to know, intuitively, that a mathematical statement is modally possibly true, I am actually just claiming that it is true - assuming that mathematical statements are necessarily true (and they seem about as close to necessity as we can expect to get). Plantinga's claim of intuitive knowledge of the "possible" existence of a God is not just a claim about "possible" existence: it is a claim of modally possible existence. Regardless of what Plantinga says (and I don't value that highly) the general public associate this with our everyday idea of "possibility" and think that this is a fairly reasonable claim - one hardly needing support. In fact, it is a super-strong claim: it is a claim that the entire set of possible worlds have some feature.

If I were to claim to you, now, that I intuitively know that it is modally possible that the Goldbach conjecture is true, while also claiming that I am not claiming to know intuitively that it is true - but that the actual truth of the Goldbach conjecture follows from my intuition that it is true and the fact that mathematics is necessary - would you find this plausible?

There is one way in which someone might try to evade this. Suppose we say that intuition may come to us in ways that we cannot understand - and we should not view intuition in terms of any kind of processing of any information that comes to us from an external source. I am saying, here: suppose we avoid thinking that we must have any kind of "mechanism" in mind to justify the intuition. Someone claims to have an intuition that X, which is necessary if true, is true in a possible world. When challenged that he is simply claiming that X is true in all possible worlds, and therefore is actually true, he looks at us surprised. He explains that S5 did not occur to him, that it did not even occur to him that what is necessary in one possible world is the case in all of them. In fact, before our discussion, this person did not even realize that his intuition, if correct, means that X is actually true! Now, that person may feel that is unfair that we say that his claim to know intuitively that X is modally possibly true is just a claim to know intuitively that X is true: after all, until now he did not even know that his intuition implies that X is actually true! Does this help at all? Does it make his intuition any more plausible? No. All that is going on here is that we are imaging a very naive person, who can have an intuition in such a specific way that something else that should clearly be seen as part of that intuition goes over his head. The idea that X is true in a possible world and the idea that X is true are so closely related - so philosophically similar to each other - that any distinction is hardly relevant. None of this matters unless we are expected to infer something from this person's intuition - and he now tries to persuade us that his intuition of X's modally possible truth, together with the argument extending this to make X true in all possible worlds, somehow makes belief X rational. How does it do this? This can only make sense if we take the person's intuition seriously. We don't necessarily have to be convinced that he is right - but we may somehow think that his intuition has a good chance of being right - and that this translates into a good chance that X is true in all possible worlds, and is therefore actually true. But why should we take this any more seriously than if he had just said, "I intuitively know that X is true" - if he had said that, and we took it seriously, we could similarly view that as making belief in X more rational. Why should an intuition that X is modally possible be any more persuasive than an intuition that X is true - in the sense that we should think that the first intuition is more likely to be correct than the other? The "power" of the intuition is the same in each case. One intuition is supposed to be about what is true in a single, actual world, while the other intuition is supposed to be about what is true in some possible world which, with regards to what is being argued about here, is exactly the same as every other possible world. There is nothing about appealing to possible worlds that makes the reliability of the intuition any more likely. Again, I refer to my Goldbach conjecture analogy: someone who claims to know intuitively that the Goldbach conjecture is true should be no less persuasive, all else being equal, than someone who claims to know intuitively that the Goldbach conjecture is modally possibly true. In both cases, an intuitive ability of similar power is being claimed. We would generally say that the two claims are equivalent, but even if we accept some difference (and it would really be nothing but pedantry) it would not matter because in any important respect they are the same kind of claim.

Plantinga could have made his argument much shorter and easier to follow if he had done it this way:

S1: I intuitively know that God exists.
Conclusion: Therefore, it is rational to believe in God. Even if you aren't convinced by my intuition, the fact I am having it shows that my belief is rational.

