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Lecture

# R November 3, 2011.pdf

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York University

Modes Of Reasoning

MODR 2640

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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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