2.1 Core readings

I begin with a well-reported split: the combination of the frustrative with eventive and stative VPs. As shown below for duplets of languages (Mapudungun being the head example of each), when marking eventives, the meaning tends to be that an intention or expectation was impeded or frustrated. The ‘locus’ of the frustration varies: while in (4a–b) the marked clause implicates the non-culmination of the described event, in (4c–d) it concerns the non-realization of a contextually salient goal. To avoid a potentially bulky terminology, I follow Copley (Reference Copley, Becker and McKenzie2005) in referring to the following examples in (4) as ‘unachieved-goal’ interpretations. I have only added the superscript ‘c’ (for context), as in ‘unachieved-goal^c’ in (4c–d), to indicate those cases in which what ‘goes wrong’ can be identified by either the conversational context or (typically) an adversative clause following the marked sentence.

As for the interaction with stative VPs, frustratives show a tendency to denote the interruption or non-continuation of the denoted state (5a–5b), although unachieved-goal^c readings are also available (5c–5d):

An issue that has raised a great deal of interest is the interaction of frustratives with the aspectual sphere. For a language where aspect is marked (e.g., Tohono O'odham), Copley (Reference Copley, Becker and McKenzie2005) has described three patterns (see also Copley and Harley Reference Copley, Harley, Copley and Martin2014, and Carol and Salanova Reference Carol, Salanova and Song2021 for more recent assessments). The first pattern relates to the interaction between the frustrative and prospective meaning, which triggers an interpretation where the intended action is impeded before it gets started (6a). The implication seems to be that the event described by the prejacent never occurred. This interpretation in Mapudungun, originally reported in Smeets Reference Smeets2008 (6b), was confirmed by my main consultant (6c). As for the imperfective and perfective, Copley shows that while both convey unachieved-goal readings (6d–e), only the perfective triggers a non-continuation interpretation (6e) (i.e., the non-continuation of the result state of an event, whose occurrence is entailed). Interestingly, in languages that lack aspectual marking, this entailment can be triggered by pastness (6f), which in several Philippine languages is linked to realis mood (see Kroeger Reference Kroeger2017: 17–20 for discussion).

Note that most of the ‘core frustrative’ examples above have a past interpretation. This raises the question as to whether pastness constitutes an analytic component of the frustrative.

2.2 The counterfactual reading

That some frustratives occur in the consequent of counterfactual conditionals has been observed for a number of languages (Copley Reference Copley, Becker and McKenzie2005 for Tohono O'odham; Carol and Salanova Reference Carol, Salanova and Song2021 for Chorote, Kroeger Reference Kroeger2017 for Kimaragang). The examples below include data from three unrelated languages.

As far as I know, no formal analysis of the occurrence of the frustrative in conditional environments has been offered in the Mapudungun literature (regardless of how the suffix is categorized). Kroeger (Reference Kroeger2017) offers a modal Kratzerian analysis of counterfactual uses of Kimaragang dara, which I will examine in section 3.2. For the distribution of -fu- and future marker -a- in conditional environments, see discussion in section 4.1.

2.3 Mapudungun -fu-: the interactions with modals

I will now provide some relevant background information on Mapudungun grammar, and introduce the frustrative-modals interactions that will be addressed in section 3.3.

As is well documented (Croese Reference Croese1984, Golluscio Reference Golluscio2000, Smeets Reference Smeets2008, Zúñiga Reference Zúñiga2006), Mapudungun possesses no temporal markers for the present and past; future interpretations, for their part, are conveyed by the verbal suffix -a- (8c). Thus, a clause that lacks -a- can be interpreted either as a present or a past, whereas one marked with -a- can only be interpreted as a future. There is no overt viewpoint aspect marker that conveys (im)perfectivity, but there is a tendency to interpret eventives as past (8a) and statives as present (8b).

