[PKop]

Isn't it sort of like Gödel's incompleteness theorem, there's no way to prove your first-principle was a correct axiom to start from. Experience will guide this.

>debunk axiomatic logic itself

He's not though. Your assumptions can be wrong, even if your incremental logic is correct according to the first principle. He's saying the correctness of axiomatic logic will lead you down the wrong path.

[dissidents]

No, he is saying that he agrees with the assumptions and the way they are used to construct other propositions, but disagrees with the outcome, and therefore there must be something wrong on a higher level with the logical system itself that is being used here. I think what's actually happening here is much more banal.

>Isn't it sort of like Gödel's incompleteness theorem

Forgive me for being curt, but no, this is absolutely nothing like either of Gödel's incompleteness theorems.

[PKop]

He's saying there's something wrong with getting fooled by a series of valid logical assertions into thinking the original axiom applied to the context in which one is making it... there are "unknown unknowns". There's something wrong with trusting that principled thinking will always hold because it held before, in what might have been a different context.

He's not debunking the validity of the chain of truth statements, but "first principles thinking"...letting this logic guide one down a path that doesn't comport with reality (which might have context one is unaware of).

I think it matches up with incompleteness quite well.

Any set of axioms can never tell you for sure if you're in a context that has other missing and more valid axioms.

You can modify your axioms with experience, but then you're back in the position of not knowing if this is the final set of axioms that will always comply with reality.