TRUE PEJORATIVE SENTENCES BEYOND THE EXISTENTIAL CORE: ON SOME UNWELCOME IMPLICATIONS OF HOM AND MAY’S THEORY*

SENTENÇAS PEJORATIVAS VERDADEIRAS ALÉM DO NÚCLEO EXISTENCIAL: SOBRE AS IMPLICAÇÕES DA TEORIA DE HOM E MAY

ABSTRACT

This paper considers one of the most significant and controversial attempts to account for the meaning of pejoratives as lexical items, namely Hom and May’s. After outlining the theory, we pinpoint sets of pejorative sentences that come out true on their account and for which the question as to whether they are compatible with the view advocated by them (so-called Moral and Semantic Innocence) remains open. Helping ourselves to the standard model-theoretical framework Hom and May (presumably) work in, we prove they are compatible with the view. Given that the issues of both the moral import of pejoratives and the practical effects of their utterance are not settled by the proof, we then highlight unwelcome moral and pragmatic implications for some of the pejorative sentences under scrutiny, thereby showing that the view, broadly understood, is not as morally and semantically innocuous as it is meant to be.

Keywords:
Pejoratives; Slurs; Moral and Semantic Innocence; Derogation; Ofensiveness

RESUMO

O presente artigo contempla uma das tentativas mais significativas e controversas de explicar o significado de pejorativos como itens lexicais, a saber, a de Hom e May. Após apresentarmos em linhas gerais a teoria, identificamos conjuntos de sentenças pejorativas que saem verdadeiras nessa teoria e para as quais a questão da sua compatibilidade com a visão por eles defendida (a chamada Inocência Moral e Semântica) permanece em aberto. Explorando o arcabouço teórico padrão da teoria dos modelos em que Hom e May (presumivelmente) trabalham, damos uma prova de sua compatibilidade com a visão. Dado que as questões relativas tanto à importância moral de pejorativos quanto aos efeitos práticos de seu proferimento não são resolvidas pela prova, destacamos, em seguida, implicações morais e pragmáticas indesejáveis para algumas das sentenças pejorativas sob escrutínio, mostrando assim que a visão de Hom e May, interpretada de maneira ampla, não é tão moral e semanticamente inócua como deveria ser.

Palavras-chave:
Pejorativos; Injúrias; Inocência Moral e Semântica; Derrogação; Ofensividade

1 Introduction

Pejoration is not a purely linguistic phenomenon. Part of it consists in a negative attitude held towards the thing judged. One way for the attitude to get linguistically realized is through the utterance of pejorative words.¹ “Bastard”, “jerk”, “nigger”, “kike” and the like intuitively belong to the same linguistic class of disparaging expressions. One thing, however, is to study their properties qua lexical items, another to study their properties as used expressions, that is, as deployed in token speech acts (see Hom and May, 2013, p. 294). Slurs, for example, arguably belong to the linguistic class of pejoratives and as such own semantic properties that make them special members of the class: in addition to expressing a disparaging attitude on the speaker’s part, they seem to make some contribution to the truth-conditions of the sentences in which they occur. As deployed in token speech acts, they display further pragmatic properties such as the properties of insulting and (potentially) ofending people.

One of the most significant and controversial attempts to account for the meaning of pejoratives as lexical items is Hom and May’s in a couple of papers (2013, 2018).² In recent years it has been criticized in many ways and respects: as semantic theory (Sennet and Copp, 2015), as a special kind of semantic (viz. truth-conditional) theory (Cepollaro and Thommen, 2019), as fictionalist theory of pejorative discourse (Marques, 2017; Orlando, 2020), as a particular instance of normative realism (Orlando, 2020). Our aim in this paper is twofold. To begin with, we aim to show that even sympathizing with the view they advocate, Hom and May’s semantic account only covers a small number of pejorative sentences (namely, those whose truth is trivially compatibility with the view), thereby leaving unanswered the question as to whether further pejorative sentences that come out true on the same account are also compatible with it. This is not to say that the view cannot get us the result beyond the set of (existential) pejorative sentences that form its core. It can, considering that Hom and May work in a standard (model-theoretic) framework and that they can help themselves to this framework to get it. The issue is, instead, whether the result obtained thanks to a suitable extension of the framework is trivially compatible with the view. We argue it isn’t and provide, accordingly, a proof of their compatibility. That a proof can be delivered does not turn the result more acceptable, though. Some authors have (rightly) pointed out that Hom and May’s semantic account yields unwelcome results with no explanation, in some cases of, why this is so.³ Another aim of this paper is to provide an explanation based on the idea that the view, broadly understood, carries unwelcome moral and pragmatic implications for the sets of true pejorative sentences under scrutiny despite their being compatible with the view (narrowly understood).

The paper runs as follows. Section 2 outlines Hom and May’s theory in such a way that the semantic account is kept distinct from the view it embodies. Section 3 pinpoints sets of true pejorative sentences for which the question can be raised as to whether they are compatible with the latter. Section 4 gives a proof of their compatibility with the view (narrowly understood) and argues that, broadly understood, it carries unwelcome moral and pragmatic implications for the sets of true pejorative sentences pinpointed in section 3.

2 Hom and May’s Theory

2.1 Truth-Conditional Monism, Different Extension and Intension Theories

Hom and May’s account of the meaning of pejoratives singles out by features that are best understood against the backdrop of general considerations. One of them has to do with the kind of approach their account exemplifes, namely (lexical) monism. On this approach, the derogatory content of pejoratives, notably those used to slur, is part of their truth-conditional (descriptive) content since there is just one (truth-conditional or descriptive) dimension of meaning. To use Hom and May’s favorite example, assuming “kike” encodes a derogatory content in addition to its descriptive content — the one also encoded by its neutral counterpart “Jew”, a defining feature of this approach is to view the former content as part of the latter and, as a result, to consider “is a kike” and the complex predicate “is a Jew and worthy of negative evaluation because of that” as truth-conditionally equivalent. Being truth-conditionally equivalent, they can arguably be substituted salve veritate in all the sentences in which they occur.

Not all semantic theories of pejoratives are monistic in the afore-explained sense, though. Or if they are, it can only be so because the term “semantics” has been used so narrowly that the only relevant semantic contribution is thought of as being truth-conditional.⁴ Of course, if you hold, like Hom and May, that the derogatory content of pejoratives is part of their truth-conditional content, you may end up holding that the only relevant semantic contribution made by a term, even when it is evaluative like “kike”, is truth-conditional. On a less narrow construal of the term ‘semantics’, this kind of approach strikes as fattening. On a narrow construal, it looks like it is the only available option qua semantic theory.

