Newsgroups: sci.logic,comp.ai.philosophy
Path: cantaloupe.srv.cs.cmu.edu!rochester!udel!gatech!howland.reston.ans.net!news.sprintlink.net!news.dorsai.org!news.ilx.com!psinntp!psinntp!psinntp!scylla!daryl
From: daryl@oracorp.com (Daryl McCullough)
Subject: Re: Deontic Logic. What is it?
Message-ID: <1995Feb10.145940.4547@oracorp.com>
Organization: Odyssey Research Associates, Inc.
Date: Fri, 10 Feb 1995 14:59:40 GMT
Lines: 104
Xref: glinda.oz.cs.cmu.edu sci.logic:9638 comp.ai.philosophy:25463

If there was a demonstration of why Chisholm's Contrary-to-Duty
Paradox is a paradox of deontic logic, I missed it. But for those who
know something about this, is the following a correct formulation:

Let H be the statement "You help your neighbor". Let T be the
statement "You tell your neighbor that you are coming (to help him)."
We use O(A) to mean "A is obligatory", or "A should be the case".
Then, the following facts about obligation sound plausible:

You should help your neighbor. This can be formalized as:

1. O(H)

It should be the case that if you go help your neighbor, you should
tell him you are coming (instead of just dropping in uninvited). This
can be formalized as: 

2. O(H -> T)

If you don't plan to help your neighbor, you really shouldn't lie and
say that you are going to. This can be formalized as (using ~ as
negation):

3. ~H -> O(~T)

Now, in addition to these facts about obligation, we will suppose
that, in spite of my obligation to help my neighbor, I choose not
to:

4. ~H

Surely these 4 assumptions must be consistent. But let's reason using
modal logic, treating O as a kind of necessity operator. A basic axiom
of necessity is:

5. O(H -> T) -> O(H) -> O(T)

(If it is obligatory that H implies T, and it is obligatory that H,
then it is obligatory that T.) Putting this axiom of modal logic together
with 1 & 2 above gives us:

6. O(T)

But putting 4 together with 3 yields:

7. O(~T)

So, I am obligated to do two contradictory things (tell my neighbor
and not tell my neighbor).

-------------------------------------------------------------------------

Here is my explanation of why Chisholm's paradox is possible, and why
Deontic logic is not really appropriate to reason about obligation.
If we think model-theoretically, what seems to be going on is
reasoning within some kind of preference relationship among
outcomes. There are many possible futures, and we are obligated to try
to bring about a good one. However, what makes a future good is, in
general, a combination of many factors. Achieving one factor alone is
neither necessarily good nor necessarily bad.

Therefore, it is not especially meaningful to say O(T), where T is
simply one small factor in the future. The interpretation of this
would be that bringing about T is necessarily good, but there are
almost no atomic facts that are necessarily good.

But this leaves us in an awkward position when it comes to reasoning
about obligation. If no single action is good, in itself, then how
could anyone ever figure out what actions to do? Well, I think that's
just life! You have to make a guess about how to bring about a
desirable outcome. However, it might work to use some kind of default
reasoning:

   When I say something like "You ought to wear your raincoat today",
this "ought" has to be taken with respect to some kind of default
assumptions about how the future will unfold. I'm assuming that you
are going to go outside, and that it will rain as the weatherman
predicted. I think that we can recover a kind of obligation operator
from a system of default reasoning as follows:


        O(A) (Meaning you are obligated to bring about A, or
              it is desirable to bring about A.)
        is defined to mean:
        w(A) > w(~A).

where w(A) means something like the most likely world (outcome) from
trying to bring about A", and > is a preference ordering on worlds.
That is, you should try to bring about A if the most likely result
of trying to bring about A is better than the most likely result of
trying to bring about its negation. (An alternative would be to say
w(A) > w(true), meaning the most likely outcome from trying to bring
about A is better than not trying to do anything in particular.)

There is no reason to think that such an obligation operator would
obey the rules of modal logic, in particular, I don't think it would
follow that O(A -> B) -> O(A) -> O(B). Well, so much the worse for logic.
We probably just shouldn't try to figure out what we should do next
from a formal logic, anyway.

Daryl McCullough
ORA Corp.
Ithaca, NY

