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Section 1.1:
Explaining the Possibility of the Impossible |
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Informal Fallacies
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Begging the question is an odd fallacy. It is odd because -- logically speaking -- it is not really invalid. As a matter of fact, "Begging the Question" makes for a perfectly valid argument. Here's an obvious example of it: Bush is the best president the US has ever had ----------------------------------- So, Bush is the best president the US has ever had The form of the argument is perfectly valid. It is: P
------- So, P Harder to get a clearer argument than that! If the premises are true (if P is true), clearly the conclusion cannot possibly be false (P). However, it should not have escaped any of you that such arguments -- while valid -- are not terribly informative. The conclusion -- which is claiming here to be proved on the basis of the premises -- isn't really proved in an interesting way. The fallacy, however, is that the argument is doing something more -- that it really is proving a conclusion in an informative non-"question begging" way.
The "false dilemma" fallacy is a derivative of the valid dilemma form in symbolic logic. The dilemma looks like this: P v Q
If P, then R If Q, then R ------------ So, R It is called a "dilemma" based on the fact that the argument is usually used against an opponent, showing the opponent that his argument has two (and only two) forms, and that no matter which of the two are chosen, some bad consequence (R) will result. However, such an argument would be a false dilemma if it were in fact the case that there was a third (or fourth, or fifth) option other than P and Q. Then (R) could be avoided. To suggest that there are only two possibilities, however, would be to state a false dilemma.
Examine the following argument: If an entity X is rational, then it has a right to life (it has a right for its existence not to be taken away). The number "2" is a rational entity. ------------------------ Thus, the number "2" has a right to life Certainly looks valid! The form looks like modus ponens! If P, then Q
P --------- Thus, Q But something must have gone wrong here. Even if we grant that the premises are true, it can't possibly be right that the conclusion follows. But if the argument is valid, the conclusion must follow (with necessity!). So what's wrong? Actually, the argument is not valid (it is not a real form of modus ponens) after all. The trick here is that a word is reused in both premises as if it had the same meaning throughout, but it really doesn't. The word here is "rational". In the first premise, it means "having a capacity to think". In the second premise, it means "non-fractional positive number greater than 0". Notice that if we insert the real meanings into the original argument, it is no longer valid. If an entity X has the capacity to think, then it has a right to life. The number "2" is a non-fractional positive number greater than 0. --------------------------------------- Thus, the number "2" has a right to life. Symbolically, this is nothing more than If P, then Q
M ------------ Thus, Q
Composition
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