#extensionalism

How Logic Became Extensional.—In early modern logical thought, such as in the Port-Royal Logic, it was a commonplace that intension and extension stood in a relationship of inverse proportion. A treatment of one, then, was by implication of treatment of the other; the two were complementary. Logic retained this traditional form through most of the nineteenth century. Russell’s theory of descriptions of 1905 marked the transition of the theory of reference to its modern form, neatly shearing off extension from intension. Frege’s approach, which retained intension after a fashion, had anticipated that of Russell, but Russell’s work was the breakthrough that created the opportunity for Frege’s work to be appreciated. In the wake of Russell’s work, many other theories of reference followed. After the field of contenders for a theory of reference was filled, intensionality was crowded out by intention and inclination, leaving only theories of extension as competitors. To the analytical mind, meaning seems “squishy” and capturing meaning is like trying to put your thumb on a drop of mercury. Better to be rid of meaning entirely, or to construct some simulacrum of meaning out of extensional elements. And so it was that, once extension and intension were put asunder, extension alone was retained, while intension was condemned to irrelevance by neglect. But with the elimination of intension from logic, the relationship between intension and extension was lost also, and, with it, an intuitive pillar of logic. Today, intension continues to languish in neglect, while extensionality reigns supreme, but the history of logic is not at an end, and the next twist in the narrative may subvert expectations about the inevitability of extensionalism.