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Discussion with Eugenio Bulygin

Let’s talk about antinomies

Normative systems reloaded
Alessio Sardo

Abstract

The author proposes new arguments in favor of Alchourrón and Bulygin’s theory presented in Normative Systems (1971), by showing how even paradigmatic examples of instantiation conflicts can be reframed as antinomies between general cases. He proceeds as follows. After a brief reconstruction of Alchourrón and Bulygin’s analysis of normative conflicts, he introduces the notion of instantiation conflict and shows how authors such as Riccardo Guastini, Jorge Rodríguez, Pablo Navarro and others rely on that notion for pointing out the existence of a “special” category of normative conflicts, which are necessarily bound to individual, actual cases and, therefore, fall out of the scope of Alchourrón and Bulygin’s analysis. The author maintains that, should they be right, several fundamental assumptions of Alchourrón and Bulygin’s theory might be seriously questioned. Against this background he argues that a reductionist approach is feasible and closes the paper by trying to save one of the main intuitions that inspired the instantiation conflicts argument.

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1 Introduction

  • 1 I am grateful to an anonymous referee of this journal for the following clarification: the logical (...)
  • 2 Alchourrón and Bulygin 1971: 49. The present investigation shall be limited to the analysis of norm (...)
  • 3 On the concept of empowerment see Paulson (1988; 1998: xlix; 2013). On the use of this concept made (...)
  • 4 See Paulson 1998: xi; 2000; 2012 and Grabowski 2013 for a discussion on the relations between posit (...)

1 Carlos E. Alchourrón and Eugenio Bulygin’s Normative Systems (from now on ‘NS’) is generally considered as one of the most groundbreaking books in legal theory, and as a major contribution to the early development of deontic logic. In this 1970’s classic, Alchourrón and Bulygin built up a complex theory that can be used to analyze both ideal and real law-application methods. The main intuition behind NS is that any legal, case-solving process consists in establishing the deontic status of a certain action, which is relative to a given universe of discourse (UD), according to the normative propositions that describe the legal system under consideration. The inference from general norms to effective individual requirements does not presuppose any sort of volitional act.1 Each ensemble of rough, normative materials can be, in principle, reshaped as a closed, deductive system.2 Generally speaking, judges and other decision-makers, by dealing with small portions of the whole system (i.e. micro-systems), take part in the law-creation process. When legislators (namely, empowered authorities)3 did not provide any clear solution, judges must find the correct answer on their own. Any legal order, taken as a whole, is a sequence of interlocking systems, connected by a specific, positivistic relation of identity qua membership.4

  • 5 Alchourrón and Bulygin 1971: ch. 1–3; Appendix.
  • 6 Hilpinen 2015: 23 ff.
  • 7 Although someone might have the impression that Alchourrón and Bulygin were not entirely aware, at (...)
  • 8 Alchourrón and Bulygin 1971: ch. 4. See also Barberis 1997: 33 ff.
  • 9 Alchourrón and Bulygin 1971: ch. 4 § 7. See also Mazzarese 1991.

2 NS contains a formal language that can be used to represent legal and, more broadly, normative reasoning. Roughly speaking, the meta-language of NS can be described as a non-conservative expansion of standard, model-theoretic first order logic, which includes: syntactic variables (x, y, z…) and constants (p, q, r…) for the individuals of the object-language, variables for sets of individuals (α, β, γ…) monadic and dyadic sentential connectives (biconditional ‘⇔’, conditional ‘⇒’, negation ‘¬’, conjunction ‘∧’), symbols for the classes-calculus (inclusion ‘⊆’, membership ‘∈’…). These elements are combined with deontic modalities (‘O’ obligatory, ‘P’ permitted, ‘Ph’ Prohibited) to generate well-formed formulae.5 Norms are conceived as “hyletic” proposition-like entities, structured as conditional statements.6 Deontic modalities are embedded in the consequent of the conditional statement, whereas the antecedent contains a partial state description of an action-type: a “generic case”, in NS-jargon. Using a well-established metaphor, we can say that norms set up a “bridge” connection between (relevant) generic cases and deontic modalities.7 Alchourrón and Bulygin designed their model under the influence of von Wright, but relying, on the one hand, on a Tarskian8 approach in semantics and, on the other, on a Kelsenian9 conception of the static/dynamic structure of the normative dimension.

  • 10 See also Barberis 2016 and 2017 for a discussion over the limitation of a traditional positivist ac (...)

3 In this essay, I will not explore in details the core of Alchourrón and Bulygin’s book-wide project, for it would be too ambitious. I will not even try to discuss the host of problems raised by this approach, which have already been analyzed by Mauro Barberis (1997).10 The aim of the present contribution is much more modest: I will set my focus to normative conflicts. I would like to invite attention to this topic because, despite their great theoretical importance, normative conflicts seem to occupy only peripheral positions in NS, and receive but a rushed overview. More specifically, as I will argue, NS does not counter the challenge raised by the existence of instantiation conflicts, which represents a serious danger for NS, insofar as it supports the claim that some “special” cases of antinomy cannot be reduced to conflicts between generic cases. NS, instead, assumes that every antinomy, by definition, is a conflict between general cases: accordingly, every antinomy stems from an inconsistent deontic modalization of two identical or overlapping general cases. In my essay I will propose new arguments in favor of NS, by showing how even paradigmatic examples of instantiation conflicts can be reframed as antinomies between general cases. I will defend the approach of NS as follows:

  • 11 In the present essay, I will use “antinomies” and “normative conflicts” as synonyms. On the notion (...)
  • 12 Alchourrón and Bulygin 1971: ch. 7.

4 Right after providing a brief reconstruction of NS’s analysis of normative conflicts, I shall introduce the notion of instantiation conflict.11 Then, I will show how authors such as Riccardo Guastini, Jorge Rodríguez, Pablo Navarro and others rely on this notion for pointing out the existence of a “special” category of normative conflicts, which are necessarily bound to individual, actual cases and, therefore, fall out of the scope of NS-model. Although these authors are very cautious in deriving dramatic implications from their argument, I will maintain that, should they be right, several fundamental assumptions of NS might be seriously questioned. This list includes the claim that legal systems correspond to sets of abstract entities, closed under the notion of logical consequence,12 and that a sharp line separates norms from facts (a version of the well-known “Hume’s guillotine”).

  • 13 Actually, the conceptual connection requirement plays a key-role for the reduction strategy, insofa (...)

5 Next, in opposition to Rodríguez, Navarro and Guastini, I will argue that a reductionist approach is feasible. As Giovanni Battista Ratti demonstrated a couple of years ago, there are compelling reasons for denying that so-called conflicts of instantiation display special logical properties, and that they necessarily arise from the facts of an actual, individual case. If we accept antecedent strengthening, every example of instantiation conflict proposed in the lively debate over antinomies can be effectively reframed as a conflict between generic cases. I will then add some fuel to Ratti’s demonstration, by exploring the idea of a conceptual connection between two apparently unrelated norms.13

  • 14 Kahneman 2013.

6 Finally, notwithstanding my objection, I will try to save one of the main intuitions that inspired the instantiation conflicts argument. Under my view, this argument, albeit incorrect, could be considered as an attempt to do justice to some reasonable intuition about our perception of normative conflicts. Those cases generally regarded as instantiation conflicts do not display any peculiar, logical structure, or feature, that confines them to the dimension of individual cases. Nevertheless, in such cases, the identification of a normative conflict seems to be a difficult task. This difficulty does not arise from the fact that certain properties have to be instantiated in order to generate a contingent normative conflict. Rather, the problem is related to the fact that the conflict is not made immediately evident by the lexical “surface” of the normative sentences under evaluation. Under uncertain circumstances, the interpreter must think slow,14 and get involved in a less intuitive kind of reasoning in order to ascertain the presence of a conflict. This amounts to say that, for some, we might say “hard”, cases, the antinomy-detection process demands a cognitive load which is much heavier than the one normally required by “easy”, stereotypical, highly intuitive cases. The instantiation conflicts argument offers a mistaken response to this reasonable intuition.

7 To come full circle, I will suggest that so-called conflicts of instantiation offer precisely good examples of “hard” cases of antinomies, which, by definition, involve generic cases, and require a heavy cognitive load by the interpreter. In this way I will move, of course, from logics to cognition.