People would have laughed at this - because it all hinges on this intuition which cannot be supported at all. In making the modal ontological argument, Plantinga has merely replaced this intuition with an intuition that "God's existence is modally possible". People get confused by this in two ways. Firstly, they conflate it with everyday possibility - this is probably how most theists view this argument - and then the whole train-wreck gets put into operation - or they recognize it as a modal claim, distinct from a claim of everyday possibility, but think that it is somehow weaker than a claim of God's actual existence - that it is more plausible to think that someone could have had this kind of intuition - that it is a more limited kind of intuitive process - however it happens or wherever all this is supposed to come from (I imagine some magical Platonic realm which looks like a Beatles album cover)- that could produce such an intuition. I should have shown here, by analogy with claims about mathematical intuition, that it is wrong to think this - that claims of intuition about possible necessity are as extreme as claims about necessity.

As an analogy for all this:

Suppose the police were looking for a serial killer. I go into the police station and say, "Look! I'm a genius. See my posts on Rational Skepticism? I won all these Orsons. I have a fantastic intuition about things - and I want to use that intuition to help you catch this murderer. I think I know where he is! I know because of my intuition! The killer is in Covent Garden, London."

The police officer who talks to me is sceptical, and ask how I know this. I explain that it is intuition. Do I really know where the killer is? the police officer wants to know. "Oh, sure I do," I reply. Every bit of the killer is in Covent Garden. His eyes are in Covent Garden, his nose is in Covent Garden, his ears are in Covent Garden, his fingers are in Covent Garden. Get the picture? Go and arrest him before he gets away!"

The police officer is not persuaded, and he throws me out. He thinks I am making an extreme claim, and he doesn't view my intuition as helping to make it rational to believe that the killer is in Covent Garden. I seem to be claiming a massive degree of intuition and he just can't plausibly see how I can do that.

The next day, I go back to the police station. The police officer reluctantly agrees to talk to me again. I now tell him that I have had another intuition. "Not another one!" he exclaims in dismay, "Are you going to make another implausible claim to have intuitive knowledge about something, even though there is no reason to think you could have come by this knowledge and that it is reliable? Is this another extreme claim that you possess some intuitive knowledge?"

"Oh, no," I say, "I'm sorry about yesterday. I realize now that my intuition wasn't to be trusted. I was claiming something very extreme- and it was hubris to think I could actually know where the killer was intuitively."

"So what is your intuition today?" the police officer ask me.

"Well, you know that yesterday I claimed that every bit of the killer was in Covent Garden: that his eyes were in Covent Garden, that his nose was in Covent Garden, that his ears were in Covent Garden and that his fingers were in Covent Garden?"

"And?"

"Well," I continue, "today I just know that the killer's ears are in Covent Garden."

"His ears are in Covent Garden?" the police officer asks me. "Why is that any more plausible than your claim yesterday?”

"Yesterday I was claiming intuitive knowledge that every bit of the killer's body was in Covent Garden. Today, I'm only claiming intuitive knowledge of where his ears are. Don't ask me how I know this: it is intuition. Have you ever lost something, and you just kind of know where it is, and you look, and it is there? Same thing. But with ears."

"Why would we want to arrest just a pair of ears?" is the reply.

"Don't you see?" I reply. "Simple human anatomy tells us that all the other parts of the killer are in the same place. Given that we now know that his ears are in Covent Garden, we can appeal to simple anatomical theory (and a reasonable belief that he has not been dismembered since his last murder), to say that all his other body parts - his eyes, nose, mouth, arms, legs, etc, are in Covent Garden. He's there right now - probably having a coffee and watching the mine artists. If you go there now, you don't just get to arrest the ears - you get to arrest the entire murderer!"

"That is one of the most stupid things I have heard!" says the police officer. "You came here yesterday with an implausible intuition that the murderer was in Covent Garden, and we didn't take you seriously. Today you have come here claiming to know that his ears…”

“and, by logical implication and appeal to anatomy, the rest of him!”

“Whatever,” Says the police officer. Why should we take you any more seriously today than yesterday?”

“Well,” I respond, “Yesterday I was claiming intuitive knowledge of where every part of the killer’s body was. Today I’m only claiming to know where his ears are!”

“You’re not!” exclaims the police officer. You’re still claiming to know where the killer is through intuition!”

