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:
“A petty reason perhaps why novelists more and more try to keep a distance from journalists is that novelists are trying to write the truth and journalists are trying to write fiction.”
—Graham Greene (1904–1991)
“But hospitality must be for service, and not for show, or it pulls down the host. The brave soul rates itself too high to value itself by the splendor of its table and draperies. It gives what it hath, and all it hath, but its own majesty can lend a better grace to bannocks and fair water than belong to city feasts.”
—Ralph Waldo Emerson (1803–1882)