For expository purposes, it is useful to draw a distinction, following Sennet and Copp, between semantic theories (in the narrow sense) “that claim or imply that, for instance, ‘black’ and ‘nigger’ difer in extension and theories that do not claim or imply this” (2015, p. 1081). Hom and May’s account of the meaning of pejoratives is clearly an instance of Different (as opposed to Same) Extension theories (hereafter, DE). The extension of a predicate is standardly conceived of as a class, namely, the class of individuals the predicate applies to (see Carnap, 1947, §§4-12). Since pejoratives used to slur like “nigger” or “kike” are predicates and since Hom and May take their extensions to be the null class, their account is an instance of DE, for there is plainly an extensional difference between the null class denoted by (the intension of) such predicates and the non-null class denoted by (the intension of) their neutral counterparts —respectively, “Afro-American” and “Jew”.

Hom and May’s account not only is an instance of truth-conditional monism and of DE theories; it is also an instance of Different Intension theories (hereafter, DI).⁵ This should come as no surprise since, in a Fregean/Carnapian perspective like the one used to frame their account, if two predicates have different extensions, they must have different intensions. In Fregean terms, if they difer as to their reference, they must have different senses (Sinne) since sense determines reference. Of course, two predicates (like the predicates “is a horse” and “is an Equus caballus”) can have the same reference while having different senses since they arguably present the same concept from different conceptual (in the case at hand, commonsensical vs. biological) perspectives (see Wiggins, 1984, p. 313). But to the extent that the reference is not the same, the senses attached to the predicates aren’t either. Given that “kike” and “Jew” do not refer, in Hom and May’s view, to the same concept, they have different senses — in Carnap’s terminology, different intensions.

2.2 The Lexical Analysis and Semantic Interpretation of Pejorative Predicates

So much for generalities. Let us turn now to the semantic analysis and interpretation of pejorative predicates. Hom and May take them to be complex lexical items analyzable at the abstract level as PEJ(N). PEJ is a lexical marker of pejoration that functionally combines with a neutral term N (the slur’s neutral counterpart) to yield a pejorative lexical item. The pejorative’s lexical complexity may be apparent as in “dirty Jew” or “Jew” uttered with a sneering tone or accompanied by a facial expression of disgust, yet it need not be as when the predicate “is a kike” is used instead. The point of the lexical analysis is to allow multiple phonological realizations of the same item analyzed at the abstract level along the same lines. In “kike” the marker is covert, yet, is still there as other possible phonological realizations (e.g., “dirty Jew” or “Jew” uttered with a contemptuous tone of voice) of the same lexical item make it conspicuous. That is why, apparent simplicity notwithstanding, “(is a) kike” is also analyzable as PEJ(Jew).

One thing is to retrieve the underlying complexity of the pejorative predicate through a lexical analysis, another to provide a semantic interpretation for it. We saw earlier that Hom and May’s account could be framed in a Fregean/Carnapian perspective as a particular instance of DE and DI theories. Although they use Carnap’s intension-extension distinction as roughly equivalent to Frege’s sense-reference one, they seem, however, closer to Frege than Carnap on their own semantic interpretation of PEJ(N) to the extent that the latter requires a threefold sense-reference-extension distinction. It is a well-known fact about Fregean semantics that, at least as far as predicates are concerned, a distinction is needed between their sense (the way their reference is presented, for Frege), their reference (the concept they denote), and their extension (roughly, for Frege, the set of individuals they apply to). It is also a well-known fact about Carnapian semantics that it simplifes Fregean semantics in distinguishing two instead of three semantic levels of analysis: the predicates’ intension (i.e. the property they denote) and extension (the class they apply to) (see Recanati, 2008, pp. 34-40) The need for a three-level Fregean semantics, when it comes to predicates on the whole and pejorative predicates in particular, can be partly justified by modus tollens as follows: if the reference of the (pejorative) predicate were its extension, as Carnap has it, the sentence in which it occurs would be truth-valueless when the class is null. An atomic sentence in which a (pejorative) predicate like “kike” occurs plainly has a truth-value: it is false. Therefore, the reference of the (pejorative) predicate is not its extension. If it is not, then what is it? — one might be tempted to ask. And how should the extension itself be viewed? Hom and May take the reference of the pejorative predicate to be a complex first-level concept resulting from the combination of a second-level concept (denoted by the sense of PEJ) with a first-level concept (denoted by the sense of N). And they take the pejorative predicate’s extension to be the null class (the empty set). This is as it should be, for, as pointed out earlier, the predicate’s Bedeutung should not be confated with its extension. And from the fact that the extension is the null class (the empty set), it does not follow that the pejorative predicate has no referent. As for the sense (Sinn) of the complex lexical item PEJ(N), one can easily figure out that it results from the combination of the sense (Sinn) of the marker of pejoration PEJ with the sense (Sinn) of the slur’s neutral counterpart N. What those senses actually are is something about which Hom and May remain silent.

Take, for instance, the pejorative predicate “(is a) kike”. Its reference is a complex first-level concept (deserves negative moral evaluation for being Jewish), outcome of the combination of a second-level concept (deserves negative moral evaluation for being G, where G is a slot for a first-level group concept) with a first-level group concept (being Jewish). Put in Fregean terms, it is a second-order function (PEJ) that takes as input a first-order function (Jewish), and maps it to a first-order function (kike). The latter in turn maps every argument to the False. Its sense is, presumably, a functional combination of modes of presentation of the corresponding functions. As for its extension, it is, like for any pejorative predicate, the null class. Hom and May even hold a stronger thesis to the effect that the extension of “(is a) kike”, like that of any other pejorative predicate, necessarily is the null class.

