Comments on: [Q] A Puzzle in Dyadic Deontic Logic

By: John Cowan

John Cowan — Thu, 04 Mar 2004 20:21:39 +0000

Now I may be only a hairy-eared engineer who owes what he knows about philosophy to his environment of upbringing, but any claim that “For all propositions p, if p is true, p ought to be true” is a clear indication that the deontic logic you are using is severely buggy. For example, we can derive immediate inferences like “Hitler murdered six million, therefore Hitler ought to have murdered six million”.

By: Xavier Parent

Xavier Parent — Wed, 25 Feb 2004 23:00:15 +0000

I’m glad you think this issue is interesting. Myselft I tried to write something on this topic some years ago when I was a PhD, but I’m not really happy with the paper (see the reference below). I didn’t refer to the Jackson account - in which you seem to be mainly interested, because I didn’t really understand what he meant

Here are two other interesting references on the issue you raise - hope it is not too late:

1) David Makinson, Five Faces of Minimality', Studia Logica, 1993, 52, p. 339-379. This paper is quite interesting (the last section deals with conditional conditional). It is argued that the difficulty vanishes as soon as futurity is taken into account 2) Henry Prakken and Marek Sergot,Dyadic deontic logic and contrary-to-duty obligations’. In Nute (ed), Defeasible deontic logic, Reidel, 1997 (you can download this paper from Henry Prakken’s webpage). It is suggested that dyadic deontic logics of the validity of O(A/A) is not problematic, because intuitively (as Hansson himself observed in his 1969 paper) the antecedent denotes a fixed, necessary, unalterable feature of the context - so that
O(A/A) sounds like OT. But some may not be satisfied with such a line of defence as I try to argue in my PhD (it is written in French)

I also give you the reference of my own paper - in case of interest: `Identity, cumulativity and time in deontic logic’, Fundamenta Informaticae, 2001, 48, pp. 237-252.

Hope this will be useful
Regards
Xavier Parent

By: Thony Gillies

Thony Gillies — Tue, 17 Feb 2004 22:58:23 +0000

If memory serves, Chellas discusses the problem (at least obliquely) in Ch. 10 of his Modal Logic textbook from 1980. One of the ending exercises is to verify by constructing a countermodel that a certain conditional logic (with a suitable definition of O( / ) in terms of the conditional) doesn’t have O(A/A) as a theorem. He may talk about the problem more directly in his 1974 paper “Conditional obligation” (or something like that) that appeared in a volume dedicated to Stig Kanger, but that is reaching much too far back into my undergraduate days to remember.

While I’m dropping references the details of the papers to which they point I can only very imperfectly remember, Dan Bonevac has a 1998 Nous paper “Against conditional obligation” that might be relevant. He argues that O( / ) can’t be taken primitive and argues for a weak conditional analysis of it. (A conditional which, e.g., only supports defeasible modus ponens.) That’s a general apporach that could very naturally make O(A/A) not a logical truth. John Horty has similar things to say about the relationship between deontic logic and nonmonotonic logic.