- 1 Narváez Mora 2024a (in English) and 2024b (in Spanish).
- 2 By ‘classical logic’ I mean first-order predicate logic in combination with model-theoretic seman (...)
1In her article ‘Norms as functions’ Maribel Narváez Mora proposes treating norms as functions in the mathematical sense and elaborates her proposal to illustrate how it would work.1 Narváez Mora’s proposal is inspired by the insight that norms are not statements and that, therefore, they are neither true nor false. In the technical terminology of logic: norms do not have a truth-value. As a result, classical logic2 cannot be used to model reasoning with norms, even though in day-to-day reasoning norms can unproblematically be used to derive conclusions. Treating norms as functions would solve this problem. My purpose in this article is to evaluate Narváez Mora’s proposal, and to propose an alternative that safeguards the strengths in her approach while avoiding the drawbacks. I assume that the reader is familiar with classical logic.
- 3 For a number of relevant distinctions, see section 7.1 below.
- 4 Here, as well as in the following, I assume that everything is ‘normal’ unless the contrary follo (...)
- 5 Anscombe 1976; Searle 1979 and 1995; Narváez Mora 2024.
2Inspired by the insight that norms are not propositions and that they are therefore neither true nor false, Narváez Mora proposes treating norms as functions. But what are norms? Narváez Mora writes that a norm is a normative qualification of an action or omission, but also that an order is a norm, that a command is a norm, and that definitions and general rules of behaviour are norms. This seems to be a mixed bag3 and to keep the following discussion simpler, I will focus on norms in the sense of mandatory rules (general rules of behaviour), such as the norm that car-drivers must carry a driver’s license.4 This norm does not inform us what drivers must do; it makes it the case that drivers must carry a driver’s license. It attaches the duty for a person to carry a driver’s license if this person drives a car. In technical terminology: the norm has the world-to-word direction of fit, while descriptive sentences have the word-to-world direction of fit.5
- 6 I ignore here the problematics of statements that deal with non-existing entities such as ‘The ki (...)
- 7 This problem is often traced back to a seminal article by Jørgensen (1937/1938), but that is a mi (...)
3In classical logic, the premises and the conclusions of arguments are all propositions — statements with a fixed meaning — and all propositions have a truth-value:6 they are either true or false. As a result, norms cannot be premises or conclusions of arguments in classical logic, and therefore, classical logic cannot be applied to norms.7 This problem cannot easily be solved by dropping the requirement of classical logic that all propositions have a truth-value. To see why this is so is not only important for a proper understanding of classical logic, but also points the way toward a solution for the logic of norms.
4Logic is the theory of valid arguments, that is, the theory of when an argument’s conclusion follows from the premises of the argument. Classical logic works with the semantic notion of logical validity. According to this notion, an argument is valid if and only if it is logically impossible that all the premises of the argument are true, while its conclusion is false. This leaves the meaning of ‘logical possibility’ open in this connection, which is where semantics enters the story. In this section, I offer an account of semantics that assigns a central role to the notion of a possible world. By means of this account, I hope to show how crucial the demand of classical logic is that premises and conclusions have a truth-value.
5The starting point of the semantics is a language L, consisting of zero or more elementary propositions, and a set of possible worlds W. In each world in the set W, all elementary propositions are either true or false, but not both. Moreover, the truth-values of these propositions are independent of each other, both inside a single world and between worlds. For example, the truth-values of the propositions that the alarm rings and that it is seven-o-clock in the morning are independent. Moreover, the truth-value of the proposition that the alarm rings is in the actual world independent of the truth-value of the same proposition in an alternative world.
- 8 I assume here that all worlds in W are distinct.
- 9 There are more compound propositions, but these examples should suffice to make the idea clear.
6If a proposition is true in a world w ∈ W, this proposition expresses a fact in w. If the proposition is false in w, it expresses a non-fact in w. A possible world is the set of all facts in that world. Let us assume that the language L contains n elementary propositions, each of which is in all worlds in W either true or false. Then, W consists of 2n possible worlds.8 Notice that these worlds are merely possible with regard to the language L. Nothing is given about whether they are also logically (or physically, or legally) possible. Logical possibility enters the stage when we also consider logically compound propositions (compound propositions, for short). A compound proposition is formed by applying a logical operator to one or two other propositions. Let us assume that p and q are propositions. In that case ~p, p & q, p ∨ q, and p → q are compound propositions.9 All compound propositions have a truth-value as well. The resulting possible world w is a logically possible world if and only if:
- w makes ~p true, if and only if w makes p false;
- w makes p & q true, if and only if w makes both p and q true;
- w makes p ∨ q false, if and only if w makes both p and q false;
- w makes p → q false, if and only if w makes p true and q false;
- w makes ~∃x(~Px) true, if and only if w makes ∀x(Px) true.
