Practitions and Deontic Logic

Practitions and Deontic Logic*

By Scott Palmer

Copyright 1982, 1998 by Scott Palmer

A note to lay readers:

This article deals with some fairly advanced topics in the logic of moral judgments (deontic logic). Moral judgments, just like factual judgments, can be used in arguments, such as "It’s wrong to steal. Therefore, you shouldn’t steal that car." However, it’s less clear what moral judgments mean. If I say that "the car is red," everyone understands what quality I’m ascribing to the car: redness, with which all non-colorblind people are familiar. But if I say that "to steal the car is wrong," then what is the quality of "wrongness," exactly? If I say that "happiness is good," what exactly do I mean by "good"? Unless we know what we mean when we say such things, we can’t be sure that our moral reasoning is correct.

The plain man sees no problem: as long as we know what is good and bad, right and wrong, why worry about the exact meanings of the terms? But philosophers are sorely vexed by such questions and have spent centuries trying to answer them. In the 20^th century, a popular answer has been that moral judgments assert nothing and that moral terms have no meaning in the ordinary sense. The statement that "It’s wrong to steal" has been variously translated as a veiled command ("Don’t steal") and even as a mere expression of emotional disapproval ("Stealing – ugh!").

To the plain man, these theories sound pretty loopy: but loopy or not, they try to answer a vital question: what is the nature of moral judgment? For if moral judgments assert nothing, then our moral choices are arbitrary and there really is no right or wrong in any way that makes sense. Arcane as they might seem, these are life-or-death questions, because their answers bear on everything we do.

Hector Castañeda’s theory that moral judgments embody what he calls "practitions" is an attempt to put morality on a solid footing. Ultimately, the attempt fails, but the flaws in Castañeda’s theory give us important clues to a correct understanding of moral judgment.

-- Scott Palmer, November 1998

Hector-Neri Castañeda’s ethical theory, which has gradually taken shape over the last 30 years or so and receives its most detailed expression in his book The Structure of Morality (Charles C. Thomas Publisher, Springfield, IL, 1974), must rank as one of the most impressive and difficult achievements of contemporary philosophy. Nevertheless, Castañeda’s theory of the nature of deontic judgments and imperatives is fatally flawed.

References in this article are to The Structure of Morality unless otherwise noted. Although Castañeda has given us a further elaboration of his ideas in a more recent book, Thinking and Doing (D. Reidel Publishing Co., Dordrecht-Holland, 1975), his later work is logically dependent on the central concepts to be discussed here. Therefore, criticisms directed against the system he presents in The Structure of Morality apply equally to later extensions of the theory.

It is absolutely essential for Castañeda that there be an intimate connection between deontic judgments and their corresponding imperatives [pp. 40, 77]. Hence, he views both a deontic judgment and its corresponding imperative as being built on the same core – a theoretical entity he calls a "practition." For example, both the deontic judgment

This being so, the imperative, whose essential function is to give Karl a psychological "push" toward going home, can reinforce the deontic judgment that Karl ought to go home. Thus, the connection between a deontic judgment and its corresponding imperative is secured by the underlying identity of their core element, a practition. Without this identity, Castañeda’s theory of the connection between deontic judgments and imperatives is in imminent danger of collapse.

Castañeda considers it an important point that practitions are not propositions. In a practition, the connection between the agent (subject) and the act (predicate) "is the idea that the agent is to do the action, and this contrasts with the way in which the very same agent and the very same action are connected in the corresponding proposition." [40] In a proposition, the connection between agent and act is asserted to be one of fact, while in a practition, the connection is one of demand.

In this context, Castañeda offers the following definition of deontic judgments:

To illustrate his definition, and to cement our confidence in the connection between deontic judgments, practitions, and imperatives, he offers an example. According to Castañeda, an imperative "can be canonically formulated in the form ‘…, do the following: ---’, where the dotted blank is to be filled in by an expression referring to the agent(s), and the hyphenated blank is to be filled in with the formulation of a practition." [77] Thus, an imperative built on a practition can be canonically expressed as:

But we can take the same practition, apply a deontic operator to it, and get a deontic judgment:

Thus, Castañeda thinks he has rendered plausible his contention that a deontic judgment and its corresponding imperative share a common core: a practition.

