Class Note for PHIL 110 at UMass(17)
Class Note for PHIL 110 at UMass(17)
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This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Massachusetts taught by a professor in Fall. Since its upload, it has received 16 views.
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Date Created: 02/06/15
INTRO LOGIC DAY 12 Derivations in SL 4 Exam 2 Format 6 argument forms 15 points each plus 10 free points Symbolic argument forms no translations For each one you will be asked to construct a derivation of the conclusion from the premises The rule sheet will be provided 1 problem from 2 problem from 2 problems from 1 problem from Set D Set E Set F Set G 91 96 Schedule Day 09 Introductory Material Day 10 Direct Derivation DD Conditional Derivation CD Negation Derivation ND Indirect Derivation Day 12 show atomic show disjunction Day11 Day 13 show conjunction Day 14 EXAM 2 Inference Rules so far amp0 amp 13 amp B amp1 B 13 3 amp B B amp v0 13 13 VI N N1 B B 3 a0 a 13 a 13 DN NN NB NN 13 N SHeW Rules so far DirectDerivation Strategy DD W DD SHe W J4 DD q 54 CD ND 39 ac ESD 39 N lADS In Direct Derivation DD SHGW C SHGWS X one directly arrives at 39 39 the very formula one is trying to show 5 Affiliated Rules ShowConditional Strategy Assumption Rule CD Ifone has a line of the form SHOW aC SHOW ADC CD then one is entitled to write down the formula A As on the very next line as an assumption SHOW C Assumption Rule ND Ifone has a line of the form SHOW N then one is entitled to write down the formula on the very next line as an assumption ContradictionIn XI if you have a formula and you have its negation N then you are entitled to infer a contradiction absurdity X ShowNegation Strategy Indirect Derivation SHCW J4 SHOW NA IN D N As J4 As SHOW X W SHGW X W X X This is exactly parallel to ND and is another version of the traditional mode of reasoning known as REDUCTIO AD ABSURDUM Can we show the following 1 P a Q Pr We are stuck 2 NPa Q Pr 3 SHOW Q we have PaQ we also have NPaQ so to apply a0 so to apply a0 we must find P we must find NP orfind NQ or find NQ 10 Using ID The difference between ID and ND is that ND applies only to negations whereas ID applies in principle to all formulas it is a generic rule like directderivation Although ID can in principle be used on any formula it is best used on two types of formulas 1 atomic formulas P Q R etc 2 disjunctions AVE 12 ShowAtomic Strategy SHGW A NA As SHOW X W X A is atomic PQR etc 13 Example 2 1 P amp Q Pr 2 P a Q CD 3 P As 4 Q ID 5 NO As 6 x DD 7 P amp Q 35 ampI 8 x 17 x1 15 Example 1 1 PsQ Pr 2 PsQ Pr 3 Q ID 4 Q As 5 X DD 6 P 14 so 7 Q 26 so 8 x 47 x1 14 ShowDisjunction Strategy sHew AVE spam As SHOW x W x 16 Affiliated InferenceRule TildeWedgeOut Example 4 v0 v B v 3 1A 3 17 Example 3 1 P Q Pr 2 P v Q ID 3 P v Q As 4 x DD 5 P 6 NQ 3 NVO 7 Q 15 0 8 X 67 x1 18 1 P QVR Pr 2 Q a P v R CD 3 Q As 4 P v R ID 5 P v R As 6 x DD 7 P 8 NR 5 NVO 9 Q v R 17 a0 10 Q 89 v0 11 x 310 x1 19 Example 5 1 PvQPPampQ Pr 2 IPampQNPampNQ ID 3 NP amp Q v NP amp NQ AS 4 x DD 5 NP ampQ 6 P amp Q 3 W0 7 NP v Q 15 a0 8 MP 9 NQ 7 NVO 10 NP amp NQ 89 ampI 11 x 610 x1 20
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