7These are the usual definitions of the logical operators and the universal and the existential quantifier. Nothing special, except that they are used here to single out the logically possible worlds from the larger set of possible worlds by the demand that these usual definitions are respected in worlds that are logically possible. Logically possible worlds form the subset of possible worlds in which the requirements of logic are respected. The definitions of the logical operators and the quantifiers function as constraints on logically possible worlds.
8Given this definition of logically possible worlds, we can provide the following definition of logical validity:
Logical validity. An argument is logically valid, if and only if the conclusion of the argument is made true by all logically possible worlds that make all the premises of the argument true.
9In this way, the notion of a logically possible world is used to define what counts as logical possibility. The truth-values of propositions play an essential role in this definition. It is therefore impossible to make minor amendments to classical logic to allow for valid arguments in which norms play a role as premise or conclusion. In logics similar to classical logic, including classical logic itself, it is not possible to reason with norms.
10However, in the definition of logical possibility that I gave above, I built on definitions of the logical operators and the universal and the existential quantifier that are customary in classical logic. It would have been possible to use another definition of what counts as a logically possible world and of logical possibility. If that were done, a different kind of logic would be defined, and different arguments would count as logically valid. In section 8 I will use this possibility to propose rule-logic, in which norms (and other rules) are treated as logical individuals. In rule-logic, which differs substantially from classical logic, it is possible to reason about and with rules, including norms.
11Narváez Mora starts from the correct assumption that norms have no truth-values and can therefore not play a role as premises or conclusions in classical logic. As an alternative, she proposes viewing norms as functions that map actions onto one of the two values, correct or incorrect. This deserves some explanation. A function maps elements of one set onto elements of another set. The former set is called the domain of the function, while the latter set is called the co-domain. We are all familiar with functions in mathematics such as plus (+) and minus (–), but I will start the explanation with a more down-to-earth example of a function — a vending machine. Let us assume that a particular vending machine only accepts button presses as input and that, depending on the button pressed, it provides one item of candy as output. For instance, the left-most button provides the lollipop, while the right-most button provides ice-cream. In the technical terminology of functions, the vending machine embodies a function that uses a button-press as its parameter and produces a candy-item as its value. If you press a button on the vending machine, this button-press functions as the parameter with which the machine operates. The vending machine outputs the corresponding candy-item, which in technical terminology is denoted as the value of the function. The domain of this function consists of button-presses, and the co-domain consists of candy-items. The elements of the domain can function as parameters of the function; the elements of the co-domain can become values.
- 10 Here I still follow Narváez Mora’s terminology. Later, I will call events of this kind acts or ac (...)
12Narváez Mora proposes treating norms as functions that take actions as their parameters and map these actions onto one of the two values correct or incorrect. For instance, the norm that car drivers must carry a driver’s license maps the action10 of some driver that (s)he carries a driver’s license onto correct, and maps the action of some other driver who does not carry a driver’s license onto incorrect.
13Let us assume for the sake of argument that norms have actions as their domain. As clear as this may seem, the word ‘action’ is ambiguous. First, it may stand for a type of action. For example, if stealing is forbidden, the prohibition applies to the type of action: actions of this type are forbidden, even if no act of this type has ever occurred. However, an action may also be an individual event. In that case it is not a type, but a token.11 To disambiguate our discussion of norms, I use the phrase ‘action type’ for the type and the phrase ‘act token’ for concrete instances of some action type. So, we have action types and act tokens.
14An important difference between action types and act tokens is that types can exist, even if no single act of that type has ever been performed. For instance, assume that chitchatting is playing ping pong with balls of different colours, with the rules of the game depending on the colour of the ball. To my knowledge, nobody ever wrote about this kind of chitchatting before, and the game has never been played. In this case, the action type chitchatting exists; it is playing the game that I just mentioned. However, there are no tokens of this action type, since the game has never been played before. An act token is always an act of a particular type, but where the type can exist without there being any token of it, tokens can only exist if the act has actually been performed.