2 Conflicts of instantiation: there is a gap in Normative Systems

8 NS considers normative conflicts as common defects of real normative systems, along with normative gaps (the system is incomplete), and conditions of redundancy (the same solution occurs more than once). From the positivistic perspective of NS, ideal systems are consistent, non-redundant and complete. A normative conflict is described as a special case of inconsistency: we face a normative conflict only if the system ascribes incompatible solutions to the same general case (for instance: smoking in general), or to overlapping general cases (for instance: abortion and therapeutic abortion) which belong to a given Universe of Cases.

  • 15 Alchourrón and Bulygin 1971: ch. 4, § 6.
  • 16 This consideration is very important for a deep understanding of the difference between internal an (...)
  • 17 Rodríguez 1995: 364 ff. deals with this problem.
  • 18 Alchourrón and Bulygin 1971: Appendix: (D20) ‘Coh (UCi, USmax) [ = Coh (UPi, UAj)] = {(UCi  USmaxj(...)

9 NS contains several important considerations about some theoretical and practical problems related to normative conflicts.15 First of all, NS points out that normative incompatibilities are not directly brought about by the fact that the contents of two norms (‘p ∧ ¬p’) are inconsistent: this holds for obligations (‘Op ∧ O¬p’) and prohibitions (‘Php ∧ Ph¬p’), but certainly does not apply to permissions (‘Pp ∧ P¬p’). Accordingly, any normative conflict comes from the interplay of the content variable and the deontic-operator.16 To put it in slightly different terms, we might say that two opposite contents are not necessarily inconsistency transmitting:17 the existence of a normative conflict is not simply the outcome of two contradictory contents, taken in conjunction, for it is always necessary to consider the role played by deontic modalizations. Second, NS weakens the notion of antinomy, by stipulating that normative inconsistencies are necessarily relative to a certain universe of cases (UCi), and that a normative set is complete and coherent with respect to a certain universe of cases (UCi), and to a certain universe of maximal solutions (USmaxi), only if the relation R between the normative set , the universe of case UCi and the universe of maximal solutions (USmaxj) is a function whose domain is UCi. Third, NS contains a formal definition of consistency.18

  • 19 The same consideration holds for analysis of two related topics: normative relevance and axiologica (...)
  • 20 Von Wright 1963: 148.
  • 21 Quine 1966: 5.
  • 22 There are several ways out: one is the rejection of ex falso quodlibet; the rejection of bivalence (...)

10 Apart from these fundamental considerations, NS does not say much more on this topic. Actually, we notice that, whereas the analysis of legal gaps offered by Alchourrón and Bulygin is very extensive and detailed, normative conflicts receive but a quick overview.19 This choice is surprising: as von Wright,20 Quine,21 and many other prominent analytic philosophers stressed, normative contradictions are one of the most serious problems in deontic logic, both from a practical and theoretical perspective. This becomes especially true if we assume the validity of ex falso quodlibet principle, which basically licenses the derivation of any proposition whatsoever from two contradictory contents, leading to the implosion of a system.22 All this deserves close attention and, just in this case, NS seems to play fast and loose.

  • 23 To be sure, Alchourrón and Bulygin 1989: 673 ff. deals with this issue. On this point see also Nava (...)
  • 24 Guastini 2011: 105 ff.
  • 25 Even though Alchourrón and Bulygin maintain that a new interpretation determines a change of the no (...)

11Among the other things, NS does not offer any explanation of how two non-cognitive (namely, non-truth conditional) propositional-like entities, such as ‘Op’ and ‘O ¬p’, bring about a genuine contradiction, or inconsistency. Is it really possible to have inconsistencies between obligations, if we assume that they do not belong to the domain of cognition and truth, just like intentions, wishes, and desires don’t? If so, how could we define ‘contradiction’ and ‘inconsistency’ without bringing back into play the concept of truth? To be sure, NS doesn’t even mention this philosophical puzzle, let alone offer a specific solution.23 Second, Alchourrón and Bulygin seem to overshadow the fact that antinomies are created through interpretation, and that they can also be avoided through interpretation.24 This detail is very important for applying their model to real, and not just to ideal, legal orders: if the model does not envisage the fact that antinomies are produced by interpretive acts it loses explicative power and opens the road to the mistaken assumption that normative conflicts are determined by the compositional or literal content of the normative statements, whereas normative conflicts are determined by the contextual content of those statement. Contextual content is incrementally determined by the interplay of literal meaning and background information: it can express a variety of proposition, or propositional-like entities, by varying background assumptions.25

  • 26 On the importance of individual case in the hermeneutic tradition see Carlizzi 2011.

12 Leaving aside these quandaries, we can consider that the most striking “gap” in Alchourrón and Bulygin’s analysis seems to be the lack of attention towards those problems related to the notion of instantiation conflict, which is entirely kept under wraps. The two authors assume straightforwardly both that normative conflicts are entirely confined within the level of general cases, and that it is possible to analyze antinomies using a conservative expansion of a basic system of first-order model theoretic logic. As we shall see, both assumptions are far from being uncontroversial. Now, the question is: were Alchourron and Bulygin right in making this assumption? This dilemma brings us to the main topic of the present essay. In the next paragraphs I shall explain why, according to my view, they made the right choice, and why we should be unconvinced by the instantiation conflict’s argument. Before offering a line of argument that justifies these considerations, I shall present briefly the distinction between generic cases and individual cases, which plays here the pivotal role: as hinted before, NS assumes that antinomies are always conflicts between general cases; on the contrary, the argument from instantiation conflicts is aimed at showing that some antinomies are necessarily conflict between individual cases.26

  • 27 Strawson 1969: 226 ff.; Lowe 1995: 512.
  • 28 Quine 1947.
  • 29 Lewis 1983: 344.
  • 30 Armstrong 1997.
  • 31 Lewis 1983: 344.

13 General cases are thought to have a so-called in abstracto dimension, for they are independent from actual and individual objects, actions, events or circumstances; individual cases, on their turn, belong to the in concreto dimension, for they correspond to actual and individual, objects, actions, events, or circumstances. This opposition very much resembles the distinction between universals, or ‘the ways things are’, and particulars, or ‘ways it is’.27 According to Russell (1911), properties (or “qualities”) are grouped together as universals, whereas individuals are particulars.28 General cases are made of properties, and properties stand for classes: the property of being a ‘farmer’ is the class of all ‘farmers’; not only the actual farmers of the world we live in, but also the unactualized farmers of other possible worlds.29 Objects instantiate properties, in the sense that they exemplify them: ‘tractor’ qua property characterizes all individual tractors, either actualized or not. When actualized objects exemplify properties, they generate state of affairs.30 Abstract entities, instead, encode set(s) of properties, without instantiating them. According to a common view, properties include relations, understood as arbitrary classes of ordered n-tuples of things (pairs, triples, and so on).31

  • 32 Ramsey 1925: 401 ff.
  • 33 Lowe 1995: 518.

14 We can thus conclude that general cases correspond to abstract sets of properties, while individual cases correspond to particulars, understood as the relevant facts or state of affairs that should be regulated by the law. Taking it forward, we might want to say that, from a psychological perspective, general cases correspond to concepts, whereas individual cases to percepts the objects of two different mental acts. From a physical perspective, instead, we observe that particulars correspond to individual objects, or entities, being thought of as existing in a concrete time and space, whereas non-particulars are abstract entities, to whom we ascribe a non-spatiotemporal nature; they can be thought independently from some other particular entity.32 According to Lowe, particulars can be defined in terms of instantiation:33

A particular is something (not necessarily an object) that instantiates but is not itself instantiated. Universals, on the other hand, necessarily have instances (or, at least, are instantiable). Thus I think of universals as Kinds.

  • 34 Russell 1948: Part IV, ch. 8.
  • 35 Von Wright 1963: ch. III postulates an analogous distinction, although expressing in terms of indiv (...)

15 An instantiation holds when a property is a constituent part of (or is present in) a particular thing: items instantiate properties when they bear, or possess, a property34. Actually, “to instantiate” basically means to create an instance by defining one particular variation of object within a class, name this variation, and locating it in some physical and temporal space. So, for instance, the prohibition of sexual harassment established by the Italian criminal law (art. 660 c.p.) regulates a general, abstract case, whereas the individual prescription that obliges Mr. Hugo to pay punitive damages for a breach of a contract previously stipulated with the x-Society, issued by a judge in flesh and bones, regulates an individual case. As hinted before, an individual case is a concrete event, which essentially possesses spatiotemporal properties and relations.35 Anyone, unaided by a legal theorist, can see the difference between some prohibited generic action of a penal code, and the concrete, real object of a lawsuit brought before courts. We might intuit offhand that the latter is a real, independent entity or event, whereas the former is essentially a property (or, better, a set of properties), which can be predicated of a whole class of x-cases. Accordingly, generic cases collect together sets of propositions: they collect at least one proposition for each atomic entity that can be used to fill the variable x; or, if you prefer, they collect together all the propositions where the property, or set of properties, might occur. Propositions about general cases are explicitly presupposed by propositions about individual cases, but they are not acquainted either with the atomic propositions that describe the facts of an individual case, or the proposition-like entities that ascribe normative qualifications to them. Rather, they can be viewed merely as schematic representations (call them generalizations, if you wish) depicting patterns that belong to classes of individual cases, which can be considered extensionally alike.

