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Argument form

The test form of an argument is what results from replacing different words, or sentences, that make up the argument with letters; the letters are called variables.

Some examples of valid arguments forms are modus ponens, modus tollens, and disjunctive syllogism. One invalid argument form is affirming the consequent.

Just as variables can stand for various numbers in mathematics, variables can stand for various words, or sentences, in logic. Argument forms are very important in the study of logic. The parts of argument forms--sentence forms (see below)--are equally important. In a logic course one would learn how to determine what the forms of various sentences and arguments are.

The basic notion of argument form can be introduced with an example. Here is an example of an argument:

A All humans are mortal. Socrates is human. Therefore, Socrates is mortal.

We can rewrite argument A by putting each sentence on its own line:


All humans are mortal.
Socrates is human.
Therefore, Socrates is mortal.

To demonstrate the important notion of the form of an argument, substitute letters for similar items throughout B:


All S is P.
a is S.
Therefore, a is P.

All we have done in C is to put 'S' for 'human' and 'humans', 'P' for 'mortal', and 'a' for 'Socrates'; what results, C, is the form of the original argument in A. So argument form C is the form of argument A. Moreover, each individual sentence of C is the sentence form of its respective sentence in A.

There is a good reason why attention to argument and sentence forms is important. The reason is this: form is what makes an argument valid or cogent.

Also see:

analytic proposition
synthetic proposition