Logical form

Consider the following argument: All men are mortal; Socrates is a man; therefore, Socrates is mortal. Intuitively, what makes this a valid argument has nothing to do with Socrates, men or mortality. Rather, each sentence in the argument exhibits a certain ‘logical form’ and those forms, taken together, constitute a pattern that guarantees the truth of the conclusion given the truth of the premises. More generally, the logical form of a sentence of natural language is what determines both its logical properties and its logical relations to other sentences.

The logical form of a sentence of natural language is typically represented in a theory of logical form by a well-formed formula in a ‘logically pure’ language whose only meaningful symbols are expressions with fixed, distinctly logical meanings (for example, quantifiers). Thus, the logical forms of the sentences in the above argument would be represented in a theory based on pure predicate logic by the formulas ‘∀x(Fx → Gx)’, ‘Fy’ and ‘Gy’, respectively, where ‘F’ and ‘G’ are free predicate variables and ‘y’ a free individual variable. The argument’s intuitive validity is then explained by the fact that the logical forms of the premises formally entail the logical form of the conclusion. The primary goal of a theory of logical form is to explain as broad a range of such intuitive logical phenomena as possible in terms of the logical forms that it assigns to sentences of natural language.