2.3 Moral and Semantic Innocence

As said earlier, our aim in this paper is, ultimately, to set out and explore unwelcome implications of the view advocated by Hom and May. But what kind of view is that? Hom and May label it Moral and Semantic Innocence (hereafter, MSI). As the name suggests, it is a view about the meaning of pejoratives that assumes the latter to be connected to a priori moral facts about the world. The justification for holding the view is clearly epistemic.⁶ This need not concern us here. What matters for our present purposes is that, on this view, pejoratives being evaluative terms, their meaning owns a moral dimension that can be accounted for, metaphysically speaking, by positing negative as well as positive moral world facts such as the fact that there are no Ss, the fact that no Ns are Ss or the fact that there are Ns.⁷ Moral Innocence (hereafter, MI) is, as the authors put it, “moral realism applied to pejoratives” (2013, p. 293). More precisely, it is the view that the negative and positive moral facts pointed above obtain, thereby making the corresponding quantified pejorative sentences true. Semantic innocence (hereafter, SI) is the view that ^┌no Ns are Ss^┐, ^┌there are no Ss^┐, ^┌there are Ns^┐ are jointly true.⁸ MSI, on the whole, is the view that Ss are not part of the world fabric while Ns are and that the extensions of both S and N and the sentences in which they occur mirror these facts.⁹

The Null Extensionality Thesis (hereafter, NET) can be understood as the semantic realization of the moral fact that no one deserves negative moral evaluation on account of being N — where N stands for any group picked out on the basis of active hateful or discriminatory ideology. More precisely, it can be understood as the outcome of the combination of a semantic fact with a non-semantic fact: the semantic fact that the intension (or sense) of “S” denotes the complex first-level concept deserves negative moral evaluation on account of being N and the moral fact that no one deserves negative moral evaluation on account of being N.¹⁰ Being the world and our language as they are —namely, respectively, morally and semantically innocent —, it follows from MSI that ^┌a is an S^┐ is false while ^┌a is an N^┐ is true, ^┌there are no Ss^┐ is true while ^┌there are no Ns^┐ is false, ^┌no Ns are Ss^┐ is true while ^┌some Ns are Ss^┐ and ^┌all Ns are Ss^┐ are false.

3 Some Non-Trivially Compatible Results

Our aim in this section is to show that the semantics picked by Hom and May yields results that are not trivially compatible with the view it is meant to embody (viz. MSI). To be sure, the set of pejorative sentences that form its core is trivially compatible with it since the members of the set wear, so to speak, on their sleeves the fact that they are. But how about the truth-value of pejorative sentences beyond the existential core? Given NET and the semantic clauses used to derive their truth-conditions, it is certainly possible to predict their truth-value. However, the fact that some come out (necessarily) true beyond the (existential) core strikes as a result that, in addition to creating moral and pragmatic discomfort, is not trivially compatible with MSI. As noted earlier, one remark by Anderson and Lepore (2013) anticipates our point. Their contribution to the on-going debate is rather limited, though, since they give but one example of what they (rightly) consider as an “unwelcome” result of the theory, namely the fact that the pejorative sentence “all chinks are spics” comes out true on the chosen semantics.¹¹ We go further and pinpoint, in addition to other instances of universally quantified pejorative sentences (see set 2 below), instances of embedded pejorative sentences (set 3) for which Hom and May’s account yields the same result. We postpone to the next section (4) the explanation of why and in what respects those results may be deemed unwelcome ones.

3.1 Semantic clauses

To the extent that the results yielded by Hom and May’s account turn on what they pick as semantic clauses for the calculus, a few words about the clauses are in order. Fortunately, there is no need to go too far to find a semantics suited to their account since one is, as they put it, “of-the-shelf, namely standard set-theoretic semantics for predicate logic applied to natural language.

Here is the standard clause for atomic (or simple) sentences: Fa = T if α e ext(F) (see Hom and May, 2018, p. 119). When it comes to quantified sentences, the relevant clauses are those governing the relations between concepts via their extensions in the theory of generalized quantifers, notably the “classical” relations universally, existentially related, and unrelated. Applied to natural language, one gets the following truth-conditions for “all”, “some”, and “no”:

$\begin{array}{c}\forall \left(X,Y\right)=T\text{iff}X\cap Y=X\\ \exists \left(X,Y\right)=T\text{iff}X\cap Y\ne \varnothing \\ \cancel{\exists }\left(X,Y\right)=T\text{iff}X\cap Y=\varnothing \end{array}$

On these clauses, a simple sentence such as “Socrates is mortal” is true if and only if Socrates belongs to the extension of the predicate “is mortal”. A universally quantified sentence such as “All men are mortal” is true if and only if the set of men is a subset of the set of mortals. An existentially quantified sentence such as “Some men are mortal” is true if and only if the intersection between the set of men and the set of mortals isn’t the empty set. The negation of an existentially quantified sentence such as “No men are mortal” is true if and only if the intersection between the corresponding sets is the empty set (i.e. if the corresponding sets do not intersect). Given these are instances of non-pejorative sentences, the predictions allowed by MSI are irrelevant here. They only matter when at least one pejorative predicate occurs in the sentence. In the latter case, the question to ask is: is the result compatible with MSI understood as a thesis about the truth-value of existential (pejorative) sentences and the obtaining of the corresponding moral facts?

3.2 Pejorative sentences (set 1)

To come up with a set of pejorative sentences for which the aforementioned semantic clauses yield, together with NET, truth-values compatible with the core of MSI is a fairly easy task. Consider (1)-(4) below.

1. (1) Woody Allen is a kike — more generally, a is an S.

2. (2) All Jews are kikes — more generally, all Ns are Ss.

3. (3) Some Jews are kikes — more generally, some Ns are Ss.

4. (4) No Jews are kikes — more generally, No Ns are Ss.

Suppose the extension of “(is a) kike” is the null class and pick as semantic clause for atomic sentences the aforementioned standard clause — namely, Fa = T if α e ext(F). (1) comes out false since it is not the case that the object referred to by “Woody Allen” belongs to the null class. (2) and (3) also come out false and (4), the contradictory of (3), true since, given both the aforementioned clauses for quantified sentences and NET, it is not the case either that the class of Jews is a subclass of the class of kikes or that the class of Jews and that of kikes intersect. These results are obviously compatible with the core of MSI: since, according to this view, ^┌ there are no Ss ^┐ is true, an atomic pejorative sentence such as (1) is false. (2) and (3) are also false — and the contradictory of (3) true — since, ^┌ there are no Ss ^┐ being true, the class of kikes is null.

3.3 Pejorative sentences (set 2)

So far so good. Now consider the couple of sentences below.

1. (5) All kikes are faggots — more generally, All Ss are S*s.

2. (6) All faggots are awful — more generally, All Ss are Φs.

The claim that (5)-(6) belong to the set of pejorative sentences is, we take it, uncontroversial since one pejorative predicate at least occurs in them.¹² The claim that they come out true on Hom and May’s account is more controversial.¹³ (5) comes out true, given NET (the semantic realization of the moral fact that no one deserves negative moral evaluation on account of being N) and the clause for universally quantified sentences, since the class of kikes is a subclass of the class of faggots. (6) also comes out true on the same assumptions, since the class of faggots is null, and the null class is a subclass of any class.

