Towards a Sigmatics of the Word ‘Norm’: An Ontological Turn in the Semiotics of the Normative

During the twentieth century, the development of semiotics and philosophy of language had a great influence on the investigation of normative phenomena, particularly within the philosophy of law: the analysis of normative language became the prevalent methodological approach among many legal philosophers, and the science of law was frequently understood as an analysis of the object language of law. This approach led to the development of a linguistic ontology of the normative and to a semiotic theory of the validity of norms, in which norms are conceived of as linguistic entities, and their validity is accordingly conceived of as a predicate of normative sentences. However, the resort to a semiotic approach for the investigation of normative phenomena does not necessarily imply the adoption of a linguistic ontology of norms. The semiotic analysis of the possible referents of the word ‘norm’ elaborated by Conte (“Studio per una teoria della validità”, Giappichelli, Torino [1970]1995; entry “Norma” in Enciclopedia filosofica, Bompiani, Milano, 2006) shows that the word ‘norm’ may alternately refer to both linguistic entities and non-linguistic entities, such as deontic states-of-affairs and deontic noemata. Such a “sigmatic” analysis exhibits the relevance of the ontological notion of deontic states-of-affairs, and of the correlative notion of “syntactical validity”. After reconstructing Conte’s theory of validity, we wonder whether validity is necessarily to be conceived of as systemic validity, or also an asystemic and factual validity of norms should be considered.

"All Questions of Law are no more than questions concerning the import of words.
Questions the solution of which depends upon skill in Metaphysics". Jeremy Bentham.

A Semiotic Turn in the Ontology of the Normative
In their critique of natural law theories, legal positivists and legal realists generally share the refusal of any metaphysical commitment implying the reference to transcendental and non-empirical entities and maintain the claim that the law must be investigated exclusively as an empirical phenomenon. 1 This approach led many authors to focus on the use of language in legal practice, and not unfrequently to conceive of law itself as language. Jeremy Bentham, who is considered one of the founding fathers of legal positivism, famously stated not only that "all Questions of Law are no more than questions concerning the import of words" [3, p. 282], but also that "a law may be defined as an assemblage of signs declarative of a volition conceived or adopted by a sovereign in a state" [2, p. 88].

The Science of Law as Analysis of Normative Language
During the twentieth century, the development of semiotics as a scientific discipline on the one hand, and the strong influence exerted by logical empiricism and the linguistic turn in philosophy on the other hand provided new and more refined conceptual tools and gave further impetus to the investigation of legal phenomena in terms of linguistic phenomena, especially among legal positivists. 2 In a pioneering work [53], Felix Oppenheim expressly outlines a plan to build a logical and semiotic analysis of law, whose starting point is the claim that "law may be viewed as language": Legal rules, decisions, commands, are generally expressed by words and expressions of a natural language, like English. If non-linguistic signs are used, e.g., the whistle of the policeman, stoplights, gestures -it is always possible to translate them into the word language. We may therefore consider the law of any given community at any given moment as a class of sentences, constituting a language which expresses the legal rules, decisions, commands of that community at that moment [p. 142]. 3 Despite the fact that many legal positivists, in light of their rejection of metaphysics, also avoid committing to any kind of ontological claim, the wide recourse to semiotics and linguistic analysis in the investigation of law and the identification of law as the object language of the science of law induced to identify norms with linguistic entities and thus to adopt a linguistic ontology of the normative. Norms are indeed conceived of by many legal positivists as linguistic entities. For instance, Bobbio expressly asserts that "from a formal point of view […] a norm is a proposition", and that "a code, a constitution are sets of propositions" [7, p. 48]. More specifically, "legal norms belong to the category of prescriptive propositions" [p. 48], where propositions are defined by Bobbio as "set[s] of words having a meaning as a whole", and the specific function of prescriptive propositions-as opposed to descriptive and expressive ones-consists, for Bobbio, in getting someone to do something [p. 53].
Scarpelli, on his part, defines norms as "linguistic propositions that have actually been uttered by certain persons on certain occasions" [66, p. 59] and gives the following characterization of juridical propositions: A juridical proposition consists in a complex of meaningful words in an intersubjective language which connects certain facts as a juridical condition (fattispecie) to other facts as juridical consequences [65, p. 42]. 6 In a later work, Scarpelli underlines the prescriptive character of imperative norms, which he defines as "propositions-i.e., sequences of meanings expressible in a language-that prescribe behaviours" [67, pp. 10-11].

