3 Unless The rule: translate “unless” as “v” But why? “p unless q” = “p if not q”Ex. You will be free of logic on Friday, unless you’re in Section X.If you’re not in Section X, you’ll be free of logic on Friday.So “p unless q” = “~q p”Next step: show that “~q p” = “p v q”
5 Unless: Recap It is natural to interpret “p unless q” as “p, if not q” “p, if not q” is equivalent to “p v q”So “p unless q” is naturally interpreted as “p v q”
6 But doesn’t ‘unless’ entail an exclusive “or”? Often, but not always.Ex. “The picnic will be held unless it rains.”What happens if it rains?Exclusive “or/unless”: no picnic.However, the speaker may mean that it will be held indoors, in which case, there is a picnic and it rains.Inclusive “or/unless.”
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