These results, the worry is, are not obviously compatible with the core of MSI. Suppose there aren’t kikes or faggots in this world; suppose, that is, that the corresponding negative existential sentences are true. Moreover, suppose that the non-pejorative existential sentences containing their respective neutral counterparts (^┌there are Ns^┐) are also true. Suppose, for the sake of argument, that ^┌no Ns are Ss^┐ is true as well. Is the claim that the truth of both (5) and (6) is compatible with the core of MSI trifing? We think not. It is up to whether one takes the universal quantifer to carry existential import. If it does, as in Aristotelian logic, both (5) and (6) are either false or without truth-value, depending on what one takes to be the effect of the emptiness of the predicate “kikes” or “faggots” on the semantic value of universal afirmative propositions.¹⁴ If it doesn’t, as is the case in modern logic, both may be true without affecting the truth of MI. Still, a proof is due of the compatibility of their truth-value with MSI as defined above.¹⁵

It might be objected that the aforementioned semantic clauses for determiners such as “all”, “some” or “no” are used to give the truth-conditions of pejorative sentences featuring paired terms like “kike” and “Jew” or “faggot” and “male homosexual” (that is, conceptually linked terms) and that sentences such as (5) and (6) do not fall within the scope of the account, which only concerns pejorative sentences like (2)-(4).¹⁶

This seems to us unduly restrictive since pejorative sentences containing paired terms are but a subset of the set of sentences used to make pejorative statements and, undoubtedly, the full set comprises sentences such as (5) and (6). And it is worth noting that even granting the restriction, one gets just the same unwelcome result. Given the aforementioned semantic clauses and NET, a pejorative statement such as (7) below comes out trivially true since, assuming all universally quantified statements are analyzable as conditionals, the antecedent of the conditional in “for all x, if x is a kike, then x is a Jew” is false, thereby turning the conditional true regardless of the truth-value of the consequent.

1. (7) All kikes are Jews — more generally, All Ss are Ns.

What we have here is a further example of pejorative sentence for which the question of its compatibility with the core of MSI remains open.

3.4 Pejorative embeddings (set 3)

It might be thought that the set identified earlier as set 2 (namely, the set of universally quantified sentences, featuring paired and unpaired terms) is the only set of pejorative sentences for which the question of the compatibility of their truth with the core of MSI remains open. This is far from being the case. Consider the set below.

1. (8) Yao is not a chink — more generally, a is not an S.

2. (9) Yao is Chinese, or Yao is a chink — more generally, a is an N or a is an S.

3. (10) Yao is a chink or Yao is not a chink — more generally, a is an S or a is not an S.

4. (11) If Yao is a chink, then Yao is Chinese — more generally, if a is an S, then a is an N.

5. (12) John, who is a bigot, believes that Yao is a chink — more generally, j, who is a bigot, believes that a is an S.

6. (13) Believing that Chinese people are chinks is racist — more generally, believing that Ns are Ss is racist.

Plainly, (8)-(13) are examples of embeddings that belong to the set of pejorative sentences, since in all these cases we have the occurrence of, at least, one pejorative. (8) is an instance of negation with a pejorative predicate within its syntactic scope. (9) is an instance of disjunction featuring a pejorative predicate in one of its disjuncts. (10) is also an instance of disjunction with a pejorative predicate in each of its disjuncts, one falling within the scope of negation. (11) is a conditional with a pejorative predicate within the syntactic scope of the antecedent clause. (12) and (13) are instances of intensional contexts with pejorative predicates within the syntactic scope of the propositional attitude verb.

Note that, in contrast to set 2, set 3 does not yield unintuitive results on Hom and May’s account, and so, should not be considered problematic in that respect. (8), for instance, is both intuitively true (from the non-bigot’s perspective, at least) and true on Hom and May’s account, being the negation of a materially false claim on the same account — see (1) above. (9) is also both intuitively true provided one, at least, of the disjuncts is true and true on Hom and May’s account, since “Yao is Chinese” is true on the same account — assuming that the class of Chinese people is non-null and Yao is a member of the class, “Yao is Chinese” is true according to the clauses for atomic sentences. The same holds for (10), being, on the one hand, an instance of the Law of Excluded Middle and, on the other hand, true on Hom and May’s account — the second disjunct being true on the same account. (11) is no exception since it is both intuitively true and true on Hom and May’s account that if a is a chink, then a is Chinese, just as it is both intuitively and materially true that for all x, if x is a kike, then x is a Jew (see 2018, p. 126). Less clear are the deliverances of their account for sentences such as (12)-(13). Nevertheless, one thing at least is certain: for the account not to yield unintuitive results, it must explain how materially false pejorative sentences can come out true within the scope of an attitude verb.

We seem to have here, the worry is, further examples of true pejorative sentences whose truth is not trivially compatible with the core of MSI. From the truth of ^┌there are no Ss^┐, one can certainly infer the truth of both (8) and (10), since the truth of ^┌there are no Ss^┐ logically entails that “Yao is not a chink” is true. From the truth of ^┌there are Ns^┐, one can also infer by logical entailment that (9) is true. And from the joint truth of ^┌there are no Ss^┐ and ^┌there are Ns^┐, one can infer that (11) is true since, by logical entailment, the antecedent clause is false and the consequent true. But how about (12)-(13)? Their being materially (in addition to intuitively) true (from the non-bigot’s perspective, at least) cannot be inferred from the core statements of MSI. According to MSI, ^┌there are Ss^┐ is false. From this it does not follow, however, that (12)-(13) have the truth-value they have, since their being true turns on the specific behavior of sentences within the scope of attitude verbs for which no semantic clauses are provided here. This is, we take it, a further example wherein the truth-value of some pejorative statements is not trivially compatible with the core of MSI although the possibility that it be is not ruled out.