Elsewhere (Fuentes Reference Fuentes2020) I argue that -a- is a prospective aspect. This might lead to the impression that Mapudungun is a tenseless language since no past, present or (authentic) future marker can be identified. Following Matthewson's approach to Gitksan and St’át'imcets (Matthewson Reference Matthewson2006, Reference Matthewson2012), however, I take Mapudungun to be only superficially tenseless. In effect, by hypothesizing a covert non-future tense, one can account for future-to-the-past (9a) and future-to-the-present (9b) meanings when -a- occurs in embedded clauses.

As for Mapudungun modal clauses, I will focus on the expression of obligations and desires. Regarding the former, and in line with several unrelated languages (see Bhatt Reference Bhatt1997 and references therein), Mapudungun expresses deontic necessity by means of an existential predicate. As shown in (10a), the predicate takes a non-finite nominalized complement, which is marked with the prospective suffix -a-. The same type of complement occurs in bouletic clauses with the attitude verb pi-, which typically expresses an attainable desire (10b). A synonymous bouletic construction can be built with the preverbal unit küpá preceding a finite form (10c), in which case the prospective marker -a- is absent.

The frustrative interacts in interesting ways with the modal constructions above. As shown elsewhere (Fuentes Reference Fuentes2020, Reference Fuentes, Klok, Rech and Guesser2023) and illustrated below, the interactions match the behaviour of what has been called ‘transparent ought/wish languages’ (von Fintel and Iatridou Reference von Fintel, Iatridou, Guéron and Lecarme2008, Reference von Fintel and Iatridou2023). An ought transparent language expresses weak necessity (as in (11a)) by marking strong necessity (have to, as in (10a)) with what has been recently referred to as ‘X-morphology’ (that is, the morphology that appears in what is traditionally known as ‘subjunctive’ conditionals; see von Fintel and Iatridou (Reference von Fintel and Iatridou2023)). As the authors have shown, a related pattern can be traced in the bouletic domain (see also Iatridou Reference Iatridou2000 for a first approach). As shown for Mapudungun below, when the X-morphology of a ‘transparent wish language’ (-fu- in Mapudungun) combines with want (typically, the expression of a desire for something attainable (10b–c)), the statement shifts into wish (typically, the expression of a desire for something unattainable (11b–c)).Footnote ⁵

2.4 The alleged link with a past tense

Traditional analyses of -fu- that link its meaning with a past component have been presented in the Mapudungun literature under different Spanish categories: ‘pretérito imperfecto’, ‘imperfecto’, ‘co-pretérito’, among others (see Croese Reference Croese1984: 64–65 and Smeets Reference Smeets2008: 233–235 for a brief summary with several references). More recently, Soto and Hasler Reference Soto and Hasler2015 (which I examine in section 4.2), make pastness an essential definitional component of the suffix. This section will cast doubt on this general tendency.

That there is at least some non-past interpretation of -fu- clauses can be seen in the three sentences in (11). As mentioned in the introduction, this does not prove that -fu- cannot convey pastness as part of its meaning: the attested interpretations might derive from a semantic (sub)component which conveys genuine past in non-conditional environments, and another related meaning in conditional and modal environments (see Iatridou Reference Iatridou2000 and Ippolito Reference Ippolito2013 for two exemplary but contrasting views, and von Fintel and Iatridou Reference von Fintel and Iatridou2023 for recent reassessments).

This may well be so. But I wish to point out that the case against the inherent pastness of -fu- can be made on independent grounds, considering data from non-conditional and non-modal environments. The following is primary data collected by the author in recent fieldwork. Examples (12a–b) are elicitations for stative VPs; (12c–d) for eventives. Crucially, these four examples have a present temporal perspective. Both judgements and voluntary translations into Mapudungun were used as elicitation techniques.

I take the above data to be solid evidence that there is no analytic link between -fu- and pastness. Past interpretations of frustrative clauses may only be a pragmatic tendency. And no matter how strong this tendency may be, the elicitation of -fu- clauses targeting present temporal interpretation struck me as very natural and productive – the four examples in (12) being only a small sample.

