Justification Via Truth Table
The validity of modus tollens can be clearly demonstrated through a truth table.
| p | q | p → q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
In instances of modus tollens we assume as premises that p → q is true and q is false. There is only one line of the truth table - the fourth line - which satisfies these two conditions. In this line, p is false. Therefore, in every instance in which p → q is true and q is false, p must also be false.
Read more about this topic: Modus Tollens
Famous quotes containing the words truth and/or table:
“... what a weak barrier is truth when it stands in the way of an hypothesis!”
—Mary Wollstonecraft (1759–1797)
“A child who is not rigorously instructed in the matter of table manners is a child whose future is being dealt with cavalierly. A person who makes an admiral’s hat out of linen napkins is not going to be in wild social demand.”
—Fran Lebowitz (20th century)