“No!” I answer. “I am only claiming to know where his ears are. That is a less extreme claim of intuitive knowledge. The rest follows from human anatomy.”

“You’re still claiming intuitive knowledge of where the killer is!” says the (by now) very impatient police officer.

“I think that is a bit unfair,” I reply. “Can’t you see that a claim of intuitive knowledge about there whereabouts of every part of the killer’s body and a claim of the whereabouts of his ears are different things?”

“But you haven’t given any explanation of how you came by this intuitive knowledge!” says the police officer.

“It’s intuition!” I answer. “Of course I don’t know how I know. I just know.”

“So you want us to accept,” says the police officer, “that your claim to intuitively know where the killer’s ears are – and therefore from knowledge of human anatomy, the rest of his body – is more plausible than your claim, yesterday, of knowing where the entire killer was intuitively?”

“Yes, you’ve got it!” I answer.

“Why should the claim about the ears be any more plausible?”

“Well, I’m not claiming as much am I? Even if you aren’t sure that I’m right, don’t you see that my intuition about the killer’s ears makes it rational to believe that he is in Covent Garden?”

“What intuition could you possibly have about the killer’s ears that you wouldn’t also have about the entire killer? None of this makes sense. For example, your intuition that the killer is in Covent Garden might be based on meeting him, or someone who knows him, in the past. Maybe you went to Covent Garden and saw him there sometimes? Maybe you’ve worked out that he likes coffee? But what could you possibly be expected to find out, in any easier or more plausible way, about ears? What exactly is going on that delivers knowledge about serial killer ears to you that it is more reasonable to believe in than some process that delivers knowledge about serial killers in general?”

“Please phone the local hospital,” I say.

“Wanting to commit yourself to a psych ward?” the police officer asks.

“No, but it occurs to me that you are out of your depth here, officer. There are complex matters of human anatomy involved, and I’m not sure that you fully appreciate the way in which the presence of the killer’s ears at Covent Garden would imply the presence of his other body parts, and therefore the presence of the killer. There has been a lot of investigation about the relationship between the different parts of the body, and I think we need to ask a surgeon to come here so he can explain it to you. It isn’t your fault. Police officers can’t be expected to know about anatomy, so don’t feel bad.”

At this stage, I get thrown out again.

What I described myself as doing in that story is exactly what Plantinga is trying to do when he suggests that an intuition about the modal possibility of a necessary truth counts for anything. The claim that the killer’s ears are in Covent Garden is equivalent to the claim that Plantinga’s being exists in a possible world. My intuition that the killer’s ears are in Covent Garden is equivalent to Plantinga’s intuition that his being exists in a possible world. My claim that the entire killer is in Covent Garden is equivalent to the claim that Plantinga’s being actually exists in the world. My intuition that the entire killer is in Covent Garden is equivalent to any intuition (which Plantinga is allegedly not claiming) that his being actually exists in the world.

It should be obvious what the problem is in my story – and the same problem exists with any intuitive support of Plantinga’s modal possibility premise. The modal possibility premise is so powerful, and requires so much knowledge about Plantinga’s being, that it may just as well be direct knowledge about the existence of this being. If we can imagine any process by which intuitive knowledge could come to us that the modal possibility premise is true, it should be no less plausible to imagine intuitive knowledge that the actual conclusion of the argument is true – except everyone would just laugh if we said that. There is no plausible process, mechanism or source of knowledge for the intuition in either course.

I actually regard Plantinga’s modal ontological argument as reality-trolling on a massive scale.

EDIT - NOTE: in the story above, I referred to "Orsons." In case anyone does not know what they are, they are awards that are given out on the Rational Skepticism website (the website you are on now) for excellent posts or series of posts. If someone made a post, or number of posts, that represented very high quality work in refuting an irrational position (for example, by explaining why an argument by a famous argument by a well-known Christian apologist is wrong), then that person would be awarded an "Orson". I am just saying that in case I confused anyone who is new here.
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Re: Why Plantinga's modal ontological argument fails

#62  Postby Thommo » Apr 05, 2011 6:14 pm

In all honesty, I wouldn't look at it that way.