A Logical-Semiotic Theory of Legal Validity
A consequence of the linguistic conception of norms consists in the fact that the theory of legal validity is accordingly elaborated as a semiotic theory of validity: the validity of a legal norm is conceived of as the belonging of a normative proposition to the object language of law, and such belonging depends upon specific conditions which are characterized in logical-semiotic terms.
The construction of the science of law as an analysis of language and the correlative elaboration of a logical-semiotic theory of legal validity are inspired by Charles Morris' conception of semiotics [47] and by Rudolf Carnap's notion of a logical syntax of language [12]. Under such a perspective, syntactical analysis is specifically concerned with the "logico-grammatical structure of language" [47, p. 14] and aims at the determination of two classes of syntactical rules: (i) formation rules, which determine "permissible independent combinations" [p. 14] of the basic elements of a language, such combinations being called sentences; (ii) transformation rules, which determine the sentences which can be obtained from other sentences.
Within this context, the theories of legal validity were mainly focused on the transformation rules that are to be satisfied in order to derive a legal norm from other pre-existing legal norms. The typical example is that of the derivation of the ruling of a court from the norms of the penal code.
From this perspective, the formal theory of validity proposed by Hans Kelsen was explicitly understood by Scarpelli as "the most serious and rigorous attempt at a syntactics of juridical language" [66, pp. 58-59], in which the assessment of the validity of a normative proposition is made through a logico-deductive line of reasoning moving from a normative proposition taken as the normative premise. 7 Scarpelli clarifies that 1 3 Towards a Sigmatics of the Word 'Norm': An Ontological Turn… the logico-deductive procedure is made possible by the linguistic nature of the propositions that constitute the premise and the consequence and by the belonging of the linguistic signs composing them to one and the same language characterised by a logical syntax [66, pp. 69-70].

Deontic vs. Dianoetic Validity
The fact that the semiotic theory of the validity of norms has long been focused mainly, if not exclusively, on the syntactical conditions of validity of normative propositions had an important drawback: it led to disregarding the difference existing between the validity of an inference-or derivation-of a proposition from other propositions on the one hand, and on the other hand the specific validity which pertains to norms. This difference has been clarified by Conte [19] through the distinction of deontic validity and dianoetic validity. The validity characterizing an inference, or a derivation, is a logical validity, and more specifically, a dianoetic validity (see [19]). On the contrary, the specific validity pertaining to norms is called by Conte "deontic validity" [19].
Dianoetic validity is the validity of a logical inference, or derivation, of a proposition (the conclusion) from another proposition, or set of propositions (the premises), and it depends upon the syntactical transformation rules of a language, which are understood as logical rules. A typical example is that of the derivation of a descriptive proposition (the conclusion), such as 'Socrates is mortal', from the two descriptive propositions (the premises) 'All men are mortal' and 'Socrates is a man'. But does the dianoetic validity of an inference or derivation of a normative proposition from other given normative propositions imply also the deontic validity of the corresponding norm within a legal system?
The distinction of deontic from dianoetic validity started to emerge from the question addressed by Kelsen [39,40] on the applicability of the logical principle of contradiction and the rule of inference to legal norms. 8 Within this debate, von Wright [76] and Conte [19] ultimately made clear that the dianoetic validity of an inference of a normative proposition from another normative proposition, or set of propositions, is not a sufficient condition for the deontic validity of the corresponding norm within a legal system.
The distinction between dianoetic and deontic validity was already implied in the dynamic principle in which consists, for Kelsen, the positivity of law [38, p. 400]. According to this principle, it is not sufficient for the existence of a norm-i.e., for its deontic validity-that its content can be logically inferred, or derived, from higher order norms; it is also necessary that the norm be posited through a normcreating act of a law-making authority.
As Conte highlights, deontic validity "is not governed by the rules and laws of logic", but rather by the specific rules, or axiotic meta-norms, of a normative system that establish the conditions of validity of other norms within that system [22, p. 360n].

An Ontological Turn in the Semiotics of the Normative: the Concept of "Deontic States-of-Affairs"
The gradual acknowledgment that the dianoetic validity of an inference between normative popositions is not a sufficient condition for the deontic validity of the inferred norm within a legal system was connected to the emerging awareness that the validity of norms cannot be investigated exclusively with reference to the semantical and syntactical properties of normative propositions, and notably to the syntactical transformation rules of normative propositions.
Kelsen's dynamic model of the legal order, which is focused on norm-creating acts rather than on normative propositions, stimulated a closer examination of the pragmatical dimension of normative language. As we have seen, according to the dynamic principle of legal positivism, the fact that a normative proposition can be derived from another normative proposition is not sufficient to determine the validity and the existence of the corresponding norm within a normative system: it is also necessary that the derived norm be posited by an act of will performed by a delegated authority. 9 This principle thus required that the theory of deontic validity be expanded to also include the pragmatical validity conditions of norm-creating acts.
In a first stage, the awareness of the pragmatical peculiarities of normative language led to a clearer distinction between the prescriptive and the descriptive usages of normative, or deontic, sentences. 10 Later, though, at least in some authors-such as Kazimierz Opałek, Jan Woleński (see [49,50,51]) and Conte-the deeper analysis of the pragmatical dimensions of language that was developed within semiotics and the philosophy of language, and notably the elaboration of the theory of performatives by Austin [1] and Searle [69], eventually led to envisage a non-linguistic conception of norms. 11 11 As we recalled in note 7 above, Oppenheim [53] already envisaged the relevance of the pragmatical peculiarities of normative language for his view of the validity of the sentences composing a legal language; however, in 1944 he did not have at his disposal the conceptual tools introduced by John L. Austin's theory of performatives [1] and never delineated a non-linguistic conception of norms. 9 As Conte made clear, in a dynamic normative system the basic norm (Grundnorm) is a necessary, but not also a sufficient condition of the validity of all the other norms of the system [13, p. 362]. 10 Kelsen [38] notoriously distinguished between the Sollnormen, or "legal norms", and the Sollsätze, or "rules of law", through which the science of law describes the legal norms. However, it is not clear whether Kelsen's distinction is connected with the distinction of the pragmatical and syntactical dimensions of normative language.

