I. Identifying conceptual norms as a category of norms

It is trivial to say that normative systems are systems of norms.¹ Yet, from such triviality immediately follows a catalogue of intricate difficulties, namely what is a norm for the purposes underlying the statement, to know if there can be (or if it makes sense to speak about) norms without prescriptive character, to see if the whole issue is not merely terminological or even, for the sake of accuracy, if one should replace that trivial statement and say instead that normative systems are systems of norms and «other entities». Assessing which might be the candidates to the broad class of «norms» as used in the statement above lies, nevertheless, outside of the scope of this article. For the present purposes it suffices to acknowledge that, as it is usually accepted, normative systems surely comprise prescriptive norms and the so called «conceptual norms».²

Under the label «conceptual norms» a specific category of norms is selected. Considering the more or less stabilized terminology, it can be said that a conceptual norm is a norm that determines an equivalence between two (or more) terms irrespective of their contents: from such norm follows that «A» is equivalent to «B», no matter the quality or the quantity of the «things» which are denoted by each one of the terms.³ And since a sentence with a logic equivalence (tautology) is self-redundant and cannot fullfil any normative function, it seems that the category is limited to norms with: (i) a biconditional (material equivalence); and (ii) a conditional (partial equivalence).⁴ So, it can be said that the category lies in the property of establishing an «equivalence», which means that it comprises norms that make something to «count as» something else.

1. (i) a sentence stated by a normative authority such as «a minor of age (m) is a minor of age» (m ≡ m) or the one expressed in «one whether is or is not a minor of age» (m ∨ ~m) have no normative content: since they express tautologies, they cannot realize any normative function.

2. (ii) a sentence stated by a normative authority such as «a minor of age (m) is a person less than 18 years old (o)» contains a biconditional (m ⇔ o): it establishes a material equivalence between «m» and «o»; that is, being «less than 18 years old» counts as being «minor of age».

3. (iii) a sentence stated by a normative authority such as «a 16 years old person old (l) is also a minor of age (m)» contains a conditional (l ⇒ m): it establishes a partial equivalence between «l» and «m»; that is, being «16 years old» counts (besides other ages that count as well) as being «minor of age».

Within the category, some subcategories can be distinguished. The first one is that of «definitory norms» (in the narrow sense). It is a kind of conceptual norm that aggregates norms with a definition of a word, specifically for interpretative purposes.

As it is known, normative authorities frequently enact norms that aim to decrease or extinguish the linguistic uncertainty coming from the way words are used by the speakers of a natural language (Alchourrón and Bulygin, 1991:448; Duarte, 2018:139). With a definitory norm, and the use of a definition, the normative authority establishes a specific meaning, precisely the one that is to be considered whenever such word appears in a norm sentence (and such sentence has to be interpreted). Definitory norms, as all conceptual norms do, determine an equivalence: the equivalence between a word and other words whose meaning is the same.⁵

1. (iv) «a minor of age (m) is a person under 18 years old (o)» (m⇔o) is an example of a norm sentence with a conceptual norm in the subcategory of definitory norms; with the equivalence between «m» and «o», a definition of being «minor» is given: those who are «under 18 years old».

A second one is that of «norms on conditions of a type»; that is, norms that establish which are the conditions for a normative act (or a document or some legal action) to belong to the type it purports to be. It is the case, for instance, of the norm «a will is a document signed by the author before an official and two witnesses».⁶ It follows that documents under analysis are not wills if and whenever each one of the conditions is not filled. Therefore, by listing those conditions, a norm of this kind specifies when the normative act is a token of the type. Although not defining the meaning of a word (it defines a «normative action»), a norm on conditions of a type also shows an equivalence: the one between the type and its necessary conditions; so, whenever these are present there is an act of the type and an act of the type means that conditions are filled.⁷

1. (v) «a will (w) is a document signed by the author (a) before an official (o) and two witnesses (t)» (w⇔a∧o∧t) is an example of a norm sentence with a norm on the conditions of a type; with the equivalence between «w» and «a∧o∧t» the necessary conditions for a token of «w» are given: there is a will if and only if the conditions «a», «o» and «t» are cumulatively present.

A third subcategory of conceptual norms is the one that can be designated as «norms on the equivalence of things»; that is, norms that determine that something (material or immaterial) values as another. For instance, it belongs to this kind of conceptual norms the one that establishes that «the Portuguese Flag is the one adopted by the Republic formed by the Revolution of October 5, 1910».⁸ From this norm follows that a specific configuration of a flag amounts to the national one. The difference between these norms and the definitory ones (in the narrow sense) is that they do not express the meaning of a word (they are not related to the natural language adopted by the system); instead, they just connect two things. There is an equivalence here as well: whenever there is the thing «A» there is the thing «B», and conversely.

1. (vi) «the Portuguese Flag (p) is the one adopted by the Republic formed by the Revolution of October 5, 1910 (f )» (p⇔f) is an example of a norm sentence with a norm on the equivalence of things; with the equivalence between «p» and «f» it is established that the Portuguese Flag is the one adopted by the Republic and that the flag adopted by the Republic is the Portuguese Flag.

Another example of a subcategory of conceptual norms is that of «norms on statuses», be it on the conditions of the status or on its consequences. Although usually conditions and consequences of a status are expressed in different sentences, the fact is that, at least under some norm individuation assumptions, it is just a norm for each side of the status at hand. The similarity between these norms and norms on conditions of type is evident; however, norms on statuses can be presented as another subcategory since, on the one hand, they have a different object (not a normative act) and, on the other, they usually present disjunctive conditions (each one is sufficient).⁹ So, norms on statuses also show equivalences: regarding conditions, between each one and the status; regarding consequences, between the status and the set of legal positions the status comprises.

1. (viii) «citizenship (c) is recognized by birth (b) or naturalization (n)» (b∨n⟹c) is an example of a norm sentence with a norm on the conditions of a status (citizenship); with the partial equivalence between «b» and «c» and «n» and «c» (each one is a sufficient condition) it follows that citizenship is the case whenever birth or naturalization is the case.

2. (ix) «a citizen (c) has the rights to vote (v) and to be designated to public bodies (d)» (c⇔v∧d) is an example of a norm sentence with a norm on the consequences of a status (citizenship); with the equivalence between «c» and «v ∧ d» being a citizen «counts as» holding the rights to vote and to be designated and holding such rights «means» that the holder is a citizen.

