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Concept
Logical form
Summary
In logic, logical form of a statement is a precisely-specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system. In an ideal formal language, the meaning of a logical form can be determined unambiguously from syntax alone. Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language.
The logical form of an argument is called the argument 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, Jan 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, and so forth 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."
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.
Official source
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