Justification Via Truth Table
The validity of modus ponens in classical two-valued logic can be clearly demonstrated by use of a truth table.
| p | q | p → q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
In instances of modus ponens we assume as premises that p → q is true and p is true. Only one line of the truth table—the first—satisfies these two conditions (p and p → q). On this line, q is also true. Therefore, whenever p → q is true and p is true, q must also be true.
Read more about this topic: Modus Ponens
Famous quotes containing the words truth and/or table:
“Why should you renounce your right to traverse the star-lit deserts of truth, of the premature comforts of an acre, house, and barn? Truth also has its roof, and bed, and board.”
—Ralph Waldo Emerson (1803–1882)
“The one happiness is to shut one’s door upon a little room, with a table before one, and to create; to create life in that isolation from life.”
—Eleonora Duse (1859–1924)