A significant feature common to the whole category of conceptual norms is that, when comprising an equivalence, such norms are enacted under a stipulative sentence. As it is visible with all subcategories showed (and the examples given), while enacting a conceptual norm the normative authority is not reporting an equivalence; such authority is, more than that, creating the equivalence: irrespective of which is the content of what counts as «A» or «B» within the norm at hand, it seems certain that, for the legal domain, the equivalence foreseen is only meaningful when the conceptual norm enters into force. So, whenever a normative authority enacts a conceptual norm nothing is being described; differently, such authority is rather «stipulating» something. Under this scheme, one cannot say, thus, that a conceptual norm might be qualified as true or false.¹⁰

1. (x) the norm expressed by «a minor (m) is a person under 18 years old (o)» contains the equivalence «m⇔o»; it is irrelevant if speakers already understood «minor» as a «person under 18 years old»; it is only due to such norm that it starts to be so (a decision about an equivalence).

It can be said, essentially when taken into account the stipulative nature of the equivalence created by the conceptual norm, that conceptual norms are, by definition, constitutive. If one understands constitutive norms as those that create a type of action (or state of affairs) that would not «exist» without the norm that makes it so, which is probably the main idea underlying the notion, then it seems consistent to say that a decision upon an equivalence implies constitutivity.¹¹ That is what one can see while observing the «count as» present in definitory norms or in norms on statuses (for instance): in the same way that the legal meaning of a word would not exist as such without the conceptual norm, the consequences of a status would not be present in the system (in the way they start to be) if the correspondent conceptual norm had not been enacted.¹²

Yet, if one can say that conceptual norms are necessarily constitutive, one cannot say that the whole set of the latter is formed by conceptual norms. One kind of norms seems to be enough to justify the statement: competence norms. As it is well-known, a competence norm is constitutive (in the sense given above) since the type of action foreseen (to produce deontic consequences) only exists for the reason of having been created by the norm itself (Frändberg, 2018:46; Peczenik, 2008:227). Nonetheless, a competence norm does not entail any equivalence: while assigning power to some agent (a body or a person) on some topic (no matter which), a competence norm is merely giving the possibility to do something otherwise impossible (not even considering now its eventual regulativeness). Accordingly, there is no equivalence here: the allocation of power does not comprise (or presuppose) any «count as».¹³

1. (xi) a norm sentence such as «the Parliament is competent on the age of majority» is a power conferring norm that assigns to such body (the Parliament) the «ability» to produce deontic consequences on some topic; here, specifically, the age of majority.

2. (xii) since having the power is just a necessary condition for «producing deontic consequences» (or at least that is assumed considering what is usual in contemporary normative systems), then one cannot say that competence norms belong to the category of conceptual norm: there is no equivalence.

II. The mainstream theory on conceptual norms: the non-prescriptive thesis

As mentioned before, comprising an equivalence works as the criterion to select norms that belong to the category of conceptual norms. In addition to such property, which might be called the «positive property», the main theory on conceptual norms (which can therefore be labeled as the «mainstream theory») adds another one: the lack of prescriptive nature (somehow, the «negative property»). Therefore, the non-prescriptive thesis on conceptual norms sustains that such norms do not regulate behavior, which is just another way to say that the category entails norms that do not have any deontic modalization (Alchourrón and Bulygin, 1991:449; Mendonca, 2000:121). So, irrespective of being a definitory norm, a norm on the conditions of a type or any other kind of conceptual norm, the whole category is formed by norms that merely present an equivalence (a definition in the broad sense).

Underlying the claim that conceptual norms do not regulate behavior and, inherently, do not have any deontic modalization, is the idea that a conceptual norm has no content other than to present a specific equivalence: a stipulation on what «A» and «B» stand for in the «A counts as B». Such an idea is relevant within the nonprescriptive thesis since it is the basis for a sharp contraposition between conceptual norms and those which are regulative (Rodríguez, 2021:52; Von Wright, 1963:6). Since the latter are somehow synthetic (making reference to the world; to human action), then it follows that conceptual norms, for the reason of only giving rise to sentences that are analytical, cannot permit, forbid or impose anything. As Alchourrón and Bulygin claim, and irrespective of the arguments that might sustain such premise, «the one and the same norm cannot be simultaneously conceptual and prescriptive».¹⁴

Such premise also comes from the underlying point, sustained by the non-prescriptive thesis, that conceptual and regulative norms bring about different kinds of sentences. Thus, while from a regulative norm one can say that such norm has been violated or not (a synthetic sentence, strictly contingent), the same is not valid whenever one deals with a conceptual norm. In the latter, a sentence on compliance with or violation of the norm does not follow. As the non-prescriptive thesis claims, in the parallel scenario of an equivalence, the conceptual norm gives rise to an impossibility. With a norm such as «a minor of age is a person under 18 years old», it follows that it is impossible for a 20 year old person to be a minor. Hence, since equivalence leads to necessity, whatever might be outside the «A counts as B» is impossible (Alchourrón and Bulygin, 1991:457).

Under the view given by the non-prescriptive thesis, conceptual norms only serve to identify other norms and that is, precisely, the function they realize in normative systems. When a normative authority enacts a norm with an «A counts as B» structure, such norm is normatively meaningless unless there is another one in which «A» or «B» play some role: the conceptual norm identifies the content of another norm where the equivalence works (and becomes normatively meaningful). Following the non-prescriptive thesis, conceptual norms are then always related to other norms, which means that, by themselves, they play no role other than presenting the «equivalence». If the thesis accepts that they have «some» normative consequences, such consequences only give rise to a «deontic normativity» through the norm with which they relate (the identified norm) (Mendonca, 2000:122).

Accordingly, a conceptual norm, by itself, does not oblige anyone, not even the judge. And, more than that, they amount to the same as any private equivalence: for the nonprescriptive thesis, there is no difference between a definitory norm with an equivalence («officially» enacted by a normative authority) and any equivalence eventually stated by some layperson (Alchourrón and Bulygin, 1991:451).The underlying argument (formulated with a definitory norm) runs as follows: since one never knows if the normative authority used the definition in another norm sentence when uttering the word defined, then it is also a fact that no one knows if that word in such sentence has the meaning given by the definition. So, considering that the normative authority might have used the word in another sense, the definition in the definitory norm «values» as much as any private one (Alchourrón and Bulygin, 1991:453).

