Freethought & Rationalism Archive

HRG · 08-15-2002, 12:24 AM

Quote:

Originally posted by Cosym:
[QB]---I never understood this mind, and I am aware I'm digressing slightly, but I don't understand what it means to say, for one characteristic, that a being would be maximally good, how can one be perfectly good?---

Normally, that would be a problem: but this proof actually has an operational definition (i.e. reasonable limits): regardless of whatever "perfectly good" means (and it's not clear that that's a characteristic this proof demonstrates in the first place), the characteristics are as maximal as _possible_. That is, they are limited by logical possibility.

Not all ordered sets have maximal elements.

Quote:

The proof also has an excellent defense for this sort of criticism, because the critic very quickly finds themselves claiming that the "greatest possible being" is not possible, which is a logically incoherent statement.

This statement is not incoherent at all. It is simply the claim that "the greatest possible being" is as ill-defined as "the largest natural number".

IOW, before you use the term "the greatest possible being" in an argument, you first have to show that the set of all possible beings, ordered by the relation "greater than" *), has a greatest - not just a maximal - element. Without that, you might as well talk about the Man in the Moon.

Regards,
HRG.

*) which would have to be defined in an unambigous way.

Adrian Selby · 08-15-2002, 12:26 AM

"Thus one may be as fluffy as one can possibly be given that he is also metallic, and vice versa. Water may be a good example as it is both hydrogen and oxygen, but too extreme in either direction it can lose one or the other quality"--Mike

The problem I have here is that if the qualities are light and heavy, then to say one is as heavy as one can possibly be without not being light, and one is as light as one can possibly be without not being heavy seems ridiculous.

I appreciate that it isn't actually important that we should be able to conceive how fluffy something can be given its metallic, but those properties that are contrary to each other do seem to cause a problem, if only because they are properties that are usually exclusive. And if these properties exemplified aren't, then there are perhaps properties that are exclusive.

The 'get out' you've described doesn't work.

Cosym · 08-15-2002, 03:19 AM

---Not all ordered sets have maximal elements.---

Too bad for those sets, then.

---IOW, before you use the term "the greatest possible being" in an argument, you first have to show that the set of all possible beings, ordered by the relation "greater than" *), has a greatest - not just a maximal - element.---

The key is the term possible. And in reference to existence, the key idea is that the most possible worlds something can exist in is: all of them.

Kassiana · 08-15-2002, 03:33 AM

Funnily enough, disproving everything Andrew insisted others do in order to show that "God" doesn't exist would not prove to me that my Gods don't exist. How is it that Andrew's belief in God rests on evolutionary theory being false? That makes no sense to me. Heck, even when I was a Christian, I would have found his position strange. Belief should be founded, after all, on a "personal relationship with God," not apparent design. /end regression into Christian thought

So Andrew, why do you let your faith rest on such....uhm....earthly principles rather than on other things? I'm confused. Most believers in Deity cite their holy books, their religious experiences, their religion's long (or short!) history, etc. as reasons they believe in their God. Why don't you believe for those reasons? Would those reasons not remain even if it were shown that abiogenesis occurred without intervention from any deity that we can discover?

Boy, I'm confused.

Cosym · 08-15-2002, 03:45 AM

---Funnily enough, disproving everything Andrew insisted others do in order to show that "God" doesn't exist would not prove to me that my Gods don't exist.---

He appears to reject the idea that existence could exist without god. I'm not sure he really bases his own theist beliefs ON these arguements alone, however.

---How is it that Andrew's belief in God rests on evolutionary theory being false?---

To get some context, check out the link that he provided to his own discussion board (assuming it's the same Andrew). It's called "Challenging Atheism," and it's premised on the idea that atheism is a belief in various things that he then lists, all of them being contrary positions to his beliefs.

Anyway, chances are he's now gone from this thread either because 1) he got enough responses of the sort that he loves to complain about on his own board or 2) he didn't get the responses he wanted, and went elsewhere to bait some more people in order to amass them.

