Skip to navigation – Site map
Pravo in logika

In Defence of the Expressive Conception of Norms

En defensa de la concepción expresiva de las normas, Doxa 37 | 2014
Andrej Kristan
p. 151-172
Translation(s):
V bran izraznemu pojmovanju pravil

Abstracts

Against a background of the past three decades of critique directed towards the expressive conception of norms, the author argues first that paradigm expressivists can well account for facultative states of affairs without introducing inconsistencies into the normative system. He then shows how to describe the propositional content of a meta-rule without semanticizing the force indicator of object-rules. Finally, the author provides a formal reconstruction of conditional norms and of permissive closure, without admitting the conceptual autonomy of acts of permitting. The first parts of this paper are of a clarifying nature, whereas the last parts purport to present an advancement in the expressivist theory. | A Spanish version of this text was published in Doxa. Cuadernos de filosofía del derecho 37 (2014).

Top of page

Dedication

I wish to thank Alejandro Calzetta and Alessio Sardo for some long and vivid discussions of the topic. I also thank Eugenio Bulygin, Damiano Canale, Diego Dei Vecchi, Alessandro Ferrari, Pablo Rapetti, Giovanni Battista Ratti, Sebastián Figueroa, José Juan Moreso, Pablo Navarro, Cristina Redondo and Jan Woleński for their valuable comments on various parts of the draft of this paper. Last, but not least, I have benefited from two negative reviews. Whereas an anonymous referee of Doxa found my formalisations erroneous, another one of Studia Logica considered them mostly simple and obvious to the extent that makes this contribution trivial. In the end, I sticked to my original formalisations with only some minor corrections. It is my impression that they shall not attract logicians, but they will spark a thought or two among legal theorists—and so I decided to leave it to the broader community to make an informed judgement.

Full text

1 The Issue in Question

  • 1 Alchourrón and Bulygin (1981: 389).

1The objective of ‘The Expressive Conception of Norms’ (1981), co-authored by Carlos E. Alchourrón & Eugenio Bulygin, was “to explore [the] possibilities [of the expressive conception] in order to uncover its limitations and show the differences” between the expressive (or pragmatic) conception of norms and the hyletic (or semantic) one. In the end, they came to the conclusion that “the same conceptual distinctions appear in both conceptions, though, of course, expressed in different languages”.1 In the past three decades, strong objections have been raised against this claim.

  • 2 Contra: Weinberger (1985 and 1986). Navarro and Redondo (1990a and 1990b). Calzetta and Sardo (2014 (...)

2 In particular, it has been argued that the expressive conception in the form presented by Alchourrón and Bulygin cannot give an account of strong permissions or (at least) of facultative states of affairs (§ 2) without introducing a contradiction into the normative system (§ 3). In the alternative, the argument continues, their Expressivist cannot successfully describe the propositional content of the rules of preference we use to resolve conflicts of ambivalence, for example, without semanticizing the indicator of illocutionary (normative) force (§ 4). This, of course, would imply adopting the hyletic conception. Some also hold that the Expressivist of Alchourrón and Bulygin (1981) cannot account for a permissive rule of closure, if she does not grant the existence of a special normative act of permitting. And, what is more, critics say that the Expressivist is unable to give an adequate representation of conditional norms (§ 5). I intend to show that the opposite is true.2

3 The following two sections of this paper are of a clarifying nature and they merely formalise the views of Alchourrón and Bulygin. Most definitions introduced in there will not be used in the last two sections, which purport to make an advancement in the expressivist theory. They serve instead to avoid confusion and misunderstanding—which is, in my opinion, the reason for an important part of the critiques mentioned in the preceding paragraph.

2 Fundamental Distinctions

  • 3 See Alchourrón and Bulygin (1981: 384–385; and 1984: 454).

4The two major conceptions of norms mentioned in the introduction both assume that ‘norm sentences’ (that is, act-sentences expressing norms) can be analysed into (a) a descriptive component—hereinafter also called ‘propositional content’—which is a description of an action or state of affairs resulting from an action, and (b) the normative operator. Where they differ is in how they view this latter, prescriptive component.3

5 The hyletic conception consists in regarding the normative operator

  • 4 Alchourrón and Bulygin (1984: 454). A footnote is omitted.

as a sign in a semantic capacity, so that it contributes to the semantic meaning of norm sentences, in which case a norm becomes the semantic meaning of a norm sentence, in much the same way in which a proposition can be said to be the meaning of a descriptive sentence.4

  • 5 Alchourrón and Bulygin (1981: 384).

Therefore, a descriptive proposition ‘p and a normative operator ‘O’ (for obligatory), ‘Ph’ (for prohibited) or ‘P’ (for permitted) both belong to the conceptual import of the norm.5

6 The expressive conception, on the other hand, takes the normative operator to be

  • 6 Alchourrón and Bulygin (1984: 454). A footnote is omitted.

a sign in a pragmatic capacity, that has no semantic meaning whatsoever and so does not form part of the conceptual import of a norm sentence.6

Norms, as such, are speech-acts and cannot be negated or combined by means of propositional connectives. For the purposes of the logical theory of systems of norms, the force of a norm shall thus be represented by the membership of its descriptive component in a set.

7 Relying on this set-theoretic approach introduced by Alchourrón and Bulygin (1981), an expressivist can account for conceptual distinctions between what is obligatory, prohibited and (strongly or weakly) permitted. This is what they say:

  • 7 Alchourrón and Bulygin (1981: 91). Square brackets are mine. The identification of the axiomatic ba (...)

‘It is obligatory that p in A’ is true if and only if p is a member of the [normative] system Cn(A)—that is, if and only if p belongs to the consequences of [the axiomatic basis of the system, also called the commanded set] A. This means that p is obligatory in A if and only if p has been [explicitly] commanded or p is a consequence of the propositions that have been commanded. In this last case we say that […] p is a derived obligation.7

8 Since the commanded set A is, by definition, a subset of the set Cn(A)

Def. 1

A ⊆ Cn(A)

their Expressivist (hereinafter: our Expressivist) can distinguish derived obligations from explicit ones by the fact that derived obligations figure only as members of the set Cn(A), whereas the explicit obligations figure as members of both sets, the axiomatic basis A and the normative system Cn(A). Although a norm can thus belong to both these two sets, the concept of derived norms and that of explicit norms are mutually exclusive:

Def. 2

p (OA(p) ⇔ p ∈ Cn(A))

Obligation (O). For every p, ‘It is obligatory in A that p’, if and only if p belongs to the set Cn(A).

Def. 3

p (OA(p) ⇔ pA)

Explicit obligation (O). For every p, ‘It is explicitly obligatory in A that p’ if and only if p belongs to the set A.

Def. 4

p (OA(p) p ∈ Cn(A) ∧ pA)

Derived obligation (O). For every p ‘It is implicitly obligatory in A that p’ if and only if p belongs to the set Cn(A), but not to its subset A.

9 In the same way, our Expressivist can define the concepts of prohibition and permission for normative propositions (or states of affairs).

  • 8 Alchourrón and Bulygin (1981: 392).

10 A proposition (or state of affairs) p is prohibited in A if and only if the negation of p (or, shortly, not-p) has been explicitly commanded or is a derived prohibition, that is a consequence of the propositions that have been commanded. To put the same in terms of sets again: “p is prohibited in A if and only if the negation of p (not-p) is a member of the [normative] system Cn(A)”,8 or of both the normative system Cn(A) and its axiomatic basis, the commanded set A.