16

  • 36 Guastini 2011: 205 ss.
  • 37 Rodríguez 2002.

17 Now, according to no less authority than Riccardo Guastini,36 Jorge Rodríguez and Pablo Navarro,37 conflicts of instantiation correspond to special kinds of antinomies, which arise only when certain factual circumstances occur. To put it in a more technical jargon, they arise only if a certain, specific property is instantiated (i.e. exemplified) in a further complex entity or state of affairs. Under their view, conflicts of instantiation cannot be reduced to antinomies in a narrow sense (that is, in abstracto), such as ‘p ⇒ Oq p ⇒ O ¬q’. instantiation conflicts transcend the in abstracto dimension, for they appear only if we reach the level of individual cases. In other words, these “special” antinomies cannot be detected by looking at the system, without taking into account also the facts of an individual case. Let us now explore the argument in greater detail.

  • 38 I prefer to use “normative sentence-type” rather than “normative formulation” because the latter de (...)

18 A first example of instantiation conflict — call it ‘the tractor case’ — is given by the following two sentence-types:38

(NST1)

“Vehicles are not allowed to enter in this area.”

(NST2)

“Agricultural machineries are allowed to enter in this area.”

19 Following the symbolism proposed by NS, endorsed also by the proponents of the argument from instantiation conflict, a possible formalization of the norms expressed by NST1 and NST2, respectively, is the following:

(N1)

p ⇒ Phs

(N2)

q ⇒ Ps

  • 39 Navarro and Rodríguez 2014: 179.

where p represents the “fact of being a vehicle”, q represents “the fact of being agricultural machinery”, ‘P’ stands for ‘permitted’, ‘Ph’ stands for ‘prohibited’, and, finally, ‘s’ stands for the action of ‘entering this area’. We use ‘⇒’ as a symbol for material implication. If we look at these formulae, we get the impression that the two norms are not contradictory at all, for they display different antecedents.39 However, this conclusion seems to be false because, according to our semantic intuitions, the proposition-like contents of NST1 and NST2 produce a normative conflict if, under specific circumstances, there is a real, individual entity ‘a’ that instantiates both the property of being a vehicle, and the property of being an agricultural machinery. Consequently, the entity ‘a’ is both permitted and prohibited to get into this area. Now, if this is correct, NS-apparatus seems to be missing something. According to the instantiation conflicts argument, what NS lacks is the following element: in such a case, the antinomy appears only when we come to decide about an actual, individual case (namely, an in concreto case). For instance, a decision-maker must determine whether “Il Lamborghini”, the tractor of Mr. Hugo – a local farmer from a small town named “Gemona” – is allowed to enter into the park.

  • 40 Rodríguez 1995: 372; 2002.
  • 41 Rodríguez 2002; Navarro and Rodríguez 2014.
  • 42 Navarro and Rodríguez 2014: 179.

20 A second example of instantiation conflict, expounded by Jorge Rodríguez in a couple of his essays, is what we might call ‘the traffic light case’.40 Also in this case we have two normative sentence-types: the first prescribes that (NST3) “Drivers ought to stop in front of red lights”, and the second prescribes that (NST4) “Drivers ought not to stop in front a military base”.41 Although these norms seem to be in abstracto consistent, an instantiation conflict arises whenever “it happens” that an actual driver finds a red light in front of a military base: let’s say, Mr. Hugo is driving “Il Lamborghini” in front of the NATO airbase located in Aviano, and he suddenly finds a red light on his way. To put it in Navarro and Rodríguez’s words:42

The example shows that two seemingly consistent norms can produce a normative conflict given the occurrence of certain factual circumstances [The stress is mine]. In our example, the joint verification of conditions p and r – red light and military zone – renders as a result the obligation and prohibition to stop (Oq and O¬q). Therefore, here is a new element that has to be taken into consideration for a proper characterization of normative inconsistency: a set of norms can be inconsistent via certain facts – under the occurrence of certain factual circumstances [The stress is mine] – and inconsistent via other facts.

21A third example, always taken from Navarro and Rodríguez’s works, is what we might label ‘the ten dollars credit case’. Let us imagine a normative system that contains a general norm which prescribes that for any x and y, if x has a credit from y, then it is obligatory for y to pay x:

(GN)

‘∀ x,y: (Axy ⇒ O(Pyx))’

  • 43 Navarro and Rodríguez 2014: 183.

where ‘x’ and ‘y’ are variables for individuals, ‘A’ stands for the relational property of having a credit and ‘P’ stands for the action of paying. According to Navarro and Rodríguez, “[a] norm such as this can contradict no other norm in a given normative system and, nevertheless, generate a conflict if applied to particular situations: for example, both ‘a’ and ‘c have credits of ten dollars from ‘b, and ‘b has only ten dollars.”43 In such a case, “[o]ur norm produces a conflict for b, because when applied to the considered situations it generates two obligations that b cannot jointly satisfy”:

(N*)

Aab ⇒ O(Pba)’

(N**)

Acb ⇒ O(Pbc)’

  • 44 Guastini 2011: 106 ff.

22 In the same vein, Guastini remarks that most of the collisions between constitutional principles can be qualified as antinomies in concreto.44 He brings ‘the unemployed tax case’ as a paradigmatic example: a constitution contains two norms N1 and N2; N1 imposes on citizens an obligation to pay the taxes, whereas N2 settles an exception to the effect that unemployed people are allowed not to pay the taxes. Considered both the possibility of unemployed foreigners, and the possibility of employed citizens, we can conclude that an instantiation conflict arises for individuals that are both citizens and unemployed – say, Mr. Hugo is an Italian citizen, and he lost his job due to the collapse of Gemona’s Agricultural Cooperative.

  • 45 Rodríguez 1995: 372.
  • 46 Guastini 2011: 106 ff.
  • 47 Guastini 2015: 45 ff.
  • 48 Navarro and Rodríguez 2014: 179.
  • 49 Navarro and Rodríguez 2014: 183.

23 Guastini, Rodríguez and others claimed that, in the abovementioned situations, a certain set of norms becomes inconsistent through certain facts,45 or through an interpretation in concreto (of the salient normative sentence-types.46 Interpretation in concreto, on its turn, is understood as a kind of individual subsumption (namely, the operation of placing an actual entity, action, or event under the scope of a quantified predicate such as ‘every citizen’, ‘every murder’, and so on).47 In other words, the proponents of the instantiation conflicts argument claim that, in all the abovementioned examples and analogous cases, normative conflicts are produced by the contingent “joint occurrence” of two consistent normative antecedents,48 and not (only) by the inferential relations between norms qua abstract semantic entities that provide solutions to general cases. Therefore, instantiation conflicts shall be considered to all effects as “facts-dependent” normative conflicts. Accordingly, a good theory of antinomies has to distinguish between two categories of normative conflicts: antinomies in abstracto, which are directly produced by inconsistencies of the normative systems (such as ‘p ⇒ Oq p ⇒ O ¬q’); antinomies in concreto (namely, conflicts of instantiation), whose existence stems from contingent, individual connections between the antecedents of two generic, non-conflictive norms:49

Situations such as this may be called conflicts of instantiation, because they involve individual norms logically derivable from at least one general norm, or instances of application of the same general norm, that generate a conflict because it is empirically impossible jointly to satisfy them.

24 Let me offer the very last example, to be even clearer on the point. According to this view, if our system contains two norms such as N1 ‘If you are a legal philosopher, then you are obliged to smoke’ and N2 ‘ If you are a legal philosopher, then you are allowed not to smoke’, it is the system itself the sole responsible for bringing about a contradiction. Apparently, this statement is shown to be true by following test: we can realize that there is a normative conflict in every possible world, even without considering any actual situation where, say, Mr. Hugo – the famous farmer and legal philosopher from Gemona – is smoking his pipe. On the opposite, conflicts of instantiations are “caused” by empirical, individual properties of an actual case. They involve consistent norms that, under peculiar circumstances, cannot be jointly satisfied, due to some factual limitation and, therefore, generate also a conflict in the system.

