The logical form of an argument is called the argument form or test form of the argument.
HistoryThe 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." 
Example of argument formTo 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.
Importance of argument formAttention 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. Some authors only define logical form with respect to whole arguments, as the schemata or inferential structure of the argument. In argumentation theory or informal logic, an argument form is sometimes seen as a broader notion than the logical form.
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.
- Categorial grammar
- Sense and reference
- Analytic proposition
- List of invalid argument forms
- List of valid argument forms
- Synthetic proposition
- The Cambridge Dictionary of Philosophy, CUP 1999, pp. 511-512
- Russell, Bertrand. 1914(1993). Our Knowledge of the External World: as a field for scientific method in philosophy. New York: Routledge. p. 53
- 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
- Hurley, Patrick J. (1988). A concise introduction to logic. Belmont, Calif.: Wadsworth Pub. Co. ISBN 0-534-08928-3.
- J. C. Beall (2009). Logic: the Basics. Taylor & Francis. p. 18. ISBN 978-0-415-77498-7.
- Paul Tomassi (1999). Logic. Routledge. p. 386. ISBN 978-0-415-16696-6.
- Robert C. Pinto (2001). Argument, inference and dialectic: collected papers on informal logic. Springer. p. 84. ISBN 978-0-7923-7005-5.
- Richard Mark Sainsbury (2001). Logical forms: an introduction to philosophical logic. Wiley-Blackwell. ISBN 978-0-631-21679-7.
- Gerhard Preyer, Georg Peter, ed. (2002). Logical form and language. Clarendon Press. ISBN 978-0-19-924555-0.
- Gila Sher (1991). The bounds of logic: a generalized viewpoint. MIT Press. ISBN 978-0-262-19311-5.
- Logical form at PhilPapers
- Logical Form entry by Paul Pietroski in the Stanford Encyclopedia of Philosophy
- Logical form at the Indiana Philosophy Ontology Project
- Beaney, Michael, "Analysis", The Stanford Encyclopedia of Philosophy (Summer 2009 Edition), Edward N. Zalta (ed.)
- IEP, Validity and Soundness