3
Towards a Sigmatics of the Word 'Norm': An Ontological Turn…

Validity as a Predicate of Prescriptive Deontic Sentences
The gradual moving from a linguistic to a non-linguistic conception of norms is clearly documented in Conte, who was originally fully involved in the linguistic conception of law and norms inaugurated by Bobbio and Scarpelli and never ceased to consider the conceptual tools of semiotics fundamental for the investigation of normative phenomena.
In a first stage of his research on normative phenomena, notably in an essay [15] originally published in 1970, Conte elaborated a strictly semiotic theory of the validity of norms in which norms are still conceived of as linguistic entities. In this work Conte shifts the focus from the traditional question: "What are the conditions of legal validity?" to the more radical, and preliminary, question: "What is a theory of, the theory of the validity of norms?" [15, p. 57]. This new question aims at making explicit what is usually acritically presupposed by the more traditional questions about the conditions of validity of norms. Conte's question may be rephrased in the following terms: "What is the validity of norms predicated of?". The apparently obvious answer that the validity of norms is predicated of norms becomes less obvious when a further question is arisen: "What is a norm?".
In this work Conte still answers that a norm is a linguistic entity, notably a deontic sentence. What kind of deontic sentence, though?
Taking advantage of the recognition of the specific pragmatical dimensions of normative language, Conte indeed distinguishes three different kinds of deontic sentences, according to their respective pragmatical function: (i) prescriptive deontic sentences are deontic sentences that can be used, for instance, by a law-making authority to prescribe an obligation, a prohibition, etc.; (ii) descriptive deontic sentences are deontic sentences that can be used, for instance, by a jurist to describe an obligation, a prohibition, etc. existing in a legal system; (iii) ascriptive deontic sentences are deontic sentences that can be formulated, for instance, by an anthropologist or a social scientist who hypothetically traces back a regularity of behaviour to the existence of an obligation, a prohibition, etc.
Which one of these three kinds of deontic sentences is the object of the theory of the validity of norms, according to Conte? Conte states that validity par excellence is the validity of prescriptive deontic sentences. The traditional questions on the validity conditions of norms are to be accordingly understood in terms of the validity conditions of prescriptive deontic sentences. Rephrasing Kelsen's famous definition of validity as the specific existence of a norm, Conte defines the validity of a norm as the existence of a prescriptive deontic sentence within a normative language, i.e., as the belonging of a prescriptive deontic sentence to the object language of the science of law [15, p. 66].

Deontic States-of-Affairs
Despite his definition of validity par excellence as the existence of prescriptive deontic sentences, and thus of a specific kind of linguistic entities, in 1970 Conte [15] also suggests that the notion of "norm" cannot be reduced to that of a prescriptive deontic sentence. Conte notably acknowledges that the term 'norm' may alternately refer to four different kinds of entities, only the first three of which are linguistic entities. The four kinds of entities are: (i) deontic sentences; (ii) deontic utterances; (iii) deontic propositions; (iv) deontic states-of-affairs.
By 'deontic sentence' Conte means a sentence of the form 'The behaviour C is D' (where D designates one of the deontic modalities), or a synonymous sentence; by 'deontic utterance' he means the actual utterance of a deontic sentence; by 'deontic proposition' he means what a deontic sentence expresses, i.e., the meaning of a deontic sentence [15, pp. 61-62]. But what does Conte mean by 'deontic state-of-affairs'?
Conte [14,15] elaborates the concept of "deontic state-of-affairs" on the basis of a parallelism between descriptive and normative language: just like the descriptive proposition expressed by the sentence 'It is raining' is not to be confused with the extralinguistic fact, or (ontic) state-of-affairs, that it is raining, the deontic proposition expressed by the sentence 'It is forbidden to smoke' is not to be confused with the extralinguistic fact, or deontic state-of-affairs, that it is forbidden to smoke. 12 In 1970 Conte [15] resorted to the notion of deontic state-of-affairs in order to give a possible account of the controversial theory of the Natur der Sache, that is, the theory according to which there are norms that immediately originate from the very nature of things (Natur des Sache). 13 Since these norms are inscribed in the nature of things, they are not created by a linguistic act of prescription of a law-making authority. Conte's hypothesis is that they can be conceived of as 12 An analogous notion of "deontic state-of-affairs" was elaborated in the same years by the Polish legal philosopher Franciszeck Studnicki [73] and by the Estonian legal philosopher Ilmar Tammelo [74]. Both Studnicki and Tammelo proposed the notion of deontic state-of-affairs in connection with the analysis of the performative features of normative language. As we show in the following § 2.3., this connection inspired also Conte's subsequent investigations on the notion of deontic state-of-affairs. A neat distinction of "linguistic expressions of normative discourse on the one hand from ontological entities called norms, imperatives and judgments of value, on the other hand" has been traced also by the Serbian philosopher Jovan Brkić [10, p. 9]. 13 On the theory of the Nature der Sache see Schambeck [68]. Conte's consideration of the theory of the Natur der Sache was also motivated by Adolf Reinach's phenomenological theory of promising, according to which from a promise immediately originate-by its very nature-an obligation and a correlative claim [61]. deontic states-of-affairs existing independently of any deontic sentence, utterance or proposition. 14 Conte, however, was initially distrustful about the notion of deontic state-ofaffairs: this notion seemed to imply "a metaphysically compromised and methodologically compromising step": the hypostatization of norms (obligations, prohibitions, permissions, etc.). However, he eventually overcame his distrust thanks to the development of further investigations into the pragmatics of normative language which were inspired by the theory of performatives.