11 Just as in the case of obligations, our Expressivist can thus distinguish derived prohibitions from explicit ones by the fact that derived prohibitions only figure as members of the set Cn(A), whereas explicit prohibitions figure as members of both sets, the axiomatic basis A and the normative system Cn(A):

Def. 5

p (PhA(p) ⇔ ¬p ∈ Cn(A))

Prohibition (Ph). For every p, ‘It is prohibited in A that p’ if and only if not-p belongs to the set Cn(A).

Def. 6

p (PhA(p) ⇔ ¬pA)

Explicit prohibition (Ph). For every p, ‘It is explicitly prohibited in A that p’ if and only if not-p belongs to the set A.

Def. 7

p (PhA(p) ⇔ ¬p ∈ Cn(A) ∧ ¬pA)

Derived prohibition (Ph). For every p, ‘It is implicitly prohibited in A that p’ if and only if not-p belongs to the set Cn(A), but not to its subset A.

  • 9 Alchourrón and Bulygin (1981: 392).

12 A proposition (or state of affairs) p is permitted in A if and only if the negation of p (shortly, not-p) has not been explicitly commanded and is not a derived prohibition, that is a consequence of the propositions that have been commanded. In terms of sets: p is permitted in A if and only if “the negation of p (not-p) is not a member of the [normative] system Cn(A)”.9 Here is a formula:

Def. 8

p (PA(p) ⇔ ¬p ∉ Cn(A))

Permission (P). For every p, ‘It is permitted in A that p’ if and only if not-p does not belong to the set Cn(A).

  • 10 Alchourrón and Bulying (1981: 393 ss and 406 ss).

13 This holds for both weak or negative permissions and strong or positive permissions (inasmuch as the sufficient conditions of the former are necessary conditions of the latter). But it does not let us distinguish between the two. So, how can the Expressivist of Alchourrón & Bulygin (1981) account for the difference between them? As we will now see, the authors faced this question directly.10

  • 11 Alchourrón and Bulygin (1981: 406).
  • 12 Moritz (1963) is the expressivist who explicitly admitted the act of permitting as a particular nor (...)
  • 13 For the act of rejection, see Alchourrón and Bulygin (1981: 394). For the act of permitting, see Al (...)

14 Say that Rex is to permit p by saying: “I hereby allow that p!” Our Expressivist can analyse this speech act in (at least) two ways.11 She can describe this act either (a) as the act of rejection of not-p or (b) as the act of permitting p. I will call the former an Ockhamite reduction and the latter a Moritzian analysis.12 In either case, the rejected or permitted content cannot be put in the commanded set A, and this for two obvious reasons:13 (i) on the one hand, we could not distinguish permitted states of affairs from the obligatory ones and the prohibited ones if we were to put all these contents together; (ii) on the other hand, we would do nothing but introduce contradictory propositions into the normative system.

  • 14 Alchourrón and Bulygin (1981: 398 and 408).

15 In order to avoid these problems, Alchourrón and Bulygin (1981) propose to form separate sets: the derogandum or the rejected set D in the first case, the permitted set P in the second.14

16 An expressivist allowing for the normative act of giving or granting permission—that is, a Moritzian expressivist—can distinguish the strongly permitted propositions or states of affairs from weakly permitted ones by the fact that only the former figure as members of the permitted set P:

Def. 9

p (PA(p) ⇔ pP)

Strong permission (P). For every p, ‘It is strongly permitted in A that p’ if and only if p is an element of the permitted set P.

Def. 10

p (PA(p) ⇔ ¬p ∉ Cn(A) ∧ pP)

Weak permission (P). For every p, ‘It is weakly permitted in A that p’ if and only if not-p does not belong to the set Cn(A) and p does not belong to the permitted set P.

17 On the alternative (Ockhamite) analysis of “I hereby allow that p!”, our Expressivist can distinguish the positively permitted propositions or states of affairs from negatively permitted ones by the fact that only the negations of the former figure as members of the derogandum or the set of the explicitly rejected propositions:

Def. 11

p (+PA(p) ⇔ ¬pD)

Positive permission (+P). For every p, ‘It is positively permitted in A that p’ if and only if not-p is an element of the rejected set D.

Def. 12

p (-PA(p) ⇔ ¬p ∉ Cn(A) ∧ ¬pD)

Negative permission (-P). For every p, ‘It is negatively permitted in A that p’ if and only if not-p belongs neither to the set Cn(A) nor to the rejected set D.

  • 15 Lat. Quod erat demonstrandum. (Eng. That which was to be demonstrated.)

18 That having been said, one can find all of the fundamental distinctions (explicit and derived obligations, explicit and derived prohibitions, strongly and weakly permitted states of affairs) in the expressive conceptions of norms. Q. E. D.15

3 Facultativity without Contradiction in the System

  • 16 Alchourrón and Bulygin (1981: 399).
  • 17 Alchourrón and Bulygin (1981: 407).

19The fact of working with separate sets (the commanded set A on the one hand and, on the other, the permitted set P and/or the derogandum D) saves us from having contradictions in the system in case there is some facultative state of affairs. This can be demonstrated by answering the following question: What effects does an act of rejection produce on the normative system Cn(A),16 and, alternatively,17 what happens with p as a result of its being permitted? — Let us play with two examples.

  • 18 See Alchourrón and Bulygin (1981: 396 and 399).

203.1. Suppose Rex is to say “I hereby allow you to smoke!” and that p stands for <you, smoking>. Now, we can describe this act of Rex as the act of rejection of not-p. This is an Ockhamite reduction. If not-p is not a member of the normative system Cn(A) (smoking has not been explicitly prohibited nor is the prohibition of smoking a consequence of other propositions that have been commanded), then the Cn(A) stays unchanged. However, if not-p were promulgated later, or if it were a consequence of some propositions commanded in the future, this fact would give rise to a ‘conflict of ambivalence’,18 which is a special case of what I would call a conflict of non-cotenability.

Def. 13

x (x ∈ Cn(A) ∧ xD)

Def. 14

Cn(A) D = { x | x ∈ Cn(A) x D } ≠ { ∅ }

Def. 15

Cn(A) \ D = { x | x ∈ Cn(A) ∧ xD } ≠ Cn(A)

Conflict of ambivalence (Cn(A), D). There is at least one x such that x belongs to the set Cn(A) and x belongs to the set D (def. 13). The intersection of Cn(A) with D is not an empty set (def. 14), the difference between Cn(A) and D–that is, the set of elements which belong to Cn(A) but not to D–is not equal to Cn(A) (def. 15).

  • 19 Alchourrón and Bulygin (1981: 397).

21 If we want a normative system capable of guiding behavior effectively, such a conflict needs to be resolved by the application of some rule of preference,19 just as it needs to be resolved when the explicitly rejected proposition is already a member of the normative system Cn(A).

22 If the explicitly rejected proposition not-p is a member of the normative system Cn(A)—that is, if smoking has been prohibited either explicitly or as a consequence of other explicitly commanded propositions before Rex uttered “I hereby allow you to smoke!”—then we have a conflict of ambivalence and need some rule of preference to resolve it. If it is resolved in favor of rejection, then the proposition not-p must be eliminated by subtraction from the commanded set A and from the normative system Cn(A). This subtraction henceforth makes the (normative) proposition OAp) false. If the conflict is resolved in favor of promulgation, then the proposition not-p must be subtracted from the rejected set D.

