26 Jun 05
2 edits
the more i think about this, the more i am sure that the logical unnecessity of U entails the existence of R', and the proof can be found in bbarr's above post.
in particular, assume no such R' exists. then there are no logically possible states of affairs without U as a constituent that are morally preferrable to S. it follows that U is logically necessary for the bringing about of greater good. this directly contradicts premise 2'. thus the theist's committing to 2' also entails his committing to the existence of R'.
my take on it is then that your premise (6.1), although correct, is redundant and unnecessary for bbarr's formulation, ie, premise 6.1 cannot be rejected unless the theist has already rejected premise 2'.
29 Jun 05
Originally posted by bbarrSomething you wrote about "quibbling over definitions" a few posts back made me think:
Let's go through this step by step, so that we may identify clearly where you are mistaken.
Here is the argument in full, without any of your additions or revisions:
[b]1) God exists.
2) There has obtained at least one fully specified state of affairs S such that S included as a constituent suffering logically unnecessary for the bringing about of g ...[text shortened]... tion available to the theist. I can't tell exactly what you think that option is, however.
Does the omnipotence of God imply that he can cause any logically possible state of affairs to attain?
Put another way:
Is the ability to do anything that is logically possible equivalent to the ability to cause any logically possible state of affairs to be the case?
Suppose it does. Then God can cause any logically possible state of affairs to attain. In other words, it is logically impossible that God cannot cause a logically possible state of affairs to attain.
Consider the following state of affairs (call it X):
"God cannot cause X to attain."
If X is logically possible, then God can cause X to attain. If God can cause X to attain, however, then it is logically impossible that God cannot cause X to attain; i.e. X is logically impossible.
A logical contradiction.
Nothing in this argument entails anything about the existence of God. The only possible sources of the contradiction are:
(1) The proposition that an entity can do anything that is logically possible.
(2) The equivalence of (1) with the proposition that an entity can cause any logically possible state of affairs to attain.
Note that (2) in this argument logically entails (6.1) in my revised version of the GAFE.
It is not clear to me why (2) should be the case. You need to either demonstrate the equivalence, or explicitly state (2) as an assumption in your argument - which is exactly what (6.1) does.
29 Jun 05
4 edits
Originally posted by lucifershammeri don't want to interrupt your discussion with bbarr, but since bbarr can answer these questions much better than i can anyway, it probably doesn't hurt for me to throw in my interpretations (even if you can show they are wrong), as i find the GAFE quite an interesting source of debate. i am also impressed with your thoroughness and your constant willingness to critique the GAFE.
Something you wrote about "quibbling over definitions" a few posts back made me think:
Does the omnipotence of God imply that he can cause any logically possible state of affairs to attain?
Put another way:
Is the a as an assumption in your argument - which is exactly what (6.1) does.
i think there must clearly be something wrong with your reasoning here. first, i interpret your use of 'equivalent' as meaning if and only if, in the sense of necessary and sufficient. but the GAFE only hinges on the following sufficiency: that omnipotence (being able to do anything that is logically possible) implies the ability to cause any logically possible state of affairs to obtain. this will clearly hold by the following proof:
suppose god is omnipotent. then he can do anything that is logically possible. it is logically possible for one to cause a logically possible state of affairs to obtain (entails no logical contradictions). thus by his omnipotence, god can cause a logically possible state of affairs to obtain. this reasoning holds for ALL logically possible states of affairs. thus god can cause ANY logically possible state of affairs to obtain. thus an omnipotent god has the ability to cause any logically possible state of affairs to obtain.
i think the fallacy in your reasoning is that your 'state of affairs' is really a proposition in this context; and this proposition "God cannot cause X to obtain" is a false proposition if X is logically possible. therefore, by starting with this assumption that X is logically possible, your contradiction argument starts with a false proposition. logical contradictions can stem from false propositions without any ramification. i think the example only shows that false propositions can lead to silly conclusions.
30 Jun 05
Originally posted by LemonJelloRemind me never to try philosophy after a full day of meetings at the office. 🙂
i think the fallacy in your reasoning is that your 'state of affairs' is really a proposition is this context; and this proposition "God cannot cause X to obtain" is a false proposition if X is logically possible. therefore, by starting with this assumption that X is logically possible, your contradiction argument starts with a false proposition. lo ...[text shortened]... tion. i think the example only shows that false propositions can lead to silly conclusions.
To complete the argument:
Suppose X is logically impossible.
Then it is impossible that God cannot cause X to attain.
i.e. God can cause X to attain.
Hence, X is logically attainable.
Hence, X is logically possible.
You get a contradiction either way.
30 Jun 05
1 edit
Originally posted by LemonJelloSee the completion of my argument above.
i don't want to interrupt your discussion with bbarr, but since bbarr can answer these questions much better than i can anyway, it probably doesn't hurt for me to throw in my interpretations (even if you can show they are wrong), as i ...[text shortened]... ty to cause any logically possible state of affairs to obtain.