Thetic Performativity and the Conventional Existence of Thetic States-of-Affairs
Starting from a work published both in Italian and in German in 1977 [16,17], Conte investigates-in the light of the theory of performatives-a specific pragmatical property of prescriptive language: its thetic character. The thetic character of prescriptive-and more generally normative-language can be understood in the light of the distinction between thetic and athetic performative acts, which was later introduced by Conte in 1994 [23]. 15 According to Conte, athetic performative acts are performative acts-like thanking or greeting-by which the speaker merely performs the act corresponding to the meaning of the performative verb used by the speaker.
In the case of thetic performative acts, on the contrary, the speaker not only performs an act, but also immediately produces a change in the world: by performing the act, he alters the world. Examples of thetic performative acts are the acts of promising, baptizing and repealing: by promising a new state-of-affairs is produced, consisting in the existence of an obligation on the promisor to do what he promised to do and a correlative claim by the promisee; baptizing is not describing the name of someone or something, it is ascribing that name to someone or something, and it thus produces a new state-of-affairs; repealing is not saying that a norm is invalid, it is making it invalid.
What is the nature, though, of the "states-of-affairs" that are produced by the performance of a thetic performative act? It is obvious that a performative act cannot immediately produce a material state-of-affairs, nor can it immediately alter a material reality. Thetic performative acts can only produce thetic states-of-affairs, that is, states-of-affairs whose existence is conventional. Thetic states-of-affairs, indeed, exist only within a convention and in virtue of that convention [17, pp. 186-188]. 16 An example of thetic state-of-affairs is the fact that Sergio Mattarella is currently the President of the Italian Republic.
Prescribing, just like promising, is a thetic act: it produces a new state-of-affairs. 17 But what is the nature of the states-of-affairs produced by prescribing? Conte's answer to this question reveals that the fruitfulness of the notion of deontic state-ofaffairs goes beyond the construction of the theory of the Natur der Sache. The thetic product of an act of prescription is, for Conte, a deontic state-of-affairs.
Just like other thetic states-of-affairs, deontic states-of-affairs are not material, but rather conventional states-of-affairs. Their conventional existence is only given within and in virtue of a normative system.
Not without considering the problem of Ockham's razor (entia non sunt multiplicanda praeter necessitatem), Conte thus introduces a specific ontological dimension in the analysis of the pragmatics of normative language-a peculiar ontological dimension that transcends the boundaries of linguistic phenomena. Conte deems necessary to introduce such an ontological dimension in order to give an account of the specific thetic character of the act of prescribing. He indeed clarifies that [i]n an act of prescription (which is a thetic act) the act does not exist if not in the hypothesis that the object of the prescription comes to being […]. The hypothesis of a thésis by which the object of the thésis does not come into being is an inherent contradiction [18, p. 204].
In this new and broader pragmatical perspective, deontic states-of-affairs are no more conceived of by Conte as elements of a metaphysically compromised, transcendent "deontic reality" pre-existing to any act of prescription; they are rather states-of-affairs whose existence is relative to a convention [17, p. 188], namely the convention of a specific legal system. For instance, the deontic state-of-affairs that in Italy it is forbidden to smoke in public premises obtains and exists only within and in virtue of the convention of the Italian legal system.

