Question

What is called a tautology?

Answer 1

A **tautology** is a statement or proposition in logic and philosophy that is always true, regardless of the truth values of its components. In other words, a tautology is a logical expression that cannot possibly be false because it repeats or restates the same thing in different terms, making it inherently true.

For example, the statement:
- "It will either rain tomorrow, or it will not rain tomorrow."

This is a tautology because one of the two possibilities must be true. Whether it rains or not, the statement will always be true.

In formal logic, tautologies are often used as the basis for reasoning and proofs because they hold under any interpretation of their components. A tautology is essentially a formula that is valid in all possible situations.

For example, the logical statement \( P \lor \neg P \) (read as "P or not P") is a tautology because it covers all possible truth conditions:
- If \( P \) is true, the statement holds.
- If \( P \) is false, then \( \neg P \) (not P) must be true, so the statement still holds.

### In summary:
A tautology is a logical statement that is **always true**, often due to its repetitive structure or inherent truth.