# Some logic texts call this the fallacy of affirming

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conclusion. [Some logic texts call this the fallacy of affirming the consequent.] (b) Why is reasoning using this argument form deemed invalid? 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) j(Frodo) ( x)(j(x) h(x)) ( x)(c(x) h(x)) Proof of validity: 1. ( x)(j(x) h(x)) : Hypothesis 2. j(Frodo) h(Frodo) : 1,Universal Instantiation 3. j(Frodo) : Hypothesis 4. h(Frodo) : 2,3,Modus Ponens 5. c(Frodo) : Hypothesis 6. c(Frodo) h(Frodo) : 5,4,Conjunction 7. ( x)(c(x) h(x)) : 6,Existential Generalization
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