Hi, I was discussing the ontological argument on another forum and I came up with the following demolition. See if it works

First the argument:
http://en.wikipedia.org/wiki/Ontologica ... modal_form

1. It is proposed that a being has maximal excellence in a given possible world W if and only if it is omnipotent, omniscient and wholly good in W; and
2. It is proposed that a being has maximal greatness if it has maximal excellence in every possible world.
3. Maximal greatness is possibly exemplified. That is, it is possible that there be a being that has maximal greatness. (Premise)
4. Therefore, possibly it is necessarily true that an omniscient, omnipotent and perfectly good being exists.
5. Therefore (by axiom S5) it is necessarily true that an omniscient, omnipotent and perfectly good being exists.
6. Therefore, an omniscient, omnipotent and perfectly good being exists.

I shall just call the proposition 'omniscient, omnipotent and perfectly good being exists' G.

Consider the definition of the term 'possibly'. In view of the comments in Wiki, the term 'possibly X' means
a) X has not been disproved.

It is clear that with this definition, P6) does not follow from P5) i.e. we have not disproved (necessarily G) does not imply (necessarily G) is true.

On the other hand, in the possible worlds semantics,
http://plato.stanford.edu/entries/logic-modal/
the statement possibly necessarily G means:
b) the statement 'G is true in all worlds in W' is true in some world W'.
In other words, to apply the S5 modal logic in the many world semantics, one has to establish 'G is true in all worlds in W' in some world and not just appeal to ignorance. Both P4) and P5) fails under interpretation b).

To conclude, saying that the S5 modal logic applies simply because the same words 'possibly' and 'necessary' are used is just a fallacy of equivocation.

Most of the objections I've seen generally fall into two categories:

1. The S5 axiom is not universally accepted, and there are arguments against it.
2. If you're already an atheist, then you probably don't think it's possible that a necessary being exists, and hence the rest of the argument doesn't work

That said, I still find it a fun puzzler.

hammiesink wrote:Most of the objections I've seen generally fall into two categories:

1. The S5 axiom is not universally accepted, and there are arguments against it.
2. If you're already an atheist, then you probably don't think it's possible that a necessary being exists, and hence the rest of the argument doesn't work

That said, I still find it a fun puzzler.

Plantinga didn't intend for it to prove or show that god exists. Instead, it was meant to show that theistic belief could be rationally held.

Given this, neither 1 nor 2 strike me as a compelling defeaters.

In regards to the OP, 'possibile'does not mean that that which is possible hasn't been disproven, or at least thats not all it means. This is more than an epistemic possibility; it's a logical possibility.

The problem this argument shares with all ontological arguments is that it can be used to define into existence literally any being. For example:

1. It is proposed that an entity has a maximal destructive tendency in a given possible world W if and only if it has both the power and the will to destroy everything in W; and
2. It is proposed that an entity has maximal destructiveness if it has maximal destructive tendency in every possible world.
3. Maximal destructiveness is possibly exemplified. That is, it is possible that there be a being that has maximal destructiveness. (Premise)
4. Therefore, possibly it is necessarily true that a being with both the power and the will to destroy everything exists.
5. Therefore (by axiom S5) it is necessarily true that a being with both the power and the will to destroy everything exists.
6. Therefore, a being with both the power and the will to destroy everything exists.
7. Therefore, nothing exists.

Mick wrote:
In regards to the OP, 'possibile'does not mean that that which is possible hasn't been disproven, or at least thats not all it means. This is more than an epistemic possibility; it's a logical possibility.

What do you mean by logical possibility? Especially, what do you mean by 'it is logically possible that (P is a tautology)'? Isn't it just equivalent to 'P is a tautology'? That is the context of S5 modal logic.

@ hammiesink
That has been addressed in the Wiki link. IMO that just misses the point. The semantic is just wrong for S5 modal logic - there is no statement of ignorance in S5 modal logic.

@ Arcanyn
That is a valid counter but does not touch WHY the argument fails.

Plantinga's ontological argument is worthless because it allows the atheist to formulate an analogous argument proving that God exists in no possible world:

Definitions:
a) Maximal excellence - the property of having omniscience, omnipotence and moral perfection with respect to a possible world.
b) Maximal greatness - the property of having maximal excellence in every possible world.

