Modus ponendo tollens
|Rules of inference|
|Rules of replacement|
MPT is usually described as having the form:
- Not both A and B
- Therefore, not B
- Ann and Bill cannot both win the race.
- Ann won the race.
- Therefore, Bill cannot have won the race.
As E. J. Lemmon describes it:"Modus ponendo tollens is the principle that, if the negation of a conjunction holds and also one of its conjuncts, then the negation of its other conjunct holds."
In logic notation this can be represented as:
Based on the Sheffer Stroke (alternative denial), "|", the inference can also be formalized in this way:
|3||De Morgan's laws (1)|
|4||Double negation (2)|
|5||Disjunctive syllogism (3,4)|
- Politzer, Guy & Carles, Laure. 2001. 'Belief Revision and Uncertain Reasoning'. Thinking and Reasoning. 7:217–234.
- Stone, Jon R. (1996). Latin for the Illiterati: Exorcizing the Ghosts of a Dead Language. London: Routledge. p. 60. ISBN 0-415-91775-1.
- Lemmon, Edward John. 2001. Beginning Logic. Taylor and Francis/CRC Press, p. 61.