Logical form

This article is about the term as used in logic. For the linguistics term, see Logical Form (linguistics).

The logical form of a sentence (or proposition or statement or truthbearer) or set of sentences is the form obtained by abstracting from the subject matter of its content terms or by regarding the content terms as mere placeholders or blanks on a form. In an ideal logical language, the logical form can be determined from syntax alone; formal languages used in formal sciences are examples of such languages. Logical form, however, should not be confused with the mere syntax used to represent it; there may be more than one string that represents the same logical form in a given language.[1]

The logical form of an argument is called the argument form or test form of the argument.


The importance of the concept of form to logic was already recognized in ancient times. Aristotle, in the Prior Analytics, was probably the first to employ variable letters to represent valid inferences. Therefore, Łukasiewicz claims that the introduction of variables was 'one of Aristotle's greatest inventions'.

According to the followers of Aristotle like Ammonius, only the logical principles stated in schematic terms belong to logic, and not those given in concrete terms. The concrete terms man, mortal, etc., are analogous to the substitution values of the schematic placeholders 'A', 'B', 'C', which were called the 'matter' (Greek hyle, Latin materia) of the argument.

The term "logical form" itself was introduced by Bertrand Russell in 1914, in the context of his program to formalize natural language and reasoning, which he called philosophical logic. Russell wrote: "Some kind of knowledge of logical forms, though with most people it is not explicit, is involved in all understanding of discourse. It is the business of philosophical logic to extract this knowledge from its concrete integuments, and to render it explicit and pure." [2][3]

Example of argument form

To demonstrate the important notion of the form of an argument, substitute letters for similar items throughout the sentences in the original argument.

Original argument
All humans are mortal.
Socrates is human.
Therefore, Socrates is mortal.
Argument form
All H are M.
S is H.
Therefore, S is M.

All we have done in the Argument form is to put 'H' for 'human' and 'humans', 'M' for 'mortal', and 'S' for 'Socrates'; what results is the form of the original argument. Moreover, each individual sentence of the Argument form is the sentence form of its respective sentence in the original argument.[4]

Importance of argument form

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, disjunctive syllogism, hypothetical syllogism and dilemma. Two invalid argument forms are affirming the consequent and denying the antecedent.

A logical argument, seen as an ordered set of sentences, has a logical form that derives from the form of its constituent sentences; the logical form of an argument is sometimes called argument form.[5] Some authors only define logical form with respect to whole arguments, as the schemata or inferential structure of the argument.[6] In argumentation theory or informal logic, an argument form is sometimes seen as a broader notion than the logical form.[7]

It consists of stripping out all spurious grammatical features from the sentence (such as gender, and passive forms), and replacing all the expressions specific to the subject matter of the argument by schematic variables. Thus, for example, the expression 'all A's are B's' shows the logical form which is common to the sentences 'all men are mortals', 'all cats are carnivores', 'all Greeks are philosophers' and so on.

See also


  1. The Cambridge Dictionary of Philosophy, CUP 1999, pp. 511–512
  2. Russell, Bertrand. 1914(1993). Our Knowledge of the External World: as a field for scientific method in philosophy. New York: Routledge. p. 53
  3. Ernie Lepore, Kirk Ludwig (2002). "What is logical form?". In Gerhard Preyer, Georg Peter. Logical form and language. Clarendon Press. p. 54. ISBN 978-0-19-924555-0. preprint
  4. Hurley, Patrick J. (1988). A concise introduction to logic. Belmont, Calif.: Wadsworth Pub. Co. ISBN 0-534-08928-3.
  5. J. C. Beall (2009). Logic: the Basics. Taylor & Francis. p. 18. ISBN 978-0-415-77498-7.
  6. Paul Tomassi (1999). Logic. Routledge. p. 386. ISBN 978-0-415-16696-6.
  7. Robert C. Pinto (2001). Argument, inference and dialectic: collected papers on informal logic. Springer. p. 84. ISBN 978-0-7923-7005-5.

Further reading

External links

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