Plantinga's Modal Ontological Proof:

1. It is possible that there is something that is maximally great.
2. It is possible that there is something that is maximally excellent in every possible world. [by definition of maximal greatness]
3. It is possible that it is necessary that there is something that is maximally excellent. [since if there is something that is maximally excellent in every possible world, then it is necessary that there is something that is maximally excellent.]
4. Necessarily, it is possible that it is necessary that there is something that is maximally excellent. [from 3 by S5-axiom: <>p -> []<>p ]
5. Necessarily, there is a possible world in which it is necessary that there is something that is maximally excellent.
6. Necessarily, if there is a possible world in which it is necessary that there is something that is maximally excellent, then in every possible world it is the case that there is something that is maximally excellent.
7. Necessarily, In every possible world it is the case that there is something that is maximally excellent. [modus ponens from 5&6]
8. Our actual world is a possible world.
9. Necessarily, in our actual world it is the case that there is something that is maximally excellent (and maximally great).


Anti-Plantinga's Modal Ontological Proof:

1*. It is possible that there is nothing that is maximally great.
2*. It is possible that there is nothing that is maximally excellent in every possible world. [by definition of maximal greatness]
3*. It is possible that it is not necessary that there is something that is maximally excellent. [since if there is nothing that is maximally excellent in every possible world, then it is not necessary that there is something that is maximally excellent.]
4*. Necessarily, it is possible that it is not necessary that there is something that is maximally excellent. [from 3* by S5-axiom: <>p -> []<>p ]
5*. Necessarily, there is a possible world in which it is not necessary that there is something that is maximally excellent.
6*. Necessarily, if there is a possible world in which it is not necessary that there is something that is maximally excellent, then in no possible world it is necessary that there is something that is maximally excellent.
7*. Necessarily, in no possible world it is necessary that there is something that is maximally excellent. [modus ponens from 5*&6*]
8*. Our actual world is a possible world.
9*. Necessarily, in our actual world it is not necessary that there is something that is maximally excellent.
10*. Necessarily, in our actual world it is possible that there is nothing that is maximally excellent.
11*. Necessarily, if in some possible world there is something that is maximally great, then in every possible world it is necessary that there is something that is maximally excellent.
12*. Necessarily, it is not the case that in every possible world it is necessary that there is something that is maximally excellent. [since in our actual world it is not necessary.]
13*. Necessarily, it is not the case that in some possible world there is something that is maximally great. [modus tollens from 11*&12*]
14*. Necessarily, in no possible world there is something that is maximally great.

See: http://plato.stanford.edu/entries/ontol ... #PlaOntArg

hammiesink wrote:Most of the objections I've seen generally fall into two categories:

1. The S5 axiom is not universally accepted, and there are arguments against it.

I have never seen this objection. Although oddly enough, you did misclassify something I said in the other thread as being this objection, I apologise if my explanation there as to what I meant wasn't clear enough, so I'll try and explain again.

Here's a rather more common objection you might hear, that you can add to your list:-

"You can't define things into existence".

And another:-

"The conclusion of the argument is no stronger than the premise, it is question begging".

On a technical note I would once again point out however that the S5 axiom isn't actually the key point of the argument anyway, it's the fact that the argument assumes S5 and a single equivalence class under the accessibility relation, which isn't a defining feature of S5 as a descriptive language anyway. The needless conflation of "in every possible world" and "necessary" isn't part of the formal Kripke semantics, it's an additional unjustified assumption.

ETA: As far as making "objections" to axiom S5, that would be like "objecting" to the commutativity axiom when discussing abelian groups. It's a nonsense concept, either one is discussing things that are abelian, or not. Similarly either one is discussing a modal logic with equivalence classes under the accessibility relation, or one is not. Neither abelian group theory nor S5 modal logic is going to describe every object we talk about, but that doesn't make them "wrong", it just means they are being applied incorrectly.

BKSo wrote:Consider the definition of the term 'possibly'. In view of the comments in Wiki, the term 'possibly X' means
a) X has not been disproved.

I'm not quite sure where on the wiki this comment is made, but it's certainly not right. Possibly has a technical definition depending on the exact structure of the modal logic being used, built on a formal Kripke semantics.

http://en.wikipedia.org/wiki/Kripke_semantics

The only key non-technical thing that can really be said about it is that the word "possibly" is not really interchangeable with the everyday word "possibly" under any circumstances relating to S5.

