Logic
Do false statements imply contradictions?
Consider the truth table for logical implication.
P...........Q.............P->Q
T...........T.............. T
T...........F...............F
F...........T...............T
F...........F...............T
Notice that for a false statement P, the last two rows of the truth table, both Q and ~Q follow. No matter what Q is, it's truth follows from false statement P, as the third row shows. We can therefore take Q to be "P is true." From here it follows that a false statement P implies it's own truth, as the third row shows.
Do false statements really imply their own truth? Do they really imply contradictions? Are false statements also true?
Accepted:June 9, 2011
Accepted:
June 9, 2011