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# Class Note for PHIL 110 at UMass(18)

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COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
5
WORDS
KARMA
25 ?

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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 26 views.

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Date Created: 02/06/15
INTRO LOGIC DAY 09 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 show that a given argument form is valid by deriving deducing its conclusion from its premises using a few fundamental modes of reasoning UNIT 2 DERIVATIONS IN SENTENTIAL LOGIC Example 1 Modus Ponens MP A gt C if A then C A A C C Example 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 8 Example 1 continued Example 2 continued P PaQ QaR RaS IS UP Q MP R VP S lt s Rss QsR PaQ P mT l R IMT Q MT Plt Example 2 Modus Tollens MT A gt C if A then C C not C A not A Example Argument Form NS R a S we can employ Q a R modus tollens MT P a Q to derive the conclusion from the premises NP Example 3 using both MP and MT A gt C A gt C A C C A Example Argument Form NS R a 8 NR a NT we can employ a combination P a T ofMP and MT NPaNQ to derive the conclusion from the premises NQ Example 3 continued Res Li NR wRaNT PeTNPaNQ Q MP Derivations How to Continue Derivations How to Start argument P PaQ QaR Res 8 1 write down premises 2 write down SHOWquot conclusion 1 2 3 4 5 P PaQ QaR Res SHOWS Pr premise Pr Pr Pr what one is trying to derive 10 3 Apply rules as applicable to available lines until goal is reached 1 P Pr premise 2 P a Q Pr premise 3 Q a R Pr premise 4 R a S Pr premise 5 SHOW 8 goal 6 Q 12MP follows from 7 R 36MP lt lines 4 and 7 8 S 47MP by modus ponens 11 Derivations How to Finish 4 Box and Cancel 1 P Pr 2 P a Q Pr 3 Q a R Pr 4 R a S Pr 5 SHOW 8 W Direct Derivation 6 Q 12MP 7 R 36MP 8 S 47MP 12 Derivation Example 2 argument NS RaS QaR PaRP 1 s Pr 2 R a s Pr 3 Q a R Pr 4 P a Q Pr 5 SHOW P W 6 R 12MT 7 Q 36MT 8 P 47MT 13 Initial Inference Rules Modus Ponens aC C Modus Tollens aC NC N Modus Tollendo Ponens 1 vB N 3 Modus Tollendo Ponens 2 vB NB 15 Derivation Example 3 argument NS Res NRaNTPaT NPaNQ NQ 1 s Pr 2 R a s Pr 3 R a T Pr 4 P a T Pr 5 P a Q Pr 6 m Q W 7 12MT 8 37MP 9 48MT 10 14 Examples of Modus Ponens A gt C PampQ gt RVS P gt Q A PampQ NP C RVS NQ 16 Examples of Modus Tollens A gt C PampQ gt RxS NP gt Q NC RVS Q NA PampQ P NP gt NQ valid argument 9 BUT P NOT an example of MT 17 Form versus ContentNalue are the dime and ten pennies the same NO are they the same in value YES actually in a very important sense they are not the same in value 2000000 Examples of MTP1 A v B PampQ v RVS NP v Q NA PampQ P B RVS NQ 19 Examples of MTPZ A v B PampQ v RVS NP v Q B RVS Q A PampQ NP 20

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