Translating the argument to English, the closest rendition one can really give is:

P1) God exists
...
C) God exists

Thommo wrote:ETA: As far as making "objections" to axiom S5, that would be like "objecting" to the commutativity axiom when discussing abelian groups. It's a nonsense concept, either one is discussing things that are abelian, or not. Similarly either one is discussing a modal logic with equivalence classes under the accessibility relation, or one is not. Neither abelian group theory nor S5 modal logic is going to describe every object we talk about, but that doesn't make them "wrong", it just means they are being applied incorrectly.

I don't think this point can be stressed enough, or explained in more than enough ways.

S5 modal logic is a formalism. You don't argue against it. At best, you just say that it's irrelevant to proving whether or not God exists.

Thommo wrote:

BKSo wrote:Consider the definition of the term 'possibly'. In view of the comments in Wiki, the term 'possibly X' means
a) X has not been disproved.

I'm not quite sure where on the wiki this comment is made, but it's certainly not right. Possibly has a technical definition depending on the exact structure of the modal logic being used, built on a formal Kripke semantics.

http://en.wikipedia.org/wiki/Kripke_semantics

The only key non-technical thing that can really be said about it is that the word "possibly" is not really interchangeable with the everyday word "possibly" under any circumstances relating to S5.

Translating the argument to English, the closest rendition one can really give is:

P1) God exists
...
C) God exists

Right. Confusing the word 'possibly' in modal logic with the everyday word is where the apologist is trying to trick us. See the second last paragraph of the Wiki section I linked:

Interestingly, Plantinga himself does not think the modal ontological argument is always a good proof of the existence of God. It depends on what his interlocutor thinks of the possibility premise. Nonetheless, Plantinga has suggested that because we do not have any evidence against the possibility premise, it might be reasonable to suppose it has a probability of 50/50.

Either Wiki misquoted Plantinga (and he is begging the question) or he is trying to equivocate.

"Scissors"
"Paper"

"Maximally powerful God, i win!!!"

BKSo wrote:

Interestingly, Plantinga himself does not think the modal ontological argument is always a good proof of the existence of God. It depends on what his interlocutor thinks of the possibility premise. Nonetheless, Plantinga has suggested that because we do not have any evidence against the possibility premise, it might be reasonable to suppose it has a probability of 50/50.

Either Wiki misquoted Plantinga (and he is begging the question) or he is trying to equivocate.

Hard to believe he really said that, is it sourced?

It's apparently based on an assumption (the princinple of equivalence) that usually leads to inconsistency when applied to an abstract definition in that way. There's no properly defined probability space to base a judgement on.

Here's an example of the inconsistency generated:

Consider:
-"Possibly there exists a maximally excellent being in exactly one possible world"

We have no evidence for or against this statement either (how could we - his definitions are maximally woolly in every possible world) so it must also be 50/50. As long as there are more than 2 possible worlds we now have 3 mutually exclusive possibilities all occuring with 50% chance. Oops.

Thommo wrote:

BKSo wrote:

Interestingly, Plantinga himself does not think the modal ontological argument is always a good proof of the existence of God. It depends on what his interlocutor thinks of the possibility premise. Nonetheless, Plantinga has suggested that because we do not have any evidence against the possibility premise, it might be reasonable to suppose it has a probability of 50/50.

Either Wiki misquoted Plantinga (and he is begging the question) or he is trying to equivocate.

Hard to believe he really said that, is it sourced?

I can't speak for that specific example, but he has made a similar error elsewhere. For instance:

What we learn from Crick and Churchland (and what is in any event obvious) is this: the fact that our hypothetical creatures have survived doesn't tell us anything at all about the truth of their beliefs or the reliability of their cognitive faculties. What it tells us is that the neurophysiology that produces those beliefs is adaptive, as is the behavior caused by that neurophysiology. But it simply doesn't matter whether the beliefs also caused by that neurophysiology are true. If they are true, excellent; but if they are false, that's fine too, provided the neurophysiology produces adaptive behavior.

