Philosophy Now Forum

I think you are actually criticising two different elements of my argument. I want to address this one first before we get to anything else though:

Wyman wrote:

I don't just say '~P' full stop, that would be like saying "◊~P at world w, therefore ~P at world w". What I'm saying, rather, is "◊~P at world w, therefore there is some other, possible world x where ~P is true, and which is morally conceivable from from the perspective of world w".

See, you snuck it in again - nothing about a proposition's being conceivable implies that the proposition is true.

Let's look at the truth conditions for propositions of the form ◊β again:

egg3000 wrote:k.) V(◊β, w)=1 if and only if: there is some x in W such that Rwx and V(β, x)=1

So, if ◊β is true within some world w, then there is at least one other possible world (let's call it x) and β is true in that possible world.

Why is this the case and how does it make sense? Well, the idea is that when we imagine some possible event or state of affairs, what we are really doing is imagining some possible scenario in which that event or state of affairs takes place. Except instead of saying that we imagine some possible scenario, we say that we access some possible scenario; instead of calling it a possible scenario, we call it a possible world; instead of saying that an event or state of affairs takes place in that possible world, we say that a proposition is true in that possible world.

This is not peculiar to deontic logic; the vocabulary, grammar, definitions of valuations and definitions of models I outlined before are the same as those that are always used modal logic. The only difference is how we use this scaffold: instead of using modal logic to talk about possibility and necessity in general, or instead of using it to talk about physical possibility and necessity, etc, we are using it to talk about moral possibility and moral necessity.

I say all of this because you seem to be continuing with your earlier criticism:

Wyman wrote:But, you perform a slight of hand:

2. ◊~P, world w

According to (2), it is permissible not to act rationally. This means that there is some world x where ~P is true:

3. ~P, world x

And similarly elsewhere. You don't give conditions to convert your modal operators to non-modal. It does not make sense to say from 'it is morally permissible not to act rationally', it follows that 'there is a world where someone acts irrationally.'

So it appears that you are taking issue with the following inference:

1. ◊~P, world w
Then w can access some world x, such that:
2. ~P, world x

But there is nothing exotic about this inference at all, it's completely uncontroversial. If that's a sleight of hand, then Saul Kripke, David Lewis and Robert Stalnaker are prolific card sharps.

Here are some links if you still disagree on this point:
http://en.wikipedia.org/wiki/Modal_logic
http://plato.stanford.edu/entries/logic-modal/

This is what you referred me to. The highlighted parts are restatements of my position.

Deontic logics introduce the primitive symbol O for ‘it is obligatory that’, from which symbols P for ‘it is permitted that’ and F for ‘it is forbidden that’ are defined: PA = ~O~A and FA = O~A. The deontic analog of the modal axiom (M): OA→A is clearly not appropriate for deontic logic. (Unfortunately, what ought to be is not always the case.) However, a basic system D of deontic logic can be constructed by adding the weaker axiom (D) to K.

(D) OA→PA
Axiom (D) guarantees the consistency of the system of obligations by insisting that when A is obligatory, A is permissible. A system which obligates us to bring about A, but doesn't permit us to do so, puts us in an inescapable bind. Although some will argue that such conflicts of obligation are at least possible, most deontic logicians accept (D).

O(OA→A) is another deontic axiom that seems desirable. Although it is wrong to say that if A is obligatory then A is the case (OA→A), still, this conditional ought to be the case. So some deontic logicians believe that D needs to be supplemented with O(OA→A) as well.

Controversy about iteration (repetition) of operators arises again in deontic logic. In some conceptions of obligation, OOA just amounts to OA. ‘It ought to be that it ought to be’ is treated as a sort of stuttering; the extra ‘ought’s do not add anything new. So axioms are added to guarantee the equivalence of OOA and OA. The more general iteration policy embodied in S5 may also be adopted. However, there are conceptions of obligation where distinction between OA and OOA is preserved. The idea is that there are genuine differences between the obligations we actually have and the obligations we should adopt. So, for example, ‘it ought to be that it ought to be that A’ commands adoption of some obligation which may not actually be in place, with the result that OOA can be true even when OA is false.

'Possible worlds' makes sense in the context of modal logic, which involves necessity and possibility. Where we may stipulate that what we mean by possible world semantics is that if A is possible, then there is a possible world where A is true; it's not the same for obligations. The semantics makes no sense, because it just means that you are drawing an equivalence between obligation and necessity - if it is necessary that p then p ought to be the case and if it is permissible that p then p is possible. I don't see any sense in this interpretation.