4 Compatibility and Unwelcome Implications

In the previous section, we identified sets of pejorative sentences for which Hom and May’s semantic account yields results that are not, or so we argued, trivially compatible with the view the account is meant to embody. This is not to say that they aren’t compatible, only that a proof of their compatibility is needed. We give the proof in section 4.1 below helping ourselves to the standard set-theoretical framework Hom and May presumably work in. However, the fact that a proof of the compatibility of, say, (5)-(6) with MSI can be delivered does nothing to ease the discomfort created by the fact that such sentences come out materially true on the chosen semantics. This is because — or so we argue — the moral import of statements such as the ones made in uttering (5)-(6) outstrips the instantiation of the corresponding normative properties. Section 4.2 pinpoints the endorsement of the semantic content encoded by these sentences as the source of the moral discomfort created by MSI, broadly understood. Section 4.3 highlights unwelcome semantically grounded pragmatic implications of the view.

4.1 Arguing for the Compatibility with MSI (Narrowly Defined)

In what follows, we provide arguments in support of the claim that the truth of pejorative sentences singled out above is compatible with the core of MSI. Since, among the sets, (8)-(11) are predicted (by logical entailment) from MSI to come out true, no argument is needed to prove the compatibility of their truth with the view. This leaves us with the task of proving the compatibility of the truth of (5)-(7) and (12)-(13) with MSI understood as a thesis about the instantiation of negative moral properties and the truth of the corresponding (negative) existential sentences — understood, that is, as Hom and May understand it, namely, narrowly.¹⁷

The way Hom and May define SI, the joint truth of the sentences picked out in the formulation (i.e. ^┌no Ns are Ss^┐, ^┌there are no Ss^┐, ^┌there are Ns^┐) follows from NET on the singular counterparts of the aforementioned semantic clauses for quantified sentences. The latter stipulate that ^┌there is no X^┐ is true if and only if the extension of X is the null class and that ^┌there is an X^┐ is true if and only if the extension of X is non-null (see 2013, p. 295 fin5).¹⁸ Given that the extension of N is non-null and that of S is the null class (according to NET), it follows that ^┌no Ns are Ss^┐, ^┌there are no Ss^┐, ^┌there are Ns ^┐ are, indeed, jointly true. This suggests that although pejorative sentences other than ^┌ no Ns are Ss ^┐ and ^┌ there are no Ss ^┐ may come out true on the same clauses, their being true must be in harmony with NET for this fact to be compatible with SI, SI being, as Hom and May put it, “a consequence of null extensionality” (2013, p. 295).

That the truth of (5)-(7) is compatible with SI, thought of as a consequence of NET, can be easily proved in model-theoretic terms. Consider a specific pejorative sentence such as “there are no kikes” the truth of which directly follows from NET on the aforementioned clause — i.e., ∄(X)= T iff X= Ø. Call it “P”. Now consider a specific pejorative sentence such as (5). Call it “ Q” . It is easy to show that there is an interpretation I that satisfes P that also satisfes Q. Suppose, for simplicity’s sake, that the (non-empty) domain D of I is a class with just one member and that, in accord with NET, the extensions of the predicates “kikes” and “faggots” in I are the null class. I is a model of P since P is satisfed by I: no member of D belongs to the extension of “kikes” in I. I is also a model of Q since the extensions of “kikes” and “faggots” being what they are, the antecedent of the conditional in (5) is false, thereby turning (5) true. In other words, Q is also (vacuously) satisfed by I. More importantly, it is easy to show that there isn’t an interpretation that satisfes P that does not satisfy Q. As is known, the number of interpretations available for quantified formulas is determined by the number of objects included in D, which in turn determines the number of instances for each formula. On the assumption that D is a singleton set, there is just one interpretation available for P and for Q — on which the extensions of “kikes” and “faggots” are the null class. Since their respective instances (say, “Woody Allen is not a kike” for “There are no kikes” and “If Woody Allen is a kike, then Woody Allen is a faggot” for “All kikes are faggots”) are satisfed by this interpretation and since no other interpretation is available, it follows that there isn’t an interpretation that satisfes P that does not satisfy Q.

The same point can be made in deductive fashion, thereby turning the argument in support of the compatibility claim even clearer. Consider arguments 1 and 2 below.

[A1]

• (2) All Jews are kikes. (Hyp)

• (14) Woody Allen is a Jew.

• (15) Woody Allen is a kike. (From 2 and 14)

• (16) There are kikes. (From 15, by existential generalization)

[A2]

• (7) All kikes are Jews. (Hyp)

• (14) Woody Allen is a Jew.

• (15) Woody Allen is a kike.

• (16) There are kikes. (From 15, by existential generalization)

In A1, there is a way to infer (16) in a small number of steps from (2) — the argument is manifestly valid. Since the conclusion, however, straightforwardly contradicts the sentence “there are no kikes” the truth of which directly follows from NET (on the aforementioned singular clause), A1 might be thought to threaten NET and, thereby, SI. But it is worth remembering that (2), while intuitively true from the bigot’s perspective, comes out materially false on Hom and May’s semantic account. Since the premise is false, the conclusion is not forced on us. Therefore, A1 is no threat to MSI, understood narrowly.

A2 is no threat to MSI either, yet for different reasons. In contrast to A1, (16) cannot be derived from (7). The crucial step here is (15). Inferring it from (7) and (14) would commit one to the fallacy of affirming the consequent. As is known, an argument that instantiates such inference pattern is formally invalid. So, in A2 MSI (narrowly understood) is compatible with the truth of (7) not because the argument isn’t sound, but because the attempt to derive (16) from (7) is unsuccessful. Presumably, the argument can be rehearsed with (5) or (6) picked as premise.

How about (12)-(13)? Remember that they cannot be predicted from MSI to come out true (although they intuitively are) since the semantics used by Hom and May to account for the truth-conditions of pejorative sentences on the whole lacks clauses for intensional contexts. It is not hard to figure out which clauses need be added, though (see, e.g., von Fintel and Heim, 2011, ch.2). It might be stipulated that sentences such as (12)-(13) are true if and only if the embedded clause is true in all the possible worlds compatible with the bigoted/racist attitude held in the actual world. Since “Yao is a chink” and “Chinese people are chinks”, respectively, are true in the relevant set of worlds, (12)-(13) come out true with respect to this set. Note that for (12)-(13) to be true, the embedded sentences need not be themselves true (in the actual world). This is fortunate since, on the aforementioned clauses for extensional contexts, “Yao is a chink” and “Chinese people are chinks” are false as a consequence of NET.

One of the marks (or effects) of intensional verbs, in addition to changing the truth-value of the embedded clause, is the suspension of the existential commitments attached to the latter.¹⁹ Whoever utters “Yao is a chink” (more generally, “a is an S”) is inferentially committed, provided the sentence is true, to the existence of chinks (more generally, of Ss) — as is clear from A1. Now, whoever utters (12) is not so committed, as the use of the restrictive relative clause (“who is a bigot”) suggests. It follows that (16) cannot be inferred from the truth of (12) or (13) either. If so, their truth is compatible with MSI, thought of as a consequence of NET.