- 12 Here I do not pay attention to permissive norms, as this category of norms is heterogeneous. Incl (...)
15Norms in the sense of rules that prescribe or proscribe behaviour12 have (at least) two functions. One is to guide future behaviour, the other is to evaluate behaviour that already took place. For example, the norm that car drivers must carry a driver’s license has the function of making car drivers carry a driver’s license, and also the function of evaluating the behaviour of a particular driver who did or did not carry such a license as lawful or unlawful, respectively. Prescribing or proscribing an act token does not make sense, as the prescribed or proscribed act was already performed. The prescription or proscription can no longer influence whether the act token will be performed. Prescriptive norms and prohibitive norms aim to guide future behaviour, and they can only do so if they deal with action types.
16However, evaluations of acts as correct or incorrect deal with tokens. So, if a norm prescribes or proscribes action types, it makes tokens of these types correct or incorrect. Only if the acts were already performed and therefore exist, does it make sense to evaluate them individually as correct or incorrect. In contrast, norms can exist without there ever being tokens of the regulated action type, and therefore without there ever being correct or incorrect instances of the types. This means that it is impossible to define prescriptive or prohibitive norms in terms of act tokens.
- 13 See Poirier (n.d.).
- 14 It may be objected that this becomes different if norms are defined in term of possible act token (...)
17It may seem that Narváez Mora has circumvented this problem by using classes as the domains of norms. A class is a set defined by the kind of its elements, for instance the class of all circles. Using classes as the domains for norms seems to allow for norms that deal with future actions, because a future case of not carrying a driver’s license would still count as an action of the kind ‘not carrying driver’s license’.13 This appearance is deceptive, however, because although it is true that the elements of classes are defined by their kinds, classes are still sets, and sets are defined by their elements. So, if a norm has actions as its domain, the norm ranges over all actions, that is, all existing actions. That leaves open the problem that norms that prescribe or forbid behaviour in their behaviour-guiding function aim to deal with behaviour that has not yet taken place, and with acts that do not (yet) exist. 14I will return to this issue in section 9.
18A second issue has to do with the co-domain of norms. Narváez Mora writes that this co-domain consists of two values, correct and incorrect. So, the norm that drivers must carry a driver’s license would attach the value incorrect to Carol’s act that consists in driving without a license. However, Narváez Mora writes in paragraph 16:
[T]he model has a semantic commitment to the thesis: “Every norm distributes correctness and/or incorrectness […] over classes of actions,” defining the deontic operators as follows:
(OA) Obligating an action A, is to qualify the performance of that action A as correct and its non-performance (A’) as incorrect: OA = CA ∪ ¬CA’
19This quotation suggests that the set of obligated actions of type A is the set-theoretical join of the set of correct actions of type A and the set of incorrect actions of type non-A. However, that is only possible if correct and incorrect are seen as characteristics of actions and not as values onto which actions are mapped. It seems that there is some ambiguity regarding the co-domain of norms. Does it contain the values correct and incorrect, or does it contain facts of the type ‘this action is correct’ and ‘this action is incorrect’? Some disambiguation is desirable.
- 15 This is a translation of the problem that it is not possible to mention all exceptions to rules i (...)
- 16 Ginsberg 1980.
20The final issue I want to mention deals with a topic unmentioned in Narváez Mora’s article. Norms can have exceptions, and treating norms as functions cannot do justice to this phenomenon. Suppose that stealing is forbidden, but that in an emergency a person stole some food and that doing so was permitted/correct given the circumstances. Of course, this particular emergency can be included in the function with the effect that the act of stealing in the emergency is evaluated as correct. However, it is not possible to include all possible exceptions in the function that maps actions onto their evaluations, as exceptions to norms are not all predictable.15 In logic, this complication is handled under the heading of defeasibility, and attempts to deal with defeasibility have led to the development of non-monotonic logics.16 If norms are functions with their strict relation between domain and co-domain, it seems impossible to develop an alternative for non-monotonicity.
