Logics of essence and accident
João Marcos · 2005
Logic and sermons never convince, The damp of the night drives deeper into my soul. (Only what proves itself to every man and woman is so, Only what nobody denies is so.) —Walt Whitman, Leaves of Grass, Song of Myself, sec.30 (1855–1881). We say that things happen accidentally when they do indeed happen, but only by chance. In the opposite situation, an essential happening is inescapable, its inevitability being the sine qua non for its very occurrence. This paper will investigate modal logics on a language tailored to talk about essential and accidental statements. Completeness of some among the weakest and the strongest such systems is attained. The weak expressibility of the classical propositional language enriched with the non-normal modal operators of essence and accident is highlighted and illustrated, both with respect to the definability of the more usual modal operators as well as with respect to the characterizability of classes of frames. Several interesting problems and directions are left open for exploration.