Editing Deductive reasoning (section)

==Validity and soundness==
[[File:Argument terminology used in logic (en).svg|thumb|400px|Argument terminology]]
Deductive arguments are evaluated in terms of their ''[[Validity (logic)|validity]]'' and ''[[soundness]]''.

An argument is ''valid'' if it is impossible for its [[premise]]s to be true while its conclusion is false. In other words, the conclusion must be true if the premises are true. An argument can be “valid” even if one or more of its premises are false.

An argument is ''sound'' if it is ''valid'' and the premises are true.

It is possible to have a deductive argument that is logically ''valid'' but is not ''sound''. Fallacious arguments often take that form.

The following is an example of an argument that is “valid”, but not “sound”:
# Everyone who eats carrots is a quarterback.
# John eats carrots.
# Therefore, John is a quarterback.

The example's first premise is false – there are people who eat carrots who are not quarterbacks – but the conclusion would necessarily be true, if the premises were true. In other words, it is impossible for the premises to be true and the conclusion false. Therefore, the argument is “valid”, but not “sound”. False generalizations – such as "Everyone who eats carrots is a quarterback" – are often used to make unsound arguments. The fact that there are some people who eat carrots but are not quarterbacks proves the flaw of the argument.

In this example, the first statement uses [[term logic|categorical reasoning]], saying that all carrot-eaters are definitely quarterbacks. This theory of deductive reasoning – also known as [[term logic]] – was developed by [[Aristotle]], but was superseded by [[propositional calculus|propositional (sentential) logic]] and [[predicate logic]]. {{citation_needed|date=April 2018}}

Deductive reasoning can be contrasted with [[inductive reasoning]], in regards to validity and soundness. In cases of inductive reasoning, even though the premises are true and the argument is “valid”, it is possible for the conclusion to be false (determined to be false with a counterexample or other means).