III. The non-prescriptive thesis and its problems

As mentioned, the non-prescriptive thesis accepts that conceptual norms have some normative consequences: they identify the content of other norms. Yet, and as also mentioned, such thesis accepts as well that a modification of a conceptual norm impacts on the content of the identified norm, which seems to be, at least partially, coherent with the statement that it is only through the regulative norm that the conceptual one produces deontic consequences. The acceptance of this second point leads, however, to serious problems. The initial one is the following (problem1): if changing the conceptual norm modifies the content of the regulative one (its scope), it is not at all clear how can one simultaneously sustain that an «official definition» (enacted by a normative authority) values as much as a private one. As it seems, one thing is incompatible with the other.¹⁵

1. (xiii) at time1, a normative system comprises a definitory norm (N₁) such as the one in «a minor is a person under 18 years old» and another norm (N₂), the one expressed in «it is forbidden to admit minors as soldiers»; when, at time₂, N₁ is substituted by N₃, the norm in «a minor is a person under 16 years old», N₂ changed its scope: after time₂, a 17 years old person may be admitted as a soldier.

2. (xiv) N₁ is an «official definition»: it has been introduced into the system by a normative authority exercising a power-conferring norm; the same applies to N₂ and to N₃; if, for some reason, Ferrando (a soldier) says that «a minor is a person under 20 years old», N₂ does not change; yet, Ferrando’s statement is a private definition; does it normatively «value» as much as N₃?

The exact same point can also be seen with a normative conflict raised with (or provoked by) a conceptual norm. If a normative system has a conceptual norm (an «A counts as B») and two regulative norms with incompatible deontic consequences for «A» and for «B», then there is a normative conflict: the equivalence places one of the terms («A») under the antecedent of both (incompatible) regulative norms. Whitin such scenario, one of two consequences must follow: whether (i) there is no conflict at all, which amounts to a contradiction with the statement that normative systems are changed by conceptual norms; or (ii) there is an effective conflict between the norms at hand and, thus, it is not true that it is just a matter of evidence to know whether the normative authority did or did not drop the definition while using again the word defined.¹⁶

1. (xv) a normative system entails simultaneously the following three norms: the one expressed in «a person deemed incapable counts as a minor» (N₁), the one expressed in «it is forbidden to admit minors as soldiers» (N₂), and the one expressed in «it is permitted to admit incapables as soldiers» (N₃).

2. (xvi) as it is visible, with the equivalence foreseen in N₁ there is a conflict: if incapables count as minors, then they are simultaneously forbidden (from N₂) and permitted (from N₃) to be admitted as soldiers; it clearly seems to be a conflict as any other (namely, if one accepts that conceptual norms «change» the law).

3. (xvii) as it is also noticeable, the conflict only occurs because of the conceptual norm: without N₁ there is no conflict whatsoever; actually, it is the equivalence between «incapables» and «minors» foreseen in N₁ that triggers simultaneously N₂ and N₃, two norms that, otherwise, would not overlap.

4. (xviii) though, the non-prescriptive thesis defends that one does not know if there is a conflict because one does not know if «incapables» in N₃ is used as «defined» in N₁; however, if this is the case, then one must admit that to enact N₁ has no normative function whatsoever (not even the identification of other norms).

Another problem (problem₂) that immediately follows from this example is the one regarding the addressees of a conceptual norm. As seen, for the non-prescriptive thesis no one is under the obligation of using the equivalence while interpreting the norm sentence with the term used: there is no more than a «technical directive» saying that those who want to comply with the law must identify the norms in force and, in order to do it, they must use the equivalences enacted by the normative authority (Alchourrón and Bulygin, 1991:450). The same does not apply to the judge: she is under the duty to give reasons and, on that account, she is under an effective obligation to identify the applicable norms (strictly under the above-mentioned duty). As it is said, the equivalence foreseen is a necessary condition to identify norms and a judicial lawsuit cannot be solved without such operation.¹⁷

This problem₂ is twofold. First, the duty to give reasons (usually) signifies that the judge ought to explain why she decided in one way or another, namely by saying how norm sentences were interpreted, how the applicable norms were identified, how facts were subsumed or how eventual conflicts of norms were solved. It follows, then, that the duty to give reasons, on the single condition of expressing a justification for the decision, is satisfied even if the judge decides wrongly or decides without taking into account the conceptual norms relevant for the case at hand. Whether the judge applies or not the conceptual norm is totally irrelevant here: it suffices to say (though wrongly) that conceptual norms are not binding. By doing so (but perhaps with some more substance), the judge is giving reasons and, thus, complying with the duty.¹⁸

1. (xix) under a norm such as the one in «judicial decisions ought to be justified», the judge is under a duty to give reasons for the decision taken; if a judge decides that «a 16 year old person may be admitted as a soldier» under «it is forbidden to admit minors as soldiers» and «a minor is a person under 18 years old», she is deciding wrongly: it is illegal to admit such person as a soldier.

2. (xx) however, the same judge gave reasons for such decision; actually, she said (because she believes so) that «definitory norms value as much as private definitions, they do not bind any legal agent, and, moreover, a 16 year old person is already apt for the military and cannot be considered a minor»; as such this judge fully complied with the duty foreseen in «judicial decisions ought to be justified».

Second, if one accepts that the judge is obliged to give reasons and, due to that, has the obligation to apply conceptual norms (which nobody else has, as the nonprescriptive thesis says), one has to admit as well that the same norm sentence can lead to two different deontic consequences depending on the agent. When the text is to be interpreted by the judge, she ought to apply the equivalence and assign to the norm sentence what follows from the «A counts as B» foreseen. However, and since no other agent is obliged, the same text can have a different meaning when interpreted by anyone else: any other agent is free to interpret such text in the way she thinks best; that is, not bearing in mind conceptual norms. So, this leads to the absurd outcome of considering that the law applied by the judge is not the same as the one regulating the behavior of other agents.¹⁹

1. (xxi) under «it is forbidden to admit minors as soldiers» and «a minor is a person under 18 years old», and in accordance with the non-prescriptive thesis, the judge (because of the duty to give reasons) is obliged to recognize that a 16 year old person may not be admitted as a soldier.