21Apparently, Narváez Mora’s proposal to treat norms as functions is not without issues. Still, its underlying ideas are correct. Norms are not statements with truth-values and they cannot function as premises or conclusions in arguments in classical logic. Moreover, norms attach — rather than describe — consequences to fact situations. Nevertheless, norms do play a role as premises in arguments, and if logic is to deal with norms it cannot be classical logic. In the rest of this article, I propose a logic that can handle norms without treating them as propositions with truth-values. Where Narváez Mora tried to do so by treating norms as functions, I will show how norms can be dealt with by treating them as logical individuals.
22The first step of my proposal is to pinpoint the notion of a norm. Narváez Mora writes that an order is a norm, that a command is a norm, and that definitions and general rules of behaviour are norms. I characterized this as a mixed bag, and this is the moment to elaborate on that. Orders and commands are both speech acts that typically aim at influencing somebody else’s behaviour. There are no precise definitions for what an order or a command are, but in earlier work17 I used the two words to mark a distinction, which I will also do here without pretending that it reflects the standard usage of ‘order’ and ‘command’.
23Orders, as I will use that term, are speech acts by which the speaker aims to influence behaviour in a purely causal matter. An example would be one person, who is in no authoritative relation to another person, telling them to close the window. This other person is not obligated by this order but may feel some psychological pressure to close the window anyhow. Strictly speaking, any person can order any other person. If the order is efficacious, its effect is psychological pressure but not a duty or an obligation. Orders as defined here have nothing to do with norms.
- 18 For the role of competences in creating legal consequences by means of juridical acts (such as co (...)
24A command, again in the use of the word proposed here, presupposes that the person giving the command has an authoritative relation to the person at whom the command is addressed. A police officer who commands traffic participants to clear a crossing would be an example, as would an army-officer who issues a command to the soldiers under his authority. In legal terms one can say that an agent needs competence to issue a valid command.18 The result of such a valid command is that the agent who received the command has the duty to do what was commanded. If the command was valid, that is, if the commander had the necessary competence and followed the right procedure, the duty will typically result. It is irrelevant here whether the commanded person recognises the duty or not. The relation between a command and the resulting duty is a normative one, not a psychological one. If the command is to be efficacious in bringing about the commanded behaviour, it is necessary that the duty is efficacious. The command creates the duty and the duty — or better, the experience thereof — leads to behaviour.
25Commands are speech acts, while norms are not, and herein lies their difference. However, the two have in common that they lead to duties. Duties have a logic of their own, which is common to duties based on commands and duties based on rules. This logic will very briefly be described in section 9.
- 19 In earlier work (e.g. Hage 2005, but also Hage 2022) I also pleaded for the complete abandonment (...)
- 20 Sometimes rules do not create new facts, but take away existing facts, or modify them. I will ign (...)
26For the purpose of this article,19 I define norms as mandatory rules, specifically, as rules the application of which lead to duties. It is often thought that all rules are there to prescribe, prohibit, and perhaps also permit, behaviour. However, there are many other kinds of rules and they have in common that they attach facts to other facts (static rules), or to the occurrence of an event (dynamic rules).20 Consider the following five examples:
27(R1) The moment that the President dies, the Vice-President becomes the new President.
This is a dynamic rule about succession. It attaches a new fact — the person who was the Vice-President becomes the (new) President — to the occurrence of an event: the (old) President died.
28(R2) Statutes are created by Parliament.
This static rule attributes the exclusive competence to create statutes to Parliament. In doing so, it attaches a state of affairs — this entity has the competence to create statutes — to another state of affairs — this entity is Parliament.
29(R3) A bachelor is an unmarried man of marriageable age.
This static rule both defines the meaning of a word and at the same time conceptually connects two kinds of entities: bachelors and unmarried men of marriageable age. Through this conceptual connection, the states of affairs that, on the one hand, somebody is a bachelor, and on the other hand, that this person is a man of marriageable age who is not married, are connected.
30(R4) If two or more parties conclude a valid contract, everything in the contract holds between the contract partners.
- 21 Following the civil law tradition, I will distinguish between obligations and duties. An obligati (...)
- 22 Hage 2018: 97-102.
This is a (strongly simplified) dynamic rule about the consequences of a contract. These consequences often — but not always — involve mutual obligations,21 even though the rule does not mention them explicitly.22 Neither does the rule mention duties or permissions. Therefore, we cannot say that it is a mandatory rule, even though its application will often lead to obligations.
31(R5) Car drivers must carry a driver’s license.
- 23 The rule is not a conditional one. Its antecedent specifies on whom the duty created by its antec (...)