[ August 15, 2002: Message edited by: Cosym ]

Cosym · 08-15-2002, 04:23 AM

Just to clarify on the second inference...

What is going on here is an arguement of this form: "If condition A is met, then (and only then) condition B is true."

That is, <>G->G can ONLY be infered to be true if G -> []G is true. <>G->G cannot be taken as a premise. Nor can you substitute anything you please for G without finding some way to properly substitute for G in G->G[] as well.

More specifically, Brouer's Theorem (I forgot the extra "r", sorry: that's what you get when speaking from memory) is of this form: "if it is true that the truth of x would imply that x is necessarily true, then (and ONLY then) the possible truth of x implies the actual truth of x."
If you'd like to find a formal explication of this theorem, you're going to have to check out a book on K logic, and skim to the bits about the modal tableu S5. I don't have access to a text at the moment, and there are no internet resources (peer-rev journals should be free, damnit!)

Thomas Metcalf · 08-15-2002, 08:43 AM

Quote:

Originally posted by Cosym:

G = []G (god is defined as the greatest existence, which in modal logic means necessary existence)
<>G (it is possible that god exists: i.e. in at least one possible world)

1. G -> []G (if god exists, then god necessarily exists, or "God must exist necessarily IF He even exists at all.")

2. (G -> []G) -> (<>G -> G) (plugging G into the valid modal form of (p -> []p) -> (<>p -> p) (i.e., that necessary existence of any p implies actual existence of p))

3.<>G -> G (if it is possible that god exists, then god exists)- found by using inference 1 with inference 2 in a modus ponens

4. G (modus ponens, using the axiom and inference 3)

It seems to me that the modal ontological argument is vulnerable to the same sorts of criticisms Kant leveled against the traditional ontological argument in Critique of Pure Reason.

First, existence is not a determining predicate. This principle is disputable but I think it holds up after argumentation. And modal statements can be thought of as statements of existence, just in the context of possible worlds, no? I would feel fairly comfortable with the position that modal "state" (necessary existence, possible existence, impossible existence) is also not a determining predicate. Therefore, "G = []G" (or 1; I'm not sure why you stated "G = []G" at the beginning) is false.

I would also say that it's hard to make sense of the statement "If a necessary being exists, then this necessary being exists necessarily," as it is to make sense of "It is possible that a necessary being exists." These are encapsulated in your "<>G" and your 1.

Kant's second criticism seems more damaging. When we try to determine whether things exist, we don't define their existence and then see if their existence is visible analytically. Rather, we define something, leaving open the question of whether it exists, and then search the universe for it or see if it follows from any necessary truths. Therefore, again, we ought not accept "G = []G". Think of Plantingan "nunicorns" as parallel to his "eunicorns."

Finally, a parody, this one inviolate, I think. Replace "G" in your above argument with G': "The Necessary God-Destroying Device." The conclusion of this argument is that G' exists, which contradicts the conclusion of your original argument. These parallel arguments have contradictory conclusions, so there must be a mistake in the form somewhere.

Hold, you might say: "<>G'" is false, because God's existence is necessary so it would be impossible to destroy Him. My response is that, then, "<>G" in the original argument is false because the Necessary God-Destroying Device is, well, necessary.

I look forward to your response. Thanks for giving us something we don't see every day.

[ August 15, 2002: Message edited by: Thomas Metcalf ]

08-15-2002, 09:23 AM

Cosym,

Quote:

It isn't assumed: it is an inference!

Given that �possible necessity� in modal logic always entails instantation, to assume <>X[] in any way shape or form is to implicitly beg the question of whether X exists.

Simply because the assumption of <>G[] is split up over several premises and definitions changes precisely nothing.

Quote:

And, unlike your chicken example, <>G cannot by itself be combined with G->G[] to demonstrate G.