2. (xxii) however, the Captain, the military official competent to approve soldiers’ applications (and no norm requires him to give reasons) only has a technical duty, which means that, if she firmly believes that a 16 year old person is apt for the military, then she is free to decide that such person may be admitted.

3. (xxiii) this means that the norm sentence «it is forbidden to admit minors of age as soldiers» has two legitimate outcomes depending on the agent: if it is a judge, «minor of age» is a person less than 18 year old; if it is the Captain competent to approve applications, «minor of age» is whatever he thinks it is.

There is yet another problem (problem₃) affecting the non-prescriptive thesis, particularly when it is assumed that the duty to give reasons fails (as it does) as the ground for the «normativity» of conceptual norms. As said, a conceptual norm is a decision upon an equivalence (a stipulative definition), which means that an «A counts as B» has been posed. However, one thing is the «stipulation» and another one is its «propositional content», being the latter, for such thesis, the sole meaning of the enacted sentence.²⁰ And the core of the problem lies exactly here: if as a decision (upon an equivalence) the conceptual norm has no truth value, the same cannot be said about the equivalence in itself. There is (some) truth-aptitude in the equivalence and, without the (irrelevant) duty to give reasons, the non-prescriptive thesis opens the door for a breach of Hume’s Guillotine.²¹

The first point is that, while enacting the equivalence, the normative authority established a «new connection» between two terms that, hereinafter, «is» the way they stand towards each other among the speaker (normative authority) and the addressees (agents). That such «new connection» exists is an undeniable fact for the reason that it has been explicitly created: one cannot deny that within the interaction among agents some «A» is now equivalent to some «B» irrespective of whether being linguistically used or not as such by the agents at stake.²² Accordingly, when assumed within the legal domain, the equivalence is also an assertion of its own existence, which means that it brings with it a clear «environment» of indicative speech. A sentence comprising only «A counts as B» expresses a true proposition regarding how «A» and «B» stand towards each other (Walton, 2003:21; Robinson, 1950:63).

The second point is that, although the decision upon an equivalence lacks true value as such, terms stipulatively coined as equivalent can lead to true or false statements. If a minor of age is a person under 18 years old it is necessarily true that a 16 years old person is a minor as, in the same way, it is necessarily false that a 21 year old person is also a minor.²³ Thus, the equivalence works a «truth-maker», which is something one cannot say about the content of a linguistic prescription: from «minors are forbidden to be admitted as soldiers» no analytical proposition can follow since it merely leads to contingent statements. Without the «prescriptive pragmatic value» given by its stipulation, such specific condition of the equivalence shows that a sentence solely containing an «A counts as B» is not at all «normative».²⁴

1. (xxiv) if the semantic content of the norm sentence «a minor (m) is a person under 18 years old (o)» is only «m⇔o», then, besides generating analytical propositions, such sentence has true value as to the existence of the reciprocal position of «m» and «o»; by itself, «m⇔o» is an «is entity».

2. (xxv) «minors of age are forbidden to be admitted as soldiers» has a prohibition whose scope depends on what a «minor» is; claiming that a «minor» ought to be understood as in «m⇔o» is to derive an ought from an is («m⇔o» as such does not oblige anyone as to what is a minor).

IV. The alternative theory: the prescriptive thesis

As it is of no surprise, contemporary normative systems are full of norms regarding mental actions. It is the case, for instance, of the norms of proportionality. When a system contains a norm imposing «the more the losses on one norm, the more the gains on the conflicting one», the system is imposing that the intellectual operation of carrying out a balancing is limited by a constant of direct proportionality, specifically regarding the losses and gains that follow from some measure instantiating two contradictory deontic consequences.²⁵ Balancing is a clear case of a mental action and cannot be confused with the action of giving reasons by a judge: one thing is to assess which one of the conflicting norms should prevail (mental action), another totally different is to write the court’s decision exposing the whole intellectual process (correspondent overt action).²⁶

This is also the case of interpretative norms. When a normative system contains a norm «imposing» that linguistic indeterminacies in norm sentences should lead to the meaning most in accordance to the relevant constitutional norms (konforme Auslegung), it clearly follows that a mental action is being regulated: to interpret the uncertain norm sentence preferring the meaning closest to the constitution.²⁷ Yet, to know how such action is supposed to be externalized is a totally different problem. Thus, if it is a judge, the usual is to write a decision explaining the interpretation carried out; but if it is a scholar giving a class, the usual is just to tell the students which is the most constitutional friendly meaning and why it ought to be chosen. Be it as it may, no doubts should exist about the difference between the mental action and the overt one.²⁸

As it is already understandable, mental actions play a relevant role in law. Whenever there are (intellectual) actions to be carried out regarding the law, the usual is to have a norm regulating such action, regardless of the overt action that might make it observable. But this is, at the same time, the main problem related to mental actions: they are not visible until some overt action exposes them and enables an assessment of compliance (or non-compliance). Yet, two points are relevant here. The first one, and as already mentioned, is that the invisibility of mental actions does not mean that they and the possible correspondent overt actions are the same. The second one, and for the same reason, is that a norm regulating a mental action only covers such action and not the overt one. Nothing justifies that a mental action, just for being invisible, should be taken as another one.

The core of the prescriptive thesis on conceptual norms lies exactly on mental actions and on their regulation by the norms of the system: a conceptual norm is an imposition to qualify an «A» as a ««B» (a mental action), commanding the agent (the primary addressee, be it a judge or any other agent) to apply the equivalence.

Accordingly, whenever there is a norm in the system such as the one expressed in «a minor is a person under 18 years old», this means that the normative authority imposed the addressees to qualify whoever is under 18 years old as a minor (irrespective of how the qualification is supposed to be used). Naturally, it follows that this norm is violated whenever the mental action is not correctly performed; that is, when the agent somehow intellectually conceives that a 20 year old person is a minor.