23 On the alternative (Moritzian) analysis of “I hereby allow you to smoke!”, we can describe this act of Rex as an act of permitting. The explicitly permitted proposition p is thus added to the permitted set P and another conflict of non-cotenability takes place (slightly different from the one of ambivalence):

Def. 16

x (x ∈ Cn(A) ∧ ¬xP)

Def. 17

Cn(A) { x | ¬x P } = { x | x Cn(A)¬x P } ≠ { ∅ }

Def. 18

{ x | x ∈ Cn(A) ∧ ¬xP } ≠ Cn(A)

Conflict of non-cotenability (Cn(A), P). There is at least one x such that x belongs to Cn(A) and not-x belongs to P (def. 16). The intersection of Cn(A) with the set of negations of the elements of P is not an empty set (def. 17). The set of elements of Cn(A) the negation of which do not belong to P–is not Cn(A) (def. 18).

  • 20 Alchourrón and Bulygin (1981: 408).

24 In order to resolve such a conflict, Alchourrón and Bulygin (1981) invite us to apply the rules of preference and subtract either p from the permitted set P—if the preference is given to prohibition—or the negation of p from A and Cn(A), if the preference is given to permission.20 In this respect, the permission of p gives rise to the same operation as the rejection of not-p.

  • 21 See Weinberger (1985: 173 s). Most recently, also Calzetta and Sardo (2014: § 2.1.1).

253.2. Suppose that Rex says also “I hereby allow you not to smoke!” To wit, there are two authoritative pronouncements: “I hereby allow you to smoke!” and “I hereby allow you not to smoke!” Following Weinberger (1985), some fear that this would bring about a contradiction in the normative system Cn(A).21 However, if we follow Alchourrón and Bulygin (1981) there is no reason for fear.

  • 22 Following Alchourrón and Bulygin (1981: 391), the normative system has been defined as Cn(A) supra (...)

26As a result of the second pronouncement of Rex, the Expressivist of Alchourrón and Bulygin (1981) will either add p to the derogandum D or not-p to the permitted set P. On the first analysis, you will now find in the derogandum D both not-p (because of the first normative act of Rex) and p (because of the second normative act of Rex); however, neither p nor not-p will be in the normative system Cn(A). On the second analysis, the permitted set P is composed of two elements: p and not-p, but again none of these two elements is part of the normative system Cn(A). In either way, the mere fact that both smoking and not smoking is permitted in the Commonwealth of Rex generates no contradiction in the normative system Cn(A) as described by our Expressivist.22 Q. E. D.

  • 23 See Redondo and Navarro (1990a: 251 and 254).

27Some may, however, be of the opinion that my response does not do the trick, because we still have p and not-p in the derogated set D. Redondo and Navarro (1990a) saw that as a problem some twenty years ago. Their argument (in different words) was this:23 From p and not-p anything follows, meaning that the set of all the logical consequences of D, say Cn(D), is all-inclusive. Consequently, everything must be eliminated by subtraction from the commanded set A and the normative system Cn(A). That would leave us with empty sets A and Cn(A), which is counter-intuitive and, at any rate, highly problematic.

  • 24 Alchourrón and Bulygin (1981: 399).
  • 25 See already Alchourrón and Bulygin (1979: 91–92).

28Indeed, the conclusion is sound but the reasoning went way too far in my opinion. The Expressivist of Alchourrón and Bulygin (1981) has no need to operate with Cn(D) as the set of all the logical consequences of D. In order to know what to eliminate from A and Cn(A), our Expressivist has to identify the “propositions and sets of propositions that imply some of the propositions belonging to [D]”.24 In other words: she needs to operate with propositions and sets of which the elements of D are a logical consequence, and not vice versa.25 The problem, therefore, does not exist.

29I know that, intuitively, some will find it hard to buy the claim that there is in general no need for our Expressivist to operate with Cn(D) or Cn(P). But I am unaware of any interesting challenge, and as long as they do not provide one, only few things can be added.

  • 26 See, at least, Alchourrón and Bulygin (1979: ch. 8), where formal representations of conditional no (...)

30One should think of two rejections, or of two permissions, that—by ways of logical inference—give rise to a third one. However, the examples of the kind usually provided by the skeptics are inadequate. (I conjecture this is because they are influenced by the Hyleticist worldview.)26 Suppose the following two rules are promulgated in the Commonwealth of Rex:

(R1) “If φ-ing is permitted, then ψ-ing is permitted.”

(R2) “φ-ing is permitted.”

31These two rules do give rise to:

(R3) ψ-ing is permitted.

  • 27 For the purpose of the present section, there is no need for a more detailed reconstruction of the (...)

But—unlike the Hyleticist—our Expressivist would analyze R1 as a command, and not as a permission. The propositional content of R1 (which is yet to be precised, but for the present purposes pretend it were: if p, then q) will, therefore, appear in the axiomatic basis A.27 The propositional content of R2 (that is, p) will appear in the permitted set P (or, in the Ockhamite alternative, its negation will appear in the derogandum D). The introduction of q in P (or the introduction of not-q in D) is thus not a logical consequence of two elements of P (or two elements of D); it is a logical consequence of an element of A and an element of P (or D). This example therefore cannot show the need to operate with Cn(P) or Cn(D) in order to explain the introduction of q in P (or that of not-q in D).

  • 28 See Alchourrón and Bulygin (1981: 395).

32 It is important to stress at this point that the introduction of a propositional content to a set, or its elimination thereof, is just a metaphor. If a content does not belong to a certain set, it never starts belonging to it. And if it belongs to a certain set, it never ceases to belong to it.28 What really happens is the performance of a normative speech act (commanding, rejecting; permitting if you will), which is an empirical fact. Each time a new fact occurs, we get new descriptions of the world in terms of sets. Thus in the course of time we have not one, but a sequence of sets (A1, A2, … An; Cn(A1), Cn(A2), … Cn(An); D1, D2, … Dn; P1, P2, … Pn). Following this proposal of Alchourrón and Bulygin (1981), a consecutive set A, D or P may always be defined in relation with the previous set of the same sort and the propositional content which is the object of the newly occurred speech act. If we use the signs ‘!’, ‘¡’ and ‘*’ to indicate the kind of normative speech act performed (command, rejection or permission), and ‘p’ for its propositional content, then we can represent as follows three (additional) axioms of the expressivist theory, which have not been explicitly formulated by the authors:

Axiom 1

p ((!p ⇒ (An = { p } An-1) ∧ (Dn = Dn-1) ∧ (Pn = Pn-1))

For every p, if p has just been commanded, then the new set An consists of p and all the elements of the previous set An-1, whereas the new sets Dn and Pn equal the previous sets D n-1 and P n-1, respectively.

Axiom 2

p (p ⇒ (Dn = { p } Dn-1) ∧ (An = An-1) ∧ (Pn = Pn-1))

For every p, if p has just been rejected, then the new set Dn consists of p and all the elements of the previous set Dn-1, whereas the new sets An and Pn equal the previous sets An-1 and Pn-1, respectively.

Axiom 3

p ((*p ⇒ (Pn = { p } Pn-1) ∧ (An = An-1) ∧ (Dn = Dn-1))

For every p, if p has just been permitted, then the new set Pn consists of p and all the elements of the previous set Pn-1, whereas the new sets An and Dn equal the previous sets An-1 and Dn-1, respectively.

  • 29 See supra the definition 1 in Section 2. See also Alchourrón and Bulygin (1981: 391).