4.2 Some Unwelcome Moral Implications of MSI (Broadly Understood): the Problem of Endorsement

Given that the truth of pejorative sentences such as (5)-(7) can be proved to be compatible with MSI, it might be thought that the issue of the moral import of pejoratives is settled by the proof. This is far from being the case. Suppose someone utters (5) in the presence of victims of discriminatory practices — be they or not members of the target groups. In getting to know that the sentence comes out true on the chosen semantics, it is very unlikely, to put it mildly, that they ever feel reassured or relieved on being told that its truth is, at the end of the day, compatible with the commonsensical belief that no one ought to be the target of negative moral evaluation on account of his/her origin, race, sexual orientation, religion, gender, etc.This suggests that Hom and May’s conception of MSI is too narrow and that it need be looked at from a wider perspective.

Consider again (5)-(7). On Hom and May’s account, they are (materially) true since the null class is a subclass of any other class. And they are compatible with MSI since no conclusion of the form ^┌there are Ss^┐ can be drawn from either of those true sentences (together with additional premises) in such a way the deductive argument be valid. Now, does the fact no one actually, or even possibly, instantiates the normative property denoted by the sense (intension) of “kikes” and “faggots”, namely the property ξ is worth of negative moral evaluation on account of being N, turn (5)-(7) morally acceptable? We think not. The non-bigot would be reluctant to endorse the thought-content expressed by such sentences even knowing that the corresponding pejorative predicates are (necessarily) empty. And the reason for this is that there seems to be no proper way “to draw the right sort of line”, as Richard (2008, p. 13) aptly puts it, between thinking that such sentences are true and thinking the very thought expressed by them; and endorsing, that is, the bigoted conceptual perspective encoded by the corresponding pejorative predicates occurring in them.²⁰ To deem them true is to endorse the bigoted conceptual perspective.²¹ Worse, to deem them materially true is to take the encoded perspective to be endorsable by any thinker whatsoever, since for them to be materially true is for them to be true irrespective of the bigot’s take on their truth-value.

Another way to put the point is to notice that whereas true pejorative sentences such as (5)-(7) are arguably innocuous for MSI understood as a claim about the instantiation of negative moral properties and the truth of the corresponding (negative) existential sentences, they do have unwelcome consequences for MSI, broadly understood.²² Hom and May’s conception of moral innocence is manifestly too narrow since the mere fact that the concept deployed in using the slur is a concept embodying the bigot’s perspective onto the world may be taken to involve some kind (or degree) of moral corruption even though no one actually or possibly falls under it. Recall that the negative moral property denoted by the sense (intension) of the predicates “kike”, “faggot” and the like is ξ is worth of negative moral evaluation on account of being N. Deeming the thought in which such a concept is deployed true looks like a major concession made to the bigot’s perspective even though the claim happens to be semantically and morally innocent in Hom and May’s narrow sense. We cannot but agree in that respect with Orlando when she writes:

[...] One may think that using a sentence that expresses a thought deploying a concept of the kind suggested [the thick ethical concept expressed by the slur] is already a violation of moral innocence, even if the concept at stake is considered not to be exemplified by anyone. [...] The main problem can be thought to be the expression of thoughts deploying bigoted concepts like the one that is associated with “spic”²³ according to Hom and May: why would anyone possess and deploy the concept PERSON WITH A LATIN AMERICAN ORIGIN WHO OUGHT TO BE THE TARGET OF NEGATIVE MORAL EVALUATION FOR THAT REASON? Why would anyone partake in the bigot’s ethical concepts structuring her bigoted beliefs and norms? Another way of making this point is claiming that Hom and May’s conception of moral innocence in terms of supporting the commonsensical belief mentioned in (ii) [the belief that no one ought to be the target of negative moral evaluation on account of his/her origin, race, sexual orientation, religion, gender, etc.] is too narrow: on a wider conception of moral innocence, even if without holding a belief contradicting commonsense, one could still be morally corrupt by taking part in what may count as a discriminatory linguistic practice deploying concepts like the one discussed earlier (Orlando, 2020, pp. 163-4).

The moral of the story is that granting NET, thought of as the semantic realization at the extensional level of MI, is not enough to ensure that no violation of MI occurs when sentences such as (5)-(7) come out materially true, as they do on Hom and May’s semantic account. This is, undoubtedly, an unwelcome implication of MSI, broadly understood as a thesis about the moral import of semantically encoded derogatory thought-contents.

4.3 Semantically Grounded Practical Effects of Derogation

In this section, we take a further step and show that an additional clue to the narrowness of Hom and May’s conception of MSI is provided by the unwelcome pragmatic implications of the theory. If Hom and May are right, that is, if true pejorative sentences such as (5)-(7) are semantically and morally innocuous, we might expect them to be inofensive. However, it is a well-known fact about pejorative sentences that they are (or keep on being) ofensive in, virtually, all contexts of use.²⁴ We conclude that the true pejorative sentences under scrutiny are neither morally nor semantically innocuous, in the broad sense of moral and semantic innocence/corruption highlighted in the previous section, and that the fact that they aren’t partly explains their ofensive potential.

One way to defuse the objection would be to draw, following Hom and May, a sharp distinction between derogation, thought of a semantic/moral phenomenon, and ofensiveness, thought of as a psychological/pragmatic phenomenon, and to ofoad the explanation of the ofensive potential of the sentences under scrutiny to some pragmatic mechanism such as conversational implicature (see Hom and May, 2013, Appendix, esp. p. 310; 2018, pp. 125-6). If this can be done, the first premise of the argument comes out false (since the consequent does not hold) and, accordingly, the conclusion is not forced on us. Indeed. But it is hard to deny that derogation can be a source of ofense and that this fact is perfectly compatible with the aforementioned distinction.²⁵ In what follows, we provide arguments in support of both claims (the claim that derogation and ofensiveness are distinct phenomena and the claim that derogation, thought of as a semantic phenomenon, is a possible source of ofense) in order to show that the objection eventually goes through.

