150 - handout 13 - 4 march 2010 - expanding truth-tables

150 - handout 13 - 4 march 2010 - expanding truth-tables -...

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PHILOSOPHY 150: INTRODUCTION TO LOGIC HANDOUT 13: 4 MARCH 2010 Alison Duncan Kerr E XPANDING O UR U SE OF T RUTH -T ABLES I. T ESTING THE V ALIDITY OF AN A RGUMENT F ORM . A. Example: If primitive people did not cross the Pacific Ocean, there will not be a strong resemblance between Polynesian artifacts and South American artifacts. There is a strong resemblance. So, primitive people did cross the Pacific. F IRST : create a dictionary. A: Primitive people did cross the Pacific Ocean. B: There is a strong resemblance between Polynesian artifacts & South American artifacts. S ECOND : symbolize the argument. ~A ~B B A T HIRD : translate the symbolized argument into variables to represent the argument form . ~p ~q q p F OURTH : create the truth-table for the argument form. p q ~ p ~ q q / p T T F T F T T T F F T T F T F T T F F T F F F T T T F F F IFTH : determine whether the argument form is valid or invalid. Recall the definition of VALIDITY : An argument (or argument form) is valid iff it is not possible for it to have all true premises and a false conclusion. To determine whether an argument form is valid takes a few steps. (i) Look to see if there are any rows where the conclusion is false. In this case, there is are two (the third and fourth rows). (ii) Check each row where the conclusion is false independently. First, consider the fourth row: are all the premises true in this case? No, while the first premise is true, the second is false. Second, consider the third row: are all the premises true in this case? No, while the second premise is true, the first is false. S IXTH : Because there is no a possible truth-value assignment (the truth-table displays all the possible combinations of truth-value assignments) that makes it such that the conclusion of this argument is false and the premises are all true, this argument is valid.

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150 - handout 13 - 4 march 2010 - expanding truth-tables -...

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