Articoli correlati a Logic for children, deductive and inductive, the substance...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1882 Excerpt: ...alone, or neither X" nor'Y". If it is not true that John called on Richard (X"), and dined with him (Y"), then either John called on Richard (X"), and did not dine with him (y"), or else John did not call on Richard at all (x"). Again, if we also know %X, or that John did call on Richard; then, as the only complex in which X occurs is X.y, we know %X.y, or that John called on Richard, and did not dine with him, and at the same time we know fla.Y, x.y). Again, if %Y, or John did dine with Richard; then, as the only complex in which Y occurs is x.Y, we know +a:.Y, or that John dined with Richard, and did not call on him. Generally, then, the expression fX.Y, which involves +i(X.y, x.Y, x.y), means that if JX then ty, or if JY, then Jit. Or, as it is frequently put, if X' happens, Y" does not happen, or if Y" happens, X" does not happen. The proper expression for either of these hypothetical assertions is therefore fX.Y. 59. It is convenient to take the whole series of complexes, X.Y, X.i/, a.Y, x.y, and study the 14 results due to the suppositions that first one, then two, and then three are absent, with the usual expressions for these cases, which the above explanations will make easy to the teacher, but which must be carefully extracted from the pupil, not put into him. All should be worked with counters first. Writing for registration is a later, but important stage. (a.) fX.Y implies i(X.y, x.Y, x.y), "X' and Y' are not true jointly," "X' alone or Y' alone is true, or both X' and Y' are false, "X' alone or Y' alone, or both X' and Y' together, are false," "if X' is true, Y' is false", "if Y' is true, X' is false." Nothing can be concluded from the supposition th...
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