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I guess it should be an Exclusive OR, although I'm not sure that is allowed in propositional logic. The argument made was that negligence could occur without b
by jsprogrammer 11y ago
I guess it should be an Exclusive OR, although I'm not sure that is allowed in propositional logic.
The argument made was that negligence could occur without benefit (ie. proof_of_negligence does not imply either proof_of_benefit or ~proof_of_benefit).
My argument is that `proof_of_benefit -> proof_of_negligence` and that `proof_of_negligence -> (proof_of_benefit v ~proof_of_benefit)` (or otherwise) is nonsense.
- thaumasiotes 11y agoSurely, if there is no benefit, then ~proof_of_benefit obtains? Are you advocating against the law of the excluded middle? How could there be proof of a benefit if there was no benefit? Exclusive or, being a logical relationship, is allowed in propositional logic. It is traditionally indicated, in mathy areas, by the symbol ⊕, but you can just compose it from the standard and, or, and not operations. And (proof_of_benefit ⊕ ¬proof_of_benefit) still simplifies to true, unless you're a hardcore constructivist.