Lecture 6(A): Logic 2 (Implication issues)

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Prof. Mark Walker, University of Arizona
Implication: a compound statement. Antecedent & consequent. Examples. Open and closed implications.
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Thanks Mark for these videos. Very helpful. I find it more intuitive to give the truth value of negation, conjunction, and disjunction compound statements. I just memorize that of implication because it does not seem intuitive. You want to reason in terms of causality: If P is true, then Q should be true; If P is false, Q should be false, and I consider only these two to be intuitively true. Consequenlty If P is true, Q should be true and if Q is false, then the statement is false. I do not understand how the statement: If P is false, Q should be true, is a true statement. It is almost as if we did not care about the antecedent in reaching the conclusion. But we can't even reason in terms of causality when considering the truth value of implications and so I do not know why the implication statements are true or false. How can one say: If P is false, then Q is true, is a true statement. Please I would appreciate some clarification. Thanks a million

tayoukachukwu
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How do we reconcile the problem where oftentimes the quantifier is left out in writing the statements (as per on the right side of the screen), but the quantifiers are actually rather important in determining the truth value of the statements (as per left hand side of the screen)?

freakedout