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Evaluating arguments - 1 Logic ~ deductive argument forms zSome common deductive argument forms yArgument forms most often used in everyday argumentation yLearning these forms will help us determine the validity of arguments

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Evaluating arguments - 2 Logic ~ deductive argument forms y1. Modus ponens A BE.G. If the car runs, it Ahas gas. BThe car runs. It has gas.

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Evaluating arguments - 3 Logic ~ deductive argument forms xAn invalid form of modus ponens the fallacy of affirming the consequent A BE.G. If the car runs, it Bhas gas. AThe car has gas. It runs.

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Evaluating arguments - 4 Logic ~ deductive argument forms y2. Modus tollens xA BE.G. If the car runs, it x~ Bhas gas. x ~ AThe car has no gas. – It does not run.

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Evaluating arguments - 5 Logic ~ deductive argument forms xAn invalid form of Modus tollens xA BE.G. If the car runs, it x~ Ahas gas. x ~ B The car does not run. It does not have gas.

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Evaluating arguments - 6 Logic ~ deductive argument forms xTo logic behind the fallacy of affirming the consequent and the fallacy of denying the antecedent. Why these two forms are invalid? xFor any given effect, more than one cause or logical condition can bring it about. Thus the occurrence of the effect does not entail the occurrence of a specific cause or condition.

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Evaluating arguments - 7 Logic ~ deductive argument forms xSimilarly, the non-occurrence of one of the causes or conditions does not entail that the effect will not occur. It could occur because of one of the other causes. a b effect c d

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Evaluating arguments - 8 Logic ~ deductive argument forms xA sophisticated variation of modus tollens reductio ad absurdum E.g., Assume I wish to show that aesthetic relativism is false. To do this, I assume it is true. Then I try to show that the consequences of this are nonsensical-- i.e., absurd. Thus I show that aesthetic relativism is false.

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Evaluating arguments - 9 Logic ~ deductive argument forms xA sophisticated variation of modus tollens reductio ad absurdum E.g., Assume I wish to show that aesthetic relativism is false. To do this, I assume it is true. Then I try to show that the consequences of this are nonsensical-- i.e., absurd. Thus I show that aesthetic relativism is false.

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Evaluating arguments - 10 Logic ~ deductive argument forms The form of reductio ad absurdum –assume A r –If A r C –~ C – ~ A r

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Evaluating arguments - 11 Logic ~ deductive argument forms y3. Disjunctive syllogism –A v BA v B – ~ A~ B – B A xThese forms are valid. Are they the only valid forms of disjunctive syllogism?

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Evaluating arguments - 12 Logic ~ deductive argument forms xThe exclusive vs inclusive “or.” exclusive -- one or the other disjunct will occur but not both inclusive -- one will occur, and possibly both will occur

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Evaluating arguments - 13 Logic ~ deductive argument forms xConsider the following where the “or” is inclusive. –A v BA v B – AB – ~ B ~ A xThese are invalid for the inclusive “or.” xBut they are valid for the exclusive “or.”

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Evaluating arguments - 14 Logic ~ deductive argument forms xSummary –A v BA v B – ~ A~ B – B A xValid for both the inclusive & exclusive “or’s.”

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Evaluating arguments - 15 Logic ~ deductive argument forms xSummary (cont’d) –A v BA v B – AB – ~ B ~ A xValid for exclusive “or”; invalid for the inclusive “or.”

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Evaluating arguments - 16 Logic ~ deductive argument forms y4. Hypothetical syllogism –A B –B C – A C This form is valid as long as the three terms are lined up as above.

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Deductive Arguments and Inference Rules Terminology: Valid Argument: – truth of the premises guarantees the truth of the conclusion – It would be contradictory.

Deductive Arguments and Inference Rules Terminology: Valid Argument: – truth of the premises guarantees the truth of the conclusion – It would be contradictory.

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