An Explanation of Some Latin Math Terms

Date: 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