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Since the proposition above is a contingency one

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Since the proposition above is a contingency, one cannot be one hundred per cent certain that the truth of the conclusion follows from the truth of the hypothesis. That, of course, is unacceptable behavior for a rule of inference, and is why we require all the implications used as rules of inference to be tautologies. [Think about betting your life on the rules of inference!!] 8. (15 pts.) c(Frodo) ¬h(Frodo) ( x)(j(x) h(x)) ( x)(c(x) ¬j(x)) Proof of validity: 1. ¬h(Frodo) : Hypothesis 2. ( x)(j(x) h(x)) : Hypothesis 3. j(Frodo) h(Frodo) : 2,Universal Instantiation 4. ¬j(Frodo) : 1,3,Modus Tollens 5. c(Frodo) : Hypothesis 6. c(Frodo) ¬j(Frodo) : 5,4,Conjunction 7. ( x)(c(x) ¬j(x)) : 6,Existential Generalization
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