This is a typical mandatory rule. It imposes a duty — to carry a driver’s license — on agents that belong to a particular category — car drivers.23 Notice that the duty itself, for instance that Henry must carry a driver’s license, is not a rule. The duty is a ‘thing’ (a logical individual), and the existence of this duty (if the duty exists) is a fact. This fact is attached by the static rule to another fact, namely, that Henry is a car driver. By attaching this fact to another fact, the rule creates a new duty.
32Given the above explanation of the different kinds of rules, it is easy to define norms in the sense that will be used in this article: norms are mandatory rules.
33If somebody does not recognise the consequences of an applicable rule without good reason, (s)he makes a mistake. Examples are:
(a) a car driver who does not see a reason to carry a driver’s license,
(b) a legal subject who does not recognise the competence of Parliament to create legislation and, thereby, rules,
(c) an English speaker who calls a married man a bachelor, or
- 24 The duty to move rooks in straight lines is an example of a duty to do something in a particular (...)
(d) a chess player who moves a rook diagonally.24
34However, making a mistake is not necessarily the violation of a duty, and from the fact that somebody who does not recognise the consequences of a rule when he ought to have done so makes a mistake, one cannot conclude that all rules impose duties.
35A slightly different way to look at the same phenomenon is to notice that there are two kinds of normativity attached to a mandatory rule.25 All rules, and therefore also mandatory rules, define the proper thing to do: if one believes that the rule conditions are satisfied, one ought pro tanto to recognise the rule consequence. This is the normativity of reason and it represents the normativity that attaches to all rules.
36If a rule is mandatory, there a second form of normativity in that such a rule imposes a duty. Let us call this second kind deontic normativity. The addressee of the duty, pro tanto ought to do what the duty prescribes. This deontic normativity only applies to mandatory rules, or to be precise, to the duties created by mandatory rules. If one does not recognise the difference between the normativity of reason and deontic normativity, it is easy to believe –— mistakenly — that all rules are mandatory, and therefore norms.
37It is a mistake to confuse, on one hand, the normativity of duties and indirectly of norms and, on the other hand, the normativity of reason, with as a special case the normativity of recognising the conclusion of an applicable rule. It is also a mistake to lump violations of both kinds of normativity together under the same label incorrect. It is true that both kinds of violation are incorrect, but they are incorrect in very different ways and that is sufficient reason not to lump them together under one label.
- 26 The idea to treat rules as logical individuals was first elaborately defended in Hage 1997. It wa (...)
38For their logic, norms do not differ from other rules, and therefore I will devote the next section to the treatment of rules as logical individuals.26
- 27 The aim of this section and the following is to give an impression of how a logic for rules and d (...)
39The complications that are attached to the fact that rules have no truth-values and can therefore not function as propositions in classical logic can be overcome by treating rules as logical individuals. Take, for instance, the following argument:
The rule [Car-drivers must carry a driver’s license] is valid.
Carol drives a car.
∴ Carol must carry a driver’s license.
40In classical logic this argument would be invalid, as the two premises have no connection. The first premise is about the validity of a rule, and the second premise is about Carol as a car-driver. Still the conclusion seems to follow, at least if we ignore the defeasibility of arguments based on rules. How can we create a logic in which this argument is valid?
- 28 This addition to the semantics can also be dealt with in the syntax of rule-logic by adding an ax (...)
- 29 The rule conditions are fulfilled (by a case) if and only if there is an instantiation of the rul (...)
41The answer is: by adding to the semantics28 the requirement that a world is only logically possible if it contains the fact that if a rule is valid in that world, the rule conclusion is true if the rule conditions are fulfilled.29 This addition means that that rule application leads to the conclusion of the rule in all logically possible worlds.
- 30 To be consistent with earlier work, I express the normative consequence of the rule as the existe (...)
42The formulation of the rule that car-drivers must30 carry a license can be formalised as:
car_driver(x) ⇒ ∃d(d = duty(x, carry_license))
43Informally, this formula can be read as denoting the rule that if somebody is a car-driver, there is a duty for this agent to carry a license. The formula is a function expression that denotes a logical individual by means of its logical structure. It is not a proposition that is true or false; in particular, it is not the statement that this rule exists. The rule formulation can therefore not be an independent part of an argument (a premise or a conclusion).