1. (xxvi) the norm in «a minor (m) is a person under 18 years old (o)» is an imposition to «qualify (q)» a «person under 18 years old» as a «minor» or, which is the same, an imposition to observe the equivalence (to mentally qualify «m» as «o» and vice-versa): «O q (m⇔o)».

2. (xxvii) from this it follows that, whenever an agent qualifies «m» as anything else than «o» (or vice-versa), such agent is violating the norm in «a minor is a person under 18 years old»; how such violation can be assessed is a totally different problem.

Understanding (and explaining) conceptual norms as norms that impose a specific «qualification», precisely the one that follows from the equivalence expressed, is a complete understanding regarding the whole category of conceptual norms. Therefore, it is valid to definitory norms (in the narrow sense), but also to norms on the conditions of a type, norms on the equivalence of things or norms on statuses, just to stick to the subcategories mentioned: in all of them it is possible to find the equivalence and the imposition to follow what has been put as equivalent. Therefore, it can be said that in conceptual norms the equivalence is merely a sort of «complement»: conceptual norms deontically modalize the action of qualifying something as something else and such complement is simply the specification of what are «A» and «B» in the «A counts as B» at hand.

1. (xxiii) «a will (w) is a document signed by the author (a) before an official (o) and two witnesses (t)» is an example of a norm sentence with a norm on the conditions of a type; as an imposition to «qualify (q)», it is: «O q (w⇔a∧o∧t)»; accordingly, the equivalence (w⇔a∧o∧t) is only a complement in the consequence: it is the specific object of the mental action «to qualify» foreseen in this norm.

2. (xxix) «the Portuguese Flag (p) is the one adopted by the Republic formed by the Revolution of October 5, 1910 (f )» is an example of a norm sentence with a norm on the equivalence of things; as an imposition to «qualify (q)», it is: «O q (p⇔f)»; accordingly, the equivalence (p⇔f) is only a complement in the consequence: it is the specific object of the mental action «to qualify» foreseen in this norm.

3. (xxx) «citizenship (c) is recognized by birth (b) or naturalization (n)» is an example of a norm sentence with a norm on the conditions of a status (citizenship); as an imposition to «qualify (q)», it is: «O q (b∧n⇒c)»; accordingly, the equivalence (b∧n⇒c) is only a complement in the consequence: it is the specific object of the mental action «to qualify» foreseen in this norm.

4. (xxxi) «a citizen (c) has the rights to vote (v) and to be designated to public bodies (d)» is an example of a norm sentence with a norm on the consequences of a status (citizenship); as an imposition to «qualify (q)», it is: «O q (c⇔v∧d)»; accordingly, the equivalence (c⇔v∧d) is only a complement in the consequence: it is the specific object of the mental action «to qualify» foreseen in this norm.

This conception calls for what seems to be another of the theoretical deficiencies of the non-prescriptive thesis: the reductive approach by which the text of the equivalence is to be taken as fully corresponding to the entire norm. As it is so frequent, while uttering a norm, and for the most various reasons, a normative authority omits some norm elements (the antecedent, the deontic operator in itself, for instance).²⁹ For the prescriptive thesis, the same is usual with conceptual norms: a conceptual norm is much more than the «A counts as B» that is frequently the unique text enacted. Besides the equivalence (only a part of the consequence) there is also an action (to qualify, also part of the consequence) and a deontic modalization. And, as with any other norm, there is an antecedent as well: applying a conceptual norm always depends on some condition (implicit or not).

1. (xxxii) understanding the norm expressed in «a minor (m) is a person under 18 years old (o)» as «O q (m⇔o)» allows one to see, besides a deontic modalization (O), a consequence formed by an action (q) and its complement (m⇔o); this is, however, still reductive.

2. (xxxiii) the obligation to qualify «m» as «o» (and vice-versa) only applies whenever «minor» is used in another norm sentence (that is, whenever there is an opportunity to perform the action foreseen); thus, there is also an antecedent: something as «whenever there is a legal mention to minor» (opp).

3. (xxxiv) not discussing now the possible correlativity under a conceptual norm, there are also (at least, primary) agents: those under the imposition to qualify; that is, everyone (or interpreters, as another possibility); a formal representation could be, then: «opp⇒oagentsq(m⇔o)».

It is claimed by the prescriptive thesis, therefore, that conceptual norms (as any other norm) are complex structures, with a conditional morphology as any other, in which the equivalence is just a small part of the story. Reducing the conceptual norm to the equivalence, besides implying a quite peculiar criterion of norm individuation (why is an equivalence a complete norm ?), is to disregard as well that nothing prevents norms on mental actions, that nothing prevents such actions to be under an imposition to observe some «rule» (mathematical or logical, for instance), and that normative systems are full of norms that deontically modalize actions with a «complement». Accordingly, when conceptual norms are seen in their completeness, there are no reasons to sustain that «the one and the same norm cannot be simultaneously conceptual and prescriptive».³⁰

1. (xxxv) the norm in «a minor (m) is a person under 18 years old (o)» can be represented as «opp⇒oagentsq(m⇔o)», showing that conceptual norms have the same complex structure visible in any other norms; particularly, it shows that the equivalence occupies only a small part of such structure.

2. (xxxvi) the norm in «constructors ought to batch concrete (bc) under the ratio of 10 of sand (s), 2 of cement (c), 5 of water (w) and 2 of gravel (g)» can be represented as «opp⇒oconstructorsbc(s:c:w:g=10:2:5:2)», showing a «current» norm in which the consequence also has a mathematical limitation for the action at hand.

On the other hand, it is important to say that the invisibility of mental actions is not particularly relevant for the prescriptive thesis. In other words, to know which are (or might be) the overt actions through which the compliance with a conceptual norm can be assessed is not decisive for that theory. Actually, it depends on the context and on the consequences that follow from the «qualification» (or the purposes aimed with it). Accordingly, two situations are possible: (i) when one can clearly see that the illegal behavior rests solely on the violation of the conceptual norm; and (ii) when such violation is not ascertainable per se, solely being possible to identify a violation of a norm regarding an overt action. However, these latter cases are of no relevance for the prescriptive thesis: rigorously, it is a strict empirical matter solely dependent on evidence.³¹

1. (xxxvii) with «a minor is a person under 18 years old» and «it is forbidden to admit minors as soldiers» one can conceive the following scenario: the Captain competent to admit soldiers in the military rejected an application from Guglielmo on the basis (as he wrote in a formal justification) that the applicant is a minor because she is 21 years old: here, it seems clear that the Captain violated the duty to qualify Guglielmo as a non-minor (unless he has given the wrong reasons).