This productivity certainly contrasts with how prevalent the past temporal interpretations are in the Mapudungun literature (although see Golluscio Reference Golluscio2000 for a view against the classical interpretation of -fu- as a past tense).Footnote ⁶ This tendency was explained to me by the fact that the ‘something going wrong’ component expressed by -fu- clauses tends to be known only retrospectively. Arguably, that María's land is not good for an orchard is only learned after (potentially many) failed attempts at planting an orchard. On the other hand, the anticipation of something going wrong with María's journey to Pitril was only accessible to the epistemically advantaged asserter in (12c), who reports that María is going to Pitril in vain as he speaks. A much more frequent narrative in the real world, however, would be María's own retrospective (and displeased) first-person account upon returning from Pitril.

3.1 The core frustrative meaning

As with ‘disappointment’, ‘frustration’ indicates that something has gone wrong with respect to some ideal standard or projection. Although the use of ‘frustrative’ in the linguistic literature only minimally evokes the ordinary notion of ‘frustration’, there is certainly something of this double-sided picture in the theoretical descriptions available. Modal analyses of frustratives (Copley Reference Copley, Becker and McKenzie2005, Kroeger Reference Kroeger2017), for instance, set forth a view which hinges on two basic claims, one ‘idealistic’ and the other ‘non-optimal’. The view is that a frustrative sentence conveys (i) that a contextually salient ideal is realized in some hypothetical scenarios in which nothing adverse interferes; and (ii) that the real world fails to satisfy such an ideal. The modal element of the view is introduced in the idealistic side of the picture: ideal scenarios can be largely translated into a possible-worlds framework through accessibility functions that calculate inertial/optimal worlds/situations. In very simple terms, that Mary is painting a vase at a certain point in time projects an inertial/optimal set of worlds/situations in which she culminates her task without interruption. When things go unexpectedly wrong with her painting, a frustrative statement expresses that the real state of things in the actual world does not belong to that ideal class of worlds/situations.

Modal approaches to grammatical features not traditionally categorized as ‘modals’ are not new to the discipline of semantics. Dowty (Reference Dowty1979) introduced the notion of possible worlds in the analysis of the progressive and the so-called ‘imperfective paradox’. Roughly speaking, ‘Mary was painting a vase’ introduces a set of modal continuations in which Mary culminates her task, leaving open the possibility that in the actual world the event reaches completion or fails to do so. The truth conditions of the progressive will ascribe the culmination for the inertial worlds, without adding any specific claim about how things (eventually) turn(ed) out in the actual world.

Frustratives across languages, on the other hand, do bring a specific nonoptimal addendum: that the actual world fails to be ideal with respect to the modal projection. In contrast to what one may initially think, though, frustratives are also (relatively) neutral regarding the culmination of what is described in the prejacent; as already mentioned for (4c–d), readings of frustrative clauses in which the described event is completely realized are regularly attested. Thus, despite their nonoptimal flavour, frustratives do not trigger a non-culmination entailment.

The definition we are after, then, needs to introduce a modal element that projects an ideal scenario (as with progressives), a nonoptimal addendum that precludes the actual world from being ideal, and an overall analytical arrangement that prevents the nonoptimal element from triggering a non-culmination entailment. This analytical challenge has been met with a very simple formulation.Footnote ⁸   The following is an adaptation as neutral as possible of the leading thread of these types of analyses.

1. (13) Meaning of frust(p)

   1. (a) Assertion: For all w′ ∈ f(w), R(w′).

   2. (b) Presupposition: The actual world is not optimal with respect to R.

(where f is a modal function from worlds to ideal continuations; and R is equal to either p or a contextually salient proposition which is a (desired or expected) successor to p in some causal chain within f(w)).

