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Information about Argument Structure

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 important arguments 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:

B
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:

C
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.[1]

Attention is given to argument and sentence form, because form is what makes an argument valid or cogent. Some examples of valid argument forms are modus ponens, modus tollens, and the disjunctive syllogism. Two invalid argument forms are affirming the consequent and denying the antecedent.

References

Hurley, Patrick J. (1988). A concise introduction to logic. Belmont, Calif. : Wadsworth Pub. Co. ISBN 0534089283

Notes

1. ^ Hurley, "1.5 Argument forms; proving invalidity"

See also

Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration.
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sound as synonymous with valid)

Each premise (there must be at least one) of an argument and its conclusion is a statement, capable of being true or false and nothing else.
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Algebra is a branch of mathematics concerning the study of structure, relation and quantity. The name is derived from the treatise written by the Arabic[1] mathematician, astronomer, astrologer and geographer,
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variable (IPA pronunciation: [ˈvæɹiəbl]) (sometimes called a pronumeral) is a symbolic representation denoting a quantity or expression.
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Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration.
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validity as it occurs in logic refers generally to a property of deductive arguments, although many logic texts apply the term to statements as well (a statement is a sentence that “has a truth value,” i.e., that is either true or false).
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An argument is cogent if and only if the truth of the argument's premises would render the truth of the conclusion probable (i.e., the argument is strong), and the argument's premises are, in fact, true.
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In logic, modus ponendo ponens (Latin: mode that affirms by affirming; often abbreviated MP) is a valid, simple argument form. It is a very common rule of inference, and takes the following form:

If P, then Q.
P.

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In logic, Modus ponendo tollens (Latin for "mode that affirms by denying") is the formal name for indirect proof or proof by contraposition (contrapositive inference), often abbreviated to MT.
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A disjunctive syllogism, is a classically valid, simple argument form:

P or Q
Not P
Therefore, Q


In logical operator notation:
¬

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Affirming the consequent is a formal fallacy, committed by reasoning in the form:

If P, then Q.
Q.
Therefore, P.

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Denying the antecedent is a logical fallacy, committed by reasoning in the form:

If P, then Q.
Not P.
Therefore, not Q.

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The analytic-synthetic distinction (or dichotomy) is a conceptual distinction, used primarily in philosophy to distinguish propositions into two types: analytic propositions and synthetic propositions.
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The analytic-synthetic distinction (or dichotomy) is a conceptual distinction, used primarily in philosophy to distinguish propositions into two types: analytic propositions and synthetic propositions.
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logical form of an argument is the representation of its sentences using the formal grammar and symbolism of a logical system to display its similarity with all other arguments of the same type.
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