Validity and Invalidity, Soundness and Unsoundness
The task of an argument is to provide statements (premises) that give
evidence for the conclusion. There are two basic kinds of arguments.
Deductive argument: involves the claim that the truth
of its premises guarantees the truth of its conclusion; the terms valid
and invalid are used to characterize deductive arguments. A deductive
argument succeeds when, if you accept the evidence as true (the premises),
you must accept the conclusion.
Inductive argument: involves the claim that the truth
of its premises provides some grounds for its conclusion or makes the
conclusion more probable; the terms valid and invalid cannot be applied.
Valid: an argument is valid if and only if it is necessary
that if all of the premises are true, then the conclusion is true; if
all the premises are true, then the conclusion must be true; it is impossible
that all the premises are true and the conclusion is false.
Invalid: an argument that is not valid. We can
test for invalidity by assuming that all the premises are true and seeing
whether it is still possible for the conclusion to be false. If
this is possible, the argument is invalid.
Validity and invalidity apply only
to arguments, not statements. For our purposes, it is just nonsense
to call a statement valid or invalid. True and false apply only
to statements, not arguments. For our purposes, it is just nonsense
to call an argument true or false. All deductive arguments aspire to validity.
If you consider the definitions of
validity and invalidity carefully, you'll note that valid arguments have
the following important property: valid arguments preserve truth.
If all your premises are true and you make a valid argument from them,
it must be the case that whatever conclusion you obtain is true.
(We shall see below, however, that valid arguments do not necessarily
preserve truth value: it is entirely possible to argue validly from
false premises to a true conclusion).
Sound: an argument is sound if and only if it is valid
and contains only true premises.
Unsound: an argument that is not sound.
Counterexample: an example which contradicts some statement
or argument (ex. a counterexample to the statement “All fifteen
year-olds have blue hair” would be a fifteen-year-old without blue
hair); for an argument, a counterexample would be a situation in which
the premises of the argument are true and the conclusion is false; counterexamples
show statements to be false and arguments to be invalid.
IV. Forms of Argument