Before we examine how this semi-formal definition can account for the attested readings in the previous section, it should be noted that nothing in (13) entails the non-realization (or non-continuation) of the event (or state) described in p in the actual world. In effect, the presupposition only says that the actual world fails with respect to the parameter proposition R. This proposition certainly can, but need not, be equated with p. Neither the assertion in (13a) nor the presupposition in (13b) forces us to do so. The definition allows R to stand for some other proposition, which can denote either a salient result that was expected to derive from p, a goal in virtue of which p is executed, a state of affairs that stands as an expected continuation of p, etc. Crucially, whenever R is equated with any of these related propositions, it is not the event/state described in p that fails to culminate/continue.

Let us see how this works for eventive VPs, starting with the case in which the denoted event does not culminate (example (4a), repeated here as (14)):

If we equate R with p, the semantic contribution of the frustrative is accounted for by our definition in (13). In effect, according to (13a), R (=p) holds in all optimal worlds accessible from the actual world; according to (13b), the actual world is not optimal for p. If we take the ideal continuations to be the natural expectations tacitly agreed to by participants, the accessible worlds are all those compatible with such expectations. The definitional clause (13a) asserts that in all those worlds, María goes to Pitril and nothing intervenes. But (the second nonoptimal element) the real world fails to satisfy that ideal. The implication is that María did not go to Pitril.Footnote ⁹

Things are slightly different when another contextually salient goal is taken as the ideal parameter – say, that María went to Pitril to meet with the local chief. This is the circumstantial arrangement that was used for the elicitation of (1b), repeated as (15). Note that the same construction is now used to assert that María went to Pitril but something else (R, not p) went wrong.

Since R is not equated to p but to another salient proposition (meeting with the chief), the fact that María arrived at Pitril does not contradict our definition, which leaves enough room for p to be realized in the actual world.

Turning now to stative predicates, the relevant expectation concerns the persistency of the described state in the prejacent. This renders accessible worlds in which p holds without any interference.Footnote ¹⁰ In example (16) below, the state consists in the possession expressed by p (which, we will assume, stands for R).

The presupposition contributed by the frustrative says that the world is not optimal for R (= p). This means that the state does not hold in the actual world anymore. The non-continuation reading is thus triggered.

Finally, that a stative VP marked with -fu- can also render unachieved-goal^c readings is also predicted by (13). Consider (12a), repeated below as (17):

Given that p describes a state that currently holds in the actual world (María's possession of land; see discourse context in (12a)), R must be linked to another salient proposition. In this particular case, the context provided in the elicitation signals the implicit goal (the intention of planting an orchard next spring). The assertion is that in all optimal worlds María's land serves that purpose; the presupposition adds that the actual world is not optimal with respect to that ideal. Crucially, the occurrence of the frustrative does not imply that the denoted state is discontinued (or even threatened). The utterance only conveys that a salient related ideal does not obtain in the actual world. The modality provides the space of possibility for the idealization; the nonoptimal presupposition excludes the real world from that space.

3.2 Counterfactual readings

It is now time to examine those interpretations of -fu- clauses that are not prima facie predictable – starting with counterfactuality. As shown in (18a–c), the suffix appears in both the antecedent and the consequent of a counterfactual conditional, the latter of these being more systematically attested than the former. Crucially, the frustrative does not occur in all Mapudungun conditionals, as example (19) shows. This bare type of construction is often referred to as ‘indicative conditional’ in the philosophic and linguistic literature. This terminology is inadequate for Mapudungun, though, since conditionals that convey counterfactuality are also marked for the indicative. The split, then, will be one between conditionals that are marked with -fu- in the consequent (=marked conditionals) and those that are not (=bare conditionals).Footnote ¹¹

Before I sketch a tentative analysis, I will clear the ground with a couple of issues. First, the consequent of (18a–b) has the same form as (most) frustrative clauses previously examined in this article, except for the future marker -(y)a- preceding -fu-. I discuss the issue in section 4.1, but I do not have, at this point, a substantial explanation of this occurrence. In the present section, I will focus the attention on the occurrence of the frustrative in the consequent.

