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PHIL12A Section answers, 6 April 2011 Julian Jonker 1 How much do you know? 1. Here are two questions from last time. Assess whether the following arguments are (a) tautologically valid, (b) logically valid but not tautologically valid, or (c) invalid. In both arguments, c is a new constant which names any large cube that exists in the world. If there are no large cubes, then c names any object. (a) (Ex 10.6) 1 x(Cube(x) Large(x)) (Cube(c) Large(c)) 2 Tet(c) → ¬ Cube(c) 3 Cube(c) 4 x ¬ (Cube(x) Large(x)) The argument has the truth-functional form: 1 A ( B C ) 2 D → ¬ B 3 B 4 E It is not tautologically valid. Nor is it logically valid: suppose that there is a large cube, and call it c . Then the premises of the argument are true, and the conclusion false. 1

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(b) (Ex 10.7) 1 x(Cube(x) Large(x)) (Cube(c) Large(c)) 2 x ¬ (Cube(x) Large(x)) ↔ ¬∃ x(Cube(x) Large(x)) 3 Tet(c) → ¬ Cube(c) 4 Tet(c) 5 x ¬ (Cube(x) Large(x)) The argument has the truth-functional form:
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