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Encyclopedia > Argument form

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. Logic, from Classical Greek Î»ÏŒÎ³Î¿Ï‚ logos (the word), is the study of the principles and criteria of valid inference and demonstration. ... In logic, an argument is a set of statements, consisting of a number of premises, a number of inferences, and a conclusion, which is said to have the following property: if the premises are true, then the conclusion must be true, or highly likely to be true. ... Algebra is a branch of mathematics concerning the study of structure, relation and quantity. ... In computer science and mathematics, a variable (IPA pronunciation: ) (sometimes called a pronumeral) is a symbolic representation denoting a quantity or expression. ... Logic, from Classical Greek Î»ÏŒÎ³Î¿Ï‚ logos (the word), is the study of the principles and criteria of valid inference and demonstration. ...

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.

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. In logic, the form of an argument is valid precisely if it cannot lead from true premises to a false conclusion. ... An argument is cogent if and only if the truth of the arguments premises would render the truth of the conclusion probable (i. ... In logic, modus ponens (Latin: mode that affirms; often abbreviated MP) is a valid, simple argument form. ... In logic, Modus tollens (Latin for mode that denies) is the formal name for indirect proof or proof by contrapositive (contrapositive inference), often abbreviated to MT. It can also be referred to as denying the consequent, and is a valid form of argument (unlike similarly-named but invalid arguments such... A disjunctive syllogism, also known as modus tollendo ponens (literally: mode which, by denying, affirms) is a valid, simple argument form: P or Q Not P Therefore, Q In logical operator notation: Â¬ where represents the logical assertion. ... Affirming the consequent is a logical fallacy in the form of a hypothetical proposition. ... Denying the antecedent (also known as vacuous implication) is a type of logical fallacy. ...

Results from FactBites:

 Argument Forms (1065 words) Each of the three arguments above is a substitution instance of this argument form, since each of them results from the substitution of an appropriate (simple or compound) statement for each of the statement variables in the argument form. Recognizing individual arguments as substitution-instances of more general argument forms is an important skill because, as we've already seen, the validity of any argument depends solely upon its logical form. An argument in the propositional calculus is valid whenever it is a substitution-instance of an argument form in which it is impossible for the premises to be true and the conclusion false.
 The Fallacy Files Glossary (2304 words) A counter-example to an argument form: This is an instance of that form which has true premisses and a false conclusion, showing that the form is non-validating. Of an argument in which the logical connection between premisses and conclusion is one of necessity. A type of argument in which an assumption is shown to imply an obviously false conclusion, thus demonstrating that the original assumption is false.
More results at FactBites »

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