25 If my understanding is correct, the relevant consequences of the argument from instantiation conflict are, at least, five:

26(1) Sometimes, the identification of a normative conflict is logically dependent from the identification of the facts of the case, regarded as actual actions, events or state of affairs or, at any rate, real, actualized objects, which literally “causes” the outbreak of the conflict, according to a notion of causation that still has to be determined.

27(2) The structure of a legal system is not entirely determined by the internal relations between the norms that it comprises but, under specific circumstances, also by the external relations between norms and individual cases, insofar as conflicts of instantiation are connected with a purely “factual” knowledge about a concrete case.

  • 50 Jackendoff 1985: 77. Categorization is a logical operation that brings a first-order logic atomic s (...)
  • 51 Marconi 1997: 64.

28(3) In order to identify an instantiation conflict, our inferential competence is not sufficient, for a referential competence is also required. In other words, the detection of a normative conflict, in some occasions, requires the cognitive ability of categorizing, that is, to “judge that a particular thing is or is not an instance of a particular category”.50 Following Diego Marconi (1997) we can draw a sharp distinction between these two different abilities: the former can be called “inferential”, for it involves our inferential performances; the latter can be called referential, for “it has been characterized as the ability to apply words to the real world”.51 As pointed out by Marconi, scientific experiments – such as the ones conducted by the neuropsychologist Glyn Humphreys on brain-injured persons – confirmed that these two abilities are separated: it is possible to know perfectly what a panda bear is, without having also the ability to recognize a real one, and vice versa.

  • 52 Rodríguez 1995: 371 ff.

29(4) If all of this is correct, a “deductivist” model that considers normative systems as closed under the notion of logical consequence, offers a misleading representation of antinomies, for it does not account for those cases where normative contradictions arise only within certain contexts, and disappear in others.52 This salient feature contributes to place limits to classic deontic logic qua method for the analysis of normative systems.

  • 53 We can thus consider that generic cases fulfill in NS one of the functions that, in Kelsen’s positi (...)

30(5) If, as I think, general cases play a special role in NS, for they seem to give determine and give unity to the content of a legal system, the argument from instantiation conflict is even more dangerous. General cases offer a minimal basis for characterizing and unifying the content of a system for three reasons: first, they establish what properties are relevant for the system; second, they characterize concrete cases (through classification); third, they are capable of repeated instantiation within a legal order. Thus, we might conclude that, under Alchourrón and Bulygin’s view, general cases carve the ‘ought’ dimension at the joints. If the proponents of the instantiation conflict argument are right, one of the fundamental functions attributed to general cases (namely: grant unity to the system) in NS cannot be entirely performed.53

31 All these dramatic implications go directly against the core of NS analysis of antinomies. If individual cases might be seen as causal relata, as explained before, then we do not have a clear-cut separation between ‘is’ and ‘ought’. Moreover, if the facts of an individual case determine the possibility of a normative conflict, then it becomes impossible to maintain that normative systems are closed under logical consequence. Finally, the fashion of giving unity to the content of a system proposed by NS encounters strong limitations.

3 A reductionist strategy

  • 54 Ratti 2013: 98.

32 In opposition to the claim raised by the argument from instantiation conflicts, I consider that a reductionist approach “NS-style” is perfectly feasible: we can remain faithful to the conservative idea that conflicts of instantiation can be treated as antinomies in abstracto, namely, conflicts between deontic modalization of general cases, which can be detected within the system, and without taking into account individual cases. In this regard, I shall invite attention to a salient detail: all the examples proposed by Rodríguez, Navarro and Guastini portrait general situations, where certain sentence-types about general actions have to be interpreted. Take the examples examined in the previous paragraph: they never involve actual interpretations of contextualized normative sentence-types, let alone normative utterance-tokens. This consideration suggests that the boundary of general cases has not been trespassed. However, this piece of evidence is not enough to score a point against the existence of instantiation conflicts: we need to build up a proper counter-argument. Now, I think that we owe to Giovanni Battista Ratti the most convincing line of argument which shows that, from a purely logical point of view, those cases presented under the label “conflicts of instantiation” are by no means different than any standard case of antinomy in abstracto, that is, conflict between general cases; his proof deservers a detailed overview.54

  • 55 Stalnaker 1984: 123–4.
  • 56 Ratti 2013: 98. This argument does not apply to the ten-dollars-credit-case.

33 Ratti argues that, if we look at the traffic light case, at the agricultural machinery case, at the ten dollars credit case, and similar cases, we can notice that, although the antecedents of the two conflictive norms, at first glance, seem completely unrelated, even after a translation into a proposition-like calculus, the norms of the system still produce a conflict in abstracto, and not an instantiation conflict. In fact, two norms such as (N1) ‘p ⇒ Oq’ and (N2) ‘r ⇒ ¬Oq’ are in conflict whenever the conjunction of the two generic cases ‘pr’ is “conceptually possible” or, in other words, when there is no strict implication between general ‘p and general ‘¬r’, or between general ‘r and general ‘¬p. In order to bring about the antinomy in the abstract dimension of general cases it is sufficient to apply antecedent strengthening either to N1 or N2. Antecedent strengthening states that the proposition ‘if p then q’ entails (is evidence or validates) the proposition ‘if p and r then q’.55 In this way, we can derive (N1*) ‘pr ⇒ Oq’ from (N1) ‘p ⇒ Oq’, and (N2*)rp ⇒ ¬Oq’ (which is equivalent to (N2**) ‘pr ⇒ ¬Oq’) from (N2) ‘r ⇒ ¬Oq’.56

  • 57 Ross 1959 would call this a partial/partial conflict, for it is an antinomy between partially overl (...)
  • 58 Ratti 2013: 99.

34 Let us take Guastini’s “unemployed citizen” as a test-case. We have (N1) ‘if x is a citizen, then x is obliged to pay the taxes’ and (N2) ‘if x is unemployed, then x is not obliged to pay taxes’. Now, by virtue of the meaning of the words ‘citizen’ and ‘unemployed’, we infer that there is no strict implication between ‘citizen’ and ‘non-unemployed’, or between ‘non-citizen’ and ‘unemployed’. Then, how could we bring about the antinomy between general cases? The answer is simple: we have to apply the antecedent strengthening’s principle, and derive, first, (N1*) ‘if x is a citizen and unemployed, then x is obliged to pay the taxes’ from (N1) ‘if x is a citizen, then x is obliged to pay the taxes’; second, we derive (N2*) ‘if x is unemployed and citizen, then x is not obliged to pay the taxes’ from (N2) ‘if x is unemployed, then he is not obliged to pay the taxes’. It is now possible to observe that the derived norms N1* and N2* are in conflict and, evidently, this is a conflict between general cases.57 In fact, it seems as clear as anything can be in philosophy that, even in this case, we have not made any reference to the singularities of individual cases. After all, we are still talking about citizens and unemployed as general categories. On these premises, Ratti concludes that the instantiation conflicts argument is flawed, for it confuses the empirical occurrence of an antinomy with the conceptual identification of the antinomy itself.58 I shall return on this point later.

  • 59 Ratti 2013: 99.

35 Now, Ratti makes his argument even stronger by showing that, relying on the same strategy adopted by Rodríguez and Guastini,59 it is well possible to build up examples of instantiation conflicts using hypothetical norms whose antecedents contain predicates that quantify over empty sets. If a predicate quantifies over an empty set, then, by definition, it cannot denote any actual, individual state of affairs, action, event, object or entity. The proof is highly intuitive, and therein lies its strength. In fact, Ratti proposes to imagine a micro-system composed by a first norm (N1) ‘The owners of unicorns shall pay a tax’ and a second norm (N2) ‘The owners of meek animals shall not pay a tax’. Considered that, according to Ratti, unicorns do not exist (his usual ontology corresponds to a non-generous form of conceptualism), the normative conflict between N1 and N2 is independent from any instantiation of the relational property of being both a unicorn and a meek animal. Once again, a “purely conceptual relation” between unicorns (which are not our world-mates) and meek animals is the ultimate source of the normative conflict between N1 and N2.

