# von Wright's Dyadic Deontic Logic System.

[Hilpinen, 1981, pages 105-119] These pages are a reprint of von Wright's "A new System of Deontic Logic", Danish Yearbook of Philosophy 1 (1964) p173-182, and combines it with his "A Correction to a New System of Deontic Logic", Danish Yearbook of Philosophy 2 (1965) p 103-107.

[Hilpinen, 1981, pages 135, 1-35] These pages are Dagfinn Fooesdal and Risto Hilpinen's "Deontic Logic: An introduction" (Pages 27-31 are on von Wright's system.)

## Notes

This system was published by Georg Henrik von Wright in 1964 in a paper called "A New System of Deontic Logic" that appeared in the "Danish Yearbook of Philosophy 1". He also had corrections to this that he published in an article titled (oddly enough): "A Correction to to a New System of Deontic Logic" that appeared in the "Danish Yearbook of Philosophy 2". Both articles are reprinted in [Hilpinen, 1981, 105-115 & 115-120]

This system was a follow on to his 1956 effort, and his 1951 monadic system

The basic operator here is a dyadic operator P. von Wright uses the notation P(r|s) as meaning r is permissible under circumstances s. I will break with his notation and use P(r,s) instead, as I find that more readable.

The operator O (obligation) is defined in terms of P in axiom K5 below.

## Based on

• PC
• Axioms (Following Hilpinen's numbering)
• K1: O(p+~p,r)
• K2: ~(O(p,r)&O(~p,r))
• K3: O(p&q,r) == (O(p,r)&O(q,r))
• K4: O(p,r+s) == (O(p,r)&O(p,s))
• K5: P(p,r) == ~O(~p,r)

[Hilpinen, 1981, page 27] Note that this is presented as K2-K4, and then K1 and K5 are presented with notes. The note for K1 says: "In the same way as in the case of the monadic system, we may exclude 'empty' normative systems by adding to (K2)-(K4) the axiom (K1) O(p+~p,r)".

## Basis for

I'm not aware of any...