Talk:Deontic logic

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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)

Contents 1 False paradox 2 The paradoxes of deontic logic 2.1 Ross's paradox 2.2 Prior's paradox 2.3 The Good Samaritan paradox 2.4 Chisholm's paradox 3 Non sequitur 4 Conditional obligations

[edit] False paradox

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. ‣ᓛᖁᑐ 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: seems to be an intended intermediate step, but why should O be distributive over ? He's also neglected the fact that . ‣ᓛᖁᑐ 20:59, 10 February 2006 (UTC)

It is indeed arguable whether the so-called "paradoxes of deontic logic" are really paradoxes. (Personally, I think it is reasonable to classify them as such, but I don't have time to argue for this at the moment.) Many writers on the topic of these "paradoxes" qualify their discussion with a remark to the effect that the problems in question are not really "paradoxes," strictly speaking. However, the term "paradoxes of deontic logic" is very widely used in the literature; and given that the point of this article is to document existing knowledge on, and theories about, the topic, it seems appropriate to stick with the standard terminology. A comment regarding the dubious application of the term "paradox" would very much be in order, though. Also, it would of course be very appropriate to discuss possible resolutions--especially those that have been proposed in the literature. Obviously, this is not the venue for original research on the topic. Dbtfz (talk - contribs) 21:51, 10 February 2006 (UTC)

Maybe the sections should just be called something other than paradoxes?JoelSCollier 14:20, 15 December 2006 (UTC)

[edit] The paradoxes of deontic logic

Please help improve this section by expanding it. Further information might be found on the talk page or at requests for expansion.

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."

[edit] Ross's paradox

The following is a theorem of D:

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.

[edit] Prior's paradox

The following is a theorem of D:

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.

[edit] The Good Samaritan paradox

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.

[edit] Chisholm's paradox

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.

[edit] 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. ‣ᓛᖁᑐ 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. ‣ᓛᖁᑐ 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.)

[edit] 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)