Definition and Examples of Valid Arguments

Glossary of Grammatical and Rhetorical Terms

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In a deductive argument, validity is the principle that if all the premises are true, the conclusion must also be true. Also known as formal validity and valid argument. 

In logic, validity isn't the same as truth. As Paul Tomassi observes, "Validity is a property of arguments. Truth is a property of individual sentences. Moreover, not every valid argument is a sound argument" (Logic, 1999). According to a popular slogan, "Valid arguments are valid by virtue of their form" (although not all logicians would wholly agree). Arguments that are not valid are said to be invalid.

In rhetoric, says James Crosswhite, "a valid argument is one which wins the assent of a universal audience. A merely effective argument succeeds only with a particular audience" (The Rhetoric of Reason, 1996). Put another way, validity is the product of rhetorical competence.

Formally Valid Arguments

"A formally valid argument that has true premises is said to be a sound argument. In debate or discussion, therefore, an argument may be attacked in two ways: by attempting to show that one of its premises is false or by attempting to show that it is invalid. On the other hand, if one concedes the truth of the premises of a formally valid argument, one must also concede the truth of the conclusion—or be guilty of irrationality." (Martin P. Golding, Legal Reasoning. Broadview Press, 2001)

"... I once heard former RIBA President Jack Pringle defend flat roofs with the following syllogism: We all like Edwardian terraces. Edwardian terraces use curtain walls to hide their sloping roofs and pretend they're flat. Ergo: we must all like flat roofs. Except that we don't, and they still leak." (Jonathan Morrison, "My Top Five Architectural Pet Hates." The Guardian, November 1, 2007)

Analyzing the Validity of An Argument

"The primary tool in deductive reasoning is the syllogism, a three-part argument consisting of two premises and a conclusion:

All Rembrandt paintings are great works of art.
The Night Watch is a Rembrandt painting.
Therefore, The Night Watch is a great work of art.
All doctors are quacks.
Smith is a doctor.
Therefore, Smith is a quack.

The syllogism is a tool for analyzing the validity of an argument. You'll rarely find a formal syllogism outside of textbooks on logic. Mostly, you'll find enthymemes, abbreviated syllogisms with one or more of the parts unstated:

The Night Watch is by Rembrandt, isn't it? And Rembrandt is a great painter, isn't he?
Look, Smith is a doctor. He must be a quack.

Translating such statements into a syllogism enables the logic to be examined more coolly and clearly than it otherwise could be. If both premises in a syllogism are true and the reasoning process from one part of the syllogism to the other is valid, the conclusions will be proven." (Sarah Skwire and David Skwire, Writing With a Thesis: A Rhetoric and Reader, 12th ed. Wadsworth, Cengage, 2014)

Valid Argument Forms

"There are a great many valid argument forms, but we shall consider only four basic ones. They are basic in the sense that they occur in everyday use, and that all other valid argument forms can be derived from these four forms:

Affirming the Antecedent

If p then q.
Therefore, q.

Denying the Consequent

If p then q.
Therefore, not-p.

Chain Argument

If p then q.
If q then r.
Therefore, if p then r.

Disjunctive Syllogism

Either p or q.
Therefore, q.

Whenever we find an argument whose form is identical to one of these valid argument forms, we know that it must be a valid argument." (William Hughes and Jonathan Lavery, Critical Thinking: An Introduction to the Basic Skills. Broadview Press, 2004)

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Nordquist, Richard. "Definition and Examples of Valid Arguments." ThoughtCo, Aug. 26, 2020, Nordquist, Richard. (2020, August 26). Definition and Examples of Valid Arguments. Retrieved from Nordquist, Richard. "Definition and Examples of Valid Arguments." ThoughtCo. (accessed June 10, 2023).