Social Rules

Origin; Character; Logic; Change

David Braybrooke

• Publisher: Routledge
• Year: 2018
• ISBN:
  9780429976902
• Edition: 1
• Topic: Social Sciences
• Subtopic: Sociology
• Index: Social Sciences

This collection is a pioneering effort to bring together in fruitful interaction the two dominant perspectives on social rules. One, shared by philosophers, lawyers, anthropologists, and sociologists, directly invites formalization by a logic of rules. The other, originating with economists, emphasizes cost considerations and invites mathematical treatment, often in game-theoretical models for problems of coordination?models that some philosophers have taken up as well.Each perspective is represented by new and recent work that moves this important topic toward increased conceptual precision and deeper insight. As a whole, the collection strikes a balance between historical illustrations and theoretical argument, offering in both a rich body of suggestions for further work.

Part One
The Logicians' and Philosophers' Approach to Rules

1
The Representation of Rules in Logic and Their Definition

David Braybrooke

We begin with a chapter outlining work that has been done in the logic of rules. From the work done specifically by the Dalhousie team the chapter draws a new definition of rules (in the third sense distinguished by Kornhauser), which avoids the circularity of definitions currently in circulation. The definition reduces to near a vanishing point the difference between rules in the third sense and conventions, though it enables us to do justice to the intentional features of both, and also to the tendency of rules to be accompanied by systematic provisions for sanctions. The chapter ends with an argument for giving a place in the work of historians to the logic of rules. (The argument extends to giving it a place in the work of social scientists as well.)

For the time being, in this chapter and in a number of chapters following, we shall be occupied with rules in Kornhauser's third sense—rules that have authority and give reasons for acting. These may or may not be settled social rules. They may be new proposals; or old counsels of perfection, honored more often in the breach than in the observance. If they are settled social rules, however, they do imply regularities of conformity and are often accompanied by regularities of enforcement in deviant cases (even if the regularities are not perfect in either case). Paying one's taxes or refraining from incest are not settled social rules if most people most of the time do neither.

Starting up closer to the concerns that ethnographers have with settled social rules than to the concerns of economists or decision-theorists, some philosophers have asked what distinguishes rules from other social phenomena, in particular, from other phenomena that involve expressions in language. Though this will not do in the end as an accurate picture of rules, we may go some distance toward the distinction demanded—most if not all the distance to a logic of rules—by thinking of a rule as standing to its linguistic expressions in a relation parallel to that in which a statement stands to the sentences that express it. We would thus make no more in either case of rule or statement than a device for talking about a variety of linguistic expressions and their instances. How do rules differ from statements (singular, existentially quantified, or universally quantified), value judgments, optatives ("Would that x were the case!")?

Work on this question has been overshadowed lately by discussions of rules as solutions to game-theoretical problems of coordination, relating to rules in Kornhauser's second perspective. A recent issue of Ethics specially devoted to the discussion of rules (norms) is typical in having contributors preoccupied mainly by such considerations.¹ Work has also been deflected year after year by a preoccupation, inspired by Wittgenstein, with what following a rule amounts to, taken up as a problem in the philosophy of mind. How does the person following a rule know "how to go on"? How do we tell that he knows? There is perhaps some consensus on Wittgenstein's position that the problem cannot be resolved without invoking, for use in every case, public criteria for identifying any rule in question, even an idiosyncratic personal one.² But this still leaves open the questions about how rules differ from other phenomena in which language and behavior intersect.

More in keeping with the aim of answering these questions than Wittgenstein's preoccupation has been the general project of deontic logic, which consists in trying to specify the features of rules crucial to their directive aims and effects on the one hand and to making visible their logical relations on the other. The chief contributor to deontic logic—several times over, producing a variety of analyses and logical formulations—has been G. H. von Wright.³ It is remarkable that in the special issue of Ethics mentioned earlier there is no reference to his work. That, however, is rather evidence of the shift of fashion in the direction of game-theoretical considerations than of the work's having been superseded in the line of thought to which it contributed. There it remains the richest contribution so far.

The Logic of Rules (Deontic Logic)

von Wright's Version (in Norm and Action) of the Logic of Rules

In his book Norm and Action,⁴ von Wright arrives at a logic of norms through a three-tier construction on top of the prepositional calculus (which concerns elementary relations between propositions taken as wholes). Each tier adds logical operators to help specify those forms of propositions which the logic of norms is especially concerned to identify among the possible substitutions available in the propositional calculus. The propositional calculus itself is so general as to accept propositions of any—i.e., wholly unspecified—forms as substitutions for the propositional variables, p, q, r, etc.; it considers those relations of such propositions to one another that are established by proposition-combining operators standing (approximately) for "if... then," "and," "or," "if and only if." ((p v q → r & s) & ~r) -> ~(p v q), for example, is a symbolic sentence belonging to the propositional calculus; it may be read, "If, if p or q then r and s yet not r, then not either p or q."

Consider a proposition ρ, which describes some state of affairs ("Ν holds office"); if the state of affairs does not obtain, then, of course, ~p. Let there be an operator, T, to be placed between propositional variables (or combinations of these) and to be read "changes into." Four basic forms of propositions in the logic of change can then be envisaged: pT~p—a world in which p changes into a world in which not-p; ~pTp—a world in which not-p changes into a world in which p; but also pTp and ~pT~p, in which, significantly, no change in the ordinary sense occurs, but to which the Toperator and the logic of change are conveniently extended by deliberate convention.

