A formal proof with 1 contradiction and 9999 correct steps is just as false as a formal proof with 10 contradictions and 9990 correct steps.
There is no “less wrong” or “more wrong” in logic, by definition.
i.e. There is no safe lower bound threshold of “wrongness” that can partially salvage the correct steps. Or conversely, 1 contradiction is already sufficient to prove anything at all.
A formal proof with 1 contradiction and 9999 correct steps is just as false as a formal proof with 10 contradictions and 9990 correct steps.
There is no “less wrong” or “more wrong” in logic, by definition.
i.e. There is no safe lower bound threshold of “wrongness” that can partially salvage the correct steps. Or conversely, 1 contradiction is already sufficient to prove anything at all.