Lecture #12 - Philosophy 12A Lecture #12 2/25/10 Expressive...

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Unformatted text preview: Philosophy 12A Lecture #12 2/25/10 Expressive Completeness: Recap Set of 4 connectives (~,&,v, ) is expressively complete It is rumored that there is gold buried on the island ( G ). You ask one of the natives, a , whether there is gold on the island. He makes the following response: There is gold on this island if and only if I am a Knight. Is there gold buried on the island? [Answer: Yes.] a says G A A (G A) logically equivalent to G because of truth table values Inhabitant a says Either I am a Knave or b is a Knight. What can we infer about a and b ? [Answer: a and b are both Knights.] a says ~ A v B therefore A (~A v B) A B A (A B) = & T T T T T T F T F F F T F F T F F F F T Three of the inhabitants a , b and c were standing together in the garden. A stranger passed by and asked a , Are you a Knight or...
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