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already. Remember that deductive arguments claim to guarantee their conclusions, while

inductive arguments merely recommend theirs. Or ask yourself whether the introduction of

any additional information, without changing or denying any of the premises, could make the

conclusion seem more or less likely; if so, the pattern of reasoning is inductive.

Truth and Validity

Since deductive reasoning requires such a strong relationship between premises and

conclusion, we will spend the majority of this survey studying various patterns of deductive

inference. It is therefore worthwhile to consider the standard of correctness for deductive

arguments in some detail.

A deductive argument is valid when the inference from premises to conclusion is

perfect:

If the premises of a valid argument are true, then its conclusion must also be true.

It is impossible for the conclusion of a valid argument to be false while its premises

are true.

(Considering the premises as a set of propositions, we will say that the premises are true

only when each and every one of those propositions is true.) Any deductive argument that is

not valid is invalid: it is possible for its conclusion to be false while its premises are true, so

even if the premises are true, the conclusion may be either true or false.

Notice that the validity of the inference of a deductive argument is independent of the

truth of its premises; both conditions must be met in order to be sure of the truth of the

conclusion. Out of eight distinct possible combinations here, only one is ruled out:

Premises

Inference

Conclusion

True

Valid

True

XXXX

Invalid

True

False

False

Valid

True

False

Invalid

True

False

The only thing that cannot happen is for a deductive argument to have true premises and a

valid inference but a false conclusion.

Some logicians designate the combination of true premises and a valid inference as a

sound argument; it is a piece of reasoning whose conclusion must be true. The trouble with

every other case, in which either one of the premises is false or the inference is invalid or

both, is that it gets us nowhere. The conclusions of such arguments may be either true or

false, so they are entirely useless in any effort to gain new information.

?1997, 1998, 1999 Garth Kemerling.

Questions, comments, and suggestions may be sent to:

gkemerling@delphi.com

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