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Traditional Logic: Third Rule for Dilemmas

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    Traditional Logic: Third Rule for Dilemmas

    In chapter 13 of Traditional Logic: Adv Formal Logic, regarding Rules for the Dilemma and The Counter-Dilemma: How does one determine whether a dilemma has violated Rule 3? The book does not appear to have answered it. For example, on page 86 in the text, the book simply states that Protagoras's Dilemma violates Rule 3 without ever saying how that was determined or why it violates Rule 3.

    Thanks ahead for any assistance.

    #2
    Sorry this took so long! I had to get help! Here's Dan Sheffler's reply:

    When it comes to counter dilemmas, there's a little bit more of rhetorical art than strict logical necessity. One must consider whether it will be easier to go after the major premise directly, providing evidence for its falsehood, or whether it would be simpler to simply propose an alternate syllogism with a contradictory conclusion that is just as plausible (or even more plausible) than the original syllogism. Protagoras's syllogism "violates rule three" for the simple reason that Euathlus is able to construct an equally plausible counter syllogism with the opposite conclusion.

    Consider a parallel example using simpler conditional reasoning, known as the "Moore inversion" (after the philosopher G.E. Moore):

    Original syllogism:
    1. If Hume's reasoning is right, then I don't know that my hand is in front of my face.
    2. Hume's reasoning is right.
    3. Therefore, I don't know that my hand is in front of my face.

    To refute this syllogism directly we would have to either show a specific mistake in Hume's reasoning (reject premise 2) or show that radical skepticism doesn't actually follow from it (reject premise 1). Moore suggested, however, that it's much simpler just to offer an alternate syllogism that is just as plausible, with the opposite claim. In the conditional case, this involves rearranging the conclusion and one of the premises, changing it from modus ponens to modus tollens:

    1. If Hume's reasoning is right, then I don't know that my hand is in front of my face.
    2. I do know that my hand is in front of my face.
    3. Therefore, there must be some mistake in Hume's reasoning (and I don't have to say where).

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