Freethought & Rationalism Archive

Thomas Metcalf · 03-25-2003, 07:15 PM

Originally posted by Bilbo :

Quote:

There is a possible world in which maximal greatness is instantiated.

I don't like that formulation, because then the statement seems to me to be patently false. Maximal greatness can't be instantiated "in" a possible world, because what's in the world itself has nothing intrinsically related to other possible worlds. Maximal greatness doesn't exist in possible worlds; it ranges over possible worlds.

Just in case the argument is presented with that statement as a premise, I offer the alternatives:

"There is a possible world in which maximal greatness is not instantiated."

"There is a possible world in which 'exists necessarily' and 'is a unicorn' are satisfied by the same object."

I see just as much reason to accept these propositions as I do to accept their cousin.

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I'm not sure that its "hard to support the modal premise", if we understand it in terms of possible property instantiation. As Kenny suggested earlier, it seems quite reasonable to say that the premise is (at worst) properly basic for some people.

I think the illusion of proper basicness occurs because of a confusion between epistemic and alethic modality. "There is a possible world in which maximal greatness is instantiated" is true if "possible" is epistemic possibility, but we have no way to tell whether it's true if "possible" is alethic modality. When you evaluate your intuitions about the alethic version, ask yourself whether your intuitions suggest that maximal greatness is instantiated in all possible worlds, because that's what the statement literally means.

Slex · 03-25-2003, 11:17 PM

OK, thanks for the answers.
Koyaanisqatsi & Christopher 13
If I understand correctly, then the premise of necessity is contigent upon the First-cause argument, isn't it? If so, then we are into a less technical and much more down-to-earth argument.

HRG · 03-26-2003, 06:48 AM

Quote:

Originally posted by Kenny
[B]Note: this post is purely explanatory (as an explanation was requested by the OP). I have no interest in arguing for or against the OA at this time.

The term �necessary,� when used in the context of the ontological argument, is being used the technical sense given to that term by various forms of modal logic. A proposition is necessary iff it is true in all logically possible worlds. A �possible world� is simply a maximal description of a coherent state of affairs. Thus, to say that God is a necessary being is to say that the proposition �God exists� is necessarily true (i.e. the proposition �God exists� is true in all possible worlds). The term �necessary,� in this sense, has nothing to do with something being necessary for something else.

Another way to understand it is that a contingent proposition about the world describes a state of affairs which could have been otherwise whereas a necessary proposition about the world describes something that could not have been otherwise. Thus, the statement �Kenny lives in Southern California� is a contingent proposition (and one that, in fact, would have been false if uttered a year ago) whereas �2+2=4� is a necessary one. To say that the proposition �God exists� is necessary, then, means that God could not have possibly failed to exist.

The two key premises of the ontological argument are:

1.) If God exists at all, then necessarily God exists.
2.) It is logically possible that God exists

It can be shown via modal logic (S5) that the conclusion �Necessarily God exists� follows from these two premises.

But has the consistency of modal logic (S5) been shown ?

Quote:

The inference is valid (the conclusion does follow from the premises), but is it sound (are the premises true)?

<SNIP>

One problem of this approach - which is often passed over sub rosa - is that "God" by itself is just a label, which needs a definition - i.e. some property G that God is the one and only entity which satisfies G. This requires that G is meaningful in all possible universes and an existence and uniqueness proof which is valid in all possible universes.

In short, for God to be a necessary being, we need a proposition G, meaningful in all possible universes. such that

"There exists an x such that G(x), and for all y with G(y), y =x"

is a tautology.

I have no idea what such a P would look like, and G�del's completeness theorem implies IMHO that it does not exist.

Regards,
HRG.

HRG · 03-26-2003, 06:54 AM

Quote:

Originally posted by Christopher13
[B]Slex, maybe you'd benefit from looking at the Nietzschean thread where I have been discussing Aquinas' "first way" to know God exists. It is similar in method to the "third way" involving the concepts of possibility and necessity. In brief, something that has its necessity of itself means that it does not receive it from another. If everything in the universe could both be and not be, given an eternity, all things would cease to be.

Maybe so, and other things would emerge in their place, such that at each point in time some things exist (let's forget for a moment that absolute time is probably undefined).

I think you attempt an interchange of quantors: from "for each thing, there is a time at which it doesn't exist" to "there is a time when no thing exists". This is obviously invalid.

Quote:

Nothing would now exist, which is plainly false.

Non sequitur, as demonstrated above.

regards,
HRG.

Thomas Metcalf · 03-26-2003, 12:03 PM

Originally posted by HRG :

Quote:

In short, for God to be a necessary being, we need a proposition G, meaningful in all possible universes. such that

"There exists an x such that G(x), and for all y with G(y), y =x"

is a tautology.

I think I missed something. Do you mean a predicate G?

Quote:

I have no idea what such a P would look like, and G�del's completeness theorem implies IMHO that it does not exist.

This is a very interesting objection. I take you to mean that there must be some primary-kind property such that the set of instantiators is a unit set, and that anything that instantiated this property must meaningfully instantiate it in all possible worlds.