I'm quite happy to let Alvin have an intuition that S5 can describe the universe. I'm quite happy to let him have an intuition that there is a possible world where it's possible that a necessary being exists - I would read this as a statement of intent about what his metaphysics are trying to capture with the formalism of "possible" and "necessary", that any statement that we lack information to decide can be represented by a member of the set of possible worlds.

Of course, he can't reach his conclusion from that, so I don't need to discuss his intuitions at all.

The thing I object to is the "intuition" that "necessary" and "in all possible worlds" need to be conflated, despite them having different formal definitions - which amounts to an assumption that not only is S5 sufficiently powerful to describe some feature of the universe (I concede that sounds ok), but that it can accomodate his desire for the meaning of "possible world" within a single equivalence class. This is a formal statement with no actual meaning regarding reality, tinkering with it is a backhanded trick that makes the proof work and is totally unjustifiable, it changes the meanings of "possible world" quite clearly against his intuition of what they should mean (some state of affairs that we can't rule out, or similar).

ETA: An attempt to explain this in a non-technical way:

Basically, we have two statements:

1) The possible worlds of Plantinga's metaphysics represent states of affairs (ways the world could be) that we do not have information to rule out - i.e. they are possibilities relative to our knowledge. (We might "intuitively" say that this is a fair enough concept and thus he can have an "intuition" that it's possible that a necessary being exists.)
2) That necessary means "in every possible world" rather than "in every possible world seen under the accessibility relation". (Which is a technical statement we define into our logic, a simple matter of choice)

You can have one, but not both. Encoding the second into our logic simply changes what sets of possible worlds we can choose, thus changing the meaning of "possible world" away from what it's supposed to mean.
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Re: Why Plantinga's modal ontological argument fails

#63  Postby Mick » Apr 05, 2011 7:56 pm

Thommo wrote:
Mick wrote:
Thommo wrote:When someone doesn't admit defeat at logical impossibility, it's time to walk away.


Logical truths and impossibilities are always truths of a system or a worldview. They might apply to "reality", but that is something to debate. Take dialetheism for instance. It's probably not the best choice tactic to walk away from a dialetheist because he doesn't admit defeat at a logical impossibility. Heck, he affirms true contradictions.


True contradictions aren't logical impossibilities in a dialethic logic. He's playing by the rules of his game, if say he's making a logic to describe "things that can be reasonably said about my couch" and he includes the phrases "it's red" and "it's not red" and even "it's red and not red".

The difference is modal logic is not dialethic. So the metaphysician who suddenly brings this up as a defence of his not playing even by his own rules (let alone the ones I would choose) is clutching at straws, he's creating new moves in his game just so he doesn't have to admit defeat.

Would you tolerate that in scrabble? I wouldn't and metaphysics isn't really such a useful or fun game, so I don't see why we should tolerate it there.

Time to walk away.

Mick wrote:
That means that you have quite literally proved their assertion false by the strictest possible rules and they still refuse to admit defeat. There's nothing that you can't say by those rules.


That'd be question begging if said to the dialetheist.


The arguments we have been discussing are in modal logics, not paraconsistent ones. That's telling me that if this had been a different conversation, with different things said to me, I'd need to produce a different response. Well, ok. So what?


No, I mean that he affirms true contradictions. That's part of it. For the classicalist, he's affirming a logical impossibility. That's all I meant.

You spoke in general terms. you did not say that if we play be classicalist rules, and if he does not admit defeat at a logical impossibility, then walk away. You simply just said: if he doesn't admit defeat at a logical impossibility, which, in this case means a contradiction of some sort, then walk away.
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Re: Why Plantinga's modal ontological argument fails

#64  Postby Mick » Apr 05, 2011 8:04 pm

Thommo wrote:
Mick wrote:One thing which caught my attention is this idea that his claiming that 'possibly god exists' is just to claim that god exists. I think that's unfair. Firstly, Plantinga doesn't refer to god as a proper name or otherwise. He talks about a being- a general term.


