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Difference between revisions of "A Prioris"
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Pay close attention to the '''Logical Representation''' column. It is equivalent to the '''Example''' column, except it is using a mathematical variable in place of the English statement. That is, <math>p</math> corresponds to, "It is raining," and <math>q</math> corresponds to "I will bring an umbrella." The <math>\rightarrow</math> symbol simply indicates that the statement is of the form "if ... then ...". | Pay close attention to the '''Logical Representation''' column. It is equivalent to the '''Example''' column, except it is using a mathematical variable in place of the English statement. That is, <math>p</math> corresponds to, "It is raining," and <math>q</math> corresponds to "I will bring an umbrella." The <math>\rightarrow</math> symbol simply indicates that the statement is of the form "if ... then ...". | ||
Now, notice that both <math>p</math> and <math>q</math> have the potential to be true or false. It could be raining, or it could not be raining. I could bring an umbrella, or I could not bring an umbrella. In fact, there are four unique combinations that <math>p</math> or <math>q</math> could hold together. | Now, notice that both <math>p</math> and <math>q</math> have the potential to be true or false. It could be raining, or it could not be raining. I could bring an umbrella, or I could not bring an umbrella. In fact, there are four unique combinations that <math>p</math> or <math>q</math> could hold together. | ||
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In the above truth table, the '''Valid''' column is meant to indicate whether the particular combination of <math>p</math> and <math>q</math> being true or false is consistent with the original conditional statement, <math>p \rightarrow q</math>. You can think about it logically. Suppose your friend tells you, "If it is raining, I will bring an umbrella." In row (1), if it is raining, and they bring an umbrella, your friend is holding true to their word. In row (2), it is not raining, yet they still chose to bring an umbrella. This might seem strange at first, but notice that your friend is not contradicting themself. They simply told you that if it would rain, then they would bring an umbrella. They told you nothing about what they would do when it is not raining. Row (4) is also fine; since it is not raining, they do not need to bring an umbrella. Row (3) presents the problem. Your friend promised that if it would rain, they would bring an umbrella. But they didn't! | In the above truth table, the '''Valid''' column is meant to indicate whether the particular combination of <math>p</math> and <math>q</math> being true or false is consistent with the original conditional statement, <math>p \rightarrow q</math>. You can think about it logically. Suppose your friend tells you, "If it is raining, I will bring an umbrella." In row (1), if it is raining, and they bring an umbrella, your friend is holding true to their word. In row (2), it is not raining, yet they still chose to bring an umbrella. This might seem strange at first, but notice that your friend is not contradicting themself. They simply told you that if it would rain, then they would bring an umbrella. They told you nothing about what they would do when it is not raining. Row (4) is also fine; since it is not raining, they do not need to bring an umbrella. Row (3) presents the problem. Your friend promised that if it would rain, they would bring an umbrella. But they didn't! | ||
Finally, we have enough background to explain the conditional logic a priori. The argument | |||
Finally, we have enough background to explain the conditional logic a priori. The argument says that the resolution should be viewed as a tacit conditional, or an <math>p \rightarrow q</math> statement. The conditional is, "If the affirmative debater wins the round, then they should get the ballot." The argument (incorrectly) says that denying the antecedent, <math>p</math> , of the statement proves that consequent, <math>q</math> , true. Therefore, if <math>p</math> is false, <math>q</math> must be true. In this context, that means that if the affirmative debater loses the round, they should still get the ballot! The implication, therefore, is that the affirmative debater must get the ballot whether they won or lost the round. | |||
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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. | |||
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. | |||
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. | |||
== How To Respond == | == How To Respond == | ||
=== General Tips === | === General Tips === | ||