# Talk:Deontic logic

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## Untitled

Nice job, User:Dbtfz! But I guess you shouldn't have deleted all the information from the previous version. For instance, the reference to Jørgensen's Dilemma and to norms. And it is not clear whether one should say that DL is a branch of modal logic, since there were (von Wright's) and there are DL systems come right from first-order predicate logic. There are also some minor spelling mistakes and the like that I'll fix as soon as I'm sober. Velho 04:25, 29 January 2006 (UTC)

I agree with your points, and encourage you to expand and edit the article accordingly. Best, Dbtfz (talk - contribs) 16:17, 29 January 2006 (UTC)
Thanks for the reply and the last edit! I'll do a tiny copy-edit within the next hours. Don't know if I mentioned it, but you did a very good job! Velho 18:24, 29 January 2006 (UTC)

The "paradoxes" claimed by the article are totally unsatisfactory. Unless valid proofs that they are paradoxical can be provided, they are not worth mentioning. Ross is clearly incorrect by reductio ad absurdum. ᓛᖁ 19:19, 10 February 2006 (UTC)

What's the point? I take it you are not disputing that they are theorems, but that the theorems are counterintuitive? --- Charles Stewart(talk) 19:54, 10 February 2006 (UTC)
None of these are paradoxes; they can all be reduced to something self-consistent. Ross's theorem doesn't seem to follow logically from D: $OA \rightarrow (OA \lor OB)$ seems to be an intended intermediate step, but why should $O$ be distributive over $\lor$? He's also neglected the fact that $B \rightarrow \lnot PA$. ᓛᖁ 20:59, 10 February 2006 (UTC)
Maybe the sections should just be called something other than paradoxes?JoelSCollier 14:20, 15 December 2006 (UTC)

So the paradoxes have been pulled, although there seems to be a consensus that they are important in the literature and are collectively known by that term? I think the article would benefit from having the deleted text reinstated as is, even though that text requires some explanation about what is, or has been to to be, at stake with them. — Charles Stewart (talk) 11:07, 17 March 2009 (UTC)

## The paradoxes of deontic logic

Standard deontic logic has several features that are found by some to be counterintuitive. These are sometimes referred to as the "paradoxes of deontic logic."

The following is a theorem of D:

$OA \rightarrow O(A \lor B)$

Thus if I ought to mail the letter, I ought to mail the letter or burn it! This is called Ross's paradox after the Danish philosopher Alf Ross.

The following is a theorem of D:

$FA \rightarrow O(A \rightarrow B)$

Thus if it is forbidden to jaywalk, the it ought to be that if I jaywalk I am given the death penalty. This is called Prior's paradox after A. N. Prior.

Consider the following statements:

• It ought to be that Alice refrains from robbing Bob.
• It ought to be that Claire (the Good Samaritan) helps Bob, whom Alice has robbed.

These statements, when expressed in ordinary language, seem perfectly consistent (i.e. they could both be true at the same time). However, when formalized in D, they entail that Claire both ought and ought not to help Bob. This paradox was first noted by the Swedish philosopher Lennart Åqvist.

Consider the following statements:

• Alice ought to go to the assistance of her neighbors.
• It ought to be that if she does go, she tell them she is coming.
• If she does not go, she ought not to tell them she is coming.
• She does not go.

When formalized in D, these entail that Alice both ought and ought not to go the assistance of her neighbors. This is called Chisolm's paradox after the philosopher Roderick Chisholm.

There has been a great deal of discussion of these and related "paradoxes." Some believe that the paradoxes can be explained away, while others believe that they jointly constitute a reductio ad absurdum of standard deontic logic.