2. (xxxviii) however, and under the same norms (and just those), if the Captain competent to admit soldiers decided to reject Guglielmo application without giving reasons or just saying that «the applicant is not fit to the demands of the military» (which is not a legal reason to reject), no one knows (and it seems hard to prove) whether the Captain complied or not with the duty imposed by the conceptual norm; yet, this is of no relevance to the prescriptive thesis: although hard to prove, it is merely a matter of evidence.

V. Answering a criticism

Recently, the prescriptive thesis has been criticized by Rodríguez, particularly with an eye on definitory norms in the narrow sense. As he says, it makes no sense to think that any agent is under an obligation to adopt a specific definition, namely when such definition is or can be (theoretically) contested; it would make sense to say that adopting an alternative definition is or can be somehow incorrect, but not that it is forbidden (Rodríguez, 2021:249). Rodríguez’s criticism is, however, misplaced. No one ever said, as far as it is known, that a definitory norm entails an obligation to use a definition tout court (namely in colloquial conversations). It is indeed devoid of sense to say that a definitory norm imposes a definition to speakers as it is to say that it follows from such definition a prohibition to use the word with other meanings. But such an idea is alien to the prescriptive thesis.³²

Rodríguez criticism is helpful, however, since it creates the opportunity to clarify one of the main pillars of the prescriptive thesis: that the mental action of «qualifying» is imposed for some purposes, irrespective of the overt action with which it can be assessed. As a matter of fact, it would be pointless to prescribe a mental action if there were no ways to «receive» the specific output given by such action. Thus, in the same manner that carrying out a balancing ought to observe some norms because the normative system does not want disproportionate balancings; the normative authority, while prescribing a certain definition, also wants a specific meaning to be ascribed to a norm sentence (containing the word defined). And, obviously, this is the sole scope of the definitory norm: no one is forbidden to use (as a speaker or whatever) such word with other meaning.

Rodríguez’s criticism seems to be, at its origins, a problem of norm individuation: it fails to understand that the definition in itself is only a specific part of a wider normative structure (specifically, a part of the norm’s consequence) and that within such structure there is also an antecedent demarcating the action of «qualifying» as mandatory only in some circumstances (when a norm sentence comprises the word defined). But, for the prescriptive thesis, it is correct to say that there is here a prohibition: it is forbidden to assign to a norm sentence a different meaning than the one foreseen in the conceptual norm. So, when an agent is not carrying out the mental action of qualifying in the way the normative authority imposed, it follows that an «illegal interpretation» has been performed, an output totally due to the violation of the conceptual norm.

1. (xxxix) the norm expressed in «a minor is a person under 18 years old» can be represented as «opp⇒oagentsq(m⇔o); if the addressee is obliged to qualify in accordance with the equivalence, then she is forbidden to qualify otherwise (0q[m⇔o]≡F∼q[m⇔o]);

2. (xl) interpreting «minor» in «it is forbidden to admit minors as soldiers» as a person under 16 years old is forbidden by the conceptual norm; consequently, the admission of a 16 years old person in the military follows from an «illegal interpretation» based on the violation of the conceptual norm.

VI. On norms on the condition of a type: illegality and sanctions

As seen before, norms on the condition of a type also have a complex structure in which the equivalence (specifically, the necessary conditions of the type) is only the final part of the conceptual norm’s consequence. Following the structure already seen, a norm on the conditions of a type also has: (i) an antecedent, regarding the possibility of qualifying some legal act as an act of the type; (ii) a deontic modalization, an imposition (as it is typical in conceptual norms); and (iii) a consequence, whose first part is the mental action of qualifying as a token of the type the legal act at hand whenever its conditions are present. Therefore, this kind of conceptual norm is violated when: (i) the conditions are present but the act is not qualified as one of the type; or (ii) the conditions are not present (at least, one of them) but the act is still qualified as a token of the type at hand.

1. xli) «a will (w) is a document signed by the author (a) before an official (o) and two witnesses (t)» is an imposition to «qualify (q)» as a will any document in which «a∧o∧t» are present; since it is only applicable when such qualification is required, the complete norm is: «opp⇒Oagentsq(w⇔a∧o∧t).

2. (xlii) an agent violates the norm whenever: (i) «a», «o» or «t» are not present and the document is taken as a will; or (ii) «a», «o» and «t» are all present and the document is not qualified as a will; if a judge qualifies some document as a will in the first case and does not in the second, she is violating the law.

An initial consideration that follows from such structure, and keeping with the will’s example, is that a conceptual norm of this kind is not a competence norm. As it normally happens in contemporary normative systems, a will is a type of act of private law that can be performed under a general competence norm that enables all agents to produce deontic consequences: be it contracts or specific unilateral acts such as a will. Accordingly, the power to produce the deontic consequences aimed with the will already existed irrespective of the norm on the condition of a type: this norm just specifies conditions for a «legal» token. Therefore, the conceptual norm does not regard power in itself; differently, it just regards the conditions that will instantiate the type. It is a norm regulating the exercise of competence, not a norm of competence.

1. xliii) a norm such as «opp⇒Oagentsq(w⇔a∧o∧t) is not a power conferring norm: it deals with the conditions to have a token of a type; the power to produce deontic consequences follows from a norm more or less similar to the one in «agents can celebrate contracts and specific unilateral acts».

2. (xliv) if Guglielmo (a soldier) complies with «opp⇒Oagentsq(w⇔a∧o∧t), but he does so in a normative system in which all agents have power to conclude private law acts except soldiers (these do not have power to enact wills), then his will is perfect regarding such conditions, but still illegal: he has no power.

The same can be said about competence in a public law environment. Usually, there is a norm conferring power on some topic to a specific body and such norm has no other content than this. Any other norm specifying the conditions of a type just lists the necessary requirements in order to exercise such competence with a token of the type. It is this other norm that can be properly designated as a norm on the conditions of a type (a conceptual norm, as seen). As it happens with the will example, also in this case there is a clear difference between the power conferring norm and this specific kind of conceptual norm. While the former merely confers the «ability», the latter establishes the conditions to exercise such power with a «proper» token. And again, if it is violated, the conceptual norm does not lead to an illegality related to competence.

