Direct Reduction and Indirect Reduction

You already trust that 2 + 2 = 4 without re-deriving it every time, but if someone doubted 57 × 23, you would break it down into steps you both already trust. Reduction does exactly that for a syllogism in Figure II, III or IV: it breaks the argument down into a Figure I argument everyone already accepts as self-evidently valid.

In two minutes

Reduction is the process of transforming a valid mood of Figure II, III or IV into an equivalent mood of Figure I, either directly (by converting propositions and reordering premises) or, for two stubborn moods, indirectly (by assuming the conclusion false and deriving a contradiction).

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