Freethought & Rationalism Archive

Kenny · 02-08-2002, 01:05 PM

Seeing how this post was based on a misunderstanding, I have deleted it

[ February 11, 2002: Message edited by: Kenny ]

bd-from-kg · 02-08-2002, 02:12 PM

Kenny:

Quote:

If that’s meant to be a dig, I think it is rather unfair.

No, not a dig. It's perfectly reasonable to post a link to an interesting article related to the discussion. But this was the third time you did so recently (in a thread I found interesting) and the last two times that was all you did. Since I have found your posts interesting in the past, I found this disappointing. When I said that it was nice to see you actually posting something substantive for a change, that's exactly what I meant.

Quote:

As this also appears to be a dig ... I would suggest being a little bit more discriminating in the future in how you give such digs out, seeing how Turtonm is an ally

Yes, I know turtonm is an ally. My comment was intended as a bit of irony (I know: I'm ironic, you're sarcastic, etc. I'll try to be more careful in the future.) Actually I'm amazed that he managed even to read the thing (over 15,000 words) in such a short time, much less understand it completely.

P.S.: After posting this I realized that the "I'm ironic, you're sarcastic" remark might itself be misunderstood. What I meant was that a comment that I might regard as merely ironic if I make it, I might consider sarcastic if you make it. And of course we all have the same perceptual bias.

[ February 08, 2002: Message edited by: bd-from-kg ]

Kenny · 02-08-2002, 10:20 PM

bd-from-kg,

Forgive me; I completely misread your tone. That's one bad thing about these message boards; sometimes it's hard to tell. Anyway, more later...

God Bless,
Kenny

Automaton · 02-08-2002, 10:41 PM

Sorry for being so cynical, but rock-so-big "arguments" are pathetic. All they really show is that logic is logical.

It's like the atheist version of the creationist "evolution violates the 2nd law of thermodynamics" plea.

You are constructing a "square circle" proposition that you claim must be forfilled in order for property x to exist. But omniscience only applies to knowing logically possible propositions. It's like asking if God can know of any married bachelors. Of course not, but that's because it's nonsense. Same thing with G�delian self-referential paradoxes. They do not challenge omniscience.

(BTW, didn't I mention this on another thread a little while back?)

Tomije · 02-08-2002, 10:57 PM

Of course, the main problem with this argument is that folks are using logic to deal with a question of faith.

To use my limited math knowledge, if it were a Venn diagram, those two circles would not intersect, at all. So these fancy proofs won't sway a single believer, and could possibly confuse those who aren't believers.

As Kierkegaard pointed out, the idea of faith is illogical, and that's where faith gains its power. To not understand that is to miss the boat, as it were.

Proving the lack of omniscience is impossible, or at least horribly complicated, as was shown. Those with faith are looking for simple answers--"there is a reason my 5 year old died", for example.

Faith is a simple answer. You don't convince those with faith by showing them horribly complex answers.

The lack of a belief in a God with omniscience is as much a matter of faith as a God with omnisience. There is no real data.

For a real atheist, the lack of data is enough. For a real theist, the lack of data can be enough. It's what makes this whole forum so delicious. But you can't prove it, no matter how many convoluted symbols you use.

I'm an atheist, but I can't prove it. I only have my gut, and circumstancial proof. So do theists. To try to prove it, one way or another, is a guarantee to fail.

Vorkosigan · 02-08-2002, 11:14 PM

But you seem to have gotten the gist of it. However, I’m not sure that you really grasped the import,

Guilty as charged. I was so busy with trying to figure out symbol-manipulation, I missed the major implications.

I guess I’m not as fast a study as turtonm, who managed to go from barely being able to understand the OP to understanding the extremely complicated argument between Plantinga and Grim in just a few hours.)

Ha! Are you kidding? I can't even remember how to spell "Plantinga." You're a much faster study than I am. I really admire the ability of you and Kenny to blithely toss these symbols around.

Michael

[ February 09, 2002: Message edited by: turtonm ]

bd-from-kg · 02-09-2002, 02:51 PM

Tomije:

Quote:

Proving the lack of omniscience is impossible, or at least horribly complicated, as was shown.

Impossible and complicated are two different things. For example, at this point it appears that proving that the equation ‘A^n + B^n = C^n’ has no nontrivial integer solutions for n > 2 is horribly complicated, but nevertheless it can be proved.

As for the argument that I presented, whether it’s “horribly complicated” depends on your point of view. If the concepts involved are unfamiliar, it does indeed look pretty complicated. But once the concepts have become familiar, the argument actually looks pretty simple.