So consider any particular belief on the part of one of those creatures: what is the probability that it is true? Well, what we know is that the belief in question was produced by adaptive neurophysiology, neurophysiology that produces adaptive behavior. But as we've seen, that gives us no reason to think the belief true (and none to think it false). We must suppose, therefore, that the belief in question is about as likely to be false as to be true; the probability of any particular belief's being true is in the neighborhood of 1/2. But then it is massively unlikely that the cognitive faculties of these creatures produce the preponderance of true beliefs over false required by reliability. If I have 1,000 independent beliefs, for example, and the probability of any particular belief's being true is 1/2, then the probability that 3/4 or more of these beliefs are true (certainly a modest enough requirement for reliability) will be less than 10(to the power -58). And even if I am running a modest epistemic establishment of only 100 beliefs, the probability that 3/4 of them are true, given that the probability of any one's being true is 1/2, is very low, something like .000001. So the chances that these creatures' true beliefs substantially outnumber their false beliefs (even in a particular area) are small. The conclusion to be drawn is that it is exceedingly unlikely that their cognitive faculties are reliable.

http://empyreus3.blogspot.com/2011/03/e ... alism.html

So, according to Plantinga, any belief we hold (e.g. that water is wet, that eating and breathing are good for our health) has only a 50% chance of being correct. And the only reason we are able to do better than that is because God goes into our brains and makes sure they operate correctly.

Shrunk wrote:http://empyreus3.blogspot.com/2011/03/evolution-vs-naturalism.html

So, according to Plantinga, any belief we hold (e.g. that water is wet, that eating and breathing are good for our health) has only a 50% chance of being correct. And the only reason we are able to do better than that is because God goes into our brains and makes sure they operate correctly.

Wow, just wow.

And this guy is a professor?

Doesn't speak much for his academic discipline does it?

ETA: Just for a moment it occured to me that it was an April Fools joke, but alas, it's dated March 25th.

If I have 1,000 independent beliefs...

I just thought I'd quote this part, for lulz.

He states they are all produced by the same mechanism, and that they are all independent. I.e. he is explicitly assuming that beliefs are generated randomly.

That would seem to be a testable hypothesis - do randomly generated beliefs have the same adaptive benefit as non-random (e.g. ones that involve biofeedback with the environment)?

We could, for example, program a robot to try and navigate a maze, by forming either experiential beliefs about where the walls are (adds a new wall to an internal map every time it bumps into a wall), then compare its learning behaviour to a robot that just randomly assumes a wall is in a particular place, regardless of whether it encounters a wall there or not.

Or, we could take Alvin, and ask him to test the belief "Humans can breathe safely underwater" and see if it has any impact on his survival chance...

Shrunk wrote:

Thommo wrote:

BKSo wrote:
Either Wiki misquoted Plantinga (and he is begging the question) or he is trying to equivocate.

Hard to believe he really said that, is it sourced?

I can't speak for that specific example, but he has made a similar error elsewhere. For instance:

What we learn from Crick and Churchland (and what is in any event obvious) is this: the fact that our hypothetical creatures have survived doesn't tell us anything at all about the truth of their beliefs or the reliability of their cognitive faculties. What it tells us is that the neurophysiology that produces those beliefs is adaptive, as is the behavior caused by that neurophysiology. But it simply doesn't matter whether the beliefs also caused by that neurophysiology are true. If they are true, excellent; but if they are false, that's fine too, provided the neurophysiology produces adaptive behavior.

So consider any particular belief on the part of one of those creatures: what is the probability that it is true? Well, what we know is that the belief in question was produced by adaptive neurophysiology, neurophysiology that produces adaptive behavior. But as we've seen, that gives us no reason to think the belief true (and none to think it false). We must suppose, therefore, that the belief in question is about as likely to be false as to be true; the probability of any particular belief's being true is in the neighborhood of 1/2. But then it is massively unlikely that the cognitive faculties of these creatures produce the preponderance of true beliefs over false required by reliability. If I have 1,000 independent beliefs, for example, and the probability of any particular belief's being true is 1/2, then the probability that 3/4 or more of these beliefs are true (certainly a modest enough requirement for reliability) will be less than 10(to the power -58). And even if I am running a modest epistemic establishment of only 100 beliefs, the probability that 3/4 of them are true, given that the probability of any one's being true is 1/2, is very low, something like .000001. So the chances that these creatures' true beliefs substantially outnumber their false beliefs (even in a particular area) are small. The conclusion to be drawn is that it is exceedingly unlikely that their cognitive faculties are reliable.

http://empyreus3.blogspot.com/2011/03/e ... alism.html

So, according to Plantinga, any belief we hold (e.g. that water is wet, that eating and breathing are good for our health) has only a 50% chance of being correct. And the only reason we are able to do better than that is because God goes into our brains and makes sure they operate correctly.