36 The gist of Ratti’s argument then is that every case of normative conflict is determined by overlapping predicates referred to placeholders for individuals, under a certain interpretation (whoever stops in front of whatever red light which is placed just in front of whatever army base), and not by rigid designators (here I am using in a somehow “liberal” fashion the jargon introduced by Kripke 1980), pointing to actual individuals or events (that traffic light just in front of that military airbase, in Aviano). The (Fregean) sense of the normative statement is not anchored to any individual entity, for the norm can be satisfied by a whole set of individuals and events that fall under the scope of those terms that fulfill a predicative function. Consequently, the instantiation conflicts enthusiast confuses the empirical occurrence of a normative conflict with the conceptual identification of the normative conflict itself.

37 I would like to add some fuel to Ratti’s argument. Let me begin with the charge of blurring the distinction between identification and occurrence of a normative conflict, which he addresses to the friends of instantiation conflicts. To be sure, we have to concede the following point: in a wholly trivial sense, it is somehow true that a certain property must be instantiated in an actual case for bringing about a “real”, “actual”, normative conflict, which might discussed by a judge in flesh and bones, provided that the property is connected to incompatible deontic modalizations (for instance: prohibited and permitted). If Mr. Hugo does not drive “Il Lamborghini” in front of a military airbase, then he will never be arraigned on a road traffic charge. Or, if our good Mr. Hugo becomes too old to drive his tractor, then he will never get into a position where he might find a red light in front of a military base while driving. Thus, we will never come to apply the traffic norms of our micro-system to him; these norms will remain, so to speak, “Hugo-inert”, and the normative conflict never arises in any “real”, actual trial concerning Hugo’s conduct as a driver considered that he simply couldn’t be a driver. These are trivial truths but, as Ratti correctly maintains, they tell us something about the empiric possibility of a normative conflict, and not about the identification of a normative conflict within a certain normative system. In other words, they involve the relation between normative micro-systems (in our case: a portion road traffic regulation) and empirical facts (Mr. Hugo’s ability/possibility to drive), but not about the relation between the items of a normative system. Moreover, what is most important, this trivial truth cannot be used to build a hard-edged case for the distinction between antinomies understood in a narrow sense and conflicts of instantiation, for it is a trivial truth about every antinomy whatsoever, including the most paradigmatic examples of conflicts between general cases.

38 Let us consider, for instance, the conflict between ‘Smoking is allowed’ and ‘Smoking is not allowed’. Even in such a case, if nobody is smoking or if, in our world, suddenly and for some obscure reasons, it becomes just impossible to smoke, the two in abstracto conflictive norms remain inert, and they will not generate a “real” normative conflict, for they cannot be instantiated. Actually, ‘Smoking is allowed/Smoking is not allowed’ really means something like ‘for every x, x is permitted to smoke/not permitted to smoke’, where ‘x is permitted’ is a function that only comes into a complete proposition-like entity through the values of this function. Thus, there is a sense in which any antinomy is a conflict in concreto, in so far as judges discuss antinomies only if they are connected with the atomic fact of a real litigation. On the other hand, this feature does not prevent us to understand that, within the system, these two norms are conflictive, just as we can realize (with a little more cognitive effort, perhaps) that, within the system, ‘vehicles are not allowed in the park’ and ‘agricultural machineries are allowed in the park’ are conflictive, as demonstrated by Ratti’s antecedent-strengthening argument. It’s worth stressing that, even in real litigations, particular cases are characterized through general cases, and conflicts between universals occur in all possible worlds. Thus, any argument based on this trivial truth would not serve as a justification for the distinction between conflicts between general cases and conflicts of instantiation. At best, it might offer good reasons for saying that every antinomy has a double dimension, actual and abstract, and that there are two different senses of ‘existence’ qua predicate of ‘normative conflict’: in abstracto-existence, or ‘existence within a system’, and in concreto-existence, or ‘existence in a actual case’. For all these reasons, Ratti recommends being careful, and keeping occurrence separate from identification.

  • 60 Hamner Hill 1987: 226.
  • 61 Hamner Hill 1987: 228.

39 It might be also objected that the confusion between empirical occurrence and (abstract) identification reaches the highest degree in the ten dollars credit case, which involves only one norm, which is clearly not a self-contradiction and, therefore, cannot be conflictive by definition. The situation represented in the example is rather a problem of purely factual impossibility: a certain agent b is facing a tragic choice, because he is unable to comply with an abstract norm, due to his scarce resources. The agent b has only ten dollars in his pocket money, but his total debt towards his creditors a and c amounts to twenty dollars. Whether he decides to pay a, or to pay c he will not comply with his obligation. It might be also objected that this confusion is a byproduct the ‘impossibility-of-joint-commitment-test’, whose inadequacy was pointed out by Hamner Hill in his 1987 essay “A Functional Taxonomy of Normative Conflicts”. Hamner Hill observed that “[m]ost philosophical analysis of the problem of normative conflict identify instances of normative conflict, through a specific test: the ‘impossibility-of-joint-commitment-test’60. According to this test, “a normative legal conflict exists when and only when it is impossible for one norm subject to comply with both of a pair of norms.” This test is “too narrow”,61 since it defines normative conflicts as impossibility of the joint compliance of two norms, it cannot account for antinomies that involve permissions; further problems arise if we want to analyze empowerments. On these premises, Hamner Hill develops a functional understanding of normative conflict, and a taxonomical classification that distinguishes between three species of conflicts: normative contradiction (a conflict between obligations), normative collision (a conflict between permissions, or between obligations and permissions), and normative competition (cases in which the conflict involve norms of distinct jurisdictions). Now, an extended analysis of Hamner Hill’s proposal goes far beyond the scope of the present contribution. However, I think it is worth stressing that the notion of impossibility of joint compliance, taken as a definitional tool for antinomy, might open the road for the confusion between empirical occurrence of a normative conflict, and a genuine normative contradiction or collision within a certain system.

40 A second issue raised by Ratti’s argument is the idea that it might subsist a “conceptual connection” between two apparently unrelated norms. As we said before, in order to prove that every antinomy is primarily a conflict between general cases, we have to explain how two apparently unrelated norms such as (N1)’p ⇒ Oq’ and (N2) ‘r ⇒ ¬Oq’ might be in abstracto inconsistent by virtue of what Ratti calls the “conceptual connections” between the two contents ‘p’ and ‘r’. The proof shall satisfy the ‘generality constraint’: the contents of the two norms must include only abstract properties and individual variables, and shall not contain individual elements of any actual case. Now, if we look at the representation of N1 and N2 it turns out that, under this formalization, N1 and N2 are unanalyzed predications: ‘p’ and ‘r’ are variables for propositional contents; but we might wonder what are their respective constituents, and how do they relate to each other. There is not such a thing as a free lunch here. An extension of first-order propositional calculus with deontic operators will not do the job. The explanation of how N1 and N2 might be conflictive necessarily passes through a reconstruction of the sub-sentential constituents of ‘p’ and ‘q’, respectively, and of their relations. The explanation must show that ‘p and ‘q have something in common. In order to reach this goal, we have to make explicit what Carnap used to call the meaning postulates of the constituent of ‘p’ and ‘q’ respectively. Going back to our examples, we have to show how agricultural machineries and vehicles, meek animals and unicorns, traffic lights and military airbases, might be brought together under the same class. This task belongs to the domain of semantics, while Ratti’s argument was essentially aimed at making a point about logic: the two strategies can be combined together.

  • 62 Carnap 1952 and 1932/1959: 63 ff.
  • 63 It’s worth stressing that meaning postulates depend on a somewhat arbitrary choice of the semantici (...)

41 Now, meaning postulates are semantic stipulations on the relation between the extensions of lexical items that specify the necessary and sufficient condition for the semantic application of a concept. For instance, (MPB) ‘(∀x) (bachelor(x) ⊆ ¬married(x))’ stipulates that every individual which is under the extension of ‘bachelor’ is not under the extension of ‘married’; in other words, it offers a mental representation of the necessary and (in Carnap’s seminal account) sufficient conditions for something to be a bachelor. These postulates become descriptive constants that have the function of validating semantically based inferences,62 which are constitutive of the meaning of a word or phrase. They can be considered as translations of lexical items into signs of a (meta-) language L constituted by customary connectives, individual variables, quantifiers, individual constants (‘a, b, c’…) and primitive descriptive predicates (‘B, M, R).63 Meaning postulates might provide partial definition, but they tend to completeness: we acquire the complete extension of a lexical by adding semantic components (individual variables, constant, quantifiers and so on) to an initial representation.

