An Explanation of Some Latin Math TermsDate: 12/11/95 at 16:26:46 From: Constance Cunningham Subject: Latin Help Dear Dr. Math, We are a small discrete math class of eight students studying logical arguments. Two arguments we have examined are "modus tollens" and "modus ponens." We understand the arguments but would like to know what the terms mean in English. Thank you. Discrete Math at Rocky Grove High School, Franklin, PA. Date: 12/12/95 at 11:2:8 From: Doctor Ken Subject: Re: Latin Help Hello! From the book _The Words of Mathematics_ by Steven Schwartzman: MODUS PONENS: Latin MODUS "standard, measure" is from the Indo-European root MED- "to take appropriate measures." The second word, PONENS, is the present participle of Latin PONERE "to put." ... In logic, MODUS PONENS is a standard form of argumentation in which you "put down" the antecedent of an if-then statement and conclude the occurrence of the consequence of that if-then statement. Modus ponens is akin to detachment. MODUS TOLLENS: ... The second word, TOLLENS, is the present participle of Latin TOLLERE "to take away," from the Indo-European root TELE- "to lift, support." In logic, MODUS TOLLENS is a standard form of argumentation in which you "take away," that is, negate, the consequent of an if-then statement and conclude the negation of the antecedent of that if-then statement. MODUS TOLLENS is equivalent to using the contrapositive of the original if-then statement. So there you have it. - Doctor Ken, The Geometry Forum |
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