Rules, facts and descriptions
Let us take a closer look at this mechanism according to which rules lead to facts which can be described by sentences that are identical to the rule formulations. To show that this has everything to do with the relation between constitutive rules and facts, and nothing in particular with regulative rules as such, I will start with a competence conferring rule. An example would be the fact to fact-rule that owners of real estate are competent to mortgage this real estate. Then, if Smith owns Blackacre, the rule makes that Smith is competent to mortgage it. The rule applies only to individual cases and makes that in all these cases the owners of real estate have the competence to mortgage it. Indirectly, via these individual cases, the rule also makes that (all) owners of real estate are competent to mortgage this real estate. And this general fact is truly described by the sentence ‘Owners of real estate are competent to mortgage this real estate’.
The same line of reasoning can—almost literally—be applied to rules that lead to deontic facts. An example would be the fact to fact-rule ‘Car drivers should drive on the right’. Let us assume that this is an existing (valid) rule. Then, if Schmidt drives a car, the rule makes that Schmidt should drive on the right. The rule is applicable to all persons who drive cars and imposes on all these persons the duty to drive on the right. The rule applies to all individual drivers and makes that they should drive on the right. As a result, car drivers should drive on the right, and this general fact is truly described by the sentence ‘Car drivers should drive on the right’.
A similar line or reasoning can be used in the case of dynamic obligation imposing rules. An example would be the dynamic rule that those who promise somebody else to do something are from then on under an obligation towards this other person to do what was promised. If this is a valid rule, then, if Smith promised Jones to pay her € 500, the rule makes that Smith is under an obligation towards Jones to pay her € 500. The rule is applicable to all individual persons who made a promise to do something and imposes on all these individuals the obligation to do what they promised. That all these individuals are under this obligation is truly described by the sentence ‘Those who promise somebody else to do something are from then on under an obligation towards this other person to do what was promised’.
2.3.3 Regulative Rules Are also Constitutive Rules
I have discussed two examples of rules that constitute deontic facts, primarily duties or obligations for individual persons, but in a derived sense also for categories of persons. These two examples represent two kinds of regulative rules, namely fact to fact-rules which impose duties on categories of persons, and dynamic rules which impose obligations on persons as the result of events. There are still other categories of regulative rules, for instance the rule of etiquette, which do not really prescribe behaviour, but which still tell agents what to do.24 Another example is the rule that if the king is in chess, the threat to the king should be removed immediately. These regulative rules are also constitutive in the sense that they make that agents should do something. Such should-facts exist in the same manner as duties and obligations, and if the latter two categories of facts are constituted by rules, so is the former. Therefore these non-mandatory regulative rules are no counter-examples against the general thesis that regulative rules are also constitutive rules. I submit here the thesis that all regulative rules are also constitutive rules, and that they only differ from other constitutive rules in that they constitute deontic facts, rather than other kinds of facts. This is not a sufficient reason to make a special category out of them.
2.4 Rules as Soft Constraints on Possible Worlds
If, as argued above, regulative rules are a subcategory of constitutive rules, one may wonder whether all rules are constitutive ones. A first reason to assume that this is indeed the case is that as yet no other kinds of rules than regulative and constitutive ones have been identified. If all these rules are constitutive, then at least it seems that all rules are constitutive. However, it is also possible to give a positive account of the nature of rules which leads to the conclusion that all rules are constitutive. According to this account, rules are a kind of ‘constraints’ on possible worlds, and more in particular a special kind of constraints, namely ‘soft’ ones.25
Possible worlds play an important role in model-theoretic semantics, an important part of modern logic. Therefore it is important to understand what these possible worlds are. The best technical approximation of logically possible worlds is the interpretation function that explains how truth values are assigned to compound sentences on the basis of the truth values of atomic sentences and to atomic sentences on the basis of individuals being elements of sets.26 The nature of possible worlds is seldom discussed in an informal manner, however.27 It may therefore be useful to say a little more about possible worlds, and to explain the role of constraints in defining which worlds count as possible ones.
2.4.1 States of Affairs, Possible Worlds and Constraints
For the purpose of this article, the terms ‘possible world’ and ‘state of affairs’ will be defined as follows:
A state of affairs is what is expressed by a declarative sentence. Notice that it is not necessary that the sentence is true. States of affairs are merely ‘potential facts’. True sentences express facts, a subset of the states of affairs.
A possible world is a complete set of compatible states of affairs. Both completeness and compatibility are defined below.
Logic cannot determine which states of affairs are compatible, because logic presupposes the notion of (logical) compatibility rather than defining it. Which states of affairs are deemed compatible is not something that is ‘objectively’ given28 but depends on the constraints that are imposed on the world. Constraints determine which states of affairs can go together in a possible word. It is possible that it rains and the sun is shining at the same time, but not that John is both a thief and not a thief.
Compatibility of states of affairs is by definition relative to a set of one or more constraints. The states of affairs that John is a thief and that he is not a thief are incompatible because of the constraints that a state of affairs cannot both exist and not. Another constraint is that the compound state of affairs that John is both a thief and a minor can only exist if both the states of affairs that John is a thief and that he is a minor exist. Such constraints are usually called logical constraints.