Second, it is worth mentioning that we are not dealing with an unachieved-goal or a non-continuation reading in addition to a counterfactual one. The utterance in (18a), for instance, does not express a failed or interrupted attempt to cry. Rather, the statement denotes a hypothetical event in a counterfactual scenario that meets the conditions stated in the antecedent. I point this out merely to delineate the general task ahead, which does not consist in clarifying how one of our attested core readings ‘pairs with’ a counterfactual yield. Rather, the task consists in determining how the meaning of the frustrative (defined in (13)) interacts with other components in the grammatical environment to render a different reading.

What are those other components? To begin with, a general grammatical form (if p, q), which hosts a frustrative component with sentential scope in the consequent, resulting in the form ‘if p, frust(q)’. This delineates a double task for an analysis of Mapudungun marked conditionals: (i) to determine the meaning of bare conditionals; and (ii) to explain what the frustative adds to that meaning. As I will show, it is important to conceive of these as two different tasks.

For the former task (to determine the meaning of bare conditionals), I will rely on a conception of conditionals that is in common use in possible world semantics, called the ‘restrictor analysis’ (Heim Reference Heim1982, Kratzer Reference Kratzer, Farley, Farley and McCullough1986). Basically, the analysis conceives of the antecedent if-clause as encoding a restriction to a modal operator elsewhere. More specifically, the idea is that the if-clause functions as a restrictive modifier of the domain that a modal operator in the consequent quantifies over. This modal operator may vary in nature. When not explicit, it tends to convey epistemic necessity (‘if John left before 10 am, he is at the station now’), although generic interpretations can also be attested (‘if it rains during cherry season, the fruit splits’). When the occurrence is overt, the modal operator has a broader range of possibilities, including deontic (‘if John killed the cat, he must confess’) and epistemic possibility (‘if John left before 10 am, he might be at the station now’), among others. Crucially, whatever its type, the modal operator hosted in the consequent quantifies over a domain restricted by the if-clause. Thus, in a sentence of the form if p, then q, the covert modal element in the consequent quantifies over the accessible worlds that are provided by its modal base and the intersection with p. It is only regarding this narrower domain of worlds that the proposition in the consequent (q) is asserted. The tree in (20) gives a rough idea of the general structure that results from this conception:

As the tree shows, the basic conditional form if p, then q constitutes a modalized proposition. The modal quantifies over a domain that intersects with the proposition introduced by the if-clause. It is for this domain that the conditional asserts q. The contribution of the if-clause, then, is simply that of a modifier: it restricts the quantificational domain that is above in the structure.

Now the question arises as to how this type of analysis can be implemented for conditional clauses marked with a frustrative – that is to say, clauses of the form ‘if p, frust(q)’. As far as I know, Kroeger (Reference Kroeger2017) was the first to attempt this. Although sketchy, the proposal illuminates some essential aspects of the clauses at issue. Interestingly, Kroeger's modal approach to Kimaragang frustrative fits very well with the basic structure implicit in the restrictor analysis, since the frustrative can be hosted as the modal operator (in Kroeger's view, of the epistemic type) represented in (20).

As a first approximation to Mapudungun marked conditionals, this general strategy seems to point in the right direction. But to reach a comprehensive account of the counterfactual readings triggered by frustrative clauses, it needs additional specifications. For one thing, as described in Kroeger's analysis, the resultant quantificational domain is entirely realistic (since in his conception, the relevant modal base is epistemic). In effect, the rendered worlds we are transported to are not counter-to-fact worlds, but possible worlds in the intersection of p (provided by the antecedent) and what is known in w. These are not yet worlds that the participants take to be counter-to-facts (that is, worlds that lie beyond the participants’ shared assumptions).

That Kroeger is aware of this problem can be seen in the fact that the author explicitly supplements his analysis with a seemingly innocuous presupposition – that the antecedent is false: “the real world does not count as an accessible world because [the antecedent p] is presupposed not to be true in the real world” (Kroeger Reference Kroeger2017: 23). Puzzlingly, though, Kroeger does not specify where this presupposition comes from. As it stands, it is a mere ad hoc stipulation, leaving the essential question (how does a frustrative trigger the falsity of the antecedent?) unanswered.