The logic of change constitutes the first tier above the propositional calculus. The logic of action, in von Wright's scheme, comes in the tier next above and relates change-propositions to human intervention by introducing d and f operators that indicate, respectively, acts and forbearances. These operators may be applied to any formula of the logic of change. While d(pT~p), for example, might symbolize in an obvious way someone's acting to remove Ν from office, f(pT~p) would symbolize forbearing to do so. But d(pTp) and f(pTp) are also intelligible formulas; and symbolize, on the one hand, acting so as to maintain a state of affairs that would otherwise change; and, on the other hand, forbearing to do this, letting it change though it could be maintained. Thus d(pTp) might stand for keeping Ν in office (when otherwise he would be ejected); f(pTp), for letting him be ejected (though he could be kept).

Finally, in the topmost tier of the construction, von Wright reveals his logic of norms, and with it two further operators: an O-operator (best thought of as standing for "must") and a P-operator (for permission). The O-operator, applied to d expressions of the logic of action, produces prescriptions—Od(pT~p) "N must be removed from office." Applied to f expressions, the O-operator produces prohibitions—Of(pT~p), "N must not be removed from office." The P-operator produces permissions, either to do something—bring about some change—or to forbear. To these permissions, as well as to the prescriptions or prohibitions formulated with the O-operator, various conditions may attach; and von Wright provides for expressing them by associating further formulas of the logic of change with the formula representing the change to be brought about or forborne Pd(pT~p/qTq & rT~r), for example, is the formula of a permissive norm showing two conditions: It might be taken to symbolize the rule, "It is permitted to eject Ν from office if he owes his office to a patron and the patron has himself left office."

However complex an O or Ρ expression may be, it can always be substituted for a propositional variable, p or q or r, in the propositional calculus.⁵ Thus all the connections, oppositions, and inferences made available by that branch of ordinary logic are available also for formulas in the logic of norms. There are, besides, some connections and oppositions peculiar to the logic of norms. Od(pTp) is, for example, incompatible with Of(pTp) (though neither may hold, they cannot both hold together). It contradicts Pf(pTp): If one must do something, then one is not permitted to forbear doing it; and vice versa. Od(pTp), in fact, entails not Pf(pTp); and Pf(pTp) entails not Od(pTp).⁶

The application of von Wright's logic can be illustrated by taking up a contention of Engels's in Socialism: Utopian & Scientific. Engels maintains that so long as artisans owned their own tools, it made no difference whether the foundation of their claims to their products was the work that they put into making them or (then a secondary consideration) the fact that they owned the tools (the capital equipment) used in making them. But once it ceased to be the case that the people who did the work were the same people as the people who owned the tools, a conflict in rules appeared, between

Od(~rTr/~wTw),

under which people were enjoined to respect a right of ownership (by some specific person to some specific product) on the condition that the work of making it had been put in by the person in question, and

Od(~rTr/~tTt),

under which the right to same product was accorded to someone on the condition that tools belonging to him had been used in making the product. For suppose—as Engels supposes became generally the case—the person who did the work was not the same person as the person who supplied the tools. Which of the two claims was to be respected by other people? So long as those other people felt the force of both rules they were in a quandary that obstructed them from acting so as to respect fully either claim.⁷

The Logic of Rules Emerging from the Dalhousie Project⁸

The multi-tier picture of rules given by von Wright in Norm and Action remains the fullest logical characterization of rules available in the literature (von Wright's remarks on aspects of rules that he does not include in the "norm-kernels" expressed in his formulas are also rich in instruction). The philosophers in the Dalhousie project have kept the multi-tier picture in mind and intend in their own work to preserve its availability as much as the balance of considerations allows.

For example, von Wright asserts that in general we must expect to have added to basic rule-formulas a statement of the conditions under which the prescription or prohibition in question comes to bear upon the people to whom it is addressed. This point is carried forward in our logic.

We distinguish three features in our formulas for rules—volk, the demographic scope; wenn, the conditions under which the rule comes to bear upon conduct; nono, the routines (sequences of actions) that the rule forbids. For example, an example drawn from Track, under the feudal social order in France, the king and nobility enjoyed the benefit of a rule under which they appropriated the social surplus and did what they pleased with it:

• volk = FRENCH
• wenn = ∃(a)(∃3x)[SURPLUS(x) & OWNS(a, x)] & aft r[DISPOSES(a,x)]
• nono = BLOCKS (r',r).

The wenn component here says that x is a part of the social surplus and somebody a owns it and disposes of it. (r stands for any routine, i.e., any action or sequence of actions.) Given this condition, which notably leaves the way in which a has disposed of x completely unspecified, the nono component forbids any action or sequence of actions r' that BLOCKS r, the disposal of x by a.

Another example from Track, which like the one just given will relate to a discussion later in this book (in the comment by Miller, below), is a technical norm consolidating advances in mechanization:

• volk = WORKERS
• wenn = (∃r)(∃w)[(TASK(t) & WORKSHOP(w) & ~MECH(t,w) & aft r[MECH(t,w)]
• nono = aft(r') (∃a)[HASRUN(r,w) & PERFORMS(a,t,w) & ~MECH(t,w)].

aft(r) signifies that after a routine r has been run the proposition that follows is true. The rule in this case forbids workers to perform in a given workshop w an unmechanized task that has been mechanized there (by running an available routine for mechanizing it). It is a rule that prudent employers would adopt and enforce; if they did not, Marx for one would hold that they would be outdistanced by competitors who were more exacting about productivity.

Thus the Dalhousie logic makes of von Wright's conditions for a rule coming to bear one (the wenn component) of the three characteristic features that it ascribes to rules. We make the doing or forbearing component (the nono component in our case) more general, refraining from specifying that it must apply to actions with the form proposed for actions by von Wright. It embraces routines that may include series of actions and we do not insist on describing actions in truth-functional propositions—we allow for three values where von Wright has one, truth. An action for us is just starting or not; is running now or not running now; has already run or not. The routines to which our formulas apply may involve many different actions; and alternative routes to the same end. They may also belong to very different overall sequences; if we are forbidden to block some ...