Wyman wrote:'Possible worlds' makes sense in the context of modal logic, which involves necessity and possibility.

Technically, modal logic isn't inherently a logic of necessity and possibility, it's just a formal apparatus that can be used to analyse the concepts of necessity and possibility (among other things). When it is used in this way, it is officially referred to as alethic logic.

Wyman wrote:The highlighted parts are restatements of my position.

I take it that the highlighted parts to which you are referring are the parts of the text you have marked in bold. Let's look at them:

The deontic analog of the modal axiom (M): OA→A is clearly not appropriate for deontic logic. (Unfortunately, what ought to be is not always the case.)

Well actually, what you have been saying until now is that neither "possibility" or "permissibility" are the same as "actually true":

Wyman wrote:nothing about a proposition's being conceivable implies that the proposition is true.

Wyman wrote:'Possible' and 'Permissible' are not the same as true in fact

So whereas the above extract, that you highlighted in bold, is saying that axioms of the form □A→A are not appropriate for deontic logic, you seem to have been arguing against axioms of the form ◊A→A. Firstly, no one in this thread is trying to claim that ◊A→A is ever appropriate. Secondly, although the above text in bold is not actually a restatement of anything you have so far said, it is basically a restatement of something that I have already said:

egg3000 wrote:Look, suppose it is impermissible to murder someone from our point of view in the actual world. Does this mean that no one does in fact murder anyone in our actual world? Of course it doesn't, people murder other people all of the time in the actual world, in spite of that fact that murder is not morally permissible.

Given the above quote, I think it is clear that I would not consider the axiom □A→A to be appropriate for deontic logic, so none of this is particularly striking. On the other hand, what is interesting is the sentence immediately succeeding the one that you put in bold:

The deontic analog of the modal axiom (M): OA→A is clearly not appropriate for deontic logic. (Unfortunately, what ought to be is not always the case.) However, a basic system D of deontic logic can be constructed by adding the weaker axiom (D) to K.

Why is this interesting? Because system K is a very weak system, whose only axioms are:

1. A→(B→A)
2. (A→(B→C))→((A→B)→(A→C))
3. (~A→~B)→((~A→B)→A)
4. □(A→B)→(□A→□B)

Because it is such a weak system, □A→A is not a theorem in K. So, what happens when we add the axiom □A→◊A to the axioms of K? The result is a different system often referred to as D. System D is slightly stronger than K, and therefore, for various reasons, arguably more appropriate for deontic logic. However, while system D is stronger than K, it is still too weak to make □A→A a theorem. In other words, if we give □ a deontic interpretation, then "it ought to be the case that P" does not imply "P" within system D, which is exactly what we want.

I find that this all makes a lot more sense when we consider these systems in terms of model theory rather than proof theory. You may recall that I mentioned the accessibility relation:

egg3000 wrote:A model for Modal Propositional Logic (MPL) consists of: a set W of possible worlds; a two place function f which, to each simple well-formed formula in each possible world, assigns either a value of 1 or 0; and a binary relation R over the set W of possible worlds. We say that some world x is accessible from some world w if and only if Rwx (call R the accessibility relation).

egg3000 wrote:j.) V(□β, w)=1 if and only if: if Rwx then V(β, x)=1
k.) V(◊β, w)=1 if and only if: there is some x in W such that Rwx and V(β, x)=1

Well, as you may know, there are different kinds of binary relations (e.g. some are serial, others are reflexive, symmetric, transitive, and so on), and the accessibility relation is no exception. In system K, there is no requirement on the accessibility relation. In system D, on the other hand, the accessibility relation is serial. In neither case, however, is the accessibility relation reflexive, which means that it is impossible for some world w to access itself in these systems. But for a proposition of the form □A to be true at some world w, it is only necessary that A be true in every world accessible from w. Since w cannot access itself, it can still be the case that '□A' is true in world w even if 'A' is not itself true in world w (and the same goes for moral reasoning: it can still be true that something ought to be the case even if it is not in fact the case).

Consider the following examples (one is new, one I have used already):

1. Suppose it is impermissible to murder someone from our point of view in the actual world. Does this mean that no one does in fact murder anyone in our actual world? Of course it doesn't, people murder other people all of the time in the actual world, in spite of that fact that murder is not morally permissible. However, suppose that we conceive, in our minds, of an imaginary, morally perfect world, where no one does anything that we actual-worlders consider to be morally impermissible. In this imaginary world, would anyone commit murder? No, because we have just said that murder is impermissible, and no one does anything impermissible in this imaginary world of ours.

