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Download QR code; Print/export ... additional citations for verification. ... written as the masculine singular form unless the generic antecedent is known to be ...
Phrased another way, denying the antecedent occurs in the context of an indicative conditional statement and assumes that the negation of the antecedent implies the negation of the consequent. It is a type of mixed hypothetical syllogism that takes on the following form: [1] If P, then Q. Not P. Therefore, not Q. which may also be phrased as
Both methods use inference rules derived from Gentzen's 1934/1935 natural deduction system, [4] in which proofs were presented in tree-diagram form rather than in the tabular form of Suppes and Lemmon. Although the tree-diagram layout has advantages for philosophical and educational purposes, the tabular layout is much more convenient for ...
The ante-in antecedent means 'before; in front of'. Thus, when a pro-form precedes its antecedent, the antecedent is not literally an antecedent, but rather it is a postcedent, post-meaning 'after; behind'. The following examples, wherein the pro-forms are bolded and their postcedents are underlined, illustrate this distinction:
ACD unfortunately gives rise to 2 issues. The first is that the elided VP must be parallel, or identical, in form with the antecedent. The second is that since the antecedent contains the VPE site, whenever the antecedent is copied in, the VPE is automatically also included. Combined, these two factors result in an infinite regress: [10]
No part of this book may be transmitted or reproduced in any form by any means without permission in writing from the publisher. Developmental Editor: John Barstow Editorial Director: Shay Totten Project Manager: Emily Foote Copy Editor: Nancy Crompton Fact-checker: Mary Fratini Book Designer: Peter Holm Printed in Canada on recycled paper.
These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths: "For any integer x, if x > 5 then x > 3." [11] – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 ...
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