tautologjës

A tautology is a statement that is true by necessity or by virtue of its logical form. It is a statement that is always true, regardless of the truth values of its component parts. For example, the statement "It is raining or it is not raining" is a tautology. This is because the statement will be true whether it is raining or not. The logical structure of this statement ensures its truth.

In propositional logic, tautologies are statements that are true for all possible assignments of truth values to their propositional variables. These can be identified using truth tables. A truth table systematically lists all possible combinations of truth values for the variables and then evaluates the truth value of the entire statement for each combination. If the final column of the truth table contains only "true" values, the statement is a tautology.

The concept of tautology is important in logic and philosophy. It distinguishes necessary truths from contingent truths (statements that are true but could have been false). While tautologies are always true, they do not provide new information about the world. Their truth is derived from the structure of language or logic itself, not from empirical observation. Examples include statements like "All bachelors are unmarried" or "If A is true, then A is true." These are considered analytically true, meaning their truth can be determined by analyzing the meaning of the words involved.