That derogation and ofensiveness are phenomena pertaining to distinct areas is a fact not always fully appreciated in the literature. We agree with Hom, and Hom and May that this can be prejudicial to a proper understanding of the issues raised by the meaning of pejoratives qua lexical items. Derogation is, as Hom (2012, p. 397) puts it, “an objective feature of the semantic contents of pejorative terms”, whereas “ofensiveness, both giving and taking, is a psychological phenomenon, and can have many sources which one may seek to understand” (Hom and May, 2018, p. 116). Derogation is “the result of the actual predication, or application, of a slur or pejorative term to its intended target group” (Hom, 2012, p. 397). So, consider an atomic pejorative statement such as (1) above. It is derogatory because it predicates (or applies) an objective semantic content, part of which involves a negative moral evaluation, to an individual (Woody Allen) in virtue of that individual’s group membership. And universally quantified statements such as (5)-(7) are also derogatory because they predicate (or apply) the same content to the target group (the group of Jews) selected on the basis of hateful ideology.

Now, one thing is to predicate this content of a group or an individual in virtue of its group membership, another the subjective or psychological effect of the predication. A remarkable feature of ofensiveness is that it only obtains qua psychological fact if the predicated content is intended and taken to ofend. Suppose my intention in using a slur (say, “kike”) is not to ofend people — as the side remark: “no ofense!” can make it clear—, but to make (what many would still rightly consider as) a (bad) joke about Jewish people. It is perfectly conceivable that at least some people do not get ofended at the joke, being warned of my intention not to ofend. And if some people do get ofended despite the warning — as it can happen if the audience is, say, hypersensitive to issues pertaining to religion or discrimination —, it can still be interpreted as an overreaction. Either way, this suggests that ofensiveness is not only up to the utterer’s intentions, but also to the hearer’s uptake. The imagined situation also illustrates another feature of ofensiveness: its variability across subjects. Some will, some won’t take ofense at the joke. Another well-known feature of ofensiveness is that it is only loosely tied to the use of language — a whistle catcall or a gesture can be just as ofensive as a linguistic utterance, because they all are instances of behavior (see Hom and May, 2018, p. 116) — and even to the use of disparaging words — words of praise can be just as ofensive: think of Veja magazine’s description of Marcela Temer (former-acting-President-of-Brazil’s wife) as “beautiful, demure, and homely (bela, recatada e do lar)”. Getting back to our examples of sentences in which objective derogatory contents are encoded by disparaging words, their ofensiveness is a psychological fact that may yet need not obtain depending on the speaker’s intention and the hearer’s uptake and, so, ought not be considered as part of the meaning of pejoratives. This does not mean, however, that derogation and ofensiveness must be viewed as unrelated phenomena.

Imagine, for the sake of argument, that a philosopher so deeply engaged in the formal treatment of philosophical problems that she ends up being inattentive to the real-life consequences of her theory asserts in the presence of a person who happens to be a male homosexual that sentence (6) — “all faggots are awful” — is true for set-theoretic reasons. Imagine she goes on arguing that the sentence being vacuously true is morally innocuous since, according to NET, no one here is deemed worth of negative moral evaluation on account of being a male homosexual. The same story could be told featuring pejorative sentences of the same form such as “all kikes are miserable” or “all niggers are monkeys”, uttered in the presence of, respectively, Jewish and Afro-American people. If no one is actually or even possibly demeaned when sentences such as these are uttered — so the argument runs —, how can they be ofensive?

That they are ofensive, and the people targeted by the slur(s), accordingly, justified in feeling outraged on hearing them are hardly disputable facts. After all, sentences (5)-(7) are paradigmatic expressions of bigotry mostly uttered with the intention to demean people on account of their group membership. The question is whether the ofense here is a strictly pragmatic matter (i.e. solely a matter of speaker’s intention and hearer’s uptake) or a semantically grounded phenomenon. If the former the same effect would be presumably achieved by uttering a non-derogatory in lieu of the derogatory term. Consider utterances of “all Jews are miserable”, “all black people are monkeys” or even “all Jews are homosexuals”. It is hard to deny that these sentences are potentially ofensive, although the derogatory terms have been replaced with their neutral counterparts. But all this shows is, arguably, that the derogatory properties lexically encoded by their pejorative counterparts are an additional, semantic source of ofense, not by any means the only (semantic) source of ofense. A theory implying, like Hom and May’s, that the true pejorative sentences scrutinized in this paper are morally innocuous, yet potentially ofensive for non-semantic reasons can hardly be taken to ft the bill.

5 Conclusion

To wrap up, let us summarize the paper’s main outcomes. In section 3, we identified sets of pejorative sentences (namely, set 2 and subsets of set 3) that come out true on Hom and May’s semantic account, yet for which it remains an open question whether they are compatible with the core of MSI. Helping itself to the standard model-theoretic framework Hom and May presumably work in, section 4.1 offered a proof of their compatibility. However, the issues of the moral import and practical effects of pejoration are far from being settled by the proof, as evidenced by the fact that the pointed semantic results do nothing to ease the discomfort felt by those (mainly, yet not exclusively from the target groups) who are told that the pejorative sentences under scrutiny come out materially true and that they are semantically (yet not practically) innocuous. If we are right — that is, if the moral import of pejoratives outstrips the instantiation of the corresponding normative properties and if the practical effect of their utterance is, at least, partly due to their being lexically encoded —, Hom and May’s theory can hardly be regarded as owning the virtues it supposedly owns. It is neither morally, nor semantically innocent.

