Scott,
For whatever it's worth, I do not think there is any guarantee that meaning is immutable in the way that you're arguing, nor that it is meaningless to consider otherwise. It seems to me that if a being had control over the physical operations of my brain, it could make me genuinely believe that "2 + 2" refers to the same concept as "5," without misusing the words insofar as that belief does not misuse them. That is, if someone or something could control our brains, it could change what constitutes "logic" to us.
As I said before, most of the time this possibility just does not matter at all. But in the case of metaphysical worldview, there can be emotional reasons to consider something that has an unknowable degree of power.
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That said, I can still interpret your argument as if 'omnipotence' does not include the power to distort meaning (in the above way or any other way).
Scott wrote:Premise 1: If there was an omnipotent creator god, we would be very intelligent designed.
Premise 2: We are not very intelligently designed.
Conclusion: There is not an omnipotent creator god.
I think my rebuttal to this particular argument mostly stands as it was: Even if the god is very logical, and incapable of intruding on our logic, it's still impossible to fathom what he might consider a good idea for a design. Sure, you can think of many standards of success which life on earth and which the rest of the universe does not meet, but how do you decide what standard of success god must use? So I disagree with the premises, as before.
Scott wrote:scientific studies of the effectiveness of prayer can help us figure out whether or not a god exists (premise 1). Scientific studies have repeatedly found that prayer is utterly ineffective regardless of who prays, of which god they pray to and of what they pray about (premise 2).
Similar answer: There is really no way to know whether god cares to answer prayers. Or whether he, e.g., rewards for them in an afterlife. Thus both premises are problematic.
Scott wrote:Premise 1: If there was an omnipotent or otherwise supernaturally powerful god, he would not cause or let utterly, unproductively awful things such as the holocaust which entailed the mass-murder of children to occur.
Premise 2: Utterly, unproductively awful things like the holocaust have happened.
Conclusion: Neither an omnipotent nor otherwise supernaturally powerful god exists.
Again, we don't know what god considers evil, or if evil now ends up having better or compensatory effects in some other way. However, I think this argument still shows that god, if he exists, is in a way very alien to us. Again, neither premise is guaranteed.
The same can be said for the last two arguments: We do not know if 'bad' things really are unproductive, purposeless, etc., and we do not know if god cares if they are bad, unproductive, purposeless, etc.
Without the possibility that god is illogical, there are only so many possible gods who could be posited, and who could then theoretically be ruled out. The problem remains, however, that nearly comprehensive knowledge of existence is needed to rule out the popular ones. As it stands, you can only rule out gods who have very specific purposes--e.g., a logical god who does not want any human being to ever have an appendix does not exist. Any general purposes may yet be explained by what we don't know of the universe; e.g. a 'good' logical god may have created future compensation, trans-dimensional compensation, etc., for apparently 'bad' things in the world.