44The operator ⇒ maps the pair of states of affairs (that somebody is a car-driver, and that (s)he has the duty to carry a license) onto the rule. The double arrow is not a logical operator and certainly not a conditional. It stands for a function with two parameters. The first parameter is the state of affairs that some agent is a car-driver. The second parameter is the state of affairs that the aforementioned agent has the duty to carry a license. The value of the function is a rule, a logical individual, and not the state of affairs that this rule exists or is valid.
45If a rule is to be used in an argument by applying it, the rule can be mentioned in a premise stating that the rule is valid. For instance:
Valid(car_driver(x) ⇒ ∃d(d = duty(x, carry_license)))
46Stating that a rule is valid means the same as stating that the rule exists:
∃r(r = (car_driver(x) ⇒ ∃d(d = duty(x, carry_license)))
- 31 Because of the technical details involved in formalising that a rule is applicable to a case, I r (...)
47If a rule is valid and the facts of a case satisfy the conditions of the rule,31 then the rule is applicable to the case:
Applicable(car_driver(carol) ⇒ ∃d(d = duty(carol, carry_license)))
- 32 A logic is said to be monotonic if the logic has the property that a conclusion that can be valid (...)
48For the rest of the logic there are two variants available, a monotonic one and a non-monotonic one.32 In the monotonic version, the conclusion of an applicable rule is true and can be derived:
∃d(d = duty(carol, carry_license))
- 33 This reasoning mechanism presupposes that there is a logic for reasoning based on reasons that ca (...)
49For the non-monotonic version, the reasoning mechanism works as follows:33
(a) If a rule is applicable to a case, this is a reason to apply the rule to the case.
(b) There can be reasons against applying a rule, for instance, that there is an applicable rule with a conflicting conclusion, or that application would violate the rule’s purpose. What would count as a reason against applying a rule is not a matter of logic.
(c) If the reasons for applying a rule to a case outweigh the reasons against applying the rule to this case, the rule applies, and its instantiated conclusion follows.
50The rule-logic that was described in this section is characterised by the fact that rules are treated as logical individuals, which are introduced in rule-applying arguments by the proposition that they are valid, or — which boils down to the same thing — that they exist. Rule-logic can be used for modelling arguments of many kinds of rules, including norms. In the case of norms, the conclusion of applying the norm to a fact situation typically leads to the conclusion that a specific agent has the duty to do something or to refrain from doing something.
51Deontic logic has in principle nothing to do with rule-logic, although that may seem different if rule-logic is applied to norms. The easiest way to see this is to compare an argument in rule-logic (example 1) with an argument in deontic logic (example 2):
Example 1
|
Valid(car_driver(x) ⇒ ∃d(d = duty(x, carry_license))) Car_driver(carol)
∴ ∃d(d = duty(carol, carry_license))
|
52The conclusion of this argument is that a specific person, Carol, has the duty to perform some action type. The argument is rule-applying, and the rule-formulation denotes an individual (the rule) and is not a proposition by itself.
Example 2
|
Valid(car_driver(x) ⇒ ∃d(d = duty∃d(d = duty(carol, carry_license))
∃a(Performed(carol, a) & Type_of(a, ¬carry_license))
∴ ∃a(~Permitted(a))
|
53The conclusion of this second argument is that some act token is incorrect (or not permitted, or unlawful, or morally wrong). This conclusion is derived from the premises that Carol has the duty to carry a driver’s license and that Carol did not carry a driver’s license.
54As these two examples illustrate, norm-applying arguments have conclusions about specific agents who stand in some deontic relation (duty, prohibition) to an action type, while arguments in deontic logic often lead to conclusions about the deontic status of some act token, typically that it was (not) permitted. It seems not to make much sense to say that act tokens were duties or that they were forbidden. As soon as there is an act token, the behaviour is already there and cannot be guided anymore. However, saying that an act was a duty or forbidden can nevertheless make sense if the purpose of saying so is to justify an evaluative judgement about the act, for instance that the act was (in)correct.
- 34 More details can be found in Hage 2018: chapters 6 and 7.
55There is much more to be said about deontic logic, but there is no space here to do so in any systematic manner.34 My main point is that deontic logic typically deals with act tokens, which are evaluated as correct or incorrect. Deontic logic is not the logic of norms, if norms are seen as mandatory rules. The logic of norms is the logic of rules, without any special role for their deontic conclusions.
