Studied by 5 people
Validity
an argument is valid if an only if it is impossible for all premises to be true and the conclusion false
Tautologically Equivalent
A + B are tautologically equivalent if and only if they have the same truth values on every valuation
Sound
An argument is sound if an only if it is valid and all of its premises are true
Jointly Consistent
Sentences are JOINTLY CONSISTENT if and only if it is possible for them all to be true together
Jointly Inconsistent
Sentences are JOINTLY INCONSISTENT if and only if it is not possible for them all to be true together
Necessary Truth
A sentence is a NECESSARY TRUTH if and only if it is true and it is not possible for it to be false
Necessary Falsehood
A sentence is a NECESSARY FALSEHOOD if and only if it is false and not possible for it to be true
Contingent
A sentence is CONTINGENT if and only if it is possible for it to be true and possible for it to be false
Tautology
A is a TAUTOLOGY iff it is true on every valuation
Contradiction
A is a CONTRADICTION iff it is false on every valuation
Tautologically Equivalent
A and B are TAUTOLOGICALLY EQUIVALENT iff they have the same truth value on every valuation
Jointly Tautologically Consistent
A1, A2, … An are JOINTLY TAUTOLOGOCALLY CONSISTENT iff there is some valuation that makes them all true
Jointly Tautologically Inconsistent
A1, A2, … An are JOINTLY TAUTOLOGOCALLY INCONSISTENT iff there is no valuation that makes them all true
Tautologically Entail
The sentences A1, A2, … An TAUTOLOGOCALLY ENTAIL the sentence C if there is no valuation of the atomic sentences
which makes all of A1, A2, … An true and C false
