Deduction

In Logic, one of two distinct systems of argumentation or reasoning. Deduction is the logical method that yields necessary conclusions.

Deductive reasoning (or argument) was first distinguished from Inductive reasoning by Aristotle. He defined the difference between the two by the direction of logical inference: deduction moved from universal (or more clearly known) propositions, to particular (less clearly known ones), while he defined induction as the inference from particular claims to universal ones.

In contemporary Logic we define the difference based on the logical status of the conclusion: deductive arguments yield necessary conclusions, while inductive arguments yield probable conclusions.

The success, and therefore the evaluation, of deduction is dependent on two distinct factors:

Form - is the structure correct?
Truth - are the premises true?

Because of the emphasis on form, deduction is sometimes called Formal logic. If the structure (form) of the argument is incorrect, the conclusion will not follow necessarily. This is what is known as a formal fallacy. But, if the form is correct, if the conclusion must follow from a given set of premises, we judge the argument to be valid.

If a deductive argument is valid AND has all true premises, it is called a sound argument.

For example:

Valid - All dogs are cats.
Kato is a dog.
Therefore, Kato is a cat.

If we assume the truth of premises one and two the conclusion MUST follow (it could not fail to be true). So, this argument is valid (it is structured correctly). However, since the first premise is false, this argument is unsound.

Sound - All dogs are mammals.
Kato is a dog.
Therefore, Kato is a mammal.

The structure of this argument is identical to the first argument, so it is obviously valid. And, in this case the first premise is also true, so this argument would be called sound.

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