  • 64 Katz 1972; Clark 1973; Burazin 2016.

42 Let us consider the term ‘unicorn’: we start by saying that all unicorns are ‘legendary objects’, and then we add that they ‘have a horn’, that they are ‘meek animals’, that they have a relational property of similarity with ‘horses’ and so forth. Through this definitional process, we might try to reduce ‘unicorn’ to primitive components, in order to obtain what Carnap used to call “observational sentences” or “protocol sentences”. However, these definitional components might not even be primitive: they might denote functional or cultural factors, other complex entities, and other non-observational elements. For instance, we can define ‘building’ in terms of ‘physical object, non-living, big, artifact’, where ‘artifact’ denotes a highly abstract, cultural concept.64 We can do pretty much the same thing with the word ‘unicorn’, which can be defined as ‘character of a fairytale world’, where ‘fairytale world’ is evidently a cultural element. According to Jackendoff (1983: 121), the sorts of conditions required to specify word meanings are, at least, three: necessary conditions, graded conditions, and conditions that are typical, but might be subject to exceptions. In our example, a necessary condition for ‘unicorn’ is being a legendary object, a graded condition is being the same size of a horse, and a condition that might be subject to exception could be having a horn (which might have been cut during a legendary battle).

  • 65 In this case, the antinomy is total/partial, for unicorns are included in the class of meek animals

43 If we bring meaning postulates into the picture, we can explain how the sentence ‘x is a meek animal’ is entirely deducible from ‘x is a unicorn’, without adding further premises, for ‘meek animal’ provides a partial definition of ‘unicorn’. The inference ‘x is a unicorn, therefore x is a meek animal’ seems to be guaranteed by the proposition to the effect that it is part of the meaning of ‘unicorn’ that unicorns are meek animals. It is not as one has to get involved in the analysis of the facts of an individual case, or in a sociological study on the behavior of unicorns. These premises can be taken as a point of departure for a rejoinder to the friends of the instantiation conflict argument.65

  • 66 Here, we are using second-order predication: we predicate something of a concept (the concept of tr (...)
  • 67 Armstrong 1978; Lewis 1983.

44 Let us examine, for instance, a little variation of the agricultural machinery case. We have a micro-system composed by two norms: the first norm (N1) prescribes: “The importation of vehicles is prohibited”; instead, the second norm (N2) prescribes: “The importation of agricultural machinery is permitted”. We can use ‘M(h)’ to symbolize the machinery of Mr. Hugo, supposing that this is a sufficiently definite description of a single object. We might even refer to the machinery as “Il Lamborghini”, and introduce an individual constant ‘a’ for denoting Il Lamborghini. Be as it may, at a certain point, we would like to predicate something about ‘M(h)’ alias ‘a’. For instance, we might want to say that Il Lamborghini, the machinery that belongs to Mr. Hugo, is a tractor. In this case we introduce the predicative constant ‘T’ (which stands for ‘tractor’, and then we obtain ‘T(a)’, which means ‘Il Lamborghini is a tractor’, or ‘T ((M)h))’, which is equivalent to ‘The machinery of Mr. Hugo is a tractor’.66 Now, the predicative constant is a general term, for it can be predicated of more than one individual:67 sure enough, terms in predicative function express properties, and refer to classes of objects. Now, as far as the meaning postulates (which here I present under the form of implications) (MPT1) ‘for every x, if x is a tractor (T) then x is also an agricultural machinery (AM)’, and (MPT2) ‘for every x, if x is a tractor (T) then x is also a vehicle (V)’, hold, ‘T(x)’ and, therefore, ‘T(a)’ have two more properties that validate ‘AM(a) ∧ V(a)’. This is not an epistemic matter, for it is related to the semantic rules that determine the use of certain expressions.

  • 68 In this paper, for simplicity, I will not introduce also causal predicates in our picture. On the l (...)

45 We shall now only introduce the action-predicate (‘I’), which stands for ‘importation’, along with the deontic modalities ‘permitted’ (‘P’) and prohibited (‘Ph’), and the deed is done.68 If we combine ‘I’ with ‘x is an agricultural machinery (AM)’ and with ‘x is a vehicle (V)’ we obtain ‘I((AM) x)’ and I((V) x)’. Then, we introduce the deontic operators ‘P’ and ‘Ph’. Remember that our starting points were the norms (N1) ‘for every x, if x is a vehicle then it is prohibited the importation of x’ and (N2) ‘ for every x, if x is an agricultural machinery then it is permitted the importation of x’. We can translate them in our toy-language as follows: (N1) ‘∀x: Ph(I((V)x))’; (N2) ‘∀x: P(I((MA)x)’ and, relying on MPT1 and MPT2, derive from them, respectively, (N1*) ‘∀x: Ph(I((T)x))’ and (N2*) ‘∀x: P(I(T)x)’. We have the whole picture now: in every tractor case, we have an antinomy between the general norms N1 and N2 because, by virtue of the meaning postulates MPT1 and MPT2, we know that every tractor is both agricultural machinery and a vehicle. Sure enough, the conflict does not concern only Il Lamborghini, the agricultural machinery/vehicle of Mr. Hugo, for it rather concerns every x that is both a vehicle (V) and agricultural machinery (AM). As we can see, all these relations are purely inferential: it is not necessary to make any reference to the individual properties of a concrete object or event. Indeed ‘tractor’ is a structured complex of other concepts such as ‘agricultural machinery’ and ‘vehicle’, for it literally has these concepts as proper parts (‘∀x: Tx AMx Vx). In other words, ‘tractor’ couldn’t be tokened without ‘agricultural machinery’ and ‘vehicle’ being tokened. On the other side, there is an inferential relation between ‘tractor’ and ‘vehicle’, and between ‘tractor’ and ‘agricultural machinery’. Even though ‘vehicle’ does not contain ‘tractor’, there is a privileged relation between the concepts: we can entertain the concept of ‘vehicle’ without having tokened tractor, but if we think about all the possible vehicles, we should have an inferential disposition that links ‘vehicle’ to ‘tractor’.

  • 69 Frege 1979: 126.
  • 70 On the limits of this approach see Marconi (1997: 107, 10): “What we feel would be needed in the ca (...)
  • 71 Marconi 1997: 114.
  • 72 Ross 1959: ch. 4.
  • 73 Of course, this does not apply to the ten-dollars-credit case.

46 We can apply this reductionist strategy also to the traffic light case and to the unemployed tax case. We might also want to develop a more accurate formalization of this semantic phenomenon. However, all this involve a lot of tiresome details that are out of place here, for they go beyond the modest purpose of this paper. Let me just make a brief clarification: in the traffic light case it will be sufficient to use a definite description of the place where the traffic light is placed, which can apply to other similar places as well. As we have seen, a model theoretic propositional semantics enriched with deontic operators (the one used in NS) won’t do the job. We have to penetrate the semantic structure of individual words in context: as Frege pointed out, these elements are the Gedankenbausteine of thought.69 This requires us to go beyond NS-semantics, which does not provide any lexical information for the use of words:70 the model has to be enriched with a system of meaning postulates, which should ideally tend to completeness.71 The theoretical payoff of the strategy that we have just proposed is twofold. On the one hand, we might even get rid of the antecedent strengthening’s principle. On the other hand, we are allowed to analyze the tractor case, the ten dollars credit case, and all the abovementioned examples as partial normative conflicts;72 namely, cases where there is a partial identity or (if you prefer a less demanding mereological claim) an overlap of the antecedents of the two norms. The intersection is determined by the presence of a common property in the meaning postulates.73

4 Normative conflicts and cognitive load

47 We saw above that every example of instantiation conflict involves a mental representation of two case-types that, taken in conjunction, bring about an antinomy. We then considered that, contrary to Rodríguez, Navarro and Guastini’s view, this antinomy is not linked to the facts of an individual case and, therefore, can be detected in abstracto. Still, we might not want to jettison altogether the intuitions that stand behind the instantiation conflicts argument. I think that there is more to say for the instantiation conflicts argument than Rodríguez, Navarro and Guastini themselves say.

  • 74 As an anonymous referee suggested, it is worth stressing that, in the lexicon of NS, there is a tec (...)