I think this is only paradoxical if you forget what a conditional is. Two plus two is necessarily four, so it ought to be four. Given that Alice does not go, she ought not to go (since A implies A is a necessary truth, it ought to be true). But she ought to go. Therefore she ought to go and ought not to go. This is obviously true and not in the least paradoxical.
Ross's paradox and the Good Samaritan are likewise obvious truths. (Ross's is so obvious that I find it strange anyone could consider it paradoxical!) Prior's paradox is an obvious truth if you remember that A->B means "either not-A or B". If it's obligatory that I not jaywalk, then it's obligatory that it be the case that either I not jaywalk or I get the death penalty. 91.107.151.20 (talk) 00:27, 24 December 2008 (UTC)
If it's obligatory that it be the case that either I not jaywalk or I get the death penalty, then it's obligatory that if I jaywalk, I get the death penalty. I don't quite understand how this analysis gets rid of the problem... Do you mean that these aren't strictly paradoxes? But they're true premises that yield false conclusions! Which shows that something seriously wrong has happened along the way. i.e., the rules of logic were faulty.--Heyitspeter (talk) 09:36, 16 March 2009 (UTC)
Er... maybe I don't understand what you mean... "Therefore she ought to go and ought not to go. This is obviously true and not in the least paradoxical." In D, this allows you to derive P and not-P. That's a contradiction. Is it that you don't think a contradiction is paradoxical?--Heyitspeter (talk) 09:46, 16 March 2009 (UTC)
Hi, I am doing my PhD on this topic, it is really absurd to leave these paradoxes out (and yes, pretty much every paper prepends paradox with the caveat "so-called"). Additionally, this article should have contrary-to-duty norms, where Mally went wrong (there is a paper from 2004 on this) and tie it in with normative frameworks. It may also be extended to include topics such as sanctions, reparation of violations, temporal aspects, normative conflict and normative system change (the latter problem which has been formalized using a variant of the AGM belief revision postulates). Having said that, I don't have time to do this, as I'm actually trying to do my own research. But a personal thank you who anyone who does. Academic Pretzel (talk) 09:18, 12 July 2013 (UTC)

## Non sequitur

The conclusion made here (1 is plausible, 2 is false) does not follow. One might equally insert "no one commits murder" in (1) and find that statement to be false as well. The problem is in attempting to use a descriptive statement where a prescriptive statement belongs. ᓛᖁ 20:44, 10 February 2006 (UTC)

Regarding: "One might equally insert "no one commits murder" in (1) and find that statement to be false as well." Insert it as a replacement for what? A, I'm guessing. In that case, we would have: "If it is necessary that no one commits murder, then no one commits murder." Surely that is true, or at least extremely plausible. (The antecedent is false, so the whole statement is automatically true, assuming we interpret the "if...then" as material implication. But the statement seems obviously true on any reasonable interpretation of "if...then.") The point of the passage is just that "Whatever is necessarily the case is actually the case" is very plausible, while "Whatever ought to be the case is actually the case" is extremely implausible. Dbtfz (talk - contribs) 22:05, 10 February 2006 (UTC)
Ah, I see. Interesting how (1) can be interpreted in different ways; I'd seen the condition as being true, as in (2). "Necessarily the case" is an improvement.
I'm not sure (2) is necessarily implausible. As a normative statement, it could be read "if A is obligatory, then A is valid", with the converse statement "if A is not valid, then A cannot be obligatory". These would be valid regardless of whether murder actually occurs. ᓛᖁ 22:31, 10 February 2006 (UTC)

The analogy is not perfect, however, for there are logical principles that seem to hold for necessary and possible but not for their deontic counterparts, obligatory and permissible. Consider the following schemas:
1. If it is necessary that A, then (it is true that) A.
2. If it is obligatory that A, then (it is true that) A.
(1) seems quite plausible, while (2) seems to be blatantly false. (For example, it ought to be that no one commits murder, but as a matter of fact people do sometimes commit murder.)

## Conditional obligations

I don't understand von Wright's objection to the first interpretation "O(smoke→ashtray)". It's true that given "O(¬forbidden)" we can derive "O(forbidden→A)", but so what? That's not the same as "if you commit a forbidden act, then you ought to commit any other act", which is "forbidden→O(A)", quite a different thing. —Ashley Y 08:21, 1 October 2007 (UTC)

No, here the forbidden act is the "smoke" and the any other act is the "ashtray", so if you used the "O(smoke→ashtray)" interpretation, then the sentence "if you commit a forbidden act, then you ought to commit any other act" would be written as "O(forbidden→A)". "forbidden→O(A)" would be used if you chose the "smoke→O(ashtray)" interpretation instead, in which case you get the gentle murder paradox.
I note that the derivation of the gentle murder paradox uses both the N and K axioms, of which I see no intuitive reason why they should apply in deontic logic. This makes me wonder if anyone has done any work on constructing a non-|normal deontic logic. N, for example, could be weakened to requiring that if p is a theorem, then P(p) is likewise a theorem (that is, if it is physically impossible not to do something, then doing that thing cannot be immoral), but O(p) need not necessarily be a theorem (which is what N demands). This seems to be enough to eliminate the gentle murder paradox under the "smoke→O(ashtray)" interpretation. -- Milo —Preceding unsigned comment added by 195.241.9.38 (talk) 05:43, 21 September 2008 (UTC)
There is a ton of literature on non-normal deontic logic. Look at some of the stuff by Lou Goble (e.g. in the nineties) using a sort of preference semantics, and Mark Brown has some stuff using neighborhood semantics. Nortexoid (talk) 09:06, 21 September 2008 (UTC)