The Sigmatics of the Word 'Norm': Beyond The Linguistic Ontology of the Normative
The investigation of the pragmatical properties of normative language and the introduction of the concept of deontic state-of-affairs eventually led Conte to shift the focus from the general semiotics of normative language to the specific semiotics of the word 'norm': what do we mean by 'norm' when we talk about norms? Starting from the 1960s, some relevant changes were indeed occurring in the semiotics of the word 'norm'-or the analogous word 'rule'. The rising of research on constitutive rules-by Searle [69], Carcaterra [11] among others-and the recognition of different kinds and degrees of normativity-for instance in Georg Henrik von Wright [75] and in Bobbio [8]-implied an enlargement of the meaning of the word 'norm' beyond the mere idea of prescription: the idea of normativity appeared to be broader and more variegated than that of strict prescription.
In this context Conte himself gave a systematic and insightful contribution to the investigation of constitutive rules [20,21], but he also explored a different and original direction in the analysis of the semiotics of the word 'norm'. Drawing inspiration from the idea of a fourth dimension of semiotics proposed by Georg Klaus [41], we propose to characterize Conte's new investigation as a "sigmatics" of the word 'norm', that is, the investigation not so much of the meaning of the word, but rather of its possible referents. 18

The Sigmatics of 'Norm': Five Possible Referents
By overcoming his distrust towards the notion of deontic state-of-affairs, Conte was able to recognize that when we speak of a norm we may actually refer to a specific referent which does not consist in a linguistic entity like a sentence or a proposition. As we have seen, indeed, deontic states-of-affairs are the extralinguistic deontic counterpart of ontic states-of-affairs.
However, this does not imply that we always and necessarily refer to deontic states-of-affairs when we talk about norms. Conte, indeed, recognizes that the word 'norm' may be used to refer to at least five different possible referents [Conte 24, pp. 26-28]-even though he suggests in some connections that norms stricto sensu are to be equated to deontic states-of-affairs. 19 Notably, the word 'norm' may alternately (but not alternatively) refer to: (i) a deontic sentence; (ii) a deontic proposition; (iii) a deontic utterance; (iv) a deontic state-of-affairs; (v) a deontic noema.
The word 'norm' refers to a deontic sentence in the following example: "The norm 'It is forbidden to smoke' consists of five words".
The word 'norm' refers to a deontic proposition in the following example: "The English sentence 'It is forbidden to smoke' and the Italian sentence 'È vietato fumare' express the same norm".
The word 'norm' refers to a deontic utterance in the following example: "Prohibiting to all Arabs to enter the United States right after 9/11 would have been an ill-timed norm".
The word 'norm' refers to a deontic state-of-affairs in the following example: "The book Sachsenspiegel is a collection of norms in force in its author's society".
Finally, the word 'norm' refers to a deontic noema in the following phrase: 'A norm presented to a legislative assembly'.
By taking into account these five possible entities that we alternately call norms, Conte's sigmatic analysis of 'norm' implies a significant rethinking and enlargement of the ontology of the normative.

The Test of Sortal Incorrectness
Conte's list of five possible referents suggests that the sigmatics-that is, the analysis of the possible referents-of the word 'norm' should be distinguished from its semantics-that is, the analysis of the possible meanings of the word.
In the aforementioned examples of sentences or phrases in which the term 'norm' occurs, each sentence or phrase selects one of the possible referents of the word 'norm'. The examples-originally elaborated by Conte [24,[26][27][28]-recall the examples used in medieval scholastic philosophy to distinguish the different "suppositions" (suppositiones, from sub-ponere) of a term rather than its different meanings, or significationes. Supposition consists in the reference relation between a linguistic expression and what it stands for in a proposition. Notably, according to Occam, supposition "is so called as, so to speak, a positing for another" (Summa Logicae, I, 63, 3), 20 and it is "a property that belongs to a term, but only when [it occurs] in a proposition" (I, 63, 1). Occam shows that different propositional contexts select one of the possible suppositions of a term. For instance, if one says: "Man is a name", the term 'man' refers to the term itself (suppositio materialis); if one says: "Man is a species", it refers to the abstract concept of "man", i.e., "an intention of the soul" (suppositio simplex), without making reference to things called "men"; finally, if one says: "Every man is an animal", it refers to the proper "significates" (significati) of the term 'man', in this particular case to a (plurality of) thing(s) outside the soul (suppositio personalis).
Analogously, Conte is not trying to give a definition-or a plurality of possible definitions-of the meaning of 'norm'; he is merely showing that the word 'norm' may be used-often acritically-in different propositional contexts to "stand for"-to refer to-ontologically different sorts of entities, and that the different 1 3 Towards a Sigmatics of the Word 'Norm': An Ontological Turn… predications about norms presuppose and select different referents for the word 'norm'. 21 By so doing Conte shows what could possibly be characterized as the "polysortality", rather than the polysemy of the term 'norm'. The five referents listed by Conte, indeed, despite being all normative entities, are not homogeneous: they are not different species of one and the same genus of entities; they are rather entities belonging to different genera, to different sorts of phenomena, which in turn belong to different ontological domains. 22 Such a sigmatic analysis of the possible referents of 'norm' is of great relevance and fruitfulness for a deeper and more comprehensive analysis of normative phenomena. This can be clarified through the test of sortal incorrectness.
Max Black [4], after introducing the distinction between rules and what he calls rule formulations-i.e., sets of words by which a rule is stated-remarks that while "it does make sense to speak of adopting a rule, following it, breaking it, and so on", it is instead absurd and nonsensical to speak of "adopting, following, or breaking a sentence", or a rule formulation [pp. 100-101]. Speaking of adopting, following, or breaking a rule formulation would be a case of sortal incorrectness. 23 Analogously, Conte shows that it would be a case of sortal incorrectness to speak of breaking, infringing, or evading a deontic sentence, a deontic proposition, or a deontic utterance, just like it is a case of sortal incorrectness to say that the number 7 (understood as a mathematical entity) is red [27, pp. 62-63]. When one speaks of breaking, infringing, or evading a norm, the sort of referent to which the term 'norm' refers can only be a deontic state-of-affairs.

