2 ms·
Proof by contradiction goes like this: You assume ~x, and from this you derive a contradiction _|_. Then you conclude x. So from ~x -> _|_ we derive x. In other
by jules 14y ago
Proof by contradiction goes like this: You assume ~x, and from this you derive a contradiction _|_. Then you conclude x. So from ~x -> _|_ we derive x. In other words: (~x -> _|_) -> x. That's the same as ((x -> _|_) -> _|_) -> x. But in any case, as you said, this is equivalent to (~x -> x) -> x because ~x -> x is equivalent to ~x -> _|_.
- DanWaterworth 14y agoI think strictly speaking, _|_ isn't a contradiction, it's an absurdity. (x, x -> _|_) is a contradiction.
- jules 14y agoAh I see, that's where the terminological differences came from.