56The logic of rules should be distinguished from deontic logic. If we do that, we can ask an interpretative question about Narváez Mora’s proposal to treat norms as functions. Is her intention to treat mandatory rules as functions, or does she want to treat duties as functions? In this section, I ignore the possibility that Narváez Mora may not have wanted to make this choice and intended her proposal to apply to norms without distinguishing between rules and duties. I claimed that deontic logic typically deals with the evaluation of act tokens and now raise the question of whether this role of deontic logic, which abstracts from the behaviour guiding function of mandatory rules and duties, can be captured by treating duties as functions.
57How can duties be interpreted as functions from actions (in a still unspecified sense) to evaluations as correct or incorrect? The answer is that the domain of a duty in this role consists of the class of all tokens of some type of action and that the co-domain consists of two values, correct and incorrect, lawful and unlawful, or morally right and morally wrong. Take again the duty to carry a driver’s license. The domain of this duty would be the class of all act tokens that have as their type either ‘carrying a driver’s license’, or ‘not carrying a driver’s license’. If this duty is treated as a function, it maps all act tokens of the type ‘carrying a driver’s license’ onto the value ‘lawful’, and it maps all act tokens of the type ‘not carrying a driver’s license’ onto the value ‘unlawful’.
- 35 In her article, Narváez Mora uses so-called ‘blockades’ to deal with conflicts of duties. I will (...)
58Interpreted along this line, Narváez Mora’s proposal seems to work. However, this interpretation comes at a cost. First, norms under this interpretation cannot guide behaviour. And second, the step from the fact that an act token falls under a type to the conclusion that this act token was (in) correct, is defeasible. This defeasibility becomes manifest if there is a conflict of duties: one duty makes an act token correct, while the other duty makes this token incorrect. There are several ways to deal with these situations, but whichever way is chosen, the choice should be incorporated in a theory of duties as functions.35
59In this article I analysed Narváez Mora’s proposal to treat norms as functions. I used this analysis as a stepping stone toward outlining an alternative theory of reasoning with norms. Narváez Mora started from two assumptions that are correct in my view. The first is that norms lack a truth value and are therefore unable to be handled adequately in classical logic. The second assumption is that norms attach evaluations to actions, or the performance thereof.
60Our difference starts where Narváez Mora proposes treating norms as functions from actions to evaluations as correct or incorrect. I discussed several drawbacks of this proposal:
61First, the proposal ignores the difference between action types and act tokens, with the result being that determining the domain of norms as functions becomes unclear.
62Second, the proposal assumes that the co-domain of all norms is the same, namely, the set {correct, incorrect}. It would be better if the co-domain consisted of facts of the type that some act token is correct or incorrect. Actually, Narváez Mora suggests this herself when she uses formulas of the form CA, where C stands for correct, and A for an action.
63Third, treating norms as functions makes it impossible to account for the defeasibility of reasoning with norms.
64Fourth, Narváez Mora uses a very broad notion of a norm, to the effect that the incorrectness of mis-applying a rule cannot be distinguished from the incorrectness of violating a duty. She ignores that there are (at least) two kinds of normativity.
65Fifth, Narváez Mora fails to distinguish between reasoning with rules and deontic reasoning, which are two completely different kinds of reasoning. The cause of this failure may be the central role she gives to norms, which, if they are interpreted as mandatory rules, are both rules and deontic.
66As an alternative to Narváez Mora’s proposal, I suggested making a strict distinction between rule-logic and deontic logic. In regard to rule-logic, I proposed treating rules as logical individuals and adding an extra constraint on logically possible worlds to the effect that the conclusion of an applicable rule is true. This constraint makes a monotonic version of rule-logic possible.
67I also indicated how a non-monotonic version could be developed. This version uses the idea that the applicability of a rule is merely a reason for applying the rule, which may need to be balanced against possible reasons against application. I pointed to the existence of Reason-based Logic as a tool that can handle this balancing.
68I have been very brief about deontic logic, pointing out that most deontic arguments lead from a duty of a specific person to perform, or refrain from, some action type, to the evaluation of a token of this type performed by this person as permitted, or unlawful, (im)moral, or (in)correct.
—Acknowledgment.— The final version of this article has benefited from comments by Maribel Narváez Mora. Obviously, she is not responsible for any of the views exposed in the article. Thanks, Maribel!