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.
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Famous quotes containing the words truth and/or table:
“Few serve truth in truth because only few have the pure will to be just, and of those again very few have the strength to be just.”
—Friedrich Nietzsche (1844–1900)
“I talk with the authority of failure—Ernest with the authority of success. We could never sit across the same table again.”
—F. Scott Fitzgerald (1896–1940)