crashfrog responds to me:
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OR, crash. God is inconsistent OR incomplete. The two are just different ways of saying the same thing.
If they're saying the same thing, why use "or"?
Because when you make your choice as to which one you want, you don't get the other. A system can be formalized so that it is either incomplete or inconsistent. The system will generate statements such that they are either undecidable (incomplete) or contradictory (inconsistent) but not both. A single system will not generate one statement that is undecidable while at the same time generating another two statements that contradict each other.
Take, for example, the question of the continuum hypothesis. The way we have set up our system, this question is considered undecidable (c = aleph-one is not contradictory and c < aleph-one is not contradictory). The system can be changed such that the statement is contradictory (c = aleph-one and c < aleph-one). What it cannot do is do both at the same time.
So you get one
or the other. The system will be either incomplete
OR it will be inconsistent.
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I wouldn't say "rich or thick" when referring to whipped cream.
Axiomatic set theories aren't whipped cream.
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Would it have simply been better to pick one of those terms, instead of both?
No, because they don't mean the same thing. "Rich" and "thick," like "all-powerful" and "omnipotent," are synonyms. "Incomplete" and "inconsistent" are not. The former means that there will be some statements for which one cannot derive any truth value. The latter means that there will be some statements for which one can derive both truth values.
Depending on how you deal with the system, incomplete can be turned into inconsistent and vice-versa, but the two are not the same thing.
So which do you pick? A system where you land on "I don't know" or a system in which you land on "both"?
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Rrhain
WWJD? JWRTFM!