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R November 3, 2011.pdf

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York University
Modes Of Reasoning
MODR 2640

R November 3, 2011 Thursday,November 03, 20110:45 AM CorrespondingConditionalof an argument - The conditional when antecedent is the conjunction of the premises and whose consequent is the conclusion ○ (A · B⊃ C - Argument is validiff corresponding conditional is a tautology 3-6 Consistency - A set of statements is consistent if it is possible that all are true - Truth table test for consistency ○ 1) Find the form of each statement ○ 2) Set up a column for each variableand a column for each statement ○ 3) Work out all truth values ○ 4) If a row in which all statements are true, then consistent. Otherwise, not. 3-7 Validityand Consistency - Valid = impossible for all premises to be true and conclusion false - Suppose P 1 P 2 ∴ C is valid. Then impossible 1 true, 2 true, and C false. Impossible 1 true, 2 true, and ~C true. - So, set 1 , 2 , and ~C is inconsistent - Argument validiff set consisting of all premises and negation of conclusion is inconsistent Note:Paradox of Implication 1. Any argument with inconsistent premises is valid. ○ Valid = impossible all premises true and conclusion false ○ Inconsistent = impossible that all premises aretrue
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