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Yes, the author seems to assume that: proof_of_breach <-> proof_of_benefit You are arguing that it could be the case that: proof_of_negligence -> pro
by jsprogrammer 11y ago
Yes, the author seems to assume that:
proof_of_breach <-> proof_of_benefit
You are arguing that it could be the case that:
proof_of_negligence -> proof_of_breach
proof_of_negligence -> (proof_of_benefit v ~proof_of_benefit)
in which case there could be a contradiction.
However, there is probably an argument that:
proof_of_negligence -> (proof_of_benefit v ~proof_of_benefit)
is wrong and that there actually is a rule:
proof_of_breach -> proof_of_benefit
For example, if someone is negligent, we already know they received a personal benefit (eg. reduced cognitive load, received compensation for work not performed, etc.).
To show a logical incorrectness, you need to show an `x` where:
proof_of_x -> (proof_of_breach ^ ~proof_of_benefit) v (~proof_of_breach ^ proof_of_benefit)
- thaumasiotes 11y agoWhat are you trying to say here? proof_of_negligence -> (proof_of_benefit v ~proof_of_benefit) easily simplifies to true and therefore doesn't need a case to be made for it. It's always true.
- jsprogrammer 11y agoI 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.