33The normative system Cn(An), on the other hand, is just the set of all the logical consequences of An — exactly as it was explicitly defined by Alchourrón and Bulygin.29

4 The Propositional Content of Rules about Rules

34It is natural to consider rules of preference as meta-rules. The question, then, is how can our Expressivist represent the propositional content of such a meta-rule without semanticizing the indicators of illocutionary (normative) force of the object-rules (cf. Weinberger 1985: 175; Calzetta and Sardo 2014: § 2.2)? — An elegant solution is to represent the propositional content of a meta-rule as operating not on object-rules, but on sets containing the (explicit or implicit) propositional contents thereof. These sets are the commanded set An, the derogated set Dn, the permitted set Pn, and the normative system Cn(An).

  • 30 Following the terminology of Alchourrón and Bulygin (1981: 397), whose Expressivist distinguishes w (...)
  • 31 The representation works both for those expressivists who admit the existence of a special act of p (...)

35The propositional content, say w, of the rule of preference (!w) usually known as lex posterior priori derogat 30 could thus be represented (see def. 19) as a conjunction of conditionals to the effect that consecutive sets do not include those propositional contents of older norm sentences (or the consequences thereof) which in relation with the newer ones bring about some conflict:31




Def. 19


x [ (xDn-1xDn) ∨ (¬xPn-1 ∧ ¬xPn) ∧ (x ∈ Cn(An-1) ∧ x ∈ Cn(An)) ⇒ (Dn+1 = Dn) ∨ (Pn+1 = Pn) ∧ (Cn(An+1) = Cn(An) \ { x }) ∧ (An+1 = An \ { x }) ][ (xDn-1xDn) ∨ (¬xPn-1 ∧ ¬xPn) ∧ (x ∉ Cn(An-1) ∧ x ∈ Cn(An)) ⇒ (Dn+1 = (Dn \ { x })) ∨ (Pn+1 = (Pn \ { ¬x })) ∧ (Cn(An+1) = Cn(An)) ∧ (An+1 = An) ] [ (x ∉ Cn(An-1) ∧ x ∈ Cn(An)) ∧ (¬x ∈ Cn(An-1) ∧ ¬x ∈ Cn(An)) ⇒ (Cn(An+1) = (Cn(An) \ { ¬x }) ∧ (An+1 = (An \ { ¬x }))) ][ ((x ∈ Cn(An-1) ∧ x ∈ Cn(An)) ∧ (¬x ∉ Cn(An-1) ∧ (¬x ∈ Cn(An)) ⇒ (Cn(An+1) = (Cn(An) \ { x }) ∧ (An+1 = (An \ { x })) ]

The propositional content of lex posterior (w): For every x, if x has just been rejected (or not-x has just been permitted), while being a member of the normative system Cn(A), then the new sets A and Cn(A) are composed of all the elements of the previous ones, except x, whereas the new set D (or the new set P) equals the previous one;

and if x has just been commanded, while being a member of the set D (or not-x a member of the set P), then the new set D is composed of all the elements of the previous one, except x (or the new set P is composed of all the elements of the previous one, except not-x), whereas the new sets A and Cn(A) equal the previous ones;

and if x has just become a member of the normative system, while not-x is also a member of the normative system, then the new sets A and Cn(A) are composed of all the elements of the previous ones, except not-x;

and if not-x has just become a member of the normative system, while x is also a member of the normative system, then the new sets A and Cn(A) are composed of all the elements of the previous ones, except x.

36 When Rex issues !w, the proposition w becomes a member of the commanded set A. As we will see, this assures the preference of a posterior normative act (irrespective of whether it is a rejection or a promulgation, or even a permission if you accept the Moritzian variety of the expressive conception) over the anterior ones.

37 Take, for example, that Rex begins his rule with the system of his late King-father still in place in which there is one (and only one) prohibition (¬p):

(t1) “Thou shall not touch the property of the King!”

38 Rex thinks to himself: This is nice! I like being king and will rule just like my father. But I want to be able to change any rule! — Consulting with the crown lawyer, Rex decides to promulgate a rule of preference called lex posterior (!w):

(t2) “Lex posterior priori derogat!”

39 To see if the system really works as he wanted, Rex decides to introduce communism and proclaims ¡(¬p) or *p:

(t3) “What is mine is yours, dear brothers!”

40 This last decision does not really help either the economy of the Commonwealth of Rex or the social relations therein and so Rex soon decides to reestablish dominium plenum !(¬p):

(t4) “Thou shall not covet your neighbor’s house. You shall not covet your neighbor’s wife, or his manservant or maidservant, his ox or donkey, or anything that belongs to your neighbor!”

41 Of course, these translations of natural language expressions into p and not-p are oversimplified. But if the above-given formal representation of w is correct, we should be able to show what is important: first, that the legislative intervention ¡(¬p) at (t3) eliminated not-p from the normative system Cn(A); and, second, that the intervention !(¬p) at (t4) reintroduced not-p into the system Cn(A).

42 At (t1) we have the following sets:

(Ockhamite analysis) A1 = { ¬p }, D1 = { ∅ }

(Moritzian analysis) A1 = { ¬p }, D1 = { ∅ }, P1 = { ∅ }

Our normative system Cn(A1) contains all the logical consequences of not-p.

43 As a result of the first promulgation of Rex, !w at (t2), we get:

(Ockhamite analysis) A2 = { ¬p, w }, D2 = { ∅ }

(Moritzian analysis) A2 = { ¬p, w }, D2 = { ∅ }, P2 = { ∅ }

and the normative system Cn(A2) contains all the logical consequences of not-p and w.

44 The second lex of Rex at (t3) may be represented as ¡(¬p) or, alternatively, as *p. This legislative intervention brings about:

(Ockhamite analysis) A3 = { ¬p, w }, D3 = { ¬p }

(Moritzian analysis) A3 = { ¬p, w }, D3 = { ∅ }, P3 = { p }

  • 32 There is a conflict of ambivalence (Cn(A), D), when there is at least one x such that x belongs to (...)

and the normative system Cn(A3) with all the logical consequences of not-p and w. As you can see, we have a conflict of ambivalence toward p,32 for the intersection of Cn(A3) and D3, or the set of elements which belong both to Cn(A3) and D3, is { ¬p } and not an empty set.

45 I will make no more representations with the elements of P instead of D from now on, for if we manage to give a successful description of how rules of preference function, without admitting the existence of a special normative act of permitting, then we could certainly be successful in the other case (that is, of the Moritzian analysis) as well. That having been said, we can move on and demonstrate how the presence of w in the commanded set A actually resolves the conflict.

46 On the basis of w, the conflict is resolved in favor of permitted p, which gives us these sets:

(Ockhamite analysis) A4 = { w }, D4 = { ¬p }

and the normative system Cn(A4) with all the logical consequences of w and without not-p or its logical consequences.

