A tautology is a statement which is always true.
What is the name for a statement which is always false?
Is it correct that a statement is either tautology, the false counterpart of tautology, or contingent?
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A tautology is not "a statement that is always true". In such case,
1>0 would be a tautology, but it is not.
A tautology is a logical structure that is true just by its logical form, not by its meaning, like on the previous example. So, "a=a" is true because of the logical structure, not because of the value of a.
The opposite would be a statement that is false due to its structure. The closest form to that is a contradiction in the structure, which has not a name as such. The term contradiction might cover it, though.
I believe the false counterpart for a tautology is a contradiction. When using truth tables to investigate statements, if the outcome is always true, the statement is a tautology. If it's always false, it's a contradiction.If it's a mixture of both, then it's neither a tautology nor a contradiction.
While the answer has been given, it might help to think in terms truth tables. In some truth table, if a proposition always evaluates to true given every possible entry, you have a tautology. Contradictions arise when the table always evaluates to false, and tables that present with a mix of true and false are contingent propositions. Contingent propositions give rise to another flavor of logic called modal logic where necessary and possible operators are introduced in statements.