He also tells us he's defending the rationality of theistic belief, and indeed has spent his whole life doing so. Does the relabelling to what we all agree he's talking about make anything less clear? Personally (I can't speak for Paul) I find it makes things more clear.

Mick wrote:Secondly, while the possibility is logically equivalent to the conclusion, it is not synonymous with the conclusion.


It is. You can prove that you can transpose any occurence of "possibly god exists" with "god exists" within the formalism under discussion, making them perfect synonyms. They aren't synonyms in English language, nor does the proof hold in English language.

Mick wrote:Neither is it obvious that it is logically equivalent to the conclusion.


It is obvious to anyone who understands the formalism, though why we would be concerned about what's obvious eludes me.

Mick wrote:Keep in mind that the possibility premise is not given as <>[](Ex)Gx; it is simply offered as <>(Ex)Gx.


Your second Gx there is not the same Gx, it's clearer if understood that he's giving it as:

<>∃x([]G(x)) ⇔ <>∃x(F(x)) where F(x) is defined to be []G(x), i.e. F is Maximal greatness and G is Maximal excellence.

Since he's chosen the rules so that he can pull the quantifier out (in fact I'm not sure if the formalism uses quantifiers there or not even) it really doesn't matter where the quantifier appears, they are the same statement.

ETA: I have switched to a conventional notation which only uses brackets as parenthesis, because I find the use of them in place of quantifiers in addition to parenthetical usage ugly and ambiguous.


I'm afraid you're wrong, Thommo. What you 'transpose' is logical equivalence. Tell me, what is or are the differences between logical equivalent statements and synonymous statements?

As for your formulation, I havent a clue what you're talking about. There's no bi-conditional or entailment given in his possibility premise. You're being awfully creative here.
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Re: Why Plantinga's modal ontological argument fails

#65  Postby Mick » Apr 05, 2011 8:15 pm

Paul Almond wrote:
Mick wrote:One thing which caught my attention is this idea that his claiming that 'possibly god exists' is just to claim that god exists. I think that's unfair. Firstly, Plantinga doesn't refer to god as a proper name or otherwise. He talks about a being- a general term.

That's a completely pointless reply. We all know what Plantinga means. You don't want this to be a claim for God? Fine - the possibility premise is that it is modally possible that a being with properties defined by Plantinga exists - and I view it is frankly bizarre to say that this isn't supposed to be God. We are doing theology here - not skiing. Whether Plantinga is claiming God's modally possible existence, some being's modally possible existence or Bugs Bunny's modally possible existence is absolutely irrelevant to the rebuttal that I gave. It doesn't matter what is being claimed to modally possibly exist. There is no plausible way in which we could regard any intuition of this modally possible existence as justified in any way that has anything to do with possible worlds or that is given anything by possible worlds. any such intuition is merely intuition about a necessary feature of the world - and anyone claiming to have such an intuition is merely claiming that he knows that something exists.

I think my point was quite simple - and I only went on for that long because some people (people like you, generally) seem to insist that modal logic is going to do anything of any use to anyone here. This is like the philosophical equivalent of a perpetual motion machine. If I showed people a wheel and claimed that if I spin it it will spin forever and generate free energy everyone will see that I am talking nonsense. However, if I build a complex machine with a complex path of causality inside it, with levers driving wheels which pull magnets and move things this way or that I can hide the fact that there is nothing on which to base such a machine - and the gullible may think that the more complex machine can give us free energy, even though we should be able to see that any simple machine we can imagine won't - and that therefore no part of this more complex machine can be producing free energy, and that the whole machine must be founded on nothing. Some people will never accept that, and will insist that there is something to be gained from an in-depth discussion of the workings of the fantastic free energy machine. If people aren't persuaded, the inventors of the machine can use mathematics to describe the behaviour of the free energy machine in the hope that this obscures the fact that it just can't work - as should be obvious from a simple consideration. Plantinga is doing nothing more than dozens of free energy machine inventors are doing on the Internet all the time - except he is doing it in philosophy instead. The whole thing is suspiciously close to the emperor's new clothes.



