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# Class Note for PHIL 110 at UMass(22)

Marketplace > University of Massachusetts > Class Note for PHIL 110 at UMass 22

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## About this Document

COURSE
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TYPE
Class Notes
PAGES
11
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KARMA
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This 11 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 25 views.

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Date Created: 02/06/15
INTRO LOGIC DAY 09 UNIT 2 DERIVATIONS IN SENTENTIAL LOGIC Basic Idea We start with a few argument forms which we presume are valid and we use these to demonstrate that other argument forms are valid We demonstrate that a given argument form is valid by deriving deducing its conclusion from its premises using a few fundamental modes of reasoning Example 1 Modus Ponens MP A a C if A then C A A C C a derivative argument form P P a Q we can employ Q a R modus ponens MP R a S to derive the conclusion from the premises S Example 1 continued P PeQ QR RS S NP Q IVIIP R MP i S lt Example 2 Modus Tollens MT A a C if A then C C not C A not A a derivative argument form S R a S we can employ Q a R modus tolens MT P a Q to derive the conclusion from the premises P Example 2 continued NS RS QR PQ P NT NR MT Q MT i P4 Example 3 using both MP and MT it a C it a C A NC C 21 derivative argument form S R a S R a T we can employ a combination P a T of MP and MT P a Q to derive the conclusion from the premises Q Example 3 continued S RaS RTPT I MT NR MP l NT I MT NP PaQ MP Derivations How to Start argument P P gtQQ gtR R gtS S 1 write down premises 2 write down SHOW conclusion 1 P Premise 2 P gt Q Pr 3 Q gt R Pr 4 R gt S Pr 5 SHOW 8 the goal 10 Derivations How to Continue A 3 apply rules as appropriate to available lines until goal is reached 1 P Pr 2 P gt Q Pr 3 Q gt R Pr 4 R gt S Pr 5 SHOW 8 goal 6 Q 12 MP 7 R 36 MP 8 8 47 MP follows from lines 1 and 2 by modus ponens 11 Derivations How to Finish 4 Box and Cancel 1 P Pr 2 P gt Q Pr 3 Q gt R Pr 4 R gt S Pr 5 8 DD 6 Q 12 MP 7 R 36 MP 8 8 47 MP DD Direct Derivation 12 W ch 6 9 LW 8 CD ch 1 8 00 LW Z L CICI Jcl O ed LO Jcl LFcl q Jcl LN PEN Jcl sea Jcl SN AAAAAAAAAO vvvvvvvvvv ON ONFdN fFlt LNFEIN SFH 9 adwexa 9L LW 1 17 LW 98 LW Z L G CICI LO Jcl 09d q Jcl EEO Jcl sea Jcl SN AAAAAAAA vvvvvvvv ANfoedfaeofseafSN z adwexa Initial Inference Rules Modus Ponens AAC 54 C Modus Tollens AAC C 54 Modus Tollendo Ponens 1 52lva 54 TB Modus Tollendo Ponens 2 52lva NTB 54 15 Examples of Modus Ponens it a C PampQ a RvS NP a Q A PampQ P C RVS Q 16 Examples of Modus Tollens it a C PampQ a RvS NP a Q C RVS Q l PampQ P P a Q valid argument E BUT P NOT an instance of MT 17 Form versus Content I Value are the dime and ten pennies the same NO are they the same in value YES these particular ten pennies are 1943 copper pennies and are worth to collectors 2000000 Examples of MTP1 A v B PampQ v RVS P v Q A PampQ P B RVs Q 19 Examples of MTP2 A v B PampQ v RVS P v Q 13 RVS Q A PampQ P 20 1O THE END

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