But I have no idea where G�del would come into this. Please say more! I only understand it at its basic level, perhaps, that you can't have a consistent, complete, axiomizable theory.

Christopher13 · 03-26-2003, 12:59 PM

HRG, thank you for your objection. Upon contemplating Aquinas' proof, I still profess that, given an infinite duration, if each thing that is does not cease to be, then for it not to be is not a possibility. This is Aquinas' reasoning. Your objection is interesting because it is hard to imagine this infinite series running out of steam, so to speak, but it still seems to beg the question of contingency as, granted your eternal scenario, how do you address the contingency problem? Aquinas' proofs, as you may know, are really quite independent of time as what is at stake is the ontology of the various problems and not their role in a temporal series;that is, they concern a causal line of dependence, being causal proofs, but I await your opinion of this.

happyboy · 03-26-2003, 02:50 PM

i still like my definition best.

happyboy

HRG · 03-27-2003, 04:30 AM

Quote:

Originally posted by Christopher13
HRG, thank you for your objection. Upon contemplating Aquinas' proof, I still profess that, given an infinite duration, if each thing that is does not cease to be, then for it not to be is not a possibility. This is Aquinas' reasoning. Your objection is interesting because it is hard to imagine this infinite series running out of steam, so to speak, but it still seems to beg the question of contingency as, granted your eternal scenario, how do you address the contingency problem?

An infinite series gets neatly rid of the contingency problem.

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Aquinas' proofs, as you may know, are really quite independent of time as what is at stake is the ontology of the various problems and not their role in a temporal series;

Temporal precedence and causal dependence are not identical, but completely analogous.

BTW, I tend to believe that ontological classifications exist only inside the minds of some philosophers.

Quote:

that is, they concern a causal line of dependence, being causal proofs, but I await your opinion of this.

Aquinas could not imagine an ordered set without minimal elements (in our case, ordered by: "X is dependent on Y"). In the meantime, we have seen many examples of such a situation.

In addition, he seems to have made the hidden postulate "Everything which exists, exists for a reason". Modern physics suggests IMHO that the postulate is false.

Regards,
HRG.

HRG · 03-27-2003, 04:38 AM

Quote:

Originally posted by Thomas Metcalf

I think I missed something. Do you mean a predicate G?

Quote:

Oops. Sorry. Of course I do

This is a very interesting objection. I take you to mean that there must be some primary-kind property such that the set of instantiators is a unit set, and that anything that instantiated this property must meaningfully instantiate it in all possible worlds.

But I have no idea where G�del would come into this. Please say more! I only understand it at its basic level, perhaps, that you can't have a consistent, complete, axiomizable theory.

This is G�del's famous Incompleteness theorem. But he has also proven a (less famous) Completeness theorem: any statement in first-order predicate calculus which is true in all possible models ( aka worlds) is a logical consequence of the axioms and deduction rules of the calculus.

I don't see how you could construct a predicate G such that it is meaningful in all possible worlds (i.e. does not depend on additional axioms) and "there exists a unique x such that G(x)" is a logical deduction from just 1st order calculus.

Of course, an opponent may claim that 1st order calculus is not sufficiently expressive to talk about God.

Regards,
HRG.

Gary Welsh · 03-27-2003, 06:27 AM

It is just an assertion masquerading as an argument:

"God exists... because, well, he just has to!"

Unfortunately, one cannot bring something into existence merely by repeatedly asserting its necessity.

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03-25-2003, 11:17 PM	#12
Slex Junior Member Join Date: Apr 2002 Location: Bulgaria Posts: 68	OK, thanks for the answers. Koyaanisqatsi & Christopher 13 If I understand correctly, then the premise of necessity is contigent upon the First-cause argument, isn't it? If so, then we are into a less technical and much more down-to-earth argument.

03-26-2003, 12:59 PM	#16
Christopher13 Junior Member Join Date: Mar 2003 Location: usa Posts: 28	HRG, thank you for your objection. Upon contemplating Aquinas' proof, I still profess that, given an infinite duration, if each thing that is does not cease to be, then for it not to be is not a possibility. This is Aquinas' reasoning. Your objection is interesting because it is hard to imagine this infinite series running out of steam, so to speak, but it still seems to beg the question of contingency as, granted your eternal scenario, how do you address the contingency problem? Aquinas' proofs, as you may know, are really quite independent of time as what is at stake is the ontology of the various problems and not their role in a temporal series;that is, they concern a causal line of dependence, being causal proofs, but I await your opinion of this.

03-26-2003, 02:50 PM	#17
happyboy Regular Member Join Date: Nov 2002 Location: on the border between here and there, WV Posts: 373	i still like my definition best. happyboy

03-27-2003, 06:27 AM	#20
Gary Welsh Regular Member Join Date: Jun 2002 Location: Saxonburg, PA, USA Posts: 134	It is just an assertion masquerading as an argument: "God exists... because, well, he just has to!" Unfortunately, one cannot bring something into existence merely by repeatedly asserting its necessity.

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