The logic of essence
The author claims that the standard accounts of essence in terms of necessity are inadequate, being unable to account for an asymmetry between a singleton set's essentially containing an individual, and the individual's not essentially belonging to the singleton set. E.g., the singleton set containing Socrates essentially contains the man, but it is not plausible to suppose that the man essentially belongs to the singleton set. There is nothing in the nature of Socrates which demands that there be any sets, let alone one that contains him. But the standard accounts of essence in terms of necessity do not account for this asymmetry. The aim of the paper is to develop an alternative account of essence, not as a fragment of a modal system, but as a system in its own right. The author introduces an operator ``\(\square_F\)'', whose role is to pick out the subjects of the essentialist claim. The intended meaning of ``\(\square_F A\)'' is that \(A\) is true in virtue of the nature of the objects which \(F\). So each class of objects is taken to give rise to its own modal operator, its own ``sphere'' of necessity; and it is the task of the logic of essence to lay down the laws which govern each of these spheres and the way they interact. The author bases this logic on classical first-order logic, axiomatized in some standard way; and adds modal axioms and rules corresponding to the standard axioms and rules for S5, predicational axioms and rules, including the principle of \(\lambda\)-abstraction, and dependency axioms. The resulting system is called ``E5'' (for ``essence'' and the underlying S5-structure). An extended system with domain axioms is called ``\(\text{E}5^+\)''. A number of theorems and meta-theorems are proved, but no semantics is provided for the system.
scientific article; zbMATH DE number 795330