Validity and Existence of Deontic States-of-Affairs Between Facticity and Normativity
The deeper analysis of the pragmatical dimension of normative language on the one hand, and the ontological turn implied by the introduction of the notion of deontic state-of-affairs on the other hand, led Conte to revise his theory of the validity of norms.
The new and more refined theory of validity proposed by Conte [22] is still marked by a wide recourse to semiotic categories-namely, the semiotic distinction between the syntactical, semantical, and pragmatical dimensions of semiotic phenomena-but it is no more a theory of the validity of exclusively linguistic entities. 21 An analysis, at the sigmatical level, of the possible referents of a word, showing that that word is acritically used to make reference to ontologically different sorts of phenomena, may obviously precede and promote a more refined determination, at the semantical level, of the meanings and acceptations of that word. 22 Polysortality refers here to the fact that a term may be alternately but acritically used to refer to entities belonging to different ontological sorts and domains. Polysortality does not seem to be reducible to polysemy, and it does not either seem to be merely a matter of the extension of a term, because it seems contradictory to think of an extension including entities belonging to different ontological domains. 23 On sortal incorrectness see Lappin [42].

The Theory of Validity Revised: Semiotic Categories for a New Ontology of Norms
In the light of the sigmatics of the word 'norm', the question "What is a theory of, the theory of the validity of norms?" [15, p. 57]-which was the starting point of Conte's previous investigation on the validity of norms-has no obvious answer. In fact, while in 1970 Conte maintained that validity par excellence is the validity of prescriptive deontic sentences, the recognition of the plurality of the possible referents of 'norm' now leads him to distinguish three different species of deontic validity. The first distinction introduced by Conte is the distinction between the validity that is predicated of deontic acts-to which linguistic norm-creating acts belongand the validity that is predicated of deontic states-of-affairs. Conte calls the former species of validity "pragmatical validity", the latter "syntactical validity".
That these two species of deontic validity are heterogeneous is demonstrated by Conte's analysis of a peculiar deontic act, namely the act of (express) repeal of a norm. Conte remarks that, on the one hand, the act of repeal has specific validity conditions within a normative system, and these validity conditions are conditions of pragmatical validity of the act. On the other hand, the act of repeal impacts on another species of validity, which is instead the syntactical validity of the repealed norm, understood as a deontic state-of-affairs. By virtue of the pragmatical validity of the deontic act of repeal, the syntactical validity of the deontic state-of-affairs is immediately repealed. Pragmatical and syntactical validity are not one and the same validity; they indeed pertain to different sorts of entities: to a deontic act and a deontic state-of-affairs, respectively.
A deontic state-of-affairs, whatever its relation to language may be, "is not a segment or fragment of language", according to Conte [15, p. 66]. Thus, the notion of syntactical validity as the specific validity pertaining to deontic states-of-affairs, despite being still modelled on semiotic categories, actually expands the theory of the validity of norms beyond the boundaries of language and linguistic entities.
It must further be remarked that Conte eventually equates the syntactical validity of deontic states-of-affairs-and no more the validity of prescriptive deontic sentences-to the validity par excellence of norms, corresponding to Kelsen's notion of the specific existence of norms (see Conte [22, p. 387]). The equation of validity and the specific existence of a norm thus means that the validity of a norm amounts to the existence of a deontic state-of-affairs.
However, Conte does not abandon the idea that validity can be predicated also of prescriptive deontic sentences: the validity pertaining to prescriptive deontic sentences is, according to Conte, a third species of validity, namely semantical validity. Conte introduces the notion of semantical validity as the correspondence of a prescriptive deontic sentence to a deontic reality, that is, to an existing deontic state-ofaffairs. This notion allows Conte to reframe a long-debated question concerning the semantics of normative language, namely the question whether truth, or a deontic análogon of truth, can be predicated of norms. If norms are understood as prescriptive deontic sentences, then their semantical validity-i.e., their correspondence to a deontic state-of-affairs-can be construed as the deontic análogon of truth and possibly as the specific logical value of norms (see Conte [22, p. 379

]).
A peculiarity of the notion of semantical validity highlighted by Conte consists in the fact that semantical validity may be strictly connected to the other two species of validity: the pragmatical validity of the deontic utterance of a prescriptive deontic sentence is a sufficient condition of the syntactical validity of the corresponding deontic state-of-affairs; and this syntactical validity of the deontic state-of-affairs is in turn a sufficient condition of the semantical validity of the deontic sentence, since semantical validity by definition consists in the correspondence to a deontic stateof-affairs, which is in this case the deontic state-of-affairs that has been thetically produced by the utterance of the prescriptive deontic sentence itself (see Conte [22, p. 380]). 24 This shows that the three species of deontic validity, despite being distinct, may be related to one another. The relationships between them can be represented in the deontic triangle (see Fig. 1).