So where exactly does this key presupposition come from? That the falsity of the antecedent does not come wired as a presupposition in the if-clause is made evident by the fact that bare conditionals do not have a counterfactual yield. From here, the only option that seems available is that the presupposition comes wired in the frustrative. Naturally, if it is the addition of some special morphology (would in English, frustrative in Kimaragang and Mapudungun) that takes us from the meaning of a bare conditional to a counterfactual yield, the presupposition may come wired in the frustrative. But there is the flaw: the presupposition in (13) does not concern the falsity of any antecedent. What the presupposition says, instead, is that the actual world is not optimal for R.

If the falsity of the antecedent comes about by a presupposition wired in the frustrative, then, it seems that it would have to be added to the one already active in core non-conditional environments… unless one proves that the definition in (13) brings about the falsity of the antecedent on its own – dispensing with any ad hoc presupposition.

This latter move seems more aligned with the relevant task pointed out above: to explain what the meaning of the frustrative contributes when it interacts with conditionals. Put this way, my aim here is to derive the falsity of the antecedent in ‘if p, frust(q)’, by combining the definition of the frustrative in (13) with the restrictor analysis of conditionals of the form ‘if p, then (q)’.

In structural terms, the first natural step would be to assume that the frustrative plays the role that the restrictor analysis assigns to the modal operator. This yields a minimal but discernible difference between the trees of marked and unmarked conditionals, as shown below.

Now I show how the counterfactual reading attested in (18a–c) can be derived from the definition in (13). Let us start with the first clause in our definition: the assertion that for all the worlds in the domain of f(w), R holds. Let us further assume that R corresponds to the marked sentence (that is, to the consequent q).Footnote ¹² Thus, the basic assertion is that in all the optimal worlds, q holds.

What are those optimal worlds, according to our definition? The worlds that are projected as ideal continuations from the modal function f(w). In Kroeger's (Reference Kroeger2017) analysis of Kimaragang frustrative, this modal function is epistemic, which the author explicitly links with ‘expectations’ readings. Kroeger's basic idea seems to be that in counterfactual conditionals, expectations are projected from what is known about the actual world, in addition to some stereotypical order. This may well be so (as far as I can see, epistemic states can be thought of as projecting ideal continuations in the same way as desires, intentions and such), although I doubt that this type of modal base can exhaust the wide range of materials involved in counterfactual interpretations.Footnote ¹³ Abstracting away from these and other difficulties, the central point here is that according to the assertion in the first clause of (13), the accessible worlds are all q-worlds.

Note how the grammatical environment impinges upon the assertion of the first clause. As the restrictor analysis posited, the contribution of the if-clause to the meaning of a conditional is to restrict the quantifier to p-worlds. Taken together with the first clause in the definition, this is what the assertion says: that all the p-worlds that intersect the domain of quantification f(w) are q-worlds. Crucially, the first clause of the definition says nothing about the truth or falsity of p in the actual world. Thus, regardless of how the ideal continuations of the frustrative are projected (from knowledge, desires, intentions, stereotypes, or what have you), the assertion clause in the definition of the frustrative leaves completely underspecified the truth-value of the antecedent in the actual world.

In effect, the falsity of the antecedent is derived, in my analysis, with the aid of the second clause in (13): the presupposition that the actual world is not optimal. Notice, however, that this is not a one-step derivation. For one thing, what the second clause of the definition entails, in the first place, is that the consequent q is false. In effect, as with many (but not all) of the core readings examined in the previous sections, if we assume that (i) the optimal worlds are q-worlds (the assertion of the first clause) and (ii) that the actual world is not optimal (the presupposition in the second clause), the falsity of the consequent q follows. From here, we can derive the falsity of the antecedent by modus tollens: from the assumption that if p, then q (the bare conditional) and the negation of q (entailed by the presupposition clause in the definition), the negation of the antecedent p obtains. The conveyed meaning is counterfactual.

