Some Basic Concepts of Deductive Logic:
Argument: A structured collection of sentences containing exactly
one sentence called a conclusion and a set of sentences called the
premises.
Conclusion: A statement supported by the premises of an argument.
Premises: A set of statements used to support the conclusion.
Validity (a property applying to arguments only): An argument
is valid if and only if necessarily if the premises are all true, the
conclusion will be as well.
• Alternatively: An argument is valid if and only if it is not
possible for the premises to all be true while the conclusion is
false (at the same time).
• From this, we can get invalidity: An argument is invalid if and
only if it is possible for the premises to all be true and the
conclusion false (at the same time).
Soundness (a property applying to arguments only): An
argument is sound if and only if it is valid and has all true premises.
Consistency (a property applying to sets of sentences only): A
set of sentences is consistent if and only if it is possible for all the
sentences in that set to be true (at the same time).
• From this, we can get inconsistency: A set of sentences is
inconsistent if and only if it is not possible for all the sentences
in that set to be true (at the same time).
Tautologousness (a property applying to single sentences only):
A sentence is a tautology (i.e., a necessary truth) if and only if it is
true in all circumstances, come what may.