2. Suppose that it is permissible for someone to eat vegetables. Does this mean that someone does in fact eat vegetables? No, not necessarily. However, if it is permissible to eat vegetables, then we can still conceive of (or access) some hypothetical, morally perfect world where someone does in fact eat vegetables. Because it is permissible to eat vegetables, no one would be violating any moral obligations by doing so, and hence we can conceive of a morally perfect world where this does in fact happen.

It isn't appropriate to analyse either of these paragraphs using a modal system whose accessibility relation is reflexive (like in S5, for example), but it certainly is appropriate to analyse such reasoning with a modal system like D (whose accessibility relation is merely serial and not reflexive or anything else).

You're right that i was arguing that a possible worlds interpretation doesn't make sense for possibility or permissibility. I'll grant that the former makes some sense if you define within the model that if something is possible, then it is true in at least one possible world. I still don't like it and think it's gimmicky and Kripke had to do it to fit his model - i.e. the (informal)interpretation is made to fit the (formal)model, not vice versa.

However, the deontic interpretation is way off, in my opinion. Assuming that 'possible worlds' are now 'morally perfect possible worlds' begs the question. We assume that there are worlds where everyone does what they ought to do. OK, but are there more than one of these worlds? Of course you have to say yes, to make it fit the formal model - but does it have anything to do with your theory of morality? In other worlds, why would there be infinitely many morally perfect worlds except for the fact that you want it to be the case that 'if p is permissible, then there is a world where p is true?'

As I said, it makes some sense in the context of our informal understanding of 'possibility' and 'necessity' to posits infinitely many possible worlds (Liebnitz defined necessity this way, for instance) - and if there are infinitely many, it is plausible to assume that every possibility is actualized in at least one (although this does not 'necessarily' follow, as I've bee arguing). But in terms of our informal, intuitive understanding of 'permissible' and 'impermissible' I think the model fails to represent and begs the question (see below).

For instance, 'ought' is usually seen as situational - the famous counter-example to Kant's categorical imperative of 'thou shalt not lie' where a murderer is chasing someone with a gun in hand and asks you where the victim went - morality rarely, if ever, applies in every situation. Whereas ethics is situational, necessity is usually viewed as not - that's the point, actually. So, in your model, you would have to say something like p is permissible in 'a morally perfect world where p is done in a morally similar context.' Unless you want to say that moral maxims are context-free, in which case you run into the same problems as Kant. It would be like saying 'P is necessary in every possible world where the context would indicate to us that it is necessary.' Circular.

Wyman wrote:We assume that there are worlds where everyone does what they ought to do. OK, but are there more than one of these worlds? Of course you have to say yes, to make it fit the formal model - but does it have anything to do with your theory of morality?

I don't see anything problematic about this. At worst, this just means that we are modifying or inventing a new way of thinking about the same moral theories, in order to formalise certain aspects of those theories. As you may know, Kant devised a number of formulations of the same categorical imperative.

Wyman wrote:In other worlds, why would there be infinitely many morally perfect worlds except for the fact that you want it to be the case that 'if p is permissible, then there is a world where p is true?'

Because if some act x is permissible, then it is possible to conceive of a morally perfect world in which everyone does what they are obliged to do and in which, at the same time, someone also does x. Well, suppose for example that it is permissible to think of any number. Then we can conceive of a morally perfect world where someone thinks of the number '1', and we can conceive of a morally perfect world where the same person thinks of the number '2' instead of '1', and so on.

Wyman wrote:As I said, it makes some sense in the context of our informal understanding of 'possibility' and 'necessity' to posits infinitely many possible worlds (Liebnitz defined necessity this way, for instance) - and if there are infinitely many, it is plausible to assume that every possibility is actualized in at least one (although this does not 'necessarily' follow, as I've bee arguing).

I'm not sure about this, you seem to be approaching possible worlds almost as though they are actual entities that exist somewhere, so that it is only plausible to think that every possibility is actualised in at least one of these worlds if there are infinitely many possible worlds. But unless you're a modal realist, which I'm not and which you don't have to be, that's not relevant at all. All we're saying is that if some happening is possible, then we can conceive of some possible scenario in which that happening takes place.

Wyman wrote:For instance, 'ought' is usually seen as situational

Even if "ought" is usually seen as situational, the mere fact that it is usually seen this way does not make it this way.

