What paradoxes are there for deontic detachment?

Question

Most people agree that if you're going kill someone, then you should kill them gently. Now suppose that you are in fact going to kill them. Then by the statement above, then on a naive application of deontic logic we might conclude that you should kill them gently, and that implies that you should kill them!

In other words, if you're going to kill someone, then you should do it, which seems absurd. One solution to this paradox of deontic logic is known as deontic detachment. Let us denote "Q ought to be the case, given P" by O(Q|P). Then according to his view, the mistake we made above is concluding O(Q) from O(Q|P) and P, known as factual detachment, and that the proper rule is that you can only conclude O(Q) from O(Q|P) and O(P), known as deontic detachment.

Deontic detachment can also be used to similarly resolve the related Chrisholm's paradox: consider the statements that you should go to the birthday party, you should RSVP if you're going, you shouldn't RSVP if you're not going, and you're not going to the party. This can be formalized as O(P), O(Q|P), O(not Q|not P), and not P. In this case, deontic detachment allows you to conclude that O(q), i.e. you should RSVP. That may seem strange, but keep in my mind that in the best possible world you both go and RSVP, so it follows that it ought to be the case that you RSVP'd, because it ought to be the case that you went.

My question is, although deontic detachment offers a resolution to these paradoxes, does it face paradoxes of its own?

Answer 1

An example of a moral quandary from inconsistent obligations

I would think that the point of obligation is a calculus of fulfilment of duty. That is: if O(p), and if q is a necessary condition for p, then O(q). That is, O(p), p⇒q ⊨ O(q). This is neither factual nor deontic detachment, of course, but in effect an evaluation of contractual dependencies.

I will borrow my example of the nature of social dimension of propositions to produce a paradox having nothing to do with factual detachment, but having the same character of the interplay between actions and obligations. If p = "you lie" and q = "you hurt other people's feelings", then we would normally say that O(¬p) and O(¬q). However, there are some circumstances where telling people the truth would hurt other people's feelings: where ¬p⇒q; and in particular to avoid hurting people's feelings you must lie, ¬q⇒p.

• From O(¬p) and ¬p⇒q we infer O(q);
• From O(¬q) and ¬q⇒p we infer O(p).

Thus we obtain the absurdities O(p) & O(¬p), and O(q) & O(¬q). This conundrum arises from simple reasoning regarding the nature of obligation: the absurdities seem to arise unavoidably due to the interplay between truth-values of propositions and obligations to fulfill them — of the same sort that factual detachment gives rise to, but by a different means.

On the interplay between is and ought in deontic logic

In the comments above, I have of course tried to suggest that simply being interested simultaneously in the truth of propositions and the obligatoriness of propositions, as deontic logic is, introduces an element of multidimensionality. The conundrum of my example above does not require one to entertain multidimensional values for propositions, but it does strongly suggest that any usable logic of obligations which also concerns itself with the actions actually taken must take into account the interplay between truth-values p and obligation-values O(p). That is: the contradiction arises not because O(¬p) and O(¬q) are inherently contradictory, but because introducing the purely logical ¬p⇒q introduces a contradiction of obligations, in precisely the same way that one observes in the Gentle Murder and Chisholm "paradoxes". That is: in my example above, we should infer

O(¬p), O(¬q), ¬O(p) ⊨ ¬(¬p⇒q)

or possibly instead either

O(¬p), ¬p⇒q ⊨ ¬O(¬q)

or

O(¬q), ¬p⇒q ⊨ ¬O(¬p).

If we adopt the corresponding purely syntactical developments as rules of inference, the absurdity of the situation would then be manifest by a logical contradiction of the form O(¬p) & ¬O(¬p), or something similar.

One might think to formulate a second-order obligation — ∀p:O(¬[O(p) & O(¬p)]), which states that there should be no catch-22s — no inconsistent obligations. We then observe the absurdities as failings of the system itself to be "morally-satisfiable" (i.e. for all of the obligations to actually be fulfillable). Formulating such a meta-obligation would not prevent the inconsistent obligations from actually arising, however; it would just make the failure slightly starker, because it would represent a transgression of the form A & O(¬A), where in this case A = O(p) & O(¬p).

It seems quite clear to me that in these cases, the absurdities O(p) & O(¬p) arise due to the fact that some non-obligational premise — "you will kill someone" in the Gentle Murder Paradox, "you will not go to the party" in Chisholm's paradox, or "telling the truth will hurt someone's feelings" in my example — is incompatible with the imposed obligations. One might say that the conditional in my own example is somehow substantially different, but I don't see how this helps. Indeed, if we recognise that the material implication ¬p⇒q is equivalent to p v q, we may immediately see that

(p & O(¬p)) v (q & O(¬q))

follows by dilemma. Thus the social transgressions p & O(¬p) which are blatant in Chisholm's and the Gentle Murder paradoxes are all but immediately manifest in my example as well: but it only uses the rule of contractual dependency. This suggests that the moral dimension of propositions, which is introduced on a syntactical level by deontic logic, is accurately represented by factual detachment.

I find it is simply more efficient to recognise that if one wishes to have operators which project propositions to truth-values regarding their social acceptability, it essentially follows that one has constructed a logic in which absurdities of a moral character might arise from statements of fact which transgress the boundaries of social acceptability. Indeed, it is difficult for me to imagine how to avoid this possibility if one wishes to reason simultaneously with propositions p and their obligatoriness O(p) in any way where one could have any bearing on the other.

Answer 2

O(Q|P) -- I should kill when a General tells me to, if I am a soldier

P -- I am a soldier

Then

O(Q) -- I should kill when a General tells me to

This does not require

O(P) -- I should be a soldier

If I am drafted against my will, you might say I should not be a soldier. In fact, lots of folks argue at some level the war should not be happening and so no one should be a soldier.

Yet if I do not perform the duties assigned, others will come to harm. So the 'factual detachment' in this case is reasonable.

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At the same time

If I kill I should kill gently

I am killing

I should kill gently

Therefore

I should kill

is just taking the modal deduction out of context. The third statement is true, but only given the conditions it was negotiated under.

Unlike material conditions, modal conditions carry around with them all of the preconditions of their context. With no context, every modal assertion is true for some situation. We evaluate the assertion only in context. So the context can never be removed. Deontic detachment oversimplifies this more realistic rule, in ways that are not necessarily reasonable.

So what is more honest is:

If I kill I should kill gently

I am killing

I should kill gently =| { I am killing }

Therefore

I should kill =| { I am killing }

This is logical, because if I am already killing, it is no longer possible for me not to be killing, and "should implies can".

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Since it never really captures what is intended by the grammar, and sometimes gives us unusual interpretations, you should discard it in favor of the proper bookkeeping.