The strength of this approach is considerable. Perhaps most importantly, it gives Castañeda a more sophisticated way of deducing imperatives from deontic judgments than has been offered by other writers on the subject, notably R.M. Hare, who he criticizes in some detail. The fact that imperatives can be deduced from deontic judgments is a thorny problem for ethical cognitivists like Castañeda. Deontic judgments seem to be propositions and, hence, are true or false: but by no stretch of the imagination does it seem that imperatives (e.g., "Ralph, shut the door") are true or false. [83, 94] How can non-truth-valued noemata be entailed by truth-valued noemata?

Castañeda divides deontic judgments into two main types: qualified and unqualified. A qualified deontic judgment invokes a particular reason for doing the act to which it refers, and does not entail its corresponding imperative. An unqualified deontic judgment does not invoke any reasons, precisely because in it, all relevant considerations have already been taken into account – and it does entail its corresponding imperative.

Castañeda is able to explain the entailment relation between an unqualified deontic judgment and its corresponding imperative, as well as the non-entailment of imperatives by qualified deontic judgments, by interpreting deontic judgments as second-order statements about the justification of imperatives. [107; see also Nahknikian & Castañeda, Morality and the Language of Conduct, p. 222] He states, for example, that "the language of oughts (etc.) is a first-order ‘reflection’ or ‘image’ of the second-order language about the justification of imperatives." [MLC, 222] Elsewhere, he says that a deontic judgment is true if and only if its corresponding imperative is justified. [107]

Qualified deontic judgments do not entail their corresponding imperatives because they only claim that a given imperative is justified relative to a certain reason or goal, and not that it is justified "all things considered." Because the essential function of an imperative, according to Castañeda, is to give the recipient a psychological "push" toward doing the indicated act, entailment of imperatives by qualified deontic judgments is not appropriate.

Unqualified deontic judgments, on the other hand, do entail their corresponding imperatives, because they come at the conclusion of a deliberation, when all relevant claims have been weighed and a push to action is appropriate. An unqualified deontic judgment states that, everything being considered, a certain course of action is the correct one: i.e., that the imperative formulating that course of action is justified. [Ch. 4] This makes the formerly problematic entailment of a non-truth-valued imperative by a truth-valued deontic judgment a simple matter, as the following sample deliberation illustrates:

Besides making the connection between deontic judgments and imperatives much more plausible, Castañeda’s approach also allows straightforward solutions to certain deontic paradoxes, most notably to the "Good Samaritan" paradox. [80-81]

Thus, the theory of deontic judgments and imperatives as built on practitions would be an enormously valuable addition to our ethical knowledge – that is, if certain crucial flaws could be adequately remedied.

There are several problems connected with viewing deontic judgments and imperatives as being built on practitions.

3.1. The Problem of Enriched Deontic Operators

First, if we look carefully at the example Castañeda gives (Section 1 of this article, (4) and (5)) to show that a deontic judgment and its corresponding imperative are both built on the same practition, we find that something rather strange is going on. What are our deontic operators supposed to be? The list that Castañeda gives in (D1) seems perfectly unobjectionable, being made up of such items as "it is required that," "it is forbidden that," and so forth. But in applying these operators we would never say:

which is what we would get if we applied a deontic operator from Castañeda’s list to the practition he uses in this example: "if it rains, open the chimney and close the windows." The case is even clearer if we simplify the example, whereupon we end up with:

which, at least apparently, is obtained by applying the operator "it is obligatory that" to the proposition or imperative "if it rains, you open the chimney and close the windows" – although indeed, how we are to determine whether such a linguistic unit represents a proposition, an imperative, or a practition is rather obscure.