Wyman wrote:the famous counter-example to Kant's categorical imperative of 'thou shalt not lie' where a murderer is chasing someone with a gun in hand and asks you where the victim went - morality rarely, if ever, applies in every situation.

Not necessarily correct. Kant simply admitted that you would be obliged to tell the murderer where the victim is hiding, which means that for Kant particular moral maxims would apply in every situation. Sure, this seems unintuitive, but it is by no means a necessary falsehood.

However, I don't even think we are forced into this position just by accepting that deontic logic has some fruitful application in moral reasoning, for we can still accept that general moral principles are context free even if their particular application is situational in a certain sense. For example, take something like the following principle: it is impermissible to exercise power over another, against their will, unless in order to prevent them from harming others. Well, can we imagine a possible world where someone exercises power over someone else? Yes, a world in which that person did so only in order to prevent the individual in question from harming another. Can we imagine a morally perfect world where someone exercises power over another, against their will, and not in order to prevent them from harming others? No, because this species of action is impermissible. In short, I just don't think it's as simple as you're trying to make it out to be, and even if it is we can just avoid circularity by taking up Kant's position.

This is an interesting topic - although apparently no one else here thinks so. It's the first time I've thought about deontic logic and as you can tell, I don't like it (but perhaps I don't understand enough to form an opinion).

My argument doesn't depend on a 'realist' interpretation. If I say 'I cannot conceive of a world in which the law of excluded middle fails to apply, therefore it is a necessary truth' - that makes sense and seems to have some claim to relevance as a model - it models the idea of 'necessity.'

If I say 'I cannot conceive of a morally perfect world in which one exercises power over another, against their will, even though they are harming no one' it all rests on my definition of 'morally perfect world.' Either the phrase is meaningless as question begging (we are examining 'moral perfection' so first we will assume a 'morally perfect' world). Or, the phrase means different things to different people, so its use won't solve any disputes.

For instance(as to my last point), someone may argue that 'Brave New World' is an example of a morally perfect world, where people are controlled against their will for their own good, even though they are harming no one. You will say that such a world is not morally perfect and the debate will proceed just as it would have if you were simply debating the underlying issue (whether your maxim is correct or not).

Wyman wrote:If I say 'I cannot conceive of a morally perfect world in which one exercises power over another, against their will, even though they are harming no one' it all rests on my definition of 'morally perfect world.' Either the phrase is meaningless as question begging (we are examining 'moral perfection' so first we will assume a 'morally perfect' world). Or, the phrase means different things to different people, so its use won't solve any disputes.

We would define a morally perfect world as one in which no one does anything considered in our world to be impermissible. Well, the next question you might ask is: ok, what is impermissibility? And if the answer to that question is "we say that an act is impermissible when there is no morally possible world where someone carries it out", then it does begin to beg the question. However, let's ask the exact same question in regard to alethic logic. We define a possible world as one in which only things considered to be possible in our world happen, and hence things which are impossible never happen. Ok, suppose we now ask: well, what is impossibility? If the answer to that question is "we say that something is impossible when there is no possible world in which it happens", then we're once again begging the question.

However, the point of possible-world semantics is not, I think, to provide a reductionist account of possibility per se. Rather, it is valuable simply because it is a useful way to think about possibility. That is, modal logic and possible-world semantics is not a theory of possibility, it's just a formal language we can use to reason about possibility given the intuitive, almost trivial, idea that a proposition being possibly true means that in some conceivable scenario it is true.

Wyman wrote:For instance(as to my last point), someone may argue that 'Brave New World' is an example of a morally perfect world, where people are controlled against their will for their own good, even though they are harming no one. You will say that such a world is not morally perfect and the debate will proceed just as it would have if you were simply debating the underlying issue (whether your maxim is correct or not).

Of course you won't be able to resolve every moral dispute using modal logic, but the mere fact that there are some moral questions that can not be immediately resolved with modal logic is not to say that there are no moral questions that can be. You will, for example, be able to totally rule out the tenability of a moral proposition of the form '◊(□P∧◊~(□P∨◊~P))'. Take the proposition "it is permissible to control people against their own will even though they are harming no one". Ok, I may disagree with this proposition in a certain sense, but assuming it to be true and then using modal logic to analyse its structure may in itself be of some use. The same proposition, for example, could just be expressed as ◊P; it's negation, ~◊P, merely implies □~P, and so it is logically possible to deny it. It's really the same as any other logic in that you're really only dealing with logical constants, and much of the time any contingent truths will just have to be inserted as postulates.