47 Here is a formal proof for Cn(A4):











Proof 1









1. A2 = { ¬p } — Description of facts. —

2. A3 = { ¬p, w } — Description of facts. —

3. Ai ⊆ Cn(Ai) — Definition 1. —

4. ¬p ∈ Cn(A2) ∧ ¬p ∈ Cn(A3) — 1, 2; conjunction; 3. —

5. D2 = { ∅ } — Description of facts. —

6. D3 = { ¬p } — Description of facts. —

7. ¬p ∉ D2 ∧ ¬p ∈ D3 — 5, 6; conjunction. —

8. ∀x [ (x ∉ Dn-1 ∧ x ∈ Dn) ∨ (¬x ∉ Pn-1 ∧ ¬x ∈ Pn) ∧ (x ∈ Cn(An-1) ∧ x ∈ Cn(An)) ⇒ (Dn+1 = Dn) ∨ (Pn+1 = Pn) ∧ (Cn(An+1) = Cn(An) \ { x }) ∧ (An+1 = An \ { x }) ][ (x ∈ Dn-1 ∧ x ∈ Dn) ∨ (¬x ∈ Pn-1 ∧ ¬x ∈ Pn) ∧ (x ∉ Cn(An-1) ∧ x ∈ Cn(An)) ⇒ (Dn+1 = (Dn \ { x })) ∨ (Pn+1 = (Pn \ { ¬x })) ∧ (Cn(An+1) = Cn(An)) ∧ (An+1 = An) ] [ (x ∉ Cn(An-1) ∧ x ∈ Cn(An)) ∧ (¬x ∈ Cn(An-1) ∧ ¬x ∈ Cn(An)) ⇒ (Cn(An+1) = (Cn(An) \ { ¬x }) ∧ (An+1 = (An \ { ¬x }))) ][ ((x ∈ Cn(An-1) ∧ x ∈ Cn(An)) ∧ (¬x ∉ Cn(An-1) ∧ (¬x ∈ Cn(An)) ⇒ (Cn(An+1) = (Cn(An) \ { x }) ∧ (An+1 = (An \ { x })) ] 2; substitution of w by its definition 19. —

9. (¬p ∉ D2 ∧ ¬p ∈ D3) ∧ (¬p ∈ Cn(A2) ∧ ¬p ∈ Cn(A3)) ⇒ (Cn(A4) = (Cn(A3) \ { ¬p })) — 8; simplification, determination of the index (n = 3) and the variable (x = ¬p). —

.: Cn(A4) = (Cn(A3) \ { ¬p }) — 9, 7, 4; modus ponens.—

48 Formal proofs for A4 and D4 reiterate the one for Cn(A4) from steps 1 to 8; at this point, I skip the obvious step 9 to reach the conclusions (D4 = D3 = { ¬p }, and A4 = (A3 \ { ¬p }) = { w }) by modus ponens. The argument for the Morizian analysis (A4 = { w }, D4 = { ∅ }, P4 = { p }) is very similar and also simple.

49 As one may see, the presence of w in the commanded set A has the expected result: it assured priority to the second lex of Rex from (t3) as a posterior normative act over the prior lex of his King-father from (t1). We could go on to demonstrate that w assures the desired result also in the case of the subsequent legislative intervention of Rex at (t4), but that seems unnecessary—for now anyone can do it for themselves, by adopting (roughly) the same argument. This would show, first, that the promulgation of not-p at (t4) brings about a conflict of ambivalence; then, you would see that on the basis of lex posterior (w) the conflict is resolved in favor (this time) of the prohibition not-p—leaving us with sets:

(Ockhamite analysis) A6 = { w, ¬p }, D6 = { ∅ }

and the normative system Cn(A6) with all the logical consequences of w and not-p.

50 At the end we can thus conclude that our Expressivist can well describe the functioning of lex posterior without semanticizing the indicators of (normative) force. Q. E. D.

  • 33 Žarnić and Bašić (2014: § 2.2). See also Alchourrón and Bulygin (1981, 400).

51 In a comment to the manuscript of this paper, Žarnić and Bašić (2014: § 2.2) showed that the definition 19 of lex posterior works only for a limited number of special cases (such as our example) where the initial norm-set is independent, that is, where no member of the set is entailed by the rest. I happily concede their point and recognize my mistake. (Alchourrón and Bulygin themselves were much more careful than me in explaining the consequences of an act of rejection, as can be observed also from the citation accompanied by footnote 24 above.) — If x has just been rejected (or not-x has just been permitted), while being a member of the normative system Cn(A), then the operation of derogation results in new sets A and Cn(A) which are—differently from what has been stated in the definition 19—maximal subsets of the previous ones that do not entail x. This means that “the operation of derogation is subdetermined since, typically, there will be more than one maximal subset” of both A and Cn(A) not entailing x. In such cases, the norm-applier will be forced to choose between these maximal subsets—and play the norm-giver’s role. The representation of the operation therefore “needs an additional choice operator γ” to pick only one of them.33 But since the exact propositional content of lex posterior is not in the scope of this contribution, I will not amend the definition 19 as needed and will leave that for some later occasion (or to the interested reader, here and now).

  • 34 The third rule of preference, lex specialis, does not raise the concerns expressed by Weinberger (1 (...)

52 For the sake of the clarity of demonstration—and brevity—I have assumed that lex posterior is the only rule of preference in the Commonwealth of Rex. Nonetheless, I owe you at least a hint to the solution for the rule of preference lex superior derogat inferiori (!s):34 we shall assume that the promulgated and rejected (or permitted) contents go to different subsets of the sets A and D (or P)—for example, to Aa, Ab, Ac, etc.—depending on the hierarchical level (a, b, c, etc.) of the normative authority which performs the normative act in question. Making use of these subsets, one should be able to formulate the propositional content s of lex superior (!s) with no trouble.

53 We can now move on to deal with one final hurdle.

5 The Rule of Closure and Other Conditional Norms

54Before we conclude with a possible representation of conditional norms, we shall tackle the problem of the rule of closure.

  • 35 For discussion see at least Alchourrón and Bulygin (1971: ch. 7 and the references thereof).
  • 36 With one practically irrelevant exception of a normative system where it can be inferred that p is (...)
  • 37 See Calzetta and Sardo (2014: § 2.1.2).

555.1. It had often been discussed and is now widely acknowledged35 that the ‘permissive rule of closure’—namely, “what is not prohibited is permitted”—is the only closing rule that does not lead to inconsistencies in the normative system.36 Calzetta and Sardo (2014) raise this claim against the Ockhamite variety of the expressive conception which denies the existence of permissive norms (or acts of permitting).37 But the claim is false or, at best, inapplicable and misleading.

  • 38 Alchourrón and Bulygin (1981: 406).

56 It is one thing to say (a) that in order to preserve consistency, a normative system can be completed with a closing rule only if this rule is to the effect that what is not prohibited is permitted. It is quite another thing to say that (b) only a permissive rule of closure will have this permissive effect, character or normative function. Whereas (a) is true, but does not bite (the Ockhamite Expressivist also admits the existence of permitted states of affairs),38 (b) is false, for a rejection of prohibition of p has that same permissive function as a permission of p. Here is a test:

  • 39 In order to avoid the ambiguity of the expression ‘permissive rule of closure’—in which the adjecti (...)

57 Suppose that Rex decides to close the system of the Commonwealth and issues the following rule of permissive closure (!c):39

(t5) “What is not prohibited is permitted!”

58 The propositional content c, which thus becomes an element of A, could be formalized as follows:

Def. 20

xx ∉ Cn(An) ⇒ ¬x Dn+1)

Rule of permissive closure (c). For every x, if x is not prohibited—that is, if not-x does not belong to the normative system Cn(An)—then not-x belongs to the derogated set Dn+1.

59 Put in this form, !c achieves the exactly desired results of a permissive closure: (i) It has no (direct) effect on private addressees of norms; the introduction of such a closing rule does not affect deontic qualifications of individual conduct. (ii) By making p positively permitted, !c eliminates normative gaps and, therefore, judicial discretion in cases of p (relative to the normative system of A). (iii) As the addition of not-p to the derogated set D is conditional, future acts of explicit rejection do not lose their relevance, as we will shortly see, and (iv) may even be made by authorities subordinated to the one that promulgated c.

