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A comment on Gödel’s first incompleteness theorem – an interactive tutorial. Parent comment

Re:Gödel’s first incompleteness theorem – an interactive tut... by plus on Monday October 17, 2022 @02:33PM (#33237766)
If your system of logic contains a contradiction, then it can be said that any statement in that system "leads to" a contradiction. Thus "proof by contradiction" can prove any statement in that system.
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Re:Gödel’s first incompleteness theorem – an interactive tut... by miga on Monday October 17, 2022 @04:02PM (#33238815)
Trying to find a formal system that encodes unbounded infinitary mathematical objects including most of maths, but yet to require that all statements are decidable within a finite number of steps...

Is it contradiction in the proof, or rather a contradiction in assumptions?

More on logic that permits all that *Bounded* Turing Machine does: https://arxiv.org/abs/2106.13309

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Re:Gödel’s first incompleteness theorem – an interactive tut... by aristofun on Wednesday October 19, 2022 @04:15PM (#33267401)
> then it can be said that any statement in that system "leads to" a contradiction

Why exactly it "leads to"? I don't get it.

Why system can't have a contradiciton for one set of inputs, and not have it for others?

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