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Difference between revisions of "A Prioris"
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→Logical a Prioris
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If you are confused how the argument reached that conclusion, good. The argument is completely invalid! If the antecedent <math>p</math> is false, the consequent <math>q</math> could be either true or false! Look to rows (2) and (4) of the above truth table. Both of these rows are valid (i.e. consistent with the conditional statement), and in row (2), the antecedent is false where the consequent is true, and in row (4), the antecedent is false where the consequent is false. Therefore, the truth or falsity of the antecedent has no bearing on the truth or falsity on the consequent. | If you are confused how the argument reached that conclusion, good. The argument is completely invalid! If the antecedent <math>p</math> is false, the consequent <math>q</math> could be either true or false! Look to rows (2) and (4) of the above truth table. Both of these rows are valid (i.e. consistent with the conditional statement), and in row (2), the antecedent is false where the consequent is true, and in row (4), the antecedent is false where the consequent is false. Therefore, the truth or falsity of the antecedent has no bearing on the truth or falsity on the consequent. | ||
This incorrect a priori, however, does not come from nowhere. If the antecedent <math>p</math> is false, the conditional as a whole, <math>p \rightarrow q</math>, is guaranteed to be true. You can see this by looking back to our truth table. In rows (2) and (4) the antecedent is false, and the '''Valid''' column is true. Because, in any situation where the antecedent is false, whether the consequent is true or false, you are guaranteed to have a true conditional statement. Returning to our example "If it is raining, then I will take an umbrella," suppose "it is not raining" (since the antecedent is false). Since it is not raining, you have the freedom to either take an umbrella or not take an umbrella – neither decision will contradict the original conditional statement. | This incorrect a priori, however, does not come from nowhere. If the antecedent <math>p</math> is false, the conditional as a whole, <math>p \rightarrow q</math>, is guaranteed to be true. You can see this by looking back to our truth table. In rows (2) and (4) the antecedent is false, and the '''Valid''' column is true. Because, in any situation where the antecedent is false, whether the consequent is true or false, you are guaranteed to have a true conditional statement. Returning to our example "If it is raining, then I will take an umbrella," suppose "it is not raining" (since the antecedent is false). Since it is not raining, you have the freedom to either take an umbrella or not take an umbrella – neither decision will contradict the original conditional statement, which means that the conditional statement as a whole is guaranteed to be true. | ||
So, if the a priori were accurate, it would say "if the antecedent <math>p</math> is false, then the conditional statement <math>p \rightarrow q</math> as a whole is true." However, this would get you nowhere in debate. Your goal is to get the ballot, <math>q</math> , not prove the conditional statement <math>p \rightarrow q</math>. Sadly, this trick has been used to exploit judges and opponents who are not aware of these facts of logic. | So, if the a priori were accurate, it would say "if the antecedent <math>p</math> is false, then the conditional statement <math>p \rightarrow q</math> as a whole is true." However, this would get you nowhere in debate. Your goal is to get the ballot, <math>q</math> , not prove the conditional statement <math>p \rightarrow q</math>. Sadly, this trick has been used to exploit judges and opponents who are not aware of these facts of logic. | ||