1. (xlv) the Captain competent to admit soldiers has a power given by a norm such as the one in «the competence to admit soldiers is assigned to the Captain»; yet, such power exists along with a conceptual norm: the one in «admission of soldiers in the military is an unilateral act signed by its author upon an opinion given by the Supreme Military Council and published under the form of a “military order”».

2. (xlvi) in this public law environment there is also the same difference: the first norm is a power conferring one, and the second a norm on the conditions of a type; therefore, if Guglielmo is admitted as a soldier by an act the Captain did not sign or by an act published under the format of a «military warning», then such act is illegal; however, it is not illegal for reasons related to power: it is just not a token of its type.

Once it is taken into consideration that a norm on the conditions of a type is not a competence norm and, moreover, that it can be violated as any other, it follows that the specific illegality provoked by such violation is sanctioned if the normative system comprises norms «with sanctions» associated to the violation of the conceptual norm. Some common possibilities are the following; the normative system has a norm: (i) stating that the act at hand does not produce deontic consequences and it is removed from the system; (ii) imposing that, although provisionally, the act produces deontic consequences until removed by a court; or even (iii) suppressing the negative relevance of the violation. Of course, if none of these norms exist in the system (or exist but are not connected with the conceptual norm), then the violation is inconsequential.

These considerations point towards a complete parallel between the consequences of violating a norm that forbids or imposes some brut (overt) action and the consequences of breaching any conceptual norm. As with the former, with the latter the normative system either associates or not a specific «sanction» to a violation: (i) if it does not, there is only a duty to «qualify» although inconsequential if breached; but (ii) if it does, then the token of the type bears the sanction specifically foreseen. It is of no surprise then that these norms with sanctions associated to norms on the conditions of a type project their sanctions on the act at hand (and not on the agent): a norm on the conditions of a type regulates the exercise of competence and a «legal act» is exactly the outcome of such exercise; sanctions could only affect acts therein produced.

Under the conception sustained by the prescriptive thesis, it seems incorrect to say, then, that conceptual norms lack an external sanction and that such aspect is a reason to differentiate them from the whole category of norms that regulate behavior: conceptual norms are regulative as any others and are (usually) associated to sanctions when violated (in the exact terms foreseen in such norms). On the other hand, it also seems wrong to say that sanctions associated to conceptual norms do not have a «motivating» component (as Hart claimed): in order to avoid the negative consequences (usually) foreseen, any holder of power «knows» that the conditions presented by a conceptual norm ought to be observed. Otherwise, a possible sanction will damage the deontic consequences aimed (leading possibly to their removal from the system).

VII. Conclusion

The two theories discussed throughout this article are totally incompatible. In such a «winner takes it all» theoretical situation there is no other alternative than to assess and evaluate the explanatory power of each one. It was argued here that the prescriptive thesis has more explanatory power. Not so much because of its merits, but because it does not share the flaws of the non-prescriptive thesis. Indeed, it seems that this thesis has unsurmountable internal inconsistencies (problem₁ and problem₂, as exposed), comprising additionally a serious confrontation with Hume’s Guillotine (problem₃) whenever one tries to solve such internal inconsistencies. Taking all into account, the best explanation for the present «why-question» (which kind of «entities» are conceptual norms) is given by the prescriptive thesis. Actually, it is claimed here that the prescriptive thesis solves all those problems without introducing new ones.

Acknowledgments

I would like to thank the participants in the 2022 Maastricht-Lisbon Seminar on Legal Theory and the participants in the V Lisbon Meeting on Legal Theory for their helpful comments on a previous draft of this paper, specifically Mathis Notermans, Jaap Hage, Antonia Waltermann, Pedro Moniz Lopes, Sara Azevedo, José Duarte Coimbra, Marek Jakubiec, Stefano Bertea and Jorge Silva Sampaio. I would also like to thank two anonymous referees for their constructive remarks. Finally, I am also grateful to the Lisbon Public Law Research Center and the Fundação para a Ciência e Tecnologia for their financial support.

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Notes

¹ Although the expression «normative systems» includes both moral and legal systems (and probably others), it is used here to refer to legal systems only (as in Alchourrón and Bulygin [1971:3]).

² Besides the usually designated «technical norms». These, however, are definitely not norms (or do not deserve the label) since they clearly are the content of a descriptive speech act: the act of informing how to reach a certain goal. It is for this reason that it would be better to designate them as «technical directives». Von Wright (1963:9), Black (1962:110).

³ On the concept of conceptual norms, Alchourrón and Bulygin (1991:463); Mendonca (2000:114). Also, as «count-as-rules», Hage (2018:102).

⁴ Understanding a tautology as a relation that is necessarily true (true in all possible worlds [m≡m]), a biconditional as the one that is true when their propositions are both true or both false in a given possible world (m⇔o), and a conditional as a relation that in a given possible world is true in all cases except when the antecedent is true and the consequent false (l⇒m).

⁵ In the system or in a specific statute (or similar set of provisions). Actually, one of the most difficult problems arising from definitory norms is exactly to grasp which is their material scope: whether the formal act in which they are formulated or the whole normative system. The solution seems to be, though, contingent (and of interpretative nature). It is also relevant to note that, rigorously, definitory norms establish the equivalence between some «word» (or words) and «other words», being the meaning of the latter the one that becomes equivalent to the meaning of the word defined.

⁶ For the sake of simplicity, only making reference to formal aspects of a will (a current example on this topic; for instance, Hart [1961:30], Rodríguez [2021:250]).

⁷ Evidently, norms on conditions of a type are also definitory norms (probably even in the narrow sense). However, the difference between the problems they raise and the ones posed by definitory norms in the narrow sense (to be addressed later on) seems to justify their autonomy.

⁸ Article 11/3 of the Portuguese Constitution.

⁹ Differently from consequences of the status that (at least usually) are conjunctive. On the conditions for a status, Hage (2018:106). As known, «sufficient conditions» in conditions and «necessary and sufficient conditions» in consequences follows the scheme presented by Ross in the middle term tû-tû (Alf Ross [1957:819]). Also, Lindhal (2004:183).