Something bbarr wrote about theodicies rejecting God's omnipotence reminded me of Godel's Incompleteness Theorem which, incidentally, can be directly applied to the definition of God's omniscience (see Rucker's version of GIT at http://www.miskatonic.org/godel.html). I've just tried to modify that argument to apply to omnipotence (very probably unsuccessfully - but I think it's possible).
The point I have been trying to demonstrate is this - that there is a logical contradiction in the logical system that bbarr set up for GAFE outside premises 1-5.
EDIT: Indeed, I think the definitions of omnipotence, omniscience and moral perfection should be assumptions/premises in the argument.
As you said, false premises lead to silly conclusions.
30 Jun 05
Originally posted by lucifershammerah...i see now where you are coming from. i have studied Godel's theorem before, but it was a rather cursory treatment, and i am not sure i fully understand the theorem or all of its ramifications yet.
See the completion of my argument above.
Something bbarr wrote about theodicies rejecting God's omnipotence reminded me of Godel's Incompleteness Theorem which, incidentally, can be directly applied to the definition of God's omniscience (see Rucker's version of GIT at http://www.miskatonic.org/godel.html). I've just tried to modify that argum ...[text shortened]... assumptions/premises in the argument.
As you said, false premises lead to silly conclusions.
30 Jun 05
1 edit
Originally posted by lucifershammerYou state that: "If X is logically possible, then God can cause X to attain." TRUE!
Something you wrote about "quibbling over definitions" a few posts back made me think:
[b]Does the omnipotence of God imply that he can cause any logically possible state of affairs to attain?
Put another way:
Is th ...[text shortened]... an assumption in your argument - which is exactly what (6.1) does.
then that:
"If God can cause X to attain, however, then it is logically impossible that God cannot cause X to attain; i.e. X is logically impossible."
This is not valid!
If God can cause X to attain, then he may instead cause (not X) to attain. In other words, just because God can do X, does not logically prevent him from being able to do the opposite.
Besides which, if the premise:
"it is logically impossible that God cannot cause X to attain" IS true,
then this would imply that:
"NOT x is logically impossible".
In other words that God must do X.
I hope you follow my reasoning and see the error in your logic!
30 Jun 05
1 edit
Originally posted by lucifershammerDoes the omnipotence of God imply that he can cause any logically possible state of affairs to attain?
Something you wrote about "quibbling over definitions" a few posts back made me think:
Does the omnipotence of God imply that he can cause any logically possible state of affairs to attain?
Put another way:
Is the a ...[text shortened]... an assumption in your argument - which is exactly what (6.1) does.
Yes.
Put another way:
Is the ability to do anything that is logically possible equivalent to the ability to cause any logically possible state of affairs to be the case?
Yes.
Suppose it does. Then God can cause any logically possible state of affairs to attain. In other words, it is logically impossible that God cannot cause a logically possible state of affairs to attain.
O.K.
Consider the following state of affairs (call it X):
"God cannot cause X to attain."
If X is logically possible, then God can cause X to attain. If God can cause X to attain, however, then it is logically impossible that God cannot cause X to attain; i.e. X is logically impossible.
Huh?
A logical contradiction.
Where’s the contradiction here? Given some state of affairs X, if X is logically possible, then God can bring about the obtaining of X. If God can bring about the obtaining of X, then it is logically impossible that God could not bring about the obtaining of X. Nothing here entails that X is logically impossible. You are simply confused on this point.
30 Jun 05
Originally posted by lucifershammerTo complete the argument:
Remind me never to try philosophy after a full day of meetings at the office. 🙂
To complete the argument:
Suppose X is logically impossible.
Then it is impossible that God cannot cause X to attain.
i.e. God can cause X to attain.
Hence, X is logically attainable.
Hence, X is logically possible.
You get a contradiction either way.
Suppose X is logically impossible.
O.K.
Then it is impossible that God cannot cause X to attain.
No. If X is logically impossible, then it is impossible that God can cause X to obtain.
You have made an elementary error in reasoning here, as should now be obvious.
30 Jun 05
Originally posted by lucifershammerFirst, the only logical contradictions in the vicinity of my argument are those that appear in your recent criticisms.
See the completion of my argument above.
Something bbarr wrote about theodicies rejecting God's omnipotence reminded me of Godel's Incompleteness Theorem which, incidentally, can be directly applied to the definition of God's omniscience (see Rucker's version of GIT at http://www.miskatonic.org/godel.html). I've just tried to modify that argum ...[text shortened]... assumptions/premises in the argument.
As you said, false premises lead to silly conclusions.
Second, if you would like to present an objection to any of my proposed definitions of the essential properties of God, then please do so. If you reject that God has these essential properties, then my argument may not apply to you (although an altered version of it may very well apply, depending on the properties you attribute to God).
30 Jun 05
Originally posted by bbarr
Consider the following state of affairs (call it X):
"God cannot cause X to attain."