48 In one way or another, so-called “instantiation conflict” require a heavy work of reconstruction of the semantic derivations of the sub-sentential expressions (such as “vehicle” and “agricultural machinery”) that constitute the contents of the norms (‘vehicles are allowed/not allowed’), in order to detect the potential, abstract conflicts between generic cases. In every example of instantiation conflicts examined before, the interpreter should penetrate the deep semantic structures expressed by the normative sentence-types under consideration, in order to realize that the two statements might express conflictive norms. If we want to put it in Carnap’s jargon, she has to identify the meaning postulates of the terms that constitute the propositions-like entities, to check whether the norms expressed are incompatible or not. If, instead, we want to remain more faithful the lexicon introduced by NS, we might say that she has to make the structure of the UD more explicit, by digging deeper, and spelling out more properties that belong to the antecedents of the conditional norms of the system.74

49 Going back to one of our examples, we can understand that the interpreter has to start an inquiry into the meaning-postulates of “vehicle” and “agricultural machinery” to understand that “Vehicles are not allowed in the park” and “Agricultural machineries are allowed in the park”, under a certain interpretation, might express conflictive norms. This mental process might not be as intuitive as the kind of reasoning that enables a competent speaker to grasp that “Smoking is permitted” and “Smoking is prohibited”, or “Vehicles are allowed in the park” and “Cars are not allowed in the park” could express conflictive norms. In the former case, the connection between “Smoking is permitted” and “Smoking is prohibited” is established by a partial identity of lexical items, for “smoking” is present in both sentences. And also in the latter case the connection between “vehicles” and “cars” is straightforward, because “cars” are normally used in extensional definitions of vehicles, due to the fact that cars are paradigmatic examples of vehicles.

  • 75 Intensions are functions from indices (for instance, possible worlds) to extensions (i.e. functions (...)
  • 76 Peacocke 1992: ch. 3.
  • 77 Longo and Barrett 2010: 66.

50 The inquiry into meaning-postulates constitutes a further level of analysis, apt at making extensions more explicit.75 In order to reach that level, we have to translate normative statements into partial definitions, and then turn these partial definitions into (relative) complete definitions. Sometimes, partial definitions are difficult to articulate,76 and also turning a partial definition into a full definition is not an easy task: there is an epistemic risk of encoding insufficient or incorrect information – after all, partial definitions are specified in a piecemeal way. This mental process might eventually require a high level of epistemic (or cognitive effort). Following Longo and Barrett,77 we can define cognitive effort as follows:

Theories of information processing consider cognitive effort as a hypothetical construct, regarded as a limited capacity resource that affects the speed of information processing. […] [I]f a task is resource limited, then the performance will improve if more cognitive effort is allocated to the task. Although cognitive effort may be a hypothetical construct, it is a subjective state that people have introspective access to. It is a multi-faceted phenomenon: it can be related to physiological states of stress and effort, to subjective experiences of stress, mental effort, time pressure and to objective measures of performance level.

51 Now, I would suggest that the fundamental distinction between the ten dollars credit case, the unemployed citizen case, the tractor case, and a paradigmatic example of antinomy such as “Vehicles are not allowed in the park” and “Cars are allowed in the park” is that, normally, the formers require a higher level of cognitive effort in order to be detected. And this is just because the cognitive connections between the meanings of “unemployed” and “citizens”, or the meanings of “vehicles” and “agricultural machineries” are less direct and intuitive than the cognitive links between the meanings “vehicles” and “cars”. Under normal circumstances, the discovery of these links requires the interpreter to undertake costly inferences (that is, thinking slow). This is precisely the source of the wrong impression that so-called “instantiation conflicts” display some logical peculiarity, or that the thinking process has necessarily analyzed the real facts of an individual case. After all, as we have said before, every normative conflict can be reduced to a clash between generic cases; the only difference is just related to cognitive process and, more specifically, concerns the level of cognitive effort required in the interpretive process. The identification of the conceptual links between ‘therapeutic abortion’ and ‘abortion’ is less demanding with respect to the identification of the conceptual links between ‘cars’ and ‘agricultural machinery’. These conceptual links rely on meaning postulates.

52 An additional argument might be adduced in favor of the hypothesis that I suggest. In fact, we can design examples of antinomies that, no doubt, involve generic cases and that: first, are cognitively demanding (even more demanding than the cases presented by Rodríguez, Guastini and Navarro); second, are intuitively similar to conflicts of instantiations. The most striking examples might be offered by conflicts between opaque norms. According to Damiano Canale (2014), we say that a norm is “opaque” if “a relevant portion of the sense of the normative text and the applied norm is totally unknown”. In spite of the fact that there is no ambiguity, vagueness, or genericity, “the norm is not completely intelligible to the decision-maker”. As Canale points out, opaque norms are generally connected with scientific thought: they have been drafted by experts (chemists, physicists, and so on), and then approved by the legislature. Analogously, judges rely on the intervention of experts in the field in order to apply these norms to individual cases, because they lack the scientific knowledge required to grasp the meaning of these norms. In other words, under opacity, decision-makers do not posses the inferential competence that is necessary to understand the cognitive content of the norms. A conflict between opaque norms, by definition, is very demanding from a cognitive point of view, for it requires complex scientific knowledge in order to be detected, and, according to our intuitions, seems very similar to an example of instantiation conflict.

  • 78 I am grateful to Lidia Fanfoni and Paolo Cinquegrana for these examples.

53 Let us imagine, for instance, a normative system composed by two norms. The first norm states: “Fires are allowed”; the second norm says: “Exothermic oxidoreduction of organic material is not allowed”. Beyond any doubt, there is a conflict in abstracto between this norms, but we don't know it immediately, because the two norms are opaque: in order to understand that there is a normative conflict, we have to start an inquiry in the meaning-postulate of “fire”, which will get us to know that “to pick up a fire” basically means to generate an exothermic oxidoreduction of organic material. Another example might be the following: (N1) “Smoking tobacco is permitted”; (N2) “The consumption of combusted leaves of solanaceae containing C10H14N2 is prohibited.”78 We must slog on the meaning postulates of tobacco in order to get its chemical formulation, and to understand that the two norms bring about a conflict between generic cases. These examples have something in common with the cases proposed by Guastini, Navarro and Rodríguez: they are all conflicts between general cases that are hard to detect, due to the fact that the decision-maker is unable to grasp intuitively the relations between the norms expressed by the normative statements that she has to interpret.

5 Conclusion

54 The purpose of my essay was to consider whether there is a fundamental distinction between normative conflicts that involve general cases and instantiation conflicts. Jorge Rodríguez, Riccardo Guastini, Pablo Navarro and others discussed this problem: their conclusion is that the distinction exists. Our conclusion was precisely the opposite: every antinomy can be reduced to a clash between contradictory regulations of generic cases. Therefore, NS was then right in assuming this position. In order to reach this conclusion, we examined three examples of instantiation conflicts. Following Ratti’s proof, we observed that, if we apply antecedent strengthening, these conflicts could be transformed into antinomies that can be detected without taking into considerations the peculiarities of individual cases. We proceeded to discuss the idea of a conceptual connection between the contents of two norms, and we found that this connection depends on what Carnap used to call “meaning postulates”, which we have analyzed as a kind of partial definition that tends to completeness. Once considered that meaning-postulates establish a purely inferential relations between the contents of two terms, by specifying the scope of their respective extensions, we concluded that we have another good reason to get rid of the distinction between conflicts between generic cases and instantiation conflicts. This argument is quite novel: among the participants to this debate, Ratti alone has seen through this muddle and offered a counter argument to the case for instantiation conflict. In the last paragraph, we suggested to displace the whole problem from logics to cognition: the examples proposed by the instantiation conflicts enthusiasts are precisely antinomies between generic cases that are cognitively costly to discover.

Acknowledgment.— I am very grateful to Alejandro Calzetta, Mauro Barberis, Giovanni Battista Ratti, Nicola Muffato, and Stanley L. Paulson for their precious comments to a previous version of this essay. A first outline of these ideas was presented at Washington’s IVR 2015. I was able to complete my research thanks to a DAAD Short-term Visiting Grant, which supported my project-proposal on normative conflicts and balancing. Prof. Stanley Paulson, at the University of Kiel, supervised the whole project.

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Notes

1 I am grateful to an anonymous referee of this journal for the following clarification: the logical derivation of individual requirements from general norms does not involve any volitional act. And it seems even dubious that the act of inference presupposes any volitional act. By contrast, individual decisions, even when grounded on general norms, do involve a volitional act.

2 Alchourrón and Bulygin 1971: 49. The present investigation shall be limited to the analysis of normative conflicts proposed in Normative Systems. Therefore, I will not explore the successive developments of Alchourron and Bulygin’s ideas, which the reader may find in various chapters of Alchourrón and Bulygin 1991 and in Bulygin 2015.