¹⁰ On stipulative definitions, Horty (2007:34), Pap (1964:50).

¹¹ For conceptions of constitutivity, Hage (2018:109), Roversi (2012:9).

¹² On this «effect» of constitutive norms, Ross (1968:53), Carcaterra (2012:103).

¹³ It could be said that a competence norm is a conceptual one given that it also advances a specific equivalence: that an «exercise of power» counts as «producing deontic consequences» (Hage [2018:206], Orunesu and Rodríguez [2022:206]). Although the whole issue might be under some contingency, this is not (usually) true. In contemporary legal systems, the action of producing deontic consequences is dependent on conditions other than power (norms on procedure, norms on the form of the act or even norms on the legitimacy of content, and several of them are mere norms of conduct). Therefore, given that the exercise of power is not a sufficient condition for the action at hand (deontic consequences depend on such norms and other norms foreseeing sanctions in case of violation), a competence norm does not contain an equivalence.

¹⁴ A statement that, as far as it is known, has never been justified in any way (the statement in, Alchourrón and Bulygin [1991:494]).

¹⁵ Thus: if a private definition changes the law, then one must admit that common people have power to change norms enacted by normative authorities (which is false, at least within the contemporary legal systems known); if a private definition does not change the law, but an official one does (as claimed by the non-prescriptive thesis), then they cannot have the same (normative) value. Be it as it may, the main point is that the nonprescriptive thesis clearly states that the scope of a regulative norm is modified by the official definition. As Alchourrón and Bulygin say «there are two ways to change a normative system: to change its norms or to change the definition of the terms foreseen in them». Alchourrón and Bulygin (1991:454).

¹⁶ Which is what the non-prescriptive thesis defends. Alchourrón and Bulygin (1991:452). The next example is an adaptation of the example used by Alchourrón and Bulygin (Alchourrón and Bulygin [1991:452]) within the pattern of examples used here.

¹⁷ Which leads to the proposition defended by the non-prescriptive thesis according to which while the judge is under a legal obligation, any other agent is subject to a technical directive. Alchourrón and Bulygin (1991:451).

¹⁸ Which undermines the explanatory power of the duty to give reasons as a justification for the normativity (only felt by judges) of conceptual norms: it is a wrong way to «explain» why judges (specifically) are bound by conceptual norms. Also with a formal conception of the duty to give reasons, Marin (2013:104), MacCormick (2005:277).

¹⁹ Other points regarding the present issue of addressees can also be considered. The first is that the duty to give reasons is contingent. It should follow for the non-prescriptive thesis, then, that in normative systems without such duty conceptual norms are mere «technical directives» (which is, somehow, a disappointing outcome when one thinks that in such systems conceptual norms would be enacted for nothing as to the wordworld direction of fit). However, and second, even if the duty to give reasons is accepted as a regularity in contemporary normative systems (working with it as if it was a necessary content), one has to accept as well that the very same systems usually foresee a norm such as «the ignorance of law is not an argument», which implies that each and every agent, in order to comply with the law, has to identify the norms as well and behave in accordance: by enacting such norm the normative authority is also imposing that law ought to be known (identified) by everyone. So, it seems that, even on this basis, no difference can be drawn between a layperson and the judge: in both cases (the judge and all the others) there would be a «parallel norm» giving equal «normativity» to conceptual norms.

²⁰ On the difference between the propositional content and the pragmatic component, Macagno (2010:200). And on the structure of definitions, Hansson (2006:9).

²¹ Which means that, under such thesis, there is no possible justification for conceptual norms to change the existent law. On Hume’s Guillotine (Hume [1888:466]), Von Wright (1998:365), Black (1964:168).

²² Already an old idea: Arnaud and Nicole (1850:81).

²³ As the non-prescriptive thesis also says. Alchourrón and Bulygin (1991:458).

²⁴ On analyticity and stipulative definitions (and the correlated broader Quinean discussion on analyticity), Lycan (1994:263), Boghossian (1996:360). On truth-makers, Restall (2009:88). On the other hand, it could be said that the conceptual norm only creates a fact and that it is such fact that triggers other norms (without derivation; only a simple and normal case of filling an antecedent). However, the argument is flawed for the reason that such (institutional) fact is legally created and depends on some normativity to meet the conditions of an antecedent. Therefore, without normativity of its own (as claimed by the non-prescriptive thesis), the conceptual norm either does not change the law or falls into an is/ought fallacy.

²⁵ The reference is to the known and so-called «substantive law of balancing» (one of the various norms of proportionality). In its original formulation, Alexy (2002:401) and in a more aseptic formulation, Duarte (2021:41).

²⁶ On mental (and overt) actions, Mele (1997:231), O’Brien (2015:58).

²⁷ On constitution-oriented interpretation, Pierluigi Chiassoni (2019:71). On interpretative norms, Duarte (2018:143).

²⁸ And, consequently, on the fact that the interpretative norm regulates the mental action and not the overt one.

²⁹ On this kind of linguistic insufficiencies, Ross (1958a:158), Grabowski (2009:137).

³⁰ As Alchourrón and Bulygin claimed (1991:494). Defending the prescriptive nature of legal definitions, although in different terms, Ross (1958b:149).

³¹ A problem that recent developments in cognitive sciences might resolve in the future, namely by picturing the brain and assessing if the violation happened regarding the conceptual norm or the one regulating a possible overt action. For instance, Pardo and Patterson (2010:1227); Mahlmann (2007:588).

³² It is not understandable as well why, while putting forward this criticism, Rodríguez remits the topic to a chapter in which he addresses Dworkin’s «one right answer» (Rodríguez [2021:249]). As far as it is understandable, there is no connection whatsoever between the prescriptive thesis and such theory: one thing is to sustain that there is only one right answer for a case no matter the linguistic indeterminacies found in norm sentences (or other problems leading to hard cases); another, totally different, is to sustain that, when a normative authority enacts a definitory norm, such authority is imposing a specific norm sentence to be interpreted in a certain way regarding one of its words. Definitory norms (somehow unfortunately) do not solve all legal problems and fall short to be the cause of judicial discretion’s death.