Not true, actually. Godel's 2nd has a lot of hypotheses, and there is one that you can change to make it false
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Replying to @FateOfTwist_ @RadishHarmers
I was directed to https://en.wikipedia.org/wiki/Self-verifying_theories … when I brought up that objection but I haven't looked into details
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Replying to @ModelOfTheory @RadishHarmers
it's powerful enough to talk about its provability, but not enough to do diagonalization and liar sentence
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Replying to @FateOfTwist_ @ModelOfTheory
"ordinary sense" for me meant theories of syntax with such basic expressivity as used in diagonalization.
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Replying to @RadishHarmers @ModelOfTheory
and that's how I know that you don't know very much logic
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the entire point of my comment was to catch people in the exact mistake you made
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Replying to @FateOfTwist_ @ModelOfTheory
Cool. Entire point of MY "ordinary sense" disclaimer was to provide "Yes, yes…" cover against such a gotcha.
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Replying to @RadishHarmers
, ok, sorry about snark, but why would you expect someone who wrote such a tweet to not know GIT?
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and how is the theory of groups or ACF_0 not a theory in the ordinary sense?
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Replying to @FateOfTwist_ @RadishHarmers
They are theories in the ordinary sense, but do not assert their own consistency in the ordinary sense.
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I am skeptical that either of those theories can prove their own consistency in an unordinary sense either.
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