Besides logical constraints there are also other constraints. Physical constraints prevent a piece of metal being heated without expanding. Conceptual or semantic constraints make it impossible that something is both a square and a circle.
What is possible depends on the constraints that are taken into account. This brings us back to the notion of a possible world. A possible world is a set of states of affairs that are compatible relative to some set of constraints C, in the sense that the facts of that world satisfy the constraints in C. For instance, a logically possible world does not contain both the fact that the capital of Belgium is Brussels and the fact that the capital of Belgium is not Brussels.
Since a set of constraints will usually not determine all the states of affairs in a possible world, every set of constraints defines a set of worlds that are possible relative to this set. For instance the set of logically possible worlds may contain one world in which Brussels is the capital of Belgium, and another possible world in which Belgium does not even exist. But, relative to a plausible set of constraints, there is no possible world that contains both facts.
If the traditional constraints of propositional logic are taken into account, a possible world cannot contain both states of affairs ‘Snow is white’ and ‘Snow is not white’. If physical constraints are taken into account, no possible world will contain the states of affairs that a piece of metal is heated without expanding. But if only proposition-logical and physical constraints are taken into account, some possible world may contain a square which is at the same time a circle. To rule out that latter possibility, also some conceptual or semantic constraints need to be taken into account
Different sets of constraints may lead to different sets of possible worlds, and there is not one single set of possible worlds. So there is the set of worlds that are both logically and conceptually possible, and this set may include a world that is physically impossible. Another set includes the worlds that are physically and conceptually possible, but not necessarily logically possible. And so on …
There are not only constraints on the states of affairs that can exist together simultaneously. Many natural laws, for instance, operate in time and make that some things must happen after something else happened. These constraints confine which possible worlds can follow after a particular possible world in time.
Not any set of states of affairs that satisfies a set of constraints c is a possible world relative to c; the set must also be complete. Intuitively completeness means that a possible world determines for every sentence whether it is true or false.29 This idea can be implemented by demanding that it is not possible to add any state of affairs to the possible world without violating a constraint on that world. For instance, if a possible world contains the states of affairs that John is a criminal and that the legal rule that criminals are punishable is valid, then it is possible (and—if the world is to be legally possible—even required) to add the state of affairs that John is punishable, but not to add the state of affairs that John is not punishable.
2.4.2 Contraints and Directions of Fit
The formulation of a constraint is very similar to a declarative sentence. For instance, one physical constraint might be that all pieces of metal that are heated expand, and a mathematical constraint would be that there is exactly one line parallel to some line L, which is through a point P which does not lie on L. However, there is a difference in the direction of fit between declarative sentences and constraints. Declarative sentences, even if they deal with what is possible, are true or false depending on the states of affairs that exist in some particular possible world, or—if they aim to describe a regularity—in the set of all worlds that are possible relative to some set of constraints.30
Constraints, even though they can be formulated in language, are not linguistic utterances, let alone declarative sentences. The existence of ‘hard’ constraints, about which we are presently talking, does not depend on the facts in a possible world, or the facts in all possible worlds. It is rather the other way round: a world only counts as possible if it satisfies the constraint, if the facts in this world are as the constraint says they are. The constraint in that sense ‘imposes itself’ on the world.31
2.4.3 Constraints and Conditionals32
Because of their nature, constraints support conditional and even counterfactual sentences. An example of a conditional sentence would be: ‘If John has committed theft, he is punishable’. This sentence tells us what is the case in the hypothetical situation that John has committed theft, without also informing us whether this hypothetical situation is actually the case. Metaphorically speaking, this sentence tells us what is the case in a possible world in which John has committed theft. Or rather, it tells us that John is punishable in all possible worlds in which John has committed theft, because it does not mention any other conditions for the punishability of John. The conditional sentence ‘If John has committed theft, he is punishable’ might be reformulated in possible world terminology as ‘In all possible worlds in which John has committed theft, he is punishable’. These possible worlds may include the actual world, but the sentence does not inform us whether this the case.
A counterfactual sentence such as ‘Even if Jane would have thrown a brick at the window, the window would still not have broken’ is very much like a conditional sentence, informing us what is the case in all possible worlds in which Jane has thrown a brick at the window. But it also tells us that Jane did not throw a brick at the window in reality, that is in the actual world.
Constraints on possible worlds are the reason why conditional sentences, including counterfactuals, are true or false. If all possible worlds would be constrained in such a way that if they contained the state of affairs that Jane threw a brick to the window, they must also contain the state of affairs that the window did not break33, then the counterfactual sentence ‘Even if Jane would have thrown a brick at the window, the window would still not have broken’ would for that reason be true. If all possible worlds would be constrained in such a way that if they contain the state of affairs that John has committed theft, they must also contain the state of affairs that John is punishable, then for this reason the conditional sentence ‘If John has committed theft, he is punishable’ is true.