About all and nothing

In § 120 of the Wissenschaftslehre, Bernard Bolzano mentions the idea of nothing as a counter-example to the principle of inverse proportionality of the intension and extension of ideas. We’ll here investigate three logical conceptions of such an idea. After having considered the standard conception of nothing as a quantifier, i.e. as a second order property accounting for the extensional vacuity/emptiness of first order properties, we’ll consider two intensional characterizations of the idea of nothing along Meinongian lines. The first one, defended by Dale Jacquette, makes “being nothing” a nuclear property and “being” the (abstract) object characterized by this sole property. We’ll show, however, that this leads to many unwanted consequences, and that it would be better to make “being nothing” an extranuclear property, the property of having no extranuclear property. The second intensional conception of nothing, defended by Thibaut Giraud, will satisfy this requirement and deal with it in mereological terms. However, for want of a convenient algebraic structure, this conception will take nothing as the empty whole and make it part of all objects, including atomic ones, which is itself questionable.