Thursday, July 3, 2014

Deduction: Deductively Valid & Deductively Sound

Deduction is the process of reasoning from one or more premises to reach a logically certain conclusion. Hence, a deductive argument is one in which if the premises were true, then the conclusion must also be true. This certainty is what distinguishes deductive arguments from other argument forms.

In informal logic circles, the term cogent is typically used to describe a good argument. To some degree, this seems to be an attempt to integrate deductive and inductive reasoning with a simple set of common terms. Among formal logicians, the term cogent is not commonly used. Instead the terms valid and sound are the standard. 

Deductively Valid Arguments - A valid deductive argument is one in which, if the premises were true, then the conclusion must also be true. The premises deductively entail the conclusion so that it would be impossible for it to be false.  Another way to think about it is to say that with deductive arguments, the premises support the conclusion 100%. If the argument does not meet these conditions then it is said to be deductively invalid.

To asses whether an argument is valid, simply assume that the premises are all true (whether they are or not) and consider if it would still be possible for the conclusion to be false. If it is possible for the conclusion to be false, the argument is invalid. If it is not possible, it is a deductively valid argument.

Applying this concept to our informal logic model we find that a deductively valid argument is one in which the premises are relevant to the conclusion and provide sufficient support to guarantee the truth of the conclusion.

Deductively Sound Arguments - A deductively sound argument is one in which the argument is valid and all of it's premises are actually true. Hence, the arguments conclusion is true.

If the argument has one or more false premises, is invalid, or both, it is deductively unsound.

For instance, if I present the argument:

P1 If I can fly over this building, I am Superman.
P2 I can fly over this building.
C  I am Superman.

This is a deductively valid argument since the form of the argument is such that if the premises were true, the conclusion must also be true. It is of course an unsound argument since one or more of it's premises are not true.

Applying the concept of soundness to the informal logic model we find that with relatively few exceptions, arguments that are sound qualify as cogent. There are, however, arguments that qualify as cogent in the ARG sense and do not qualify as sound in the classical sense. One reason is that the standard used to evaluate premises in formal logic is whether they are true or not true. In informal logic, premises are judged by the less stringent criteria of being either acceptable or unacceptible.

The two types of deductive arguments are categorical syllogisms and propositional arguments.