A logical conflict: a statement that is necessarily false.

Example for a contradictive statement:

⊥: It is raining and it is not raining.

Since it cannot rain and not rain at the same time, the statement as a whole is necessary false.

A contradiction is a statement that is necessary false under all circumstances. Usually it is the result of putting two contradictory statements together, as in the example above.

No contradictions are statements that only evaluate as false due to experience or additional information. For example, take the following statement:

It is raining.

If looking out of the window proves that it is actually not raining at the moment, then the statement is false, but it is not a contradiction, because we need additional information to know if it is true or false.

Contradictory statements can not be used as premises for logical conclusions. Even if they appear in the concluding sentence, they only signify that something must have gone wrong at some point – which can of course be used to prove the invalidity of a statement.

The opposite of a contradiction, i.e. a statement that is always (necessary) true, is called a tautology.

On this site, the logical symbol ⊥ is used to indicate a contradiction. Since every contradiction is always inherently false, it can also be replaced or described by the expression “false” or “F” or the equivalent expression in the respective formal system (e.g. 0).

• Tautology
• Vacuous truth

• Contradiction in Wikipedia