Wow!!! All I was trying to do is point out that you need to be careful. I never said that what we say is always true, or even makes any sense at times. In logic, if you can (in fact) determine the truth value of a statement then double negation does change its truth value.
Point---by adding the word "it" into the statement you changed the sentence and its meaning. You can not determine if the sentence is true or false since she never took the class, therefore it is no longer a statement. That does not change how logic works only how someone could get confused when trying to use it or understand it.
Point---the second sentence can not be assigned a value since it makes no logical sense. For any sentence (string of words in any language) to be considered a logical statement, it must be determined that it can be assigned a truth value (either true or false but not both).
> Date sent: Mon, 28 Jul 1997 20:05:26 -0500 (CDT) > Send reply to: email@example.com > From: Genevieve Boulet <firstname.lastname@example.org> > To: Multiple recipients of list <email@example.com> > Subject: Re: neg * neg = pos; why?
> > >Be very careful here!!! In logic, double negation does in fact > >result in what you refer to as "cancel each other out." > > I am being careful, maybe a little more than others. > > >Change to a statement like "she did not fail" and it would then be > >the same as "she did pass." > > > Consider Mary who never took my math class. She did not fail it, nor did > she pass it. > > Or from something like "number two is not unmarried", it does not follow > that the number two is married! > > > By the way, there is extensive literature concerning logical negation (first > order predicate logic is not all there is to logic). For more on logical > negation, see Lawrence Horn (1989) A NATURAL HISTORY OF NEGATION, University > of Chicago Press; George Englebretsen (1981) LOGICAL NEGATION, Assen, Van > Gorcum; Englebretsen (1996) SOMETHING TO RECKON WITH, Ottawa, Ottawa > University Press; Fred Sommers (1982) THE LOGIC OF NATURAL LANGUAGE, Oxford > University. > > > Genevieve Boulet > Professeure > Departement d'enseignement au prescolaire et au primaire > Faculte d'education > Universite de Sherbrooke > Sherbrooke, Quebec > J1K 2R1 > > tel: (819)821-8000 ext. 1207 > fax: (819)821-8048 > email: firstname.lastname@example.org > > Raymond E. Lee, Ph.D. Department of Mathematics and Computer Science The University of North Carolina at Pembroke P.O. Box 1510 Pembroke, NC 28372-1510 (910) 521-6309 FAX 521-6649