Perhaps this step-by-step derivation is just a more intricate version of what is implicitly sketched in Kroeger (Reference Kroeger2017). But I think it is important to stress that the falsity of the antecedent does not come wired either in the if-clause, nor in -fu-. It is the usual semantic contribution of the frustrative to the meaning of the bare conditional that triggers the falsity of the antecedent.

The proposed analysis defends the view that despite the divergence of interpretations in conditional and non-conditional -fu- clauses, the semantic contribution of the morpheme is one and the same. This should not surprise us – after all, the core modality inherent to the meaning of the frustrative would most naturally yield different interpretations in different environments. Combined with the fact that there is no analytical link to the past in the definition (as shown in section 2.4), the result is not trivial: unlike ‘fake past’ conceptions of counterfactuality (Iatridou Reference Iatridou2000), the Mapudungun morphology responsible for such readings seems to play an ‘authentic’ role. This behaviour leaves considerable space for the second of the three strategies identified by Iatridou with respect to the expression of counterfactual meanings across languages: that the relevant morpheme “does mean what it always does, but that other interpretative parts of the environment contribute to the final interpretation” (Iatridou Reference Iatridou2000: 245).

3.3 The frustrative-modal interactions

I now turn to the interactions between -fu- and deontic and bouletic modals.

3.3.1 Transparency: endo-X and exo-X

As far as I know, the notion of ‘transparent language’ was first introduced in the seminal article by von Fintel and Iatridou (Reference von Fintel, Iatridou, Guéron and Lecarme2008) with respect to weak necessity. According to the view sketched by the authors, a transparent language uses X-morphology (that is, the special morphology that appears in marked conditionals) to mark strong necessity constructions (have to) and denote, by these means, either weak necessity (ought) or counterfactual necessity (would have to).Footnote ¹⁴ Spanish offers a clear example: the conditional mood morphology that occurs in the consequent of Spanish marked conditionals (X-conditionals, in the authors’ terminology), marks strong necessity tener que (have to_ind) to obtain tendría que (have to_cond), a form that is ambiguous between weak and counterfactual necessity. A language like English, on the other hand, lexicalizes the former of these shifts with ought (while would (in would have to) occurs as predicted, since it is would that appears in the consequent of English marked conditionals). The observed pattern has been attested in a significant number of Indo-European languages (see von Fintel and Iatridou Reference von Fintel, Iatridou, Guéron and Lecarme2008 for crosslinguistic examples).

A more recent contribution of the same authors (von Fintel and Iatridou Reference von Fintel and Iatridou2023) shows that the attested pattern is somewhat paralleled in the bouletic domain (see also Iatridou Reference Iatridou2000 for an earlier approach). When X-marking is applied to want (typically, the expression of a desire for something attainable, like Spanish querer (want_ind)), the ascription turns into a wish (typically, the expression of a desire for something unattainable, like Spanish querría (want_cond)). As expected, the resulting construction is also used to express counterfactual desires (typically, a desire in a hypothetical situation). Again, a language like English lexicalizes these shifts with wish (while would in would want to occurs as predicted, for the same reason pointed out above).

As shown in section 2.3 and recast below, Mapudungun follows this pattern systematically. Example (22) shows a Mapudungun marked conditional. Example (23) illustrates Mapudungun deontic transparency, and example (24) does the same for the bouletic domain. As can be seen, the morphology that occurs in the language's marked conditionals (-fu- in (22)), serves to turn (i) a strong necessity (23a) into either a weak necessity (23b) or a counterfactual one (23c), and (ii) an attainable desire (24a–b) into either an unattainable desire (24c–d) or a counterfactual one (24e–f).

Table 1 summarizes the previous facts. I adopt the endo-X/exo-X distinction (von Fintel and Iatridou (Reference von Fintel and Iatridou2023: 21)), according to which endo-X constructions correspond to modalized claims about the actual world (namely, ought and wish), while exo-X readings constructions are about hypothetical scenarios (namely, would have to and would want to). The attested ambiguities run horizontally for each of the domains: modal constructions marked with -fu- trigger either endo-X or exo-X readings.