Quote:

The lack of a belief in a God with omniscience is as much a matter of faith as a God with omniscience. There is no real data.

For a real atheist, the lack of data is enough. For a real theist, the lack of data can be enough... But you can't prove it, no matter how many convoluted symbols you use.
I'm an atheist, but I can't prove it. I only have my gut, and circumstantial proof. So do theists. To try to prove it, one way or another, is a guarantee to fail.

The position that I’m arguing for here is not atheism, but noncognitivism. I do not deny that an omniscient God exists, but rather deny that the statement “an omniscient God exists” expresses a proposition at all. This is not a matter of faith or lack of faith, of evidence or lack of evidence, of proof or lack of proof. The argument is not that those who claim to have “faith” in an omniscient God are wrong, but that they are literally talking nonsense.

Drange’s essay <a href="http://www.infidels.org/library/modern/theodore_drange/definition.html" target="_blank">Atheism, Agnosticism, Noncognitivism</a> gives a more complete explanation of the various possible attitudes toward the statement “God exists” (for any given definition of “God&#8221).

[ February 09, 2002: Message edited by: bd-from-kg ]

jpbrooks · 02-09-2002, 06:40 PM

Quote:

Originally posted by bd-from-kg:


God must know, for every proposition p, either that it’s true or that it’s false. Not only that, but He knows all of these things simultaneously, and thus knows, of the class TP of all true propositions, that each proposition in it (and no other) is true, and of the class FP of false propositions FP that each element of it is false. So God’s mind must contain the concepts of TP and FP themselves. It follows that God’s mind must include the concept of P, the class of all propositions, since this is just the union of TP and FP. [Note: the point of this is just to establish that P exists as a conceptual entity – a “set” if you will – since it exists as a concept in God’s mind.]

Now for any set of propositions m, let T(m) be “every proposition in m is true”. [Note: it doesn’t seem to matter just what T(m) asserts; the only thing that matters is that T(m) is a proposition, and that if m and n are different sets of propositions, T(m) and T(n) are also different.]

Now God’s mind must include, for each such m, the knowledge of whether T(m) is itself one of the propositions in m. And thus God’s mind must include the knowledge of exactly which T(m)’s are members of their corresponding m’s. That is, He knows the contents of w* == {m: T(m) is not a member of m} and hence of w, whose elements are T(m) for every m which is an element of w*. That is, w consists of all of the propositions T(m) which are not elements of the set m to which they refer. [Note: Once again the statements about “God’s mind” are used only to establish the existence of w as a conceptual entity – i.e., a “set”.]

Since w is a set of propositions, we also have the proposition T(w). Now consider the question whether T(w) is a member of w.

If T(w) is an element of w, then it isn’t, because w consists of precisely those T(m) which are not elements of the corresponding m.

But if T(w) is not an element of w, then it is, again because w consists precisely of those T(m) which are not elements of the corresponding m.

This is an unavoidable consequence of the fact that w is a set – i.e., a conceptual entity - which is in turn an unavoidable consequence of the fact that God knows which propositions of the form T(m) are elements of their corresponding m. And this in turn is an unavoidable consequence of the fact that God knows, for any set of propositions m, whether T(m) is an element of that set.

In short, the logical paradox is an unavoidable consequence of the assumption that God is omniscient.

So God cannot be omniscient. In fact, the concept of omniscience is logically incoherent.

Therefore the concept of an omniscient God is logically incoherent.

Comments?

Bd,

much of Russell is still (admittedly) a little beyond my grasp. However, though I agree that there cannot be a "set of all sets", I am quite suspicious about this attempt to extend Russell's argument to the concept of omniscience.

At the moment, you are losing me on the inference from the fact that there is a paradox involved in the inclusion/exclusion of T(w) in/from w to the notion that omniscience is impossible.
God would simply know (as would you and I) that T(w)'s inclusion involves a paradox, in addition to all of the other truths that He knows. In other words, God knows the ("meta") truth about this problem. Thus, there would seem to be no reason to assume that any such argument involving paradoxes about truth or knowledge presents any real problem for God's omniscience.

[ February 09, 2002: Message edited by: jpbrooks ]

bd-from-kg · 02-10-2002, 08:49 PM

Automaton:

Quote:

But omniscience only applies to knowing logically possible propositions. It's like asking if God can know of any married bachelors.

The point is not that God doesn’t know any married bachelors. The point is that saying that God is omniscient is like saying that God is a married bachelor.