Hi, it matters in the formulatization whether Plantinga uses a proper noun, name or whatever. These have different commitments given his actualism n' stuff.

I'm not too sure what I should reply to here. You're just making allegations. There's no argument which I can make sense out of, and your subsequent post is bludgeoning in terms of its length despite my request for brevity.

I read and type quickly on my phone. I don't have the time or.resources to answer such replies.

:(
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Re: Why Plantinga's modal ontological argument fails

#66  Postby Paul Almond » Apr 05, 2011 8:31 pm

I understand your point, Thommo, and I don't have any problem with it - despite still maintaining the objection that I have given. In my objection, I don't explicitly say what a "possible world" is. In fact, I leave that to whoever is trying to use the modal ontological argument. My own view would be that the set of possible worlds should be the set of all worlds which we do not know to be inconsistent with our knowledge - and I would actually admit logically inconsistent worlds into this set. As far as I am concerned, there should not be any problem with saying that there are possible worlds in which the Goldbach conjecture is true and possible worlds in which it is false. All we are doing is defining what might be the case. Someone may say, however, that there must be a set of possible worlds that share things like mathematical and logica properties with our own. Specifically, for Plantinga's argument, we are talking about a set of worlds for which truths about the existence of God are all the same. Plantinga's intuition is claimed to be about the existence of a possible world in which God exists in that set - whether it is meaningful to talk about possible worlds outside that set does not concern me: Plantinga is clearly claiming that intuition can inform him about the set of possible worlds for which truths about God are the same as they are in ours, and can inform him more reliably that it could just inform him about our world alone. I dispute that - regardless of what other possible worlds are being considered beyond all this.
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Re: Why Plantinga's modal ontological argument fails

#67  Postby IIzO » Apr 05, 2011 8:40 pm

2. It is proposed that a being has maximal greatness if it has maximal excellence in every possible world.

Seriously , how is this not begging the question ?"maximal excellence in every possible world" is rejecting every possible worlds where maximal greatness is less than maximal excellence without justification .
The proposition is not acceptable to me ,there are no direct equivalence between maximal greatness and maximal excellence.
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Re: Why Plantinga's modal ontological argument fails

#68  Postby Paul Almond » Apr 05, 2011 8:47 pm

IIzO wrote:
2. It is proposed that a being has maximal greatness if it has maximal excellence in every possible world.

Seriously , how is this not begging the question ?"maximal excellence in every possible world" is rejecting every possible worlds where maximal greatness is less than maximal excellence without justification .
The proposition is not acceptable to me ,there are no direct equivalence between maximal greatness and maximal excellence.

I don't have any real problem with that really: it's just a definition. I view it as extremely vague, but I'm sure an apologist could tighten it up if he had too.
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Re: Why Plantinga's modal ontological argument fails

#69  Postby Thommo » Apr 05, 2011 8:48 pm

Mick wrote:I'm afraid you're wrong, Thommo. What you 'transpose' is logical equivalence. Tell me, what is or are the differences between logical equivalent statements and synonymous statements?


Two words or phrases are synonymous if they have the same meaning in context.

What did you mean when you tried to draw a distinction between logical equivalence and synonymity? How do you think your point impacts the explanations that were given?

Mick wrote:As for your formulation, I havent a clue what you're talking about. There's no bi-conditional or entailment given in his possibility premise. You're being awfully creative here.


It (trivially) provably follows from <>∃x([]G(x)) that <>∃x(F(x))

and it (trivially) provably follows from <>∃x(F(x)) that <>∃x([]G(x))

I.e. under the definition of the entailment relation for S5 logic <>∃x([]G(x)) ⇔ <>∃x(F(x))

I'm not quite following where the confusion or "creativity" is there, it's all perfectly standard. :scratch:

Edit: Fixed an error.
Edit2: Perhaps you are misreading the notation? It maybe wasn't clear. For the sentence in question, you can replace the ⇔ sumbol with the words "or equivalently".
Last edited by Thommo on Apr 05, 2011 9:25 pm, edited 2 times in total.
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Re: Why Plantinga's modal ontological argument fails

#70  Postby Thommo » Apr 05, 2011 8:52 pm

Paul Almond wrote:My own view would be that the set of possible worlds should be the set of all worlds which we do not know to be inconsistent with our knowledge - and I would actually admit logically inconsistent worlds into this set.


