Algebra of Deontic Notions Cover Image

Algebra pojęć deontycznych
Algebra of Deontic Notions

Author(s): Edward Nieznański
Subject(s): Philosophy
Published by: Towarzystwo Naukowe KUL & Katolicki Uniwersytet Lubelski Jana Pawła II
Keywords: deontic notions; deontic modalities; connection of deontic concepts with the moral values; algebra of sets; the Boolean algebra; pojęcia deontyczne; modalności deontyczne; związek pojęć deontycznych z wartościami moralnymi; algebra zbiorów; algebra Boole’

Summary/Abstract: Leibniz suggested that deontic modalities can be defined in terms of the alethic modalities; according to him, the permitted (licitum) is what possible for a good man to do and the obligatory (debitum) is what is necessary for a good man to do. The paper starts from specifying a connection of deontic concepts with the moral values. The connection comes down to define an isomorphism of two Boolean algebras: from deontic one onto axiological one. The work presents theories of two algebras of deontic notions: the algebra of sets and the Boolean algebra. The theory of deontic set is based on the two axioms: 1) an act x is an element of the set of acts subordinated to some norm or law and 2) an act x is identical with double denial of x. By means of definitions following notions are introduced: Λ (the empty set of acts), N (the set of ordered acts), Z (the set of forbidden acts), P (the set of obligatory acts), F (the set of optional acts), D (the set of permitted acts), I (the set of indifferent acts).The calculus is structured by rules of the Słupecki-Borkowski’s suppositional deduction. Forty five theorems are proven in this calculus. The second theory presented in the paper, is a Boolean algebra of deontic notions. Added to the theory of equality, it takes axioms from the theory of Boolean algebras with addition of a specific axiom for the deontic system. Sixty four theorems are proven in this calculus.

  • Issue Year: 56/2008
  • Issue No: 1
  • Page Range: 239-251
  • Page Count: 13
  • Language: Polish