Yes, several additional steps are required. That you think this makes any difference demonstrates that you do not understand question-begging, assurances to the contrary notwithstanding. <a href="http://www.swif.uniba.it/lei/foldop/foldoc.cgi?begging+the+question" target="_blank">http://www.swif.uniba.it/lei/foldop/foldoc.cgi?begging+the+question</a>

It does not matter how complex or indirect the assumption is. As long as what you are trying to prove (namely the modal possibility of God�s modal necessity) is assumed, you have begged the question at hand.

That means the assumption that anything is (modally) possibly necessary implicitly assumes instantiation.

Quote:

That it is merely possible that G necessarily exists does not demonstrate either G or G[]. All it could say is that it is possible that G exists, and thus only possible that G is necessary. One could claim the same about anything.

You�re right. One can claim that anything is modally possibly necessary and hence exists. That�s why such forms of argument have no force.

Quote:

Where in the proof is found something equivalent to <>J[]?

Don�t be such a fool. It follows directly from the definition of God (being necessary), the assumption of his possibility and from the structure of modal logic (wherein the instantiation of a necessary being in some possible world

Quote:

How can you possibly critique the arguement without examining the second inference, which is the key to the whole thing?

I�m not criticizing the validity of the argument. The only relevant structural consideration is the notion of possible necessity which is assumed in both your argument and my argument. There is no relevant disanalogy save in the language with which the argument is expressed.

Regards,
Synaesthesia

ex-preacher · 08-15-2002, 10:59 AM

Quote:

Originally posted by Mike:
Roger,

Seriously investigate? Maybe not. Keep an open mind, certainly. Many apparently impossible things have become possible in recent years. I try not to draw conclusions about things I know nothing about. If you know nothing about God and don't wish to, fine, but don't pretend you know what he is or is not if you haven't made the effort.

Right now alien abductions don't concern me, but whether I have 72 years of life or infinity may be worth consideration since the meaning of life itself hangs in the balance.

Are you under the false impression that most of us haven't seriously considered the existence of God? That's the whole reason we're here! We have seriously considered that possibility and have found it sorely lacking.

Most of us were Christians until we discovered that both reason and reality dictate strongly against the supernatural, specifically the God(s) of the Bible.

I was raised as a "Hebrew of Hebrews" on the mission field, the son of a preacher of the Church of Christ (maybe not the true religion, you say? Right.) My great-great grandfather studied under Alexander Campbell.

I attended an accredited Christian liberal arts university, earning a B.A. in Bible (4.0). I next earned a Master of Divinity (top student) and a Doctor of Ministry at Abilene Christian University. I ministered at a church in Dallas for 10 years. I then spent 3 years teaching Bible at another Christian university. It was during that final phase that I resolved to honestly and thoroughly study all sides of certain issues which had long troubled me. Within 6 months I was an atheist. I quit my job and sacrificed my career as a minister/professor.

I continue to study the Bible, listen to Christian radio and read Christian books. I would love to be able to believe again and to please my family (including a wife and 3 children). But I cannot lie to myself and I cannot make myself believe something which deep down I think is false.

To what extent have you "seriously considered" that God might not exist?

HRG · 08-15-2002, 11:29 AM

Quote:

Originally posted by Cosym:
---Not all ordered sets have maximal elements.---

Too bad for those sets, then.

But using a term like "greatest possible" assumes uncritically that they do.
[quote]

---IOW, before you use the term "the greatest possible being" in an argument, you first have to show that the set of all possible beings, ordered by the relation "greater than" *), has a greatest - not just a maximal - element.---

The key is the term possible.
[quote]

That won't help you with infinite sets. The "largest possible natural number" is just as ill-defined as the "largest natural number".

HRG.

