#intension

Ontological Saturation.—One way in which a concept can be considered narrow would be because only one (or a few) objects fall under its extension. This is the case of “natural satellite of the Earth”—an example employed by Frege. This example, however, isn’t necessarily narrow in the sense of having a narrow extension; it is in another sense a highly general concept because it is a special case of the very general concept of a moon. If, at some future date, the solar system is flooded with many asteroids, say, from some extraterrestrial close encounter, the Earth could acquire many additional natural satellites, and then the concept “natural satellite of Earth” could have a great many objects fall under its extension. The fact that this concept can have a changing extension reflects a generality compatible with its current narrowness. The conceptual simplicity of “natural satellite of Earth” betrays its generality, even if a single object, or no object at all, falls under the concept; in this case, the intension is simple, and that simplicity can yield a narrow or a wide extension. A complex intension more readily yields a narrow extension, and an intension might be narrow in more than one way, but that is because there are an infinitude of forms of particularism that could render an intension narrow. We can arrive at particularism by specifying many properties (restricting the extension by expanding the intension) or through the use of highly particularistic concepts, but highly particularistic concepts are naturally complex, i.e., they tacitly incorporate a greater complexity of intension. The concept “natural satellite of Earth” can be made less complex by eliminating the qualifier “natural” and by substituting any planet for “Earth,” but it can also be made more complex by specifying the diameter or orbital distance or even surface features of the natural satellite. When we think of “The Moon” in all is particularity we could be said to entertain the concept of the Moon, but this is misleading, like Hegel’s “concrete universal,” which isn’t a concept at all. A concept is, as Frege noted, “unsaturated,” but any concrete individual is particular in virtue of its ontological saturation.

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.

the spirit is willing but the flesh is weak

With Pure Precisions and Intentions I Can Climb Any Mountains

#poetry