ln2-page3 - the scene of the crime. Therefore, Macavity did...

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the scene of the crime. Therefore, Macavity did not steal the diamonds. Simply put, if an if-then statement is true, but the then-part is false, the if-part must be false as well. Modus ponens is Latin for “afFrming mode”. Modus tollens is Latin for “denying mode”. Here are some derivations that make use of this form of ! O”. 1. 2. 3. 4. 5. 6. X ! Y Y ! Z Z SHOW: X Y X Pr Pr Pr DD 2,3 ! O 1,5 ! O 1. 2. 3. 4. 5. 6. ( M _ N ) ! Q Q ( R S ) ! ( M _ N ) SHOW: ( R S ) ( M _ N ) ( R S ) Pr Pr Pr DD 1,2 ! O 3,5 ! O Here are some that use both forms of “ ! O”. 1. 2. 3. 4. 5. 6. A ! B A ! C B SHOW: C A C Pr Pr Pr DD 1,3 ! O (MT) 2,5 ! O (MP) 1. 2. 3. 4. 5. 6. ( P _ Q ) !⇠ S S !⇠⇠ S S SHOW: ⇠⇠ ( P _ Q ) ⇠⇠ S ⇠⇠ ( P _ Q ) Pr Pr Pr DD 2,3 ! O (MP) 1,5 ! O (MT) This last example shows that our rules are very strict. Modus tollens takes the form: p ! q q p
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This note was uploaded on 11/22/2011 for the course PHIL 110 taught by Professor Bohn during the Spring '08 term at UMass (Amherst).

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