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In logic, the argument form or test form of an argument results from replacing the different words, or sentences, that make up the argument with letters, along the lines of algebra; the letters represent logical variables. The sentence forms which classify argument forms of common arguments important are studied in logic.
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 are 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.
Attention is given to argument and sentence form, because form is what makes an argument valid or cogent. Some examples of valid arguments forms are modus ponens, modus tollens, and the disjunctive syllogism. Two invalid argument forms are affirming the consequent and denying the antecedent.