Algebra of Deontic Notions

  • Edward Nieznański Cardinal Stefan Wyszynski University in Warsaw
Keywords: deontic notions, deontic modalities, connection of deontic concepts with the moral values, algebra of sets, the Boolean algebra

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: xÎV (an act x is an element of the set of acts subordinated to some norm or law) and x''=x (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 i.e., N = N∩D. Sixty four theorems are proven in this calculus.

Author Biography

Edward Nieznański, Cardinal Stefan Wyszynski University in Warsaw

Prof. Dr Edward Nieznański – Chair of Logic, Institute of Philosophy, Cardinal Stefan Wyszynski University

References

Dubish R.: Lattices to Logic, New York 1964.

Hilpinen R.: Deontic Logic, [w:] L. Goble (ed.), The Blackwell Guide to Philosophical Logic, Oxford 2001.

Kalinowski J.: Logika norm, Lublin 1972.

Tokarz M.: Wprowadzenie do logiki, Katowice 1984.

Wojciechowska A.: Elementy logiki i teorii mnogości, Warszawa 1979.

Published
2020-09-03
Section
Articles