Syntactical Validity of Deontic States-of-Affairs as Systemic Validity
As we have shown in § 3.2., Conte ascribes to the notion of deontic state-of-affairs a pre-eminent role among the five referents of 'norm': when we speak, for instance, of breaking, infringing, or evading a norm, we are in fact speaking of the norm in terms of deontic state-of-affairs. To deontic states-of-affairs pertains, as we have Fig. 1 The deontic triangle of the three species of deontic validity 24 This phenomenon may be likened to the phenomenon of the self-verification of performative sentences-which seems to contradict the thesis that performative sentences are non-apophantic sentences. To be true, Conte's remark requires a specification: the pragmatical validity of the deontic utterance of a deontic sentence is obviously a sufficient condition of the syntactical validity of the corresponding deontic state-of-affairs only inasmuch as such syntactical validity is not repealed by a subsequent act, fact, or event.

3
seen, syntactical validity, which is now considered by Conte the deontic validity par excellence, the validity of norms par excellence.
If Conte [15] in 1970 conceived of the validity of prescriptive deontic sentences as the belonging of a prescriptive deontic sentence to the language of law, in 1988, on the contrary, he conceives of the syntactical validity of deontic states-of-affairs as the belonging of a deontic state-of-affairs to a legal system, understood as a system of norms-namely, of deontic states-of-affairs [22].
The validity of a deontic state-of-affairs is called "syntactical validity" by Conte because it depends on the relations between that deontic state-of-affairs and other deontic states-of-affairs of the same legal system, notably what Conte calls the "axiotic meta-norms" of the system. The axiotic meta-norms of a legal system are the constitutive norms that determine the conditions of validity of other norms within that legal system, and thus "determine the syntax of validity" of the system [25, p. 48].
In many cases, the conditions of syntactical validity of a deontic state-ofaffairs are obviously connected to the conditions of pragmatical validity of a linguistic deontic norm-creating act: the pragmatical validity of a norm-creating act is a sufficient condition of the syntactical validity of the corresponding deontic state-of-affairs.
However, this is not always and necessarily so. Not every legal norm is in fact created through a thetic linguistic norm-creating act: a paradigmatic counterexample are customary norms.
This raises the question whether the validity and the existence of customary norms can be conceived of in the same terms as the syntactical validity-and existence-of deontic states-of-affairs that are created through thetic norm-creating acts. In the hypothesis that the validity of customary norms is still a kind of syntactical validity, it cannot obviously be dependent on the pragmatical validity of a linguistic norm-creating act. Conte proposes, thus, to distinguish two kinds of syntactical validity: (i) thetic syntactical validity is the validity of a deontic state-of-affairs which is the product of a linguistic thetic norm-creating act, as in the case of statutory legal norms; (ii) athetic syntactical validity is the validity of a deontic state-of-affairs which is not the product of a linguistic thetic norm-creating act, as in the case of customary legal norms. 25 Both the conditions of thetic syntactical validity and the conditions of athetic syntactical validity of a deontic state-of-affairs may be determined by the axiotic meta-norms of a legal system. According to this perspective, both kinds of syntactical validity-and thus of existence-of deontic states-of-affairs are twofold relative: first, they are relative to a legal system; second, they are relative to the axiotic constitutive meta-norms about validity within that legal system [25, p. 48]. This conception of the syntactial validity of deontic states-of-affairs can be characterized as a form of "systemic validity". 26 If this is true, then it seems that the existence of a legal deontic state-of-affairswhich is a conventional existence consisting in its syntactical validity-cannot be an isolated and autonomous existence; it is, on the contrary, always a systemic existence, an existence that can be given only within a legal system of norms containing some specific axiotic meta-norms.