60 Please bear with the logical exercise for one final simulation, especially if you are skeptical about my claims sub (iii) and (iv). Otherwise, just skip the next four paragraphs.

  • 40 See supra the definition 20 in this section.
  • 41 For every p, ‘It is positively permitted in A that p’ if and only if not-p is an element of the rej (...)

61 Suppose that the axiomatic basis A1 is composed of constitutional norms { a, c, s, w } and that ¬x ∉ Cn(A1). Therefore, ¬xD2 on the basis of the (conditional) rule of permissive closure c (saying that if x is not prohibited in Cn(An), then not-x belongs to Dn+1).40 Moreover, A1 = A2 and ¬x ∉ Cn(A2). This means that x is positively permitted.41

  • 42 See supra the definition 19 in Section 4.

62 Now, imagine two different scenarios. On the first scenario, a town council issues b with the content (a ⇒ ¬x). As a consequence of !b, we get A3 = { a, b, c, s, w } and ¬x ∈ Cn(A3)—which brings about a conflict of ambivalence between Cn(A3) and D3 (= D2). On the basis of lex posterior (w),42 the conflict is resolved so that D4 = (D3 \ ¬x), whereas A4 = A3 and ¬x ∈ Cn(A4). In other words: x gets prohibited as a consequence of the town council provision b, even though it had been hitherto positively permitted on the basis of the conditional (constitutional) rule of permissive closure c. Note that lex superior (s) played no role in the resolution of our conflict of norms.

63 Now, think of another scenario in which not-x is rejected (unconditionally) by the legislator before the town council issues b. Consequently, ¬xD3, whereas A3 = A2 = A1 and ¬x ∉ Cn(A3). This, too, means that x is positively permitted. However, the consequences of the provision b issued later by the town council will be quite different in this case. The conflict of ambivalence will now be resolved on the basis of lex superior (s) and not on that of lex posterior (w). The preference will be given to the rejection of not-x. As a consequence, x will not be prohibited but will remain positively permitted.

64 The two simulations demonstrate: (iii) that future acts of explicit rejection do not lose their relevance under the rule of permissive closure c with the above given formalisation—just as they actually do not lose it in legal systems with permissive closure; and (iv) that future acts of explicit rejection may well be made by authorities subordinated to the one that promulgated c.

65 Here is not the place to discuss the four characteristics of a permissive closure just described. The point is elsewhere. We have shown that the permissive function of the closing rule to the effect that what is not prohibited is permitted may well be represented without granting the existence of a special illocutionary (normative) act of permitting. Q. E. D.

  • 43 The example is from Alchourrón and Bulygin (1979: ch. 8).

665.2. What is more, our Ockhamite Expressivist has already exposed by now all the necessary tools to reconstruct conditional norms, including this one:43

(R4) “If and only if it is raining, you ought not to leave the house!”

67Whereas the Hyleticist would represent R4 as a conditional imperative, our Expressivist shall make use of one further set—namely, F, the set of relevant facts and actions occurring in the context of application of the rule—to represent R4 as an imperative conditional or, more precisely, a command that the conditional proposition be made true:

(R4) in the Hyleticist representation

p ⇔ O¬r

(R4) in the Expressivist representation

!((p Fn) ⇔ (¬r An+1))

where p stands for <raining> and r for <leaving the house>.

  • 44 See Alchourrón and Bulygin (1979: ch. 8), whose tentative representation of conditional norms admit (...)
  • 45 The definitions have been introduced supra in Section 2 and will also be reported in the following (...)

68One may prefer the first representation or the second one for reasons of intellectual and other tastes. Yet as far as instrumental power is concerned, the Expressivist representation provides every expected result of R4: If it is raining (p), you have an explicit prohibition to leave the house. If it is not raining (not-p), you are negatively permitted (and thus not obliged) to leave the house.44 This can easily be verified, if we recall our definitions of explicit prohibition (def. 6) and of negative permission (def. 12).45

  • 46 For every x, ‘It is negatively permitted in A that x’ if and only if not-x belongs neither to the s (...)
  • 47 For every x, ‘It is explicitly prohibited in A that x’ if and only if not-x belongs to the set A. S (...)

69When R4 is issued, its propositional content enters the axiomatic basis An. For the sake of simplicity, suppose this is the only rule we have in the Commonwealth of Rex and that Dn is an empty set, whereas Cn(An) contains all the logical consequences of R4. Now, if it is not raining, leaving the house (r) is negatively permitted,46 since Dn remains an empty set and Cn(An) does not contain staying in the house (¬r). On the other hand, if it is raining, you are explicitly prohibited to leave the house,47 since ¬r belongs to An+1.

  • 48 See Weinberger (1985: 175 s). See also Alchourrón and Bulygin (1991: xxvii), but especially Caracci (...)

70This is how one could rebut the objection posed by Weinberger (1985 and 1986) and finally conceded even by Alchourrón and Bulygin (1991): namely, that Expressivist cannot give a satisfactory reconstruction of conditional norms.48

71If the Expressivist makes use of i) sequences of ii) separate sets (including the set F of relative facts and actions occurring in the context of application), and if she renders conditional norms not as conditional imperatives, but as iii) commands that conditionals be made true, then she can easily translate the Hyleticist representation of conditional terms (first column) into the Expressivist one (second column):

Def. 21

If p, then Oq ...

!((pFn) ⇒ (qAn+1))

Def. 22

If p, then Phq ...

!((pFn) ⇒ (¬qAn+1))

Def. 23

If p, then Pq ...

!((pFn) ⇒ (¬qDn+1))

  • 49 Indeed, for some, the very idea of a normative system is appealing only if it does not change toget (...)

72Admittedly, however, some will find the price is too high to be paid—for now our axiomatic basis and, therefore, our normative system changes along with the weather conditions and other factual circumstances over and above commands and derogations.49 But there are at least two ways to avoid the alleged problem (for those who care):

73a) From the general norm R4 (“If, and only if, it is raining, then you ought not to leave the house!”) and the fact p (it is raining), we want to obtain as a consequence the obligation to stay in the house. But this may be regarded as an individual obligation in a particular case at hand. The said obligation is derived from a general norm (or its propositional content) and a factual premise. Now, if we assume that such individual obligations are not part of the normative system itself, but are rather applications of its contents to factual circumstances, then we can preserve the normative system’s independence from the ever-changing facts: Instead of putting ¬r (or, staying in the house) in the axiomatic basis An+1, we shall simply put it in a separate set of individual obligations in a case at hand: say, In+1. R4 shall then be represented as !((p Fn) ⇔ (¬r In+1)). Accordingly, we shall also modify the above given definitions of what is obligatory, prohibited and permitted (def. 2 – def. 12); but that cannot undermine the claim that conditional norms may be adequately represented by Expressivists.

  • 50 See Žarnić and Bašić (2014: especially § 1.1 and § 2.1). Their references to John Broome, Lou Goble (...)