I think this is indeed the standard practise. Although there may be some formal details when you get into it (e.g. is a possible world where we guess pidig incorrectly inconsistent in a theory in which we have not embedded PA or some other suitable system).

It's this understanding of the set of possible worlds that would appear to justify modal intuition. However, when you start messing around with the definition of possible worlds any justification for intuition would seem to disappear.
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Re: Why Plantinga's modal ontological argument fails

#71  Postby Shrunk » Apr 05, 2011 8:58 pm

Mick wrote:I'm not too sure what I should reply to here. You're just making allegations. There's no argument which I can make sense out of, and your subsequent post is bludgeoning in terms of its length despite my request for brevity.


I don't see how it can be possible that someone could be unable to "make sense out of" Paul's clear, precise and specific arguments, lengthy though they may be, while claiming to be able to understand Plantinga's convoluted, obscure and misleading bafflegab. I guess those God-goggles only work when you want them to.
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Re: Why Plantinga's modal ontological argument fails

#72  Postby Mick » Apr 05, 2011 9:27 pm

IIzO wrote:
2. It is proposed that a being has maximal greatness if it has maximal excellence in every possible world.

Seriously , how is this not begging the question ?"maximal excellence in every possible world" is rejecting every possible worlds where maximal greatness is less than maximal excellence without justification .
The proposition is not acceptable to me ,there are no direct equivalence between maximal greatness and maximal excellence.


Here's something I'm sympathetic to at least to some degree. It seems to me that a maximal greatest being should (at most) just be required to be maximally excellent in every world in which it exists. Why, every world? What's so repugnant about not being maximally excellent in a world wherein you, a maximally great being, do not exist?

If we grant this, then it only follows that, possibly, a maximally excellent being exists.



BTW, Paul, I forgot to mention that I don't think we are doing theology here. Probably the most accepted conceptual difference between theology and philosophy is that only the former uses (and has to use at least once) premises which are from revelation. Plantinga, a philosopher, does not such thing.
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Re: Why Plantinga's modal ontological argument fails

#73  Postby Mick » Apr 05, 2011 9:31 pm

Shrunk wrote:
Mick wrote:I'm not too sure what I should reply to here. You're just making allegations. There's no argument which I can make sense out of, and your subsequent post is bludgeoning in terms of its length despite my request for brevity.


I don't see how it can be possible that someone could be unable to "make sense out of" Paul's clear, precise and specific arguments, lengthy though they may be, while claiming to be able to understand Plantinga's convoluted, obscure and misleading bafflegab. I guess those God-goggles only work when you want them to.


Pick out the premises within that post then. I'm not talking about the lengthy post, but just the one I recently replied to.
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Re: Why Plantinga's modal ontological argument fails

#74  Postby Paul Almond » Apr 05, 2011 9:41 pm

Okay Mick, suppose I give you some mathematical problem, which I have just devised today and which has one of two answers - "Yes" or "No". You have to work out whether the answer is "Yes" or "No". You can't solve the problem, though you may intuitively have some suspicion that the anwer is a particualr value - "Yes" or "No". You take the problem to a university and see two mathematics professors, Professor A and Professor B. You don't know anything about these professors, apart from the fact that they are mathematics professors at this university: just assume that they are both randomly selected mathematics professors at the university. You show them both my problem.

Professor A says that he has an intuitive belief that the answer to the problem is "No".
Professor B says that he has an intuitive belief that it is modally possible that the answer to the problem is "Yes".

You ask each professor to justify his belief and he doesn't know on what he bases it. Also, neither professor makes any special impression in you in conversation: beyond the answers I have given above, you get no information from or about each professor, such as about his previous record on intuition, how reliable he is, his IQ, papers published, etc. All you know is what is in this scenario.