Factual and Asystemic Existence of Deontic States-of-Affairs: Two Hypotheses
Conte's theory of validity, including the distinction between thetic and athetic validity of deontic states-of-affairs, seems to fit well the structure of legal normative systems.
However, the range of normative phenomena is wide and variegated: it obviously transcends the boundaries of legal normative systems and includes normative phenomena that do not seem, at first sight, to imply a presupposed normative system nor some specific meta-norms or criteria of validity.
One can think, among many others, of the following phenomena: (i) informal and unofficial norms created through a linguistic act of commanding or promising outside any specific institutional framework; (ii) spontaneous norms emerging in one's consciousness on the basis of intuitive normativity; (iii) norms imposed by a gangster under the threat of coercion; (iv) norms imposed to a pet under the threat of coercion; (v) norms implied in the Natur der Sache or in the Natur der Dinge; (vi) non-legal customary norms; (vii) norms emerging from social practice before their recognition and validation within a legal system; (viii) norms of mute law (which have been investigated by Rodolfo Sacco). 27 We cannot specifically investigate all of these normative phenomena in the present paper. However, the mere recognition of the existence of these variegated phenomena arises an important question: Are there any forms of asystemic normativity?
To be more precise: Are there any forms of normativity that are not relative to a normative system and to a set of axiotic meta-norms? In other terms: Is it possible for a norm-understood as a deontic state-of-affairs-to come to existence independently of (the meta-norms of) any presupposed normative system? These questions are worth to be thoroughly investigated, but this goes beyond the scope of the present paper. 28 On the hypothesis that they can all be given an affirmative answer, 29 we envisage two further theoretical hypotheses that can explain such an answer.
The first hypothesis is that, besides normative validity-that is, the validity that is determined by some set of axiotic meta-norms-also forms of factual validity exist, that is, forms of validity of deontic states-of-affairs that directly emerge from the facts of human life without any normative pre-condition. 30 Should this first hypothesis prove to be correct, it would contradict the equationmaintained, among others, by Kelsen and Conte-according to which the validity of norms consists in their specific existence within and in virtue of a normative system. The validity of norms, understood as deontic states-of-affairs, would thus go beyond the boundaries of systemic and syntactical validity.
The second hypothesis is that deontic states-of-affairs, besides an existence in terms of validity, may also have an existence in terms of mere facticity. In other terms, according to this second hypothesis, it should be recognized that deontic states-of-affairs-while still being deontic-may also have a merely factual existence devoid of any validity. 31 Should this second hypothesis prove correct, it would contradict the equationalso maintained by Kelsen and Conte-according to which the specific existence of a norm is (exclusively) validity. The existence of norms, understood as deontic states-of-affairs, would thus go beyond the boundaries of validity tout court.

From the Polysortality of 'Norm' to the Plurality of the Modes of Existence of a Norm
In the present paper we have shown that the recourse to the tools and categories developed by semiotics and the philosophy of language allowed for many fruitful advancements in the investigation of normative phenomena, particularly of legal phenomena. However, a possible drawback of such a semiotic approach to the investigation of normative phenomena lies in being induced to characterize normative phenomena exclusively in terms of linguistic entities. This possible drawback may be overcome thanks to the tools offered by semiotics itself: the sigmatic analysis of the different referents of the word 'norm' has highlighted the polysortality of this term. Such a polysortality depends on the fact that, despite their apparent conceptual homogeneity, normative phenomena intersect different ontological domains: the domains of sentences, of propositions, of utterances, of states-of-affairs, of noemata.
The recognition of the polysortality of 'norm' led to deal with the problem of the modes of existence of norms and the relation between the existence and validity of norms in a renovated and more articulated perspective. Conte, for instance, distinguished three species of deontic validity: pragmatical validity, which pertains to norm-creating acts, semantical validity, which pertains to deontic sentences, and syntactical validity, which pertains to deontic states-of-affairs.
The introduction of the notion of deontic states-of-affairs allows for a more rigorous definition of the equation of the existence of a norm with its systemic validity. However, the existence of normative phenomena seemingly independent of the existence of correlated normative systems arises a theoretical dilemma: these phenomena, indeed, seem to imply either the introduction of a notion of a factual and asystemic validity of deontic states-of-affairs-in opposition to their normative and systemic validity-or the renouncement to the equation between the existence and the validity of norms, and the acceptance that the existence of norms, understood as deontic states-of-affairs, may sometimes consist in an autonomous facticity rather than in a systemic validity.
Author Contribution This paper is the joint work of two authors. Both authors contributed to the paper conception and elaboration. Paragraphs 1., 3. and 5. of the manuscript were written by Paolo Di Lucia paragraphs 2. and 4. were written by Lorenzo Passerini Glazel. Both authors commented on previous versions of the manuscript. Both authors read and approved the final manuscript. The quotations for which there is no available English translation are translated by the authors. A previous version of this paper was discussed at the webinar Global Semiotics, Intercultural Legal Space and the Interplay between 'Facticity' and 'Normativity' held on September 16th, 2021. The authors are grateful to the organizers, Stefano Bertea, Mario Ricca and Anne Wagner, as well as to the participants to the webinar for their insightful comments. The authors are also grateful to three anonymous reviewers of this Journal for their comments on a previous version of this paper.
Funding Open access funding provided by Università degli Studi di Milano -Bicocca within the CRUI-CARE Agreement. No funding was received to assist with the preparation of this manuscript.

Conflict of interest
The authors have no competing interests to declare that are relevant to the content of this article.
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