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Thursday, July 12, 2007 10:01 AM Arguments in sentential logic. We have translated English arguments into sentential logic (replacing with variables and symbols). SF S /F Can become SF;S/F S T T F F F T F T F SF T F T T S T T F F /F T F T T If there is smoke there is fire SF There is no smoke ~S There is no fire /~F S T T F F F T F T F SF T F T T ~S F F T T ~F F T F T Invalid argument We can turn the above into one part of a conditional argument ((SF)&~S)F Validity & invalidity Arguments Tautology & Contradiction & contingent Formulas We are now dealing with turning arguments into formulas. What if the argument isn't false in any cases? ((SF)&S)F SF T F T T & T F F F S T T F F T T T T F T F T F Valid Tautology InvalidContradiction or Contingent Intro to Logic Page 1 An argument with premises P1, P2.... And conclusion C is valid IFF if the formula constructed from it (P1 &P2...C) is a tautology. A conditional that is a tautology is also said to be a logical implication. So the Ps must logically imply C. Modus Ponens ('afirming the antecedent') Modus Tollens ('denying the consequent') Modus Tollendo Ponens ('disjunctive syllogism') Modus Ponens If there is smoke there is fire We have a conditional There is smoke Confirms the antecedent There is fire we infer the consequent VALID Not Modus Ponens If there is smoke there is fire We have a conditional There is no smoke Deny the antecedent There is no fire we deny the consequent This is invalid Modus Tollens If there is smoke there is fire We have a conditional There is no fire We deny the consequent Then there is no smoke We infer the antecedent VALID PQ T F T T & F F F T ~Q F T F T T T T T ~P F F T T Not Modus Tollens If there is smoke there is fire We have a conditional There is fire Confirm the consequent There is smoke We infer the antecedent PQ T F T T & T F T F Q T F T F T T F T P T T F F Modus Tollendo Ponens P v Q We have a disjunction ~P We deny one of the antecedents /Q We infer the other (P T v T Q) T & F ~P F T Q T Intro to Logic Page 2 T F F VALID T T F F T F F T F F T T T T T F T F Examples: Logical implications Pg 78 #10 P T T F F Q T F T F PQ T F F T T T T F P&Q T F F F & T F F F QP T F T T AB is not a logical implication BA is a logical implication AB are not logically equivalent. Pg 79 #26 P T T T T F F F F Q T T F F T T F F R T F T F T F T F (((PQ) & T T F F T T T T T F F F T F T T (QR)) & T F T T T F T T T F F F F F F T (RP)) T T T T F T F T T T T T T T T T (PR) T F T F F T F T Intro to Logic Page 3 ...
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This note was uploaded on 04/07/2008 for the course PHILOSOPHY 201 taught by Professor Morgan during the Spring '08 term at Rutgers.
- Spring '08