Think Again: How to Reason and Argue by Walter Sinnott-Armstrong

Author:Walter Sinnott-Armstrong [Sinnott-Armstrong, Walter]
Language: eng
Format: epub, mobi, azw3, pdf
Publisher: Oxford University Press
Published: 2018-05-31T22:00:00+00:00

WHEN IS VALIDITY FORMAL?

Some arguments are valid because of their specific words or sentences. The argument “My pet is a tiger, so my pet is a cat” is valid, because it is not possible to be a tiger without being a cat. However, this validity is destroyed if we substitute certain other words, such as in “My pet is a tapir, so my pet is a dog.” Thus, what makes the original argument valid is the (semantic) meanings of its words—“tiger” and “cat.”

In contrast, other arguments are valid by virtue of their form. Consider “My pet is either a tiger or a tapir. My pet is not a tiger. Therefore, my pet is a tapir.” If the conclusion is false (my pet is not a tapir), and the second premise is true (my pet is not a tiger), then the first premise has to be false (my pet is not either a tiger or a tapir). Thus, this argument is valid. Moreover, it remains valid no matter which words are substituted for “tiger” and “tapir” as well as “My pet.” This argument is also valid: “Your pet is either a dog or a pig. Your pet is not a pig. Therefore, your pet is a dog.” So is this one: “My country is either at war or in debt. My country is not at war. Therefore, my country is in debt.” In every case with this form, it is not possible for the conclusion to be false in circumstances where the premises are both true. Thus, this argument is valid by virtue of its form. This argument form is called denying a disjunct (because the “either” and “or” propositions are called disjuncts) or process of elimination (because the second premise eliminates one of the alternatives in the first premise).

It is useful to remember a few other argument forms that are formally valid as well as a few that are not valid by virtue of their form but are often mistakenly thought to be valid. The variables “x” and “y” can be replaced by any sentence as long as the same sentence replaces the same variable wherever that variable occurs. These argument forms are valid:

Modus Ponens: If x, then y; x; so y.

Modus Tollens: If x, then y; not y; so not x.

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