What has happened? To find out, let’s take another look at (5), where Castañeda allegedly obtained a deontic judgment by applying a deontic operator to a practition:

We can now see that a subtle shift in the content of the "deontic operator" has occurred. The operator is no longer "it is obligatory that," which appears in Castañeda’s innocuous-sounding list, but has been enriched to "it is obligatory that you do the following."

Moreover, "if it rains, open the chimney and close the windows" is not a practition, since a practition unites a subject (agent) and a predicate (act) by the demand that the agent do the act. "If it rains, open the chimney and close the windows" is rather what Castañeda and others have called an "act." An act is a subjectless formulation of something that somebody does or might do, while a practition, which formulates an action, has both a subject and a predicate. ("Act" is also, of course, used ambiguously to denote the events referenced by act-formulations.)

Thus, Castañeda’s example misses the mark. It does not show that a deontic judgment and its corresponding imperative can be built on the same practition. Instead, if anything, it shows that a deontic judgment and its corresponding imperative can both be built on the same act.

3.2. The Problem of Deontic Stuttering

Nevertheless, it is worthwhile to go through the example again, this time using a subject-predicate structure, which has at least some claim to be considered a practition. To clarify matters, let’s make the practition a little less complex: "you close the windows." Then, using the suggested canonical notation, we have:

This formulation looks a little better. It certainly fits better when we rewrite (5*) using a standard deontic operator:

In spite of this apparent improvement, substituting a practition for an act has put us in even deeper trouble than before. We can see this when we ask ourselves what it is that Ralph is supposed to do. In the original version of (4),

which is without question a perfectly legitimate imperative, Ralph is told to do an act, formulated by "close the windows." In (4*), however, he is told to do an action, formulated by a practition: "you (Ralph) close the windows." So what he is doing when he carries out imperative (4), built on an act, is closing the windows. What he is doing when he carries out imperative (4*), built on a practition, is Ralph-closing the windows.

It seems plain, then, that practitions cannot serve as a basis on which to erect imperatives. Otherwise, we will end up with an incurable "deontic stutter," being forced to say things like "Ralph Ralph close the windows." Obviously, these same considerations apply, mutatis mutandis, to any attempt to base imperatives or deontic judgments on noemata with a subject-predicate structure – on propositions, in particular.

3.3. The Problem of Deontic Redundancy

But practitions are in still more trouble. Recall that what differentiates a practition from a proposition is that in a practition, subject and predicate are united by a relation of demand: as Castañeda puts it, "the idea that the agent is to do the action." [40] Even without the problems noted above, this alone is enough to give us a severe case of deontic stuttering. Castañeda’s canonical formulation of the practition in question,

does not capture very perspicuously the connection of demand between "Ralph" and "closing the windows." We can do better by taking a hint from Castañeda’s own explanation of the demand-relation, and canonically expressing (8) as:

Then, however, we clearly run into paradox when we try to use this as a basis for formulating deontic judgments by applying deontic operators to practitions. This method gives, from (8*),

But "Ralph is to close the windows" plainly carries within itself the obligation, i.e., the "demand," as Castañeda puts it, that Ralph close the windows. Hence, what we would actually get by applying a deontic operator to practition (8*) is:

which, if it is not nonsense, is certainly not what we meant to say. (An even more bizarre result is obtained by applying "it is forbidden that" to (8*).) On Castañeda’s view, of course, it is nonsense, since he interprets "It is obligatory that Ralph close the windows" as meaning "The imperative ‘Ralph, close the windows’ is justified." Under this reading, we would have to render (10) as:

which is perilously close to gibberish. (Castañeda makes it an official principle that deontic operators cannot be piled on top of one another: see p. 97, principle DP.) Of course, this particular problem would not arise if we tried to base deontic judgments on propositions: but then, as noted before, we would simply be afflicted with another variant of deontic stuttering.

