# Attacking Factual Detachment in Deontic Logic

Let OB(q/p) represent the conditional ought statement: "If p, we ought q".

(Note that depending on your views of deontic conditionals, the statement "If p, we ought q" could be taken to be wide-scoped or narrow-scoped; for now we leave this distinction purposely ambiguous).

Consider now two different versions of modus ponens involving deontic conditionals:

Factual Detachment (FD): p & OB(q/p) --> OBq

Deontic Detachment (DD): OBp & OB(q/p)--> OBq

Of particular interest to me now is finding ways in which factual detachment is implausible. One method of attacking factual detachment is by finding by finding inferences which follow the technical form of factual detachment yet nevertheless strike us as absurd. The Gentle Murder Paradox provides one such example:

(1) You ought not murder someone.

(2) If you are going to murder someone, then you ought to murder them gently.

(3) You are going murder someone.

Absurd Conclusion via Factual Detachment: You ought to murder someone gently.

Now this is all well and good, but I am curious if anyone is aware of any other arguments (structural or otherwise) against factual detachment? A bit looser: is one aware of any good resources to check out arguments for/against both factual and deontic detachment other than the Stanford Encyclopedia of Philosophy?

• I'm not sure how the absurdity of the conclusion is anything but a manifestation of the inappropriate behaviour of premise #3 in the example. For comparison, an entirely mathematical paradox such as the Banach Tarski paradox often gets mileage from its blatantly unphysical seeming outcome, because a blatantly unphysical operation which one requires to achieve that outcome is glossed over. What we are seeing is the effects of a logical system which is effective at preserving absurdity. May 4, 2013 at 9:54

Expanding on my comment concerning the apparent source of absurdity in the Gentle Murder Paradox, I think that the apparent absurdity of the Gentle Muyrder Paradox arises from the transgressive behaviour premised in "you will kill someone", and that this is unavoidable. I'd argue that in this case, propositions have multidimensional value — social acceptability/transgressiveness, in addition to truth/falsehood (where "OBx" simply transforms the social value of x to a logical value regarding social normatives) — and that it also arises because there is a sense in which social obligations can hold with greater or lesser force.

I present an example below which more explicitly demonstrates these features of the Gentle Murder Paradox, in another context.

### On factual detachment with socially transgressive well-formed formulae

It is not clear that there is more to Factual Detachment than modus ponens. Using the notation OBq ("we ought q") allows us to re-express the conditional OB(q/p) as (p ⇒ OBq) — which we would gloss equivalently as "if p, we ought q". Then factual detachment is simply

p ,  p⇒OBq
——————
OBq

as a straightforward application of modus ponens.

Indeed, it is not clear that deontic detachment is any improvement in the case of the Gentle Murder paradox. If you forbid factual detachment, you can avoid deriving OBq from the premise p and OB(q/p), but one might argue that — in addition to being special pleading against modus ponens — this obscures the facts of the matter multimodal valuation of propositions, and the consequences of propositions which may be true, but are socially transgressive. If we consider the inference

OBp ,  OB(q/p)
————————
OBq

then the only thing which differs here is that, in the case that p is "you will kill someone" and q is "you will kill someone gently", the absurd conclusion OBq follows from an absurd premise OBp. If we use factual detachment, then the fact that we obtain the false conclusion OBq is that, while p may or may not be absurd, it is socially transgressive — regardless of its positive or negative logical value, it has a negative social value. One can express this by OB¬p, perhaps, to reduce constructive behaviour to truth values; or one can see the Gentle Murder Paradox as hinting that in this system, well-formed formulae may be valued in a multidimensional way, where OB discards the logical value of a proposition and promotes the moral component to the place held by the logical value.

### An example of a moral quandary from inconsistent obligations

This can be illustrated with a case where one has multiple, inconsistent, logical obligations. Suppose that

• p = "you lie"

• q = "you hurt other people's feelings"

then we would normally say that OB¬p and OB¬q. However, there are some circumstances where telling people the truth would hurt other people's feelings: where ¬p⇒q. Consider

• r = "you will make them become angry and violent"

• s = "you will make them cry"

and suppose that q ⇒ (r v s). On the whole, we would tend to say OB¬r and OB¬s. However, given the choice, it is reasonable to suppose that it would be better to make them cry than to make them violent. That is: there is a sense in which OB¬r holds more force than OB¬s. This would suggest that OB(s/q). Suppose that you decide to tell someone a hard truth: then we have

¬p ,  ¬p⇒q ,  OB¬s ,  OB(s/q)
——————————————
OB¬s & OBs

which is a moral absurdity which follows from the fact that telling a hard truth is socially transgressive, and that while making someone cry is not a good course of action, it is a better choice of action than the other possible consequences of telling a hard truth.

Indeed, the crux of the paradox here is that the triad of OB¬p, OB¬q, and ¬p⇒q form a moral dilemma. If ¬p, we obtain (q & OB¬q), which, while not a contradiction, is an expression of a violation of one's social obligations. The alternative in this case is to choose ¬q, in which case we may derive (p & OB¬p); which is also a violation of obligations. This is the same as the transgression (p & OB¬p) in the Gentle Murder paradox.

In any case, the issue here seems entirely to be based upon a socially transgressive premise, from which one can derive a formula of the form (p & OB¬p); and that there are different strengths of obligation, so that some moral absurdities (you should make someone cry, you should kill someone gently) are less terrible than others (you should make someone angry and violent, you should kill someone brutally).

This sounds sort of like Kolondy & MacFarlane's "Ifs and Oughts" (though it's not quite FD). They present a scenario where ten miners are trapped in either shaft A or shaft B (we don't know which), and flood waters might drown them. We can either block shaft A, block shaft B, or do neither. If we block the right shaft, all miners are safe. If we block the wrong shaft, all miners drown. If we do neither, one miner dies. In this case, it seems we have the following:

(0) (Given) The miners are either in shaft A or shaft B.

(1) If the miners are in shaft A, we should block shaft A.

(2) If the miners are in shaft B, we should block shaft B.

(3) We shouldn't block either shaft.

It's not quite FD, but it's closely related. You might want to read that paper for more details (though to be honest, SEP is not a bad place for references either; and those references most likely have more references).

In fact, you could modify the example and just stipulate that the miner's are in shaft A. Then by FD, you'd get that we should block shaft A. But if we don't know they're in shaft A, that seems somewhat implausible. So you could probably generate failures to FD just by introducing epistemic elements of this sort. (Again, I'd suggest reading Kolondy & MacFarlane's paper to see how they treat this).