As Grim puts it (in the article cited by Kenny):

Quote:

[This] ... is "a short and sweet Cantorian argument against omniscience." Were there an omniscient being, what that being would know would constitute a set of all truths. But there can be no set of all truths, and so can be no omniscient being.

jpbrooks:

Quote:

... there would seem to be no reason to assume that any such argument involving paradoxes about truth or knowledge presents any real problem for God's omniscience.

Well, I don’t know. I would have thought that if the concept of omniscience is logically incoherent, this would present a bit of a problem for God’s omniscience.

jpbrooks · 02-10-2002, 10:35 PM

Quote:

Originally posted by bd-from-kg:


Well, I don’t know. I would have thought that if the concept of omniscience is logically incoherent, this would present a bit of a problem for God’s omniscience.

And I would agree that it would. But you have not established that the concept of omniscience is logically incoherent. Not knowing the truth of a proposition whose truth value involves a logical paradox (and is hence logically impossible to determine) is no limitation on omniscience.
One might as well argue that the fact that no one (including God) can determine whether the barber (in the mythical town where the barber shaves everyone who doesn't shave himself) shaves himself or not demonstrates that our knowledge of truth is limited.
If it is logically impossible to determine the truth of a proposition, how can not knowing its truth be considered an actual limitation on the knowledge of any being?

[ February 10, 2002: Message edited by: jpbrooks ]

02-08-2002, 01:05 PM	#11
Kenny Senior Member Join Date: Jul 2000 Location: South Bend IN Posts: 564	Seeing how this post was based on a misunderstanding, I have deleted it [ February 11, 2002: Message edited by: Kenny ]</p>

02-08-2002, 11:14 PM	#16
Vorkosigan Contributor Join Date: Jan 2001 Location: Barrayar Posts: 11,866	But you seem to have gotten the gist of it. However, I’m not sure that you really grasped the import, Guilty as charged. I was so busy with trying to figure out symbol-manipulation, I missed the major implications. I guess I’m not as fast a study as turtonm, who managed to go from barely being able to understand the OP to understanding the extremely complicated argument between Plantinga and Grim in just a few hours.) Ha! Are you kidding? I can't even remember how to spell "Plantinga." You're a much faster study than I am. I really admire the ability of you and Kenny to blithely toss these symbols around. Michael [ February 09, 2002: Message edited by: turtonm ]</p>

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02-08-2002, 10:20 PM	#13
Kenny Senior Member Join Date: Jul 2000 Location: South Bend IN Posts: 564	bd-from-kg, Forgive me; I completely misread your tone. That's one bad thing about these message boards; sometimes it's hard to tell. Anyway, more later... God Bless, Kenny

02-08-2002, 10:41 PM	#14
Automaton Senior Member Join Date: Jan 2002 Posts: 717	Sorry for being so cynical, but rock-so-big "arguments" are pathetic. All they really show is that logic is logical. It's like the atheist version of the creationist "evolution violates the 2nd law of thermodynamics" plea. You are constructing a "square circle" proposition that you claim must be forfilled in order for property x to exist. But omniscience only applies to knowing logically possible propositions. It's like asking if God can know of any married bachelors. Of course not, but that's because it's nonsense. Same thing with G�delian self-referential paradoxes. They do not challenge omniscience. (BTW, didn't I mention this on another thread a little while back?)

02-08-2002, 10:57 PM	#15
Tomije Junior Member Join Date: Feb 2002 Posts: 16	Of course, the main problem with this argument is that folks are using logic to deal with a question of faith. To use my limited math knowledge, if it were a Venn diagram, those two circles would not intersect, at all. So these fancy proofs won't sway a single believer, and could possibly confuse those who aren't believers. As Kierkegaard pointed out, the idea of faith is illogical, and that's where faith gains its power. To not understand that is to miss the boat, as it were. Proving the lack of omniscience is impossible, or at least horribly complicated, as was shown. Those with faith are looking for simple answers--"there is a reason my 5 year old died", for example. Faith is a simple answer. You don't convince those with faith by showing them horribly complex answers. The lack of a belief in a God with omniscience is as much a matter of faith as a God with omnisience. There is no real data. For a real atheist, the lack of data is enough. For a real theist, the lack of data can be enough. It's what makes this whole forum so delicious. But you can't prove it, no matter how many convoluted symbols you use. I'm an atheist, but I can't prove it. I only have my gut, and circumstancial proof. So do theists. To try to prove it, one way or another, is a guarantee to fail.

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