08-15-2002, 03:45 AM	#85
Cosym Junior Member Join Date: Aug 2002 Location: New York Posts: 22	---Funnily enough, disproving everything Andrew insisted others do in order to show that "God" doesn't exist would not prove to me that my Gods don't exist.--- He appears to reject the idea that existence could exist without god. I'm not sure he really bases his own theist beliefs ON these arguements alone, however. ---How is it that Andrew's belief in God rests on evolutionary theory being false?--- To get some context, check out the link that he provided to his own discussion board (assuming it's the same Andrew). It's called "Challenging Atheism," and it's premised on the idea that atheism is a belief in various things that he then lists, all of them being contrary positions to his beliefs. Anyway, chances are he's now gone from this thread either because 1) he got enough responses of the sort that he loves to complain about on his own board or 2) he didn't get the responses he wanted, and went elsewhere to bait some more people in order to amass them. [ August 15, 2002: Message edited by: Cosym ]</p>

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08-15-2002, 12:26 AM	#82
Adrian Selby Senior Member Join Date: Jan 2002 Location: Farnham, UK Posts: 859	"Thus one may be as fluffy as one can possibly be given that he is also metallic, and vice versa. Water may be a good example as it is both hydrogen and oxygen, but too extreme in either direction it can lose one or the other quality"--Mike The problem I have here is that if the qualities are light and heavy, then to say one is as heavy as one can possibly be without not being light, and one is as light as one can possibly be without not being heavy seems ridiculous. I appreciate that it isn't actually important that we should be able to conceive how fluffy something can be given its metallic, but those properties that are contrary to each other do seem to cause a problem, if only because they are properties that are usually exclusive. And if these properties exemplified aren't, then there are perhaps properties that are exclusive. The 'get out' you've described doesn't work.

08-15-2002, 03:19 AM	#83
Cosym Junior Member Join Date: Aug 2002 Location: New York Posts: 22	---Not all ordered sets have maximal elements.--- Too bad for those sets, then. ---IOW, before you use the term "the greatest possible being" in an argument, you first have to show that the set of all possible beings, ordered by the relation "greater than" *), has a greatest - not just a maximal - element.--- The key is the term possible. And in reference to existence, the key idea is that the most possible worlds something can exist in is: all of them.

08-15-2002, 03:33 AM	#84
Kassiana Veteran Member Join Date: Jun 2000 Location: USA Posts: 5,046	Funnily enough, disproving everything Andrew insisted others do in order to show that "God" doesn't exist would not prove to me that my Gods don't exist. How is it that Andrew's belief in God rests on evolutionary theory being false? That makes no sense to me. Heck, even when I was a Christian, I would have found his position strange. Belief should be founded, after all, on a "personal relationship with God," not apparent design. /end regression into Christian thought So Andrew, why do you let your faith rest on such....uhm....earthly principles rather than on other things? I'm confused. Most believers in Deity cite their holy books, their religious experiences, their religion's long (or short!) history, etc. as reasons they believe in their God. Why don't you believe for those reasons? Would those reasons not remain even if it were shown that abiogenesis occurred without intervention from any deity that we can discover? Boy, I'm confused.

08-15-2002, 04:23 AM	#86
Cosym Junior Member Join Date: Aug 2002 Location: New York Posts: 22	Just to clarify on the second inference... What is going on here is an arguement of this form: "If condition A is met, then (and only then) condition B is true." That is, <>G->G can ONLY be infered to be true if G -> []G is true. <>G->G cannot be taken as a premise. Nor can you substitute anything you please for G without finding some way to properly substitute for G in G->G[] as well. More specifically, Brouer's Theorem (I forgot the extra "r", sorry: that's what you get when speaking from memory) is of this form: "if it is true that the truth of x would imply that x is necessarily true, then (and ONLY then) the possible truth of x implies the actual truth of x." If you'd like to find a formal explication of this theorem, you're going to have to check out a book on K logic, and skim to the bits about the modal tableu S5. I don't have access to a text at the moment, and there are no internet resources (peer-rev journals should be free, damnit!)

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