PHIL 110 Lecture Notes - Lecture 16: First-Order Logic, Vacuous Truth, Universal Quantification
16 Mar 2017
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Dr mc"s philosophy 110 (1171) part notes 10#1 . Four section: t/f, mc, mc with a twist, proofs. It will cover everything up until the end of the last lecture. Last time, we were talking about contradictories pairs of sentences that cannot both true at the same time and also cannot both be false at the same time. and. If it is true that: (x) (ax bx) then it is false that ( x)(ax ~bx) If it is false that: (x) (ax bx) If it is true that: (x) (ax ~bx) If it is false that: (x) (ax ~bx) The arrows on the square of opposite point to contradictory pairs. In ordinary english, we also have the notion of contraries : sentences that cannot both be true but that could both be false. And surely they could, logically speaking, both be false . (x)(fx ~rx) (x)(fx rx): (fa ra) (fb rb) (x)(fx ~rx): (fa ~ra) (fb ~rb)
