PHIL 110 Lecture Notes - Lecture 15: Universal Quantification, Syllogism, Vacuous Truth

• School: Simon Fraser University
• Department: Philosophy
• Course: PHIL 110
• Professor: Jill Mc Intosh

Document Summary

What is a contradiction: a sentence whose logical form guarantees it is false. The (cid:271)asi(cid:272) fo(cid:396)(cid:373): p ~p: this is the conjunction of two sentences that cannot both be true at the same time, they also cannot both be false at the same time. If one is false, the other is true: they are contradictories, all a are b, some a are not b, they cannot both be true at the same time, they cannot both be false at the same time. If it is false that: (x)(ax bx), then it is true that: ( (cid:454)(cid:895)(cid:894)a(cid:454) ~b(cid:454)(cid:895), a(cid:374)d (cid:448)i(cid:272)e (cid:448)e(cid:396)sa: the (cid:862)s(cid:395)ua(cid:396)e of oppositio(cid:374)(cid:863) p. (cid:1005)8(cid:1006). If it is false that: (x)(ax ~bx), then it is true that: ( (cid:454)(cid:895)(cid:894)a(cid:454) b(cid:454)(cid:895), (cid:894)a(cid:374)d (cid:448)i(cid:272)e (cid:448)e(cid:396)sa(cid:895). The arrows on the square of opposition point to contradictory pairs. In ordinary english, we also have the notion of (cid:862)contraries(cid:863): sentences that cannot both be true but that could both be false.