74b) Another way to avoid the alleged problem of an ever-changing normative system consists in identifying the normative system with the commanded set A and not with the set Cn(A) which includes all the logical consequences of the explicitly commanded propositions. One could thus stick with the initially proposed representation of conditional norms (def. 21 – def. 23) and with the idea that normative systems do not change together with factual circumstances different from the acts of promulgation and derogation. This solution is also in line with the objections Žarnić and Bašić (2014) raise against the usual definition of a normative system (with deductive closure) which I have adopted in this paper. I find their arguments convincing and although I will not repeat them here—since they do not go against the expressive conception as such—we can conclude by putting their (general) proposal in connection with our (special) issue of conditional norms: A norm-applier performs deduction from the general norm R4 (“If, and only if, it is raining, then you ought not to leave the house!”) and the fact p (it is raining), but there is “no deductively closed set Cn(A) that needs to precede or can result from the thus obtained determination of the deontic status of the state of affairs brought about by a norm-subject act or by forbearance” (Žarnić and Bašić 2014: § 2.1). The relation between R4 and the individual obligation (in the case of raining) or individual permission (in all other circumstances) concerns one’s reasoning with ought-statements. In other words, the rules of inference that make us derive implicit and/or individual norms from the explicit and general ones define the metanormative context for the norm-appliers and have no necessary connection with a normative systems itself.50 In this view, the issue of the ever-changing normative system disappears.

  • 51 I will not take positions on other issues here and will stop at indicating further readings. Althou (...)

75Of course, the expressive conception (and, in particular, its Moritzian variety) may have other flaws and even serious problems.51 But if the above demonstrations are correct, the Expressivist of Alchourrón and Bulygin (1981) can perfectly account for facultative states of affairs (§ 2) without introducing inconsistencies into the normative system Cn(A) (§ 3). She can successfully describe the propositional content of a meta-rule without semanticizing the indicator of (normative) force of the object-rules (§ 4). And she can give an account of a permissive closure—and of other conditional norms—even if she denies the conceptual autonomy of acts of permitting or, in different words, their irreducibility to other normative forms (§ 5).

Top of page

Bibliography

Josep AGUILÓ, 1995: Sobre la derogación. Ensayo de dinámica jurídica. Mexico: Fontamara (Biblioteca de ética, filosofía del Derecho y política; 41).
Carlos E. ALCHOURRÓN & Eugenio BULYGIN, 1971: Normative Systems. Wien/New York: Springer (Library of Exact Philosophy; 5).
Carlos E. ALCHOURRÓN & Eugenio BULYGIN, 1979: Sobre la existencia de las normas jurídicas. Valencia (Venezuela): Universidad de Carabobo. Page numbers in my text refer to the reprint in Mexico: Fontamara 1997.
Carlos E. ALCHOURRÓN & Eugenio BULYGIN, 1981: The Expressive Conception of Norms. In New Studies in Deontic Logic, ed. Risto Hilpinen, 95–124. Dordrecht: Reidel. Page numbers in my text refer to the reprint in Normativity and Norms, ed. Bonnie Litschewski-Paulson and Stanley Paulson, Chapter 21, 383–410. Oxford: Oxford University Press 1998.
Carlos E. ALCHOURRÓN & Eugenio BULYGIN, 1984: Pragmatic Foundations for a Logic of Norms. Rechtstheorie 15: 453–464.

Alejandro CALZETTA & Alessio SARDO, 2014: The Expressive Conception Revisited. (Under review.) In Spanish: Una nueva visita a la concepción expresiva de las normas. Doxa. Cuadernos de filosofía del Derecho 37.

Ricardo CARACCIOLO, 1993: Entrevista a Eugenio Bulygin. Doxa. Cuadernos de filosofía del Derecho 14: 499–513.
Ricardo CARACCIOLO, 1996: Esistenza di norme e di sistemi normativi. In Struttura e Dinamica dei Sistemi Giuridici, ed. Paolo Comanducci & Riccardo Guastini. Torino: Giappicheli Editore 1996. In Spanish: Existencia de normas. Isonomía. Revista de teoría y filosofía del Derecho 7: 159–178. Reprinted in Ricardo Caracciolo, El Derecho desde la filosofía. Madrid: Centro de estudios políticos y constitucionales 2009 (El Derecho y la Justícia).

Jordi FERRER BELTRÁN & Jorge Luis RODRÍGUEZ, 2011: Jerarquías normativas y dinámica de los sistemas jurídicos. Madrid: Marcial Pons (Filosofía y Derecho).

Manfred MORITZ, 1963: Permissive Sätze, Erlaubnissätze und deontische Logik. In Alf Ahlberg, Rolf Ekman et al., Philosophical Essays Dedicated to Gunnar Aspelin on the Occasion of His Sixty-fifth Birthday. Lund: Gleerups. 108–121.

Pablo E. NAVARRO & José Juan MORESO, 1992: Normas permisivas, sistemas jurídicos y clausura normativa. Un analisis de la evolución de las ideas de Carlos Alchourrón y Eugenio Bulygin. Theoría. Revista de Theoría, Historia y Fundamentos de la Ciencia. Segunda época. Vol. 7, Nos. 16-17-18, Tomo B: 1079–1100.
Pablo E. NAVARRO & María Cristina REDONDO, 1990a: Permisiones y actitudes normativas. Doxa. Cuadernos de filosofía del Derecho 7: 249–255.
Pablo E. NAVARRO & María Cristina REDONDO, 1990b: Derogations, Logical Indeterminacy and Legal Expressivism. Rechtstheorie 21: 233–239.

Kazimierz OPAŁEK & Jan WOLEŃSKI, 1986: On Weak and Strong Permissions Once More. Rechtstheorie 17: 83–88.
Kazimierz OPAŁEK & Jan WOLEŃSKI, 1987: Is, Ought, and Logic. Archiv für Rechts- und Sozialphilosophie LXXIII: 373–385.
Kazimierz OPAŁEK & Jan WOLEŃSKI, 1991: Normative Systems, Permissions, and Deontic Logic. Ratio Juris 4: 334–348.

Ota WEINBERGER, 1985: The Expressive Conception of Norms: An Impasse for the Logic of Norms. Law and Philosophy 4: 165–198. Reprinted in Normativity and Norms, ed. Bonnie Litschewski-Paulson & Stanley Paulson, 411–432. Oxford: Oxford University Press 1998.
Ota WEINBERGER, 1986: Der normenlogische Skeptizismus. Rechtstheorie 17: 13–81.
Jan WOLEŃSKI, 1972: Logiczne problemy wykładni prawa. Krakow.

Berislav ŽARNIĆ & Gabriela BAŠIĆ, 2014: Metanormative Principles and Norm Governed Social Interaction. Revus. Journal for Constitutional Theory and Philosophy of Law (2014) 22: 105–120.

Top of page

Notes

1 Alchourrón and Bulygin (1981: 389).

2 Contra: Weinberger (1985 and 1986). Navarro and Redondo (1990a and 1990b). Calzetta and Sardo (2014). But even Alchourrón and Bulygin (1991: xxvii), who conceded one major point to Weinberger: the Expressivist’s inability to give a satisfactoriy reconstruction of conditional norms. See also Caracciolo (1993: 507). I pressume that the reader is familiar with the notations of classical logic and axiomatic set theory. The notations in this paper follow the ISO standard 31-11 (with the addition of ‘⇔’ for the biconditional connective). We will assume all the usual inventory of classical logic and axiomatic set theory (if not stated otherwise), plus three axioms which will be introduced later on.

3 See Alchourrón and Bulygin (1981: 384–385; and 1984: 454).

4 Alchourrón and Bulygin (1984: 454). A footnote is omitted.

5 Alchourrón and Bulygin (1981: 384).

6 Alchourrón and Bulygin (1984: 454). A footnote is omitted.

7 Alchourrón and Bulygin (1981: 91). Square brackets are mine. The identification of the axiomatic basis of the system with the set A, and the normative system with the set Cn(A) is made on the same page.