• 1
  The linguistic means of pejoration are much more diverse than the usual focus on words (or terms) may prompt us to think, though. For an overview of the different grammatical levels involved in the linguistic realization of pejoration, see Finkbeiner, Meibauer, and Wiese (2016, pp. 2-9).
• 2
  Henceforth, referred to — whenever possible — as follows: date, followed by page number.
• 3
  Anderson and Lepore are a case in point, as evidenced by the following comment added in footnote: “In Hom and May [2013] they give the following semantics: ∀(X, Y) = T if X ∩ Y = X; ∃(X, Y) = T if X ∩ Y ≠ Ø; 3 (X, Y) = T if X ∩ Y = Ø. Notice that the clause for the universal yields the following result, ‘All chinks are spics’, given that the intersection of chink and spic are [sic!] trivially identical to chink (since Hom and May claim slurs’ extensions are null). This is an unwelcome result.” (2013, p. 361, fn. 20) See also Camp (2013), Sennet and Copp (2015), Nunberg (2018), Rappaport (2019).
• 4
  For an example of narrow use, see Sennet and Copp (2015, p. 1081).
• 5
  “[…] It is a consequence of null extensionality that paired terms like ‘kike’ and ‘Jew’ difer not only extensionally, but also intensionally; they have different meanings.” (2013, p. 296).
• 6
  “It stems”, as the authors put it, “from the simplicity of the explanation that semantic innocence afords for the epistemic query that is fundamental to any account of pejoratives: how can a competent, rational speaker of a language know the meaning of a pejorative without being committed to, or even complicit with, racist attitudes?” (2013, p. 293).
• 7
  “S” and “N” stand here, respectively, for any pejorative used to slur and its neutral counterpart.
• 8
  Here and in what follows, we use quasi-quotations (Quine, 2009, §6) to talk about sentences containing an unspecified slur or a neutral counterpart to a slur, or both. The first quantified sentence, for instance, reads roughly as follows: “the result of putting a plural neutral counterpart predicate for ‘N’ and a plural slur for ‘S’ in ‘No Ns are Ss’ is true”.
• 9
  Our wording is a bit sloppy here. The linguistic and the non-linguistic levels should be more neatly distinguished.
• 10
  We owe this point to R. Jeshion, Embracing Moral Corruption: A Response to Hom and May, unpublished.
• 11
  See footnote 3 above.
• 12
  Although “awful” involves a negative evaluation, the attribute does not count as a slur since it does not encode a content targeted at an identifable group. Hence, the choice of a different symbol for it — also considering that a non-evaluative predicate may occur in the attribute placeholder.
• 13
  This is because it is a widely shared assumption in semantics that quantifer phrases such as “All Ps” (whatever P) trigger the presupposition that the extension of P is non-empty (see Beaver et al., 2021: 1.1). Given NET, the presupposition triggered by “All Ss” fails, which means that, strictly speaking, neither (5) nor (6) comes out true on Hom and May’s account. A way to come around this difficulty is to consider cases in which the presupposition is cancelled, as in: “If there are Ss, then all Ss are Ps (Ss, Φs)”, for in these cases the claim that the pejorative sentence comes out true on their account is uncontroversial. To simplify, we shall take from now on all pejorative sentences of the form “All Ss are Ps”, including (7) below, to be elliptical for “If there are Ss, then all Ss are Ps”. Thanks to an anonymous referee for drawing our attention to this difficulty.
• 14
  In reply to Sennet and Copp’s criticism, Hom and May allow this possibility: “We could forego the Fregean assumption that universals do not carry existential import for the Aristotelian assumption that they do. Then both “All kikes are Jews” and “All kikes are Mormons” would be both either false or without truth-value.” (2018, p. 126).
• 15
  This is done in section 4.1 below.
• 16
  “We begin with an obvious observation, namely that pejorative terms are typically paired with non-pejorative terms with which they are conceptually linked — “Jew” and “kike” are paradigmatic in this regard — and an equally obvious question as to what is the nature of this relation?” (2013, p. 294).
• 17
  On the distinction between two possible understandings of MSI, narrow and broad, see next section.
• 18
  As a reminder, “X” stands for a concept, be it pejorative or not.
• 19
  See Forbes (2020) for a fuller account applied to transitive verbs.
• 20
  On a dualistic account of the meaning of pejoratives on which the derogatory significance of slurs is ofoaded to another, non-truth-conditional dimension, there might be a way of drawing “the right sort of line”. But remember that the account under scrutiny is monistic.
• 21
  Endorsement is to be understood here as an acceptance relation borne to a given linguistic content. On this understanding, a speaker S or hearer H endorses the content of a declarative sentence s if and only if S or H bears an acceptance relation to s (or the content thereof). For S or H to accept s, she must take the content of s to be true regardless of whether it is (materially) true. No one can endorse the content of a declarative sentence held to be false, although it may be false. So, in our view, the bigot and the non-bigot difer with respect to the sentence “Yao is not a chink” in just the same way as the fat-Earther and the science friend do with respect to the sentence “Earth isn’t fat”: while the former has no reason to endorse it, being held false, the latter has all the reasons in the world to endorse it, being both held true and materially true. Thanks to an anonymous referee for urging us to make this clear.
• 22
  As for (8)-(13), one might be tempted to add that the fact that they (arguably) leave the derogatory content unaffected also speaks in favor of interpreting Hom and May’s account as violating moral innocence broadly understood. For, clearly — so the argument runs — the fact that the bigot’s perspective is lexically encoded and left untouched by such constructions seems to strengthen our point. We resist, however, the temptation to take this step, for we are not at all convinced that the non-displaceability (or hyperprojectability) of derogatory content in those embeddings is a hard (semantic) fact about pejoratives. Perhaps embeddings such as (11) are clear instances of non-displaced derogatory content. But consider (12)-(13). Unless some evidence is provided to the effect that the word chink is mentioned rather than used, it seems more natural to construe them as instances of displacement to the attitude holder (if any) in the context of a debate about racism. For further examples of displacement of derogatory content in intensional contexts, see Schlenker (2003, p. 98), Anand (2007, p. 200), and Hom (2008, p. 429; 2012, p. 388).
• 23
  Orlando’s example.
• 24
  In some contexts, a slur can be used to praise rather than denigrate (or belittle) members of the target group, as in: “I’m glad we have so many spics at our school: they always bring the best food to our fund-raising functions” (Camp, 2013, p. 332). Claiming that this kind of use causes no ofense is far from uncontroversial, though, since, as will become clear soon enough, ofensiveness is not only up to the speaker’s intention, but also to the hearer’s uptake. Less controversial is, in our opinion, the claim that the slur keeps on encoding a derogatory content in such contexts of use.
• 25
  A delicate issue is whether true belief reports like (12)-(13) are also liable to ofend, considering they are instances of displaced derogatory content. In our opinion, they are because ofensiveness is a psychological/ pragmatic phenomenon that can yet need not have its source in derogation.

Acknowledgments

Research for this paper has benefited from the financial support of both CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brazil) via Research Productivity (#312815/2017-4) and Senior Post-Doctoral (#101052/2020-0) Grants and CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brazil, #001). We are grateful to these institutions. We also thank Marco Rufino, Arthur Pagani, Marcos Rosa, the LEME Seminar participants (especially, Guido Imaguire, Célia Teixeira, and Filipe Carijó) and two anonymous referees for significant feedback.

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Publication Dates

• Publication in this collection
  06 Jan 2023
• Date of issue
  Dez 2022

History

• Received
  22 Sept 2021
• Accepted
  28 Oct 2021