Evidence for atheism

[Angrboda]

The entailment implied by the argument is false. That says nothing about the conclusion, in or out of the system. (And imo, equating not necessarily true with false is as likely to make a mess of things as not. In classical logic, the liar's paradox is stated as, "This sentence is false." Logicians have gotten around this by claiming that the sentence is meaningless and therefore it isn't false, it's just meaningless. This prompted the improved liar's paradox which is stated as "This sentence is not true," which evades the meaning objection. Clearly 'false' and 'not true' have different implications in the system, even in classical logic. And this is assuming classical logic, as opposed to something like dialetheic logic in which a statement can be both true and false.)

I understand the desire to say something about the conclusion in the context of an unsound or invalid argument, but in doing so, I think you are overreaching, with potentially unwanted consequences. (Can we use the invalidated argument in another argument in the place of the value 'false' ? Absolutely not.) Your objection runs perilously close to the fallacy fallacy; it's a fallacy that because an argument employs a fallacy in reaching a conclusion that the conclusion is false.

Anyway, I don't fully understand what you're trying to say Rhythm. I side with CD on this one. Not necessarily true is the appropriate conclusion, not 'false'.