Being closed minded is a justifiable defense in some circumstances. The ability to consider counter-factuals is often (and perhaps inherently) leakly. I mean, that once someone has entertained an idea, and relied on it to think about secondary and tertiary effects, they’re more likely to believe the premise… even if they have no additional information about the accuracy the initial premise. It’s an effective form of manipulation / gaslighting.
Lol, it is not gaslighting/manipulation. Are you really so unable to resist the temptation to believe an idea that you must choose not to even consider it?
Proof by contradiction[1] has quite a number of important results. We shouldn't denigrate that machinery.
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G. H. Hardy described proof by contradiction as "one of a mathematician's finest weapons", saying "It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game."
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