Two intimately related themes in Castañeda’s theory are that first, deontic judgments and imperatives are based on practitions; and second, that sentences formulating actions (as opposed to acts) are the proper objects of deontic operators. The latter, of course, is a natural position to adopt if we want to treat deontic logic on the model of alethic and epistemic modal logics, both of which deal with subject-predicate structures, albeit with propositions rather than practitions. In terms of obligations, at the ontological level, it might appear that this cashes out to the view that it is actions, not acts, which are obligatory, forbidden, and so forth.

Nor is this view without support from our ways of talking about obligations. The astute reader will already have noticed that a supporter of practitions (or propositions) can turn one of Section 3’s arguments around to attack the view that acts are the objects of obligation. Is it possible that imperatives and deontic judgments do not share a common core element, whether that element is a practition, proposition, act, or whatever? The following chart should clarify what imperatives and deontic judgments can and cannot be based on, and why:

and we have seen how substituting the action "you close the windows" can lead to deontic stuttering. But the supporter of practitions (or propositions) can justifiably retort that we have looked at only half of the linguistic evidence. Try to base a deontic judgment on an act, he says, and you will come down with a malady just as bad as deontic stuttering, e.g., as in

We might call this problem "deontic skipping." Here, the linguistic evidence unequivocally supports the view that deontic operators must be applied to subject-predicate structures, as in

This suggests, once again, that actions, not acts, are what is obligatory, forbidden, and so forth.

As plausible as this sounds, I must demur, at least on the ontological level. Castañeda himself has taught us well that not everything occurring within the scope of a deontic operator is bound by it. [Ch. 3, Section 2] Put simply, deontic operators are properties attach only to certain elements of sentences or situations, and not to others. For example, in

two actions are referenced within the scope of the deontic operator: "John returns to Mary the book he stole from her" and "John steals a book from Mary." However, even though the latter action occurs within the scope of the deontic operator, it is not bound by the operator, precisely because it is only mentioned to identify one element of the obligatory action. In Castañeda’s terms, the action "John steals a book from Mary" is not practically considered in (11), but occurs only as an identifier.

If this is so, and if not everything occurring within the scope of a deontic operator is bound by it, then nothing prevents us from maintaining that the indexical "you" which stands for the subject-term in (5**),

is not practically considered and that, hence, what is obligatory is the act of closing the windows rather than the action of Ralph closing the windows.

Moreover, this view is supported by reflection on the nature of deontic properties. It amounts to the following structural interpretation of deontic judgments:

a formulation which takes into account the pre-philosophical datum that an obligation is always for someone to do something, and that the "something" which is to be done does not include the "someone" who is supposed to do it. To take an example formulated in terms of duties, if I have a duty to give Castañeda five dollars, then I have the duty, and the duty is to give Castañeda five dollars, not redundantly to Scott-give Castañeda five dollars. Deontic properties attach to things that I can do or refrain from doing, but not to me personally.

There is one important misunderstanding which ought to be avoided (i.e., Reader: to avoid this misunderstanding is obligatory: for you), and that is over-estimating the implications for deontic logic of acts being the proper objects of deontic properties. True enough, in

the indexical "you" which refers to Ralph is not bound by the deontic operator "it is obligatory that." However, we would cause ourselves unnecessary theoretical left-footedness if from this fact, we jumped to the conclusion that in a proper deontic logic, the deontic operators would only be allowed to apply to acts – e.g., as in

A partial parallel exists in alethic and epistemic modal logics. In alethic modal logic, for instance, as in

the modal operators apply straightforwardly to whole sentences, and not to any of their sub-sentential parts. Hence, it does not occur to us to demand that since "Scott," standing by itself, fails to be bound by the alethic operator, that we should therefore have

or even worse, since "marry Drew Barrymore" standing alone isn’t bound, either, that we should have the totally ridiculous

It is plain, however, that in this respect, the cases of alethic and deontic modal logics are analogous. Hence, we need not have any qualms about simultaneously maintaining the theses that (a) deontic properties attach only to acts, not to actions; but that (b) deontic operators can be applied to linguistic units which formulate actions.

