Property of statements and of ideas: A statement is
false iff what the statement
means does not
represent a fact. And an idea is false iff a
statement of which the meaning is the idea does
Note there sometimes is a difference between what is false and what is not true, depending on one's assumptions or system of logic. In that case, the false corresponds to the strong notion of having verified that a statement is in contradiction with the facts, while what is not true is either what is false or else what is (merely) not true.
In standard bi-valent logic, the false and the not true coincide; in other systems (e.g. for dealing with paradoxes) they may not. This need not introduce three or more truth-values, though sometimes it does: Two ways to do without are using truth-value gaps (one sets up truth-tables and leaves entries open rather than T or F) or extending a logical system so that it comprises probability theory.
See also: Evidence,
Negation, Not, Philosophy of Science, Proof,