Abstract
Not much is certain in deontic logic. There are not many theorems, in any system, which are undisputed, i.e. with regard to which one or more authors have not stated that they cannot be accepted as a rational reconstruction of normative reasoning. There is, nevertheless, a formal system on which, although it has been disputed as a whole as well as with regard to its theorems, several other systems are founded, which other systems can be regarded as extensions of the first-mentioned system. One may therefore to a certain extent rightly speak of a ‘standard system of deontic logic’. This is even more justified by the fact that alternative systems have often been developed as a reaction to this system. Every deontic logician has to determine, in one way or another, his attitude towards this standard system.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes
Von Wright, 1951–1; and 1951–2, p.36–41; independently of Von Wright comparable systems have been developed by O. Becker, 1952 and G. Kalinowski, 1953.
Von Wright, 1951–1, p.7.
Von Wright, 1951–1, p.9.
Von Wright, 1951–1, p.11.
In this method a formula which is to be examined is reduced to a conjunction of disjunctions, with which every disjunction contains all the parameters occurring in the formula which are preceded or not preceded by a negation symbol. By means of this reduction it is fairly easy to determine whether the formula represents a logical tautology. Cf.a.o. Tammelo, 1969, p.143 ff.
Føllesdal and Hilpinen, 1971, in Hilpinen, 1971, p.13.
The reverse is valid: if the system is not empty (i.e. if not all is permitted) than ax.l can be proven within this system (cf.also Prior, 1973, p.221–223), which means that it is possible to say that ax.l has to be valid within every system of positive norms. Cf. J.F. Lindemans, 1982, I, p.104, 105, who (following S. Kripke) presents a semantics which distinguishes between normal possible worlds in deontic semantics and non-normal possible worlds in deontic semantics. The latter are worlds in which no obligations or prohibitions are in force and which are called anarchistic worlds by Lindemans (I doubt the appropriateness of the name). Lindemans demonstrates that in such an anarchistic world O(pv-p) is not a theorem. Oq ⊃ O(pv-p), however, is a theorem (in fact, Lindemans only demonstrates that Op ⊃ O(pv-p) is a theorem, but his reasoning does not depend on the same variable being present in the antecedent as well as in the consequent of this implication).
U1, U2,... Un and Z are here used by me as meta-variables which serve as indications of random (elementary) normative judgements.
It is not possible to say that the prohibition to perform r follows from the conjunction of the two mentioned prohibitions if r ⊃ (p&q) is a tautology of the proposition-calculus. Rule Ab’ follows directly from rule Aa’ and the definition of F. Suppose that (p&q) ⊃ r is a tautology of the proposition-calculus. It is then valid that Or follows from Op & Oq (Aa’). According to the definition of F this is: F-r follows from F-p & F-q. If p is replaced by -p, q by -q and r by -r, then Fr follows from Fp & Fq iff (-p & -q) z> -r is a tautology of the proposition-calculus. This latter formula is equivalent with r ⊃ (pvq).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Soeteman, A. (1989). A Standard System of Deontic Logic. In: Logic in Law. Law and Philosophy Library, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7821-9_5
Download citation
DOI: https://doi.org/10.1007/978-94-015-7821-9_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4035-0
Online ISBN: 978-94-015-7821-9
eBook Packages: Springer Book Archive