Do false statements imply contradictions?

Do false statements imply contradictions?

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?

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