PHIL 110 Lecture Notes - Lecture 14: Free Variables And Bound Variables

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The scope of a quantifier is the extent of the expression (cid:862)covered by that quantifier(cid:863). We use brackets to disambiguate, though we may assume, as with negation, which the scope is the smallest unit to its right, if not otherwise indicated. In sentential, it is easy to disambiguate these: ~ (p v q, ~p v q. No expression with a free variable is a sentence. The domain of discourse is just the individuals we"re talking about: unless otherwise specified, the domain is unrestricted. Domain: some people are happy and some are not. ( (cid:454)(cid:895)(cid:894)p(cid:454) h(cid:454)(cid:895) (cid:894) (cid:454)(cid:895)(cid:894)p(cid:454) ~h(cid:454)(cid:895) Domain: people ( (cid:454)(cid:895)(cid:894)h(cid:454)(cid:895) (cid:894) x)(~hx: not ( (cid:454)(cid:895)(cid:894)h(cid:454) ~h(cid:454)(cid:895, not ~(cid:894)(cid:454)(cid:895)(cid:894)h(cid:454)(cid:895) ~(cid:894)(cid:454)(cid:895)(cid:894)~h(cid:454)(cid:895) No mathematician philosophers are snazzy dressers. (cid:894)(cid:454)(cid:895)[(cid:894)m(cid:454) p(cid:454)(cid:895) ~sx: ~( (cid:454)(cid:895)[(cid:894)m(cid:454) p(cid:454)(cid:895) ~ (cid:454)] Nobody is a snazzy dresser unless she is also a mathematician and a philosopher. (cid:894)(cid:454)(cid:895)[~(cid:894)m(cid:454) p(cid:454)(cid:895) ~sx] (x)[sx (cid:894)m(cid:454) p(cid:454)(cid:895): ~( (cid:454)(cid:895)[ (cid:454) ~(cid:894)m(cid:454) p(cid:454)(cid:895)]

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