Thanks, I think this makes sense, and it's quite a trip! But I'm a little foggy about any differences between "externally inconsistent", "indeed inconsistent",

Thanks, I think this makes sense, and it's quite a trip! But I'm a little foggy about any differences between "externally inconsistent", "indeed inconsistent", and "inconsistent overall". I'm also guessing at a few pieces like what you mean by "our theory" - I assume that is "our system of ZFC + ~Con(ZFC)". Does this corollary have a name? > This whole pile of stuff is why I think using the word "truth" hurts more than helps unless everyone has a model theory background. I don't agree at all, and you have not addressed my other point. Formal systems which are used for science aren't designed to be paradox-systems, and truth in those systems is always intended to correspond with reality.