3 On the concept of empowerment see Paulson (1988; 1998: xlix; 2013). On the use of this concept made by Alchourrón and Bulygin, have a look at Calzetta (2017).

4 See Paulson 1998: xi; 2000; 2012 and Grabowski 2013 for a discussion on the relations between positivism, validity and membership.

5 Alchourrón and Bulygin 1971: ch. 1–3; Appendix.

6 Hilpinen 2015: 23 ff.

7 Although someone might have the impression that Alchourrón and Bulygin were not entirely aware, at that time, of the problem related to the distinction between “insular” and “bridge” models of deontic conditionals.

8 Alchourrón and Bulygin 1971: ch. 4. See also Barberis 1997: 33 ff.

9 Alchourrón and Bulygin 1971: ch. 4 § 7. See also Mazzarese 1991.

10 See also Barberis 2016 and 2017 for a discussion over the limitation of a traditional positivist account, and the advantages of a truly realistic account of law.

11 In the present essay, I will use “antinomies” and “normative conflicts” as synonyms. On the notion of antinomy see Barberis 2008: 158 ff. and Mazzarese 1984 and 1987. On the distinction between non-antinomy and non-contradiction see Muffato 2010.

12 Alchourrón and Bulygin 1971: ch. 7.

13 Actually, the conceptual connection requirement plays a key-role for the reduction strategy, insofar as it settles a semantic, abstract link between the antecedents of two apparently unrelated.

14 Kahneman 2013.

15 Alchourrón and Bulygin 1971: ch. 4, § 6.

16 This consideration is very important for a deep understanding of the difference between internal and external negation of a norm. This problem was analyzed by Ross 1968; Caracciolo 1994; Ratti 2013: 95 ff.

17 Rodríguez 1995: 364 ff. deals with this problem.

18 Alchourrón and Bulygin 1971: Appendix: (D20) ‘Coh (UCi, USmax) [ = Coh (UPi, UAj)] = {(UCi  USmaxj) ∈ Fun, where ‘Coh’ stands for ‘Coherence’, ‘UC’ for Universe of cases, ‘UP’ universe of properties, ‘USmax’ for Universe of maximal solutions, ‘UA’ universe of actions,. The symbol ‘{  … ’ represents the set of entities that satisfy condition and, finally, ‘Fun’ stands for the set of functions.

19 The same consideration holds for analysis of two related topics: normative relevance and axiological relevance.

20 Von Wright 1963: 148.

21 Quine 1966: 5.

22 There are several ways out: one is the rejection of ex falso quodlibet; the rejection of bivalence is another. See Moreso, Navarro and Redondo 2003: 127 ff.

23 To be sure, Alchourrón and Bulygin 1989: 673 ff. deals with this issue. On this point see also Navarro and Rodríguez 2014: 176.

24 Guastini 2011: 105 ff.

25 Even though Alchourrón and Bulygin maintain that a new interpretation determines a change of the normative system.

26 On the importance of individual case in the hermeneutic tradition see Carlizzi 2011.

27 Strawson 1969: 226 ff.; Lowe 1995: 512.

28 Quine 1947.

29 Lewis 1983: 344.

30 Armstrong 1997.

31 Lewis 1983: 344.

32 Ramsey 1925: 401 ff.

33 Lowe 1995: 518.

34 Russell 1948: Part IV, ch. 8.

35 Von Wright 1963: ch. III postulates an analogous distinction, although expressing in terms of individual/general actions (instead of cases).

36 Guastini 2011: 205 ss.

37 Rodríguez 2002.

38 I prefer to use “normative sentence-type” rather than “normative formulation” because the latter denotes a broader notion, which includes: normative sentence-types, normative sentence-tokens, normative utterance-types and normative utterance-tokens. The distinction is salient for the present discussion: as I will suggest later, the fact that a normative conflict comes from normative types, and not tokens, offers a good reason to think that it involves general cases.

39 Navarro and Rodríguez 2014: 179.

40 Rodríguez 1995: 372; 2002.

41 Rodríguez 2002; Navarro and Rodríguez 2014.

42 Navarro and Rodríguez 2014: 179.

43 Navarro and Rodríguez 2014: 183.

44 Guastini 2011: 106 ff.

45 Rodríguez 1995: 372.

46 Guastini 2011: 106 ff.

47 Guastini 2015: 45 ff.

48 Navarro and Rodríguez 2014: 179.

49 Navarro and Rodríguez 2014: 183.

50 Jackendoff 1985: 77. Categorization is a logical operation that brings a first-order logic atomic sentence (the token) under the scope of a complex ontological category (the type) by a predicative sentence of the form ‘a is ’ (for instance: ‘Il Lamborghini is a Tractor’) or, if you prefer a set-theoretic approach, by a two-place relational function ‘a ∈ T’ (Jackendoff 1985: 78 ff.).

51 Marconi 1997: 64.

52 Rodríguez 1995: 371 ff.

53 We can thus consider that generic cases fulfill in NS one of the functions that, in Kelsen’s positivistic theory, can be ascribed to the Grundnorm: namely, granting “unity” to the system. I take this interpretation of Kelsen’s work, and the whole idea of functions, from Stanley L. Paulson’s most up-do-date reading of the Basic Norm. See, at least, Paulson 2012.

54 Ratti 2013: 98.

55 Stalnaker 1984: 123–4.

56 Ratti 2013: 98. This argument does not apply to the ten-dollars-credit-case.

57 Ross 1959 would call this a partial/partial conflict, for it is an antinomy between partially overlapping cases.

58 Ratti 2013: 99.

59 Ratti 2013: 99.

60 Hamner Hill 1987: 226.

61 Hamner Hill 1987: 228.

62 Carnap 1952 and 1932/1959: 63 ff.

63 It’s worth stressing that meaning postulates depend on a somewhat arbitrary choice of the semanticist: therefore, it is well possible that different persons assign different meaning postulates to a phrase or word. In a similar way, different legal interpreters can assign different meaning postulates to the same lexical item. Moreover they can vary, and they are always context-dependent.

64 Katz 1972; Clark 1973; Burazin 2016.

65 In this case, the antinomy is total/partial, for unicorns are included in the class of meek animals.

66 Here, we are using second-order predication: we predicate something of a concept (the concept of tractor) rather than an object (Il Lamborghini). See Kremer 1985.

67 Armstrong 1978; Lewis 1983.

68 In this paper, for simplicity, I will not introduce also causal predicates in our picture. On the logical structure of causal predicates see Davidson 1967a and 1967b.

69 Frege 1979: 126.

70 On the limits of this approach see Marconi (1997: 107, 10): “What we feel would be needed in the case of such word as ‘walk’ or ‘painting’, ‘sepia’ or ‘inducement’ is close to a truth function in being an explicit instruction for the use of a word. This is what Tarskian semantics (or Montague semantics, for that matter) does not provide us with, for such instructions would be different for non-synonymous words, whereas whatever information we get from Tarskian semantics is the same for ‘table’, ‘book’, and ‘walk’ […].”

71 Marconi 1997: 114.

72 Ross 1959: ch. 4.

73 Of course, this does not apply to the ten-dollars-credit case.

74 As an anonymous referee suggested, it is worth stressing that, in the lexicon of NS, there is a technical device to deal with such cases: the analysis of the relations between finer and less fine universes of cases.

75 Intensions are functions from indices (for instance, possible worlds) to extensions (i.e. functions that assign to each possible world a set of individuals). See Carnap 1956b: 181. Eventually, during this process, the interpreter might extend and restrict the domain of quantifications over properties, in order to create or prevent normative conflicts.

76 Peacocke 1992: ch. 3.

77 Longo and Barrett 2010: 66.

78 I am grateful to Lidia Fanfoni and Paolo Cinquegrana for these examples.

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References

Electronic reference

Alessio Sardo, « Let’s talk about antinomies », Revus [Online], in print | 2018, Online since 29 March 2018, connection on 25 September 2018. URL : http://journals.openedition.org/revus/4089 ; DOI : 10.4000/revus.4089

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About the author

Alessio Sardo

Researcher with grant at Bocconi University (Milan). Member of the Tarello Institute for Legal Philosophy (Genoa).

Address: Università Bocconi, Dipartimento di Studi giuridici “Angelo Sraffa”, Via Röntgen 1, 20136 Milano, Italia.

E-mail: alessio.sardo@unibocconi.it

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