Here is my question: Has it now become more rational or less rational to think that the answer is "Yes", or has the visit told you nothing?

The similarity with what Plantinga's modal ontological argument is supposed to achieve should be obvious.
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Re: Why Plantinga's modal ontological argument fails

#75  Postby Teuton » Apr 05, 2011 9:54 pm

Paul Almond wrote:
modally possible


"Possible" is per se a modal term, so the phrase "modally possible" is redundant. Anyway, I have no idea what "nonmodally possible" might mean.
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Re: Why Plantinga's modal ontological argument fails

#76  Postby Thommo » Apr 05, 2011 9:58 pm

Teuton wrote:
Paul Almond wrote:
modally possible


"Possible" is per se a modal term, so the phrase "modally possible" is redundant. Anyway, I have no idea what "nonmodally possible" might mean.


It means "possible" in its everyday sense of the word - an event which cannot be ruled out. You might notice that the formal S5 definition of "possible" does not mean this.
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Re: Why Plantinga's modal ontological argument fails

#77  Postby Teuton » Apr 05, 2011 9:59 pm

Thommo wrote:
Paul Almond wrote:My own view would be that the set of possible worlds should be the set of all worlds which we do not know to be inconsistent with our knowledge - and I would actually admit logically inconsistent worlds into this set.

I think this is indeed the standard practise.


I don't think that most logicians use "possible world" in the sense of "epistemically possible world" rather than "logically possible world" or "ontologically/metaphysically possible world". And internally inconsistent or contradictory worlds are impossible worlds rather than possible worlds.
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Re: Why Plantinga's modal ontological argument fails

#78  Postby Paul Almond » Apr 05, 2011 10:04 pm

I merely mean that Mathematician B is making the kind of statement about possibility that Plantinga thinks he can intuitively justify: people can phrase that as they want. I mean that Mathematician B is actually asserting the equivalent of the possibility premise in Plantinga's argument. Mathematician B could have simply said "I have no idea" - and we might infer from this that he thinks it is possible that the answer is "Yes" and possible that the answer is "No" - but what I am saying here is that Mathematician B is not just relying on uncertainty to say that something is possible - which would be the default position in the absence of certain knowledge one way or the other. He is doing something stronger: he is actually asserting a possibility premise in modal logic. Now, it is not my job to sort that out and decide whether it is a meaningful thing to do - but Plantinga's argument relies on a distinction between the kind of possibility we may say to apply because we can't prove something to be otherwise and the kind of possibility that you can, somehow, know something to have that is a stronger sort of possibility that justifies statements about possible worlds.
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Re: Why Plantinga's modal ontological argument fails

#79  Postby Teuton » Apr 05, 2011 10:05 pm

Thommo wrote:
It means "possible" in its everyday sense of the word - an event which cannot be ruled out.


By what? By the rules of logic, physics, or metaphysics?
The problem is that it's the everyday senses of the words "possible" and "necessary" that are in need of interpretation and clarification.
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Re: Why Plantinga's modal ontological argument fails

#80  Postby Thommo » Apr 05, 2011 10:06 pm

Teuton wrote:
Thommo wrote:
Paul Almond wrote:My own view would be that the set of possible worlds should be the set of all worlds which we do not know to be inconsistent with our knowledge - and I would actually admit logically inconsistent worlds into this set.

I think this is indeed the standard practise.


I don't think that most logicians use "possible world" in the sense of "epistemically possible world" rather than "logically possible world" or "ontologically/metaphysically possible world". And internally inconsistent or contradictory worlds are impossible worlds rather than possible worlds.


I don't think most logicians mean anything by "possible world" beyond its formal definition. But we aren't talking about logicians, we are talking about what philosophers intend to capture with the concept of a possible world. And I really can't be bothered to get into the ins and outs of whether we can be judged to formally "know" the logical consequences of all the things we know. It doesn't matter one way or the other in practise.

Obviously we do know that logically contradictory worlds are not possible, their accidental inclusion in the set of possible worlds in some model is only ever going to be a mistake, it really doesn't matter how you then classify that mistake in your own mind.
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