Let’s sum up. Deontic properties apply to acts, while deontic operators apply to linguistic units formulating actions: and as we have seen, there’s no special problem there. We do have a problem, however, in drawing the connection between deontic judgments and imperatives: a problem which, in spite of its other flaws, the practitional theory handles very nicely.

But is there really such a problem? Castañeda’s interpretation of deontic judgments as second-order statements about the justification of imperatives is in no way dependent on their both being erected on practitions: it would work just as well if both were erected on propositions which formulate actions. If imperatives could be based on actions rather than acts, we would be home free.

As it turns out, we are home free. Looking back at Castañeda’s canonical notation for expressing imperatives, e.g., as in

we can see that we were again misled by a faulty notation into thinking that a subject-predicate structure could not serve as the basis for constructing an imperative. If we were actually to apply Castañeda’s canonical notation to an act, what we would get is

since an act-formulation lacks a subject term. Hence, we apply Castañeda’s imperatizing operator to the proposition "Ralph closes the windows," split off the agent from the act, put the verb in the imperative mood, and Voila!, we have an imperative. On the other hand, we can apply the deontic operator "it is obligatory that," put the verb in the subjunctive mood, and Voila!, we have a deontic judgment, based on the same proposition as the imperative which it entails. Hence, there are no significant problems involved in simply co-opting Castañeda’s account of deontic judgments as veiled statements about the justification of imperatives – but substituting propositions for practitions.

I conclude that the ontological and linguistic evidence present no barrier to the view that deontic judgments and imperatives are based on propositions. Castañeda’s practitional theory of imperatives and deontic judgments, while it has advanced our insight in many respects, is unacceptable as it stands.

It has been shown, I think, that Castañeda’s theory will not do as it stands, and that a proposition-based substitute is the most sensible alternative. However, Castañeda has been kind enough to point out what he thinks is a weakness in the foregoing argument. Here, I will explain his objection and why it seems unconvincing to me.

Castañeda writes: "Your Section 3 suffers a very serious defect, namely, the confusion of sentences with propositions. … Obviously, the subject of ‘open the chimney’ and ‘close the windows’ is the second person, or ‘Ralph’. But this is a grammatical point, not a logical or semantical point. … The same confusion between linguistic expressions and thought-contents appears in your contrast between the operators ‘it is obligatory that’ and ‘it is obligatory that you do the following’. … There are several logical operators, linguistically speaking, but it does not follow that such different expressions do not express the same logical operator."

While I am in complete agreement with Castañeda on the distinction between sentences and propositions, it seems to me that to push the distinction far enough to save the practitional theory is to invite total linguistic anarchy. If language is to be workable at all, there must be at least some regular correspondence between linguistic entities and what they express.

Granted that the same content can be expressed with different words. But to claim that (in the context under discussion) "close the windows" expresses the same content as "you close the windows" and "it is obligatory that" expresses the same content as "it is obligatory that you do the following" is to push the flexibility of language beyond all rational bounds.

It is worth mention that practitions cannot be saved even if we accept Castañeda’s defense. Let us stipulate that

which under Castañeda’s reading is supposed to mean the same as the redundant

this defense simply won’t do the job of making practitions viable, even as it cripples our confidence in the viability of language. We are still faced with the deontic redundancy involved in applying deontic operators to a subject-predicate structure whose central connection is that of demand (see Section 3 of this paper, (8*) and (9)).

*Hector Castañeda, Mike Dunn, and Earl Conee commented on this paper, with the result that it is much improved over the original version. Any remaining errors are my own.

	Imperatives	Deontic Judgments
Practitions	No: deontic stuttering, e.g., "Ralph, do the following: Ralph close the windows."	No: deontic redundancy, e.g., "It is obligatory that it is obligatory that Ralph close the windows."
Propositions (formulating actions)	No: deontic stuttering, e.g., "Ralph, do the following: Ralph close the windows."	Yes, e.g., "It is obligatory that Ralph close the windows."
Acts	Yes, e.g., "Ralph, do the following: close the windows."	No: deontic skipping, e.g., "It is obligatory that close the windows."