ln2-page4 - p p DN It is worth noting that _ I, &O, $ O...

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1. 2. 3. 4. 5. 6. 7. 8. 9. 10. P ! [( Q ! R ) _ S ] S S !⇠ R R ! P SHOW: Q R P ( Q ! R ) _ S Q ! R Q Pr Pr Pr Pr DD 2,3 ! O 4,6 ! O 1,7 ! O 2,8 _ O 6,9 ! O Pitfalls to Avoid The following argument forms are invalid and must never be used! p ! q q p p ! q p q p _ q p q p _ q q p These may appear superFcially similar to the real rules, but a little re±ection shows that the slight differences matter. The Frst two are not cases of “ ! O” and the latter two are not cases of “ _ O”. Another problem that must be avoided is applying the rules to parts of lines. These rules only apply when the whole statement is of the right form. ! O” cannot be used if the main connective of a statement is not the arrow. One cannot go from ( P ! Q ) _ R and Q either to P or to R ! Rules must be applied to whole lines . D. Other Direct Derivation Rules So far we have learned ! O and _ O. To review: p ! q p q p ! q q p ! O p _ q p q p _ q q p _ O To these we now add: p q p p q q p q p q p $ q p ! q p $ q q ! p $ O p ! q q ! p p $ q $ I p p _ q p q _ p _ I p ⇠⇠ p ⇠⇠
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Unformatted text preview: p p DN It is worth noting that _ I, &O, $ O and DN require only one line for justiFcation, whereas _ O, ! O, &I, and $ I require two. The OUT rules are rules for using statements of a certain form (with a certain main operator). The IN rules are rules for deriving or getting statements of a certain form. With all of these rules in place, we can prove the validity of a wide variety of different arguments. Here are some sample derivations. 1. 2. 3. 4. 5. 6. ( F _ G ) ! ( H & J ) F SHOW: H F _ G H & J H Pr Pr DD 2 _ I 1,4 ! O 5 &O 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. ( A & B ) ! C A D _ C A ! B SHOW: D & B B A & B C D D & B Pr Pr Pr Pr DD 2,4 ! O 2,6 &I 1,7 ! O 3,8 _ O 6,9 &I 4...
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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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