We know this though that is why we have the reproducibility of the scientific method. Plantinga is not telling anyone anything new.

Our beliefs about the world around us are always suspect if we have derived these beliefs ourselves. If results can't be reproduced by us or by others then they are suspect. Within an experiment you would repeat tests to see what the margin for error is and between researchers the tests would ideally be duplicated.

This process allows us to trust the empirical "beliefs" even though we can't trust our own beliefs nor our own cognition. This is why we do double-blind testing. This is why we use statistical sampling and use good sources of entropy for random samples.

For obvious reasons, Plantinga twists the already known and accepted untrustworthy nature of individual beliefs against naturalism so he can use this as a proxy attack on Evolution in that sadly American parochial way whilst ignoring the mechanisms we have created to overcome these flaws. For some reason the science of Evolution is specially picked out leaving the other sciences. Plantinga really needs to honestly explain why this gets such special attention.

The clues lie in the closing remarks - Plantinga does not extend the same lack of trust in the process to the canonical beliefs of Christianity. I suspect it will be a cold day in Hell when Plantinga honestly criticises both sides of the coin and whilst he only takes one side, we can honestly consider his cognition suspect too. By his own petard he is hung.

byofrcs wrote: We know this though that is why we have the reproducibility of the scientific method. Plantinga is not telling anyone anything new.

Our beliefs about the world around us are always suspect if we have derived these beliefs ourselves. If results can't be reproduced by us or by others then they are suspect. Within an experiment you would repeat tests to see what the margin for error is and between researchers the tests would ideally be duplicated.

Strictly speaking, however, this still does not mean that the conclusions derived from this process are "true." The scientific method simply allows us to generate conclusions that are independent of an individual's subjective impression. And, even though these conclusions have a demonstrated utility in understanding, predicting and influencing the behaviour of entities and processes that we collectively perceive to be real, this still does not mean that they are true. But it also doesn't mean that Plantinga is correct in saying the possibility of their being true is only 50%. In fact, if he is able to assign a probability to it at all, that can only be if he is in fact endowed with the ability to objectively and truthfully perceive reality, an ability that he denies exists!

The real problem with his argument is that he tries to claim that this problem (i.e. of determining whether the conclusions we draw based on our perceptual and cognitive apparatus are true) only arises if one accepts naturalism. I see no reason to justify that claim. In fact, I would go so far and say that if Christianity is true, then we know for a fact that at least some of our perceptions are false. My reasoning: According to Christianity, only God is omniscient and infallible. So if we are created as beings who are lesser than God, we must be wrong in at least some of the things we believe. This should be self-evident to Plantinga, since some of the greatest minds that have ever existed (and which Plantinga believes were created by God) have come to the conclusion that God does not exist.

Shrunk wrote:Strictly speaking, however, this still does not mean that the conclusions derived from this process are "true." The scientific method simply allows us to generate conclusions that are independent of an individual's subjective impression. And, even though these conclusions have a demonstrated utility in understanding, predicting and influencing the behaviour of entities and processes that we collectively perceive to be real, this still does not mean that they are true. But it also doesn't mean that Plantinga is correct in saying the possibility of their being true is only 50%. In fact, if he is able to assign a probability to it at all, that can only be if he is in fact endowed with the ability to objectively and truthfully perceive reality, an ability that he denies exists!

That isn't really true, he's denying an objective and truthful perception of reality exists if god does not exist since he believes that god exists, he believes he's justified.

It's circular nonsense. But there you go.

The scientific method simply allows us to generate conclusions that are independent of an individual's subjective impression. And, even though these conclusions have a demonstrated utility in understanding, predicting and influencing the behaviour of entities and processes that we collectively perceive to be real, this still does not mean that they are true.

That is just confusing what 'empirical truth' is. If a theory is consistent and works, what more can we ask for?

Also, as a matter of fact,
1) people have been believing things that are not true
2) humans cannot intuitively understand the likes of quantum mechanics, we use formal mathematics instead.