8 Alchourrón and Bulygin (1981: 392).

9 Alchourrón and Bulygin (1981: 392).

10 Alchourrón and Bulying (1981: 393 ss and 406 ss).

11 Alchourrón and Bulygin (1981: 406).

12 Moritz (1963) is the expressivist who explicitly admitted the act of permitting as a particular normative speech act different in nature from that of commanding. Consequently, he also admitted two types of norms: imperative norms (establishing obligations and prohibitions) and permissive norms (conferring power and permissions). Ockham’s name, on the other hand, is employed here to allude to the principle of parsimony used in problem-solving (also known as Ockham’s razor).

13 For the act of rejection, see Alchourrón and Bulygin (1981: 394). For the act of permitting, see Alchourrón and Bulygin (1981: 408).

14 Alchourrón and Bulygin (1981: 398 and 408).

15 Lat. Quod erat demonstrandum. (Eng. That which was to be demonstrated.)

16 Alchourrón and Bulygin (1981: 399).

17 Alchourrón and Bulygin (1981: 407).

18 See Alchourrón and Bulygin (1981: 396 and 399).

19 Alchourrón and Bulygin (1981: 397).

20 Alchourrón and Bulygin (1981: 408).

21 See Weinberger (1985: 173 s). Most recently, also Calzetta and Sardo (2014: § 2.1.1).

22 Following Alchourrón and Bulygin (1981: 391), the normative system has been defined as Cn(A) supra in Section 2.

23 See Redondo and Navarro (1990a: 251 and 254).

24 Alchourrón and Bulygin (1981: 399).

25 See already Alchourrón and Bulygin (1979: 91–92).

26 See, at least, Alchourrón and Bulygin (1979: ch. 8), where formal representations of conditional norms in the expressive conception are clearly put in the Hyleticist key: If p, then [commanded] q. We will face this problem infra in Section 5.

27 For the purpose of the present section, there is no need for a more detailed reconstruction of the propositional content of conditional norms. As announced above, I will return to this point later.

28 See Alchourrón and Bulygin (1981: 395).

29 See supra the definition 1 in Section 2. See also Alchourrón and Bulygin (1981: 391).

30 Following the terminology of Alchourrón and Bulygin (1981: 397), whose Expressivist distinguishes what they call lex posterior from what they call auctoritas posterior, this rule would correspond to lex posterior & auctoritas posterior. I decided to give a unitary formal presentation for the sake of simplicity, though the two rules might easily be separated.

31 The representation works both for those expressivists who admit the existence of a special act of permitting and for those who do not. In case of the latter, the set Pn will simply be an empty set.

32 There is a conflict of ambivalence (Cn(A), D), when there is at least one x such that x belongs to the set Cn(A) and x belongs to the set D. The intersection of Cn(A) with D is thus not an empty set. See supra the definitions 13 and 14 in Section 3.1.

33 Žarnić and Bašić (2014: § 2.2). See also Alchourrón and Bulygin (1981, 400).

34 The third rule of preference, lex specialis, does not raise the concerns expressed by Weinberger (1985) and Calzetta and Sardo (2014). See also Alchourrón and Bulygin (1979: 86).

35 For discussion see at least Alchourrón and Bulygin (1971: ch. 7 and the references thereof).

36 With one practically irrelevant exception of a normative system where it can be inferred that p is not facultative (¬Ip = ¬(Pp ∧ P¬p)). “As p is not forbidden, we may infer by means of the [permissive] rule of closure that p is permitted. But as ¬p is not forbidden either, the permission of ¬p may also be inferred. However, the joint permission of p and ¬p is incompatible with ¬[I]p, so that the [permissive] rule of closure has introduced an inconsistency.” Alchourrón and Bulygin (1971: 140, n. 4).

37 See Calzetta and Sardo (2014: § 2.1.2).

38 Alchourrón and Bulygin (1981: 406).

39 In order to avoid the ambiguity of the expression ‘permissive rule of closure’—in which the adjective ‘permissive’ may be used to specify the function of the rule, the form of the rule, or both—, I choose to use the term in question only in the second sense (fixing the reference to the form), and express the first sense (that of the function) with the ‘rule of permissive closure.’

40 See supra the definition 20 in this section.

41 For every p, ‘It is positively permitted in A that p’ if and only if not-p is an element of the rejected set D. See supra the definition 11 in Section 2.

42 See supra the definition 19 in Section 4.

43 The example is from Alchourrón and Bulygin (1979: ch. 8).

44 See Alchourrón and Bulygin (1979: ch. 8), whose tentative representation of conditional norms admittedly fails to meet this challenge.

45 The definitions have been introduced supra in Section 2 and will also be reported in the following paragraph.

46 For every x, ‘It is negatively permitted in A that x’ if and only if not-x belongs neither to the set Cn(A) nor to the rejected set D. See supra the definition 12 in Section 2.

47 For every x, ‘It is explicitly prohibited in A that x’ if and only if not-x belongs to the set A. See supra the definition 6 in Section 2.

48 See Weinberger (1985: 175 s). See also Alchourrón and Bulygin (1991: xxvii), but especially Caracciolo (1993: 507).

49 Indeed, for some, the very idea of a normative system is appealing only if it does not change together with factual circumstances different from the acts of norm-promulgation and norm-derogation. I shall thank Moreso (private conversation) for bringing up this issue.

50 See Žarnić and Bašić (2014: especially § 1.1 and § 2.1). Their references to John Broome, Lou Goble, and Jürgen Habermas are here omitted.

51 I will not take positions on other issues here and will stop at indicating further readings. Although already mentioned, Weinberger (1985 and 1986) is the best starting point, as it dwells on various issues not touched upon in this paper. The argument of Opałek and Woleński (1986, 1987 and 1991) goes against the Expressivist treatment of permissions. Navarro and Redondo (1990b: 238 s) point out some questions related to the configuration of the rejected set (with its subsets) as lacking a clear answer in the works of Alchourrón and Bulygin. Moreso and Navarro (1992: 1089) purport to identify an ambiguity of positive permission. Aguiló (1995: 59 ss and 63 ss) invokes a problem with derogations for reasons of incompatibility. Caracciolo (1996: nn. 15, 25 and 31) raises the issue of identifying the normative system of the expressive conception with the law. Finally, see also Ferrer Beltrán & Rodríguez (2011: ch. 1), claiming that there are two different conceptions of meaning, and not of norms.

Top of page

References

Bibliographical reference

Andrej Kristan, « In Defence of the Expressive Conception of Norms », Revus, 22 | 2014, 151-172.

Electronic reference

Andrej Kristan, « In Defence of the Expressive Conception of Norms », Revus [Online], 22 | 2014, Online since 14 November 2014, connection on 25 June 2017. URL : http://revus.revues.org/2883 ; DOI : 10.4000/revus.2883

Top of page

About the author

Andrej Kristan

Research fellow (Ital. assegnista di ricerca) and doctoral candidate at Tarello Institute for Legal Philosophy, University of Genoa (Italy). Lecturer (Span. profesor asociado) at the University of Girona (Spain).

 Andrej Kristan
Tarello Institute for Legal Philosophy
Via Balbi 30/18
16126 Genoa
Italy

E-mail: andrej.kristan@gmail.com

By this author

Top of page

Copyright

All rights reserved

Top of page
  • Revues.org