Logical form

In philosophy and mathematics, a logical form of a syntactic expression is a precisely-specified semantic version of that expression 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.• Unilalianism In philosophy and mathematics, a logical form of a syntactic expression is a precisely-specified semantic version of that expression 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 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.' To demonstrate the important notion of the form of an argument, substitute letters for similar items throughout the sentences in the original argument. 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. Attention is given to argument and sentence form, because form is what makes an argument valid or cogent. All logical form arguments are either inductive or deductive. Inductive logical forms include inductive generalization, statistical arguments, causal argument, and arguments from analogy. Common deductive argument forms are hypothetical syllogism, categorical syllogism, argument by definition, argument based on mathematics, argument from definition. The most reliable forms of logic are modus ponens, modus tollens, and chain arguments because if the premises of the argument are true, then the conclusion necessarily follows. 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.