If X is logically possible, then God can cause X to attain. If God can cause X to attain, however, then it is logically impossible that God cannot cause X to attain; i.e. X is logically impossible.
Huh?
Do it step by step:
X is logically possible
=> God can cause X to attain (God's omnipotence)
=> It is logically impossible that God cannot cause X to attain (essentially a double negative)
=> "God cannot cause X to attain" is logically impossible (just re-ordering the sentence)
=> X is logically impossible (definition of X)
Similarly:
X is logically impossible
=> "God cannot cause X to attain" is logically impossible (definition of X)
=> It is logically impossible that God cannot cause X to attain (re-ordering the sentence)
=> God can cause X to attain (double negative)
=> X is logically attainable
=> X is logically possible
Cheers,
LH
30 Jun 05
Originally posted by bbarrFirst of all, I have to thank bbarr and LJ for helping me clarify my thoughts. This thread is not so much a finished counter-argument as it is a counter-argument in development.
Second, if you would like to present an objection to any of my proposed definitions of the essential properties of God, then please do so. If you reject that God has these essential properties, then my argument may not apply to you (although an altered version of it may very well apply, depending on the properties you attribute to God).
My objection to your proposed definitions of omnipotence and omniscience would simply be that they are logically untenable; in themselves, they entail logical contradictions. I've attempted to show that your definition of omnipotence is untenable in the last 3-4 posts (and I have to thank you for giving me the idea); it is relatively easy to show that your definition of omniscience is untenable using Rucker's version of the proof of Godel's Incompleteness Theorem in the link I provided earlier (essentially, your definition says that God is a Universal Truth Machine).
It should come as no surprise, therefore, that an argument you've built off these definitions would entail a contradiction at some point.
30 Jun 05
Originally posted by howardgeeWhat are you talking about??
You state that: "If X is logically possible, then God can cause X to attain." TRUE!
then that:
"If God can cause X to attain, however, then it is logically impossible that God cannot cause X to attain; i.e. X is logically impossible."
This is not valid!
If God can cause X to attain, then he may instead cause (not X) to attain. In other words, just ...[text shortened]... her words that God must do X.
I hope you follow my reasoning and see the error in your logic!
If God can cause X to attain, it is irrelevant to my argument whether he can cause (not X) to attain.
30 Jun 05
3 edits
Originally posted by lucifershammerYou are still making the same simple error. Perhaps your notation has confused you, so I’m going to make it clearer for you below.
Originally posted by bbarr
Consider the following state of affairs (call it X):
"God cannot cause X to attain."
If X is logically possible, then God can cause X to attain. If God can cause X to attain, however logically attainable
=> X is logically possible
Cheers,
LH
For any state of affairs X, either X is logically possible or X is logically impossible. If X is logically possible, then God can bring about the obtaining of X. If X is logically impossible, then God cannot bring about the obtaining of X.
Now, start your argument by supposing some state of affairs M (I’m using ‘M’ to keep states of affairs clear, instead of confusingly using the same variable in two different ways, as you did above) where:
M = ‘God cannot cause X to obtain’
Presumably, the variable ‘X’ in M just denotes some state of affairs or other.
Now, since M is itself a state of affairs, either M is logically possible or logically impossible.
Suppose M is logically possible.
If so, then it is logically possible that God cannot cause X to obtain.
Thus, it is logically possible that X is logically impossible.
Thus, X is logically impossible.
Alternatively, suppose M is logically impossible.
If so, then it is logically impossible that God cannot cause X to obtain.
Thus, it is logically impossible that X is logically impossible.
Thus, X is logically possible.
There is no contradiction here, regardless of whether M itself is logically possible or logically impossible
Of course, you can derive a contradiction from the supposition that M is logically possible together with the further supposition that X is logically possible, but all this shows is that you can derive a contradiction from supposing two propositions that are inconsistent with each other. Similarly, you can derive a contradiction from the supposition that M is logically impossible together with the further supposition that X is logically impossible, but all this shows is that you can derive a contradiction from supposing two propositions that are inconsistent with each other.
In short, you are not deriving a contradiction from anything in my argument, but merely from starting off supposing two things that are inconsistent (the logical possibility of both M and X, or the logical impossibility of both M and X). This is your mistake, and it has nothing to do with my argument.
Cheers.
30 Jun 05
Originally posted by lucifershammerYou have shown nothing concerning my notion of omnipotence other than that you can get yourself confused.
My objection to your proposed definitions of omnipotence and omniscience would simply be that they are logically untenable; in themselves, they entail logical contradictions. I've attempted to show that your definition of omnipotence is untenable in the last 3-4 posts (and I have to thank you for giving me the idea); it is relatively easy to show tha ...[text shortened]... that an argument you've built off these definitions would entail a contradiction at some point.
Did you even read Rucker's reconstruction of Godel's argument? If so, go back and re-read premise (2). Can you see why Godel's argument doesn't apply here? If not, here is a hint: So-called "Godel sentences" only result from the supposition that there is some UTM with a finitely specifiable instruction set.