4 ms·
For me, proof by contradiction only clicked (recently!) once I understood that logical consequence and unsatisfiability are equivalent. Once I understood that
by sunday_serif 3mo ago
For me, proof by contradiction only clicked (recently!) once I understood that logical consequence and unsatisfiability are equivalent.
Once I understood that and reframed the contradiction as a statement about unsatisfiability… I could then see directly how the positive result you get is the equivalent logical consequence.
Unfortunately, I feel like this intuition only really helps if you are pretty immersed in formal logic… otherwise it just sounds like jibberish.
- SkiFire13 3mo agoIf you are into constructive logic then this will only work for proving negative statements (where indeed the definition is the same as what a proof by contradiction would give you). For positive statements you won't get back a direct proof term of your initial statement, but rather a proof of a double negation of it.