On 5/13/07, Taral <[EMAIL PROTECTED]> wrote:
The axiom I quoted is actually part of some "standard" deontic logic,
apparently. (See wikipedia: Deontic logic.)
I do not dispute that it is an axiom of the standard deontic logic.
But as I said, that axiom is Bentham's law that ``ought implies may''
(Of -> Pf), not Kant's principle that ``ought implies can''
(Of -> \diamond f).
In ``On the Logic of Norms and Actions'', von Wright gives a hierarchy
of deontic logics, using the propositional operators O, P, F as
representing ``it is obligatory'', ``it is permissible'', and ``it is
forbidden''. Using the common notation, which can be found for
example in section 6.3 of David Lewis's _Counterfactuals_, von Wright
gives the following systems:
I. The Minimal System
Rules: (1) Modus ponens.
(2) Leibniz's Law: Given |- p <-> q and a deontic operator Q,
infer |- Q(p) <-> Q(q).
Axioms: (1) Tautologies of propositional logic.
(2) P = ~O~, F = O~.
II. The Classical System.
The Minimal System plus the axiom
(3) D (Bentham's Law): Op -> Pp.
III. The Standard System.
Rules: (1) Modus ponens.
(2) From |- p, infer |- O(p).
Axioms: (1) Tautologies of propositional logic.
(2) P = ~O~, F = O~.
(3) D (Bentham's Law): Op -> Pp.
This looks almost like the modal logic D, except that I don't think von
Wright uses the Kripke schema
(4) O(p -> q) -> (O(p) -> O(q))
here, although the Stanford Encyclopedia of Philosophy in its article
http://plato.stanford.edu/entries/logic-deontic/
disagree, including it as an axiom schema for standard deontic logic.
I'm trying to work through von Wright in part because he says that
using modal logic to model deontic logic is ultimately a Bad Idea. In
``On the Logic of Norms and Actions'' he develops a system to model
the logic of sentences of the form
Agent a acts on occasion o to perform p,
which he writes as
[ p ] (a, o).
This sort of notation allows him to distinguish between
~ [ p ] (a, o) and [ ~p ] (a,o),
which in turn allows him to model the distinction between simply *not*
doing something and actually *omitting* doing something. Ultimately
he has propositional operators O, P, F as well as act-category
operators script-O, script-P, and script-F, which act in different
ways I don't yet understand.
--
C. Maud Image (Michael Slone)
You know you're not abusing your station enough when people don't want
you out.
-- root, in agora-discussion