Table 1: Transparency

Three tasks emerge from these facts. The first relates to the empirical question as to whether the attested semantic patterns can be verified in other ‘frustrative languages’. The second, more theoretical task, is to determine whether the attested semantic shifts (in transparent-via-frustrative languages) can be accounted for by a unifying modal conception of the frustrative. Finally, a third and more abstract enterprise is to reflect on what a semantic theory of the frustrative (potentially resulting from the second task) can tell us about X-marking more generally. This section addresses only the second of these three questions.

3.3.2 And yet another ambiguity: (core) unachieved readings

Before we proceed, it should be said that in contrast to other transparent languages, Mapudungun deontic and bouletic constructions that are marked with -fu- make available an additional interpretation. In effect, since the language does not mark either past or present, a past unachieved obligation/desire is expressed with the same constructions exemplified above. Thus, while (25a) expresses an unachieved obligation (in contrast to (25b), which is specifically used for achieved ones), (25c–d) exemplify unachieved desire statements. Note that in contrast to weak necessity (23b) and unattainable desires (24c–d), unachieved obligations/desires have a past temporal perspective (had to/wanted but…).

These constructions share the same form as their (deontic/bouletic) matches in Table 1. Since they denote obligations/desires in the actual world, one would naturally be tempted to categorize them as an endo-X type of construction. This is misleading, however. Although past unachieved statements are about the actual world (the endo aspect of things), the link between unachieved obligations/desires and X-readings seems only incidental. For one thing, the ambiguity that these constructions generate is not attested in transparent languages. In Spanish, for instance, past unachieved desires/obligations are conveyed using the imperfective aspect, not X-morphology. Accordingly, I will set these readings aside and treat them not as transparent but as core readings. Although I still have not shown how core and transparent readings differ semantically, setting apart these interpretations right from the outset will clear the ground for the central hypothesis about the frustrative-modal interactions that I defend in this section – namely, that there are three possible interpretations: (i) a core interpretation (unachieved obligations/desires); (ii) an endo-X interpretation (weak necessity and unattainable desires), and (iii) an exo-X interpretation (counterfactual obligations/desires). Whereas (i) and (ii) constitute claims about the actual world, (iii) is about hypothetical worlds beyond the actual.

Let us rearrange Table 1 into Table 2, then, to have a full preview of the semantic landscape.

Table 2: Mapudungun frustrative-modal interactions

3.3.3 An informal sketch

I will proceed by first examining the core column in Table 2: past unachieved readings (both for obligations and desires). I will then address the (more problematic) second column: endo-X readings (ought and wish). This will be done by first showing that these interpretations cannot be reduced to the core reading, to then speculate on other options. As for the third column (that is, exo-X constructions denoting counterfactual obligations and desires), the analysis should proceed in the same way as it was proposed for marked conditionals in section 3.2, so I will leave it aside here.Footnote ¹⁶

For concreteness, (26) identifies two types of discourse contexts used in the elicitations for the core column: past unachieved obligations (26a) and desires (26b).

How can our definition of the frustrative in (13) account for these attested readings? A natural move would be to take the modalized sentence p as R. However, this does not take us very far, since we end up with the real world not being optimal with respect to that proposition. What would this mean? The modalized sentence p expresses an obligation/desire. Since obligations and desires are states, we have two interpretative possibilities open: either a non-continuation or an unachieved-goal^c reading. The non-continuation interpretation can be easily discarded, since neither of the sentences elicited by (26a) and (26b) expresses the discontinuation of an obligation or desire. In effect, in the same way that María's missing an appointment does not entail that María does not have to go to the doctor (anymore), her not being able to go to a friendly meeting does not entail that her desire to do so has vanished. The intended meaning is much more conservative: that María was under the obligation/had the desire of going to Pitril but failed to do so.

So we need to consider the other possibility: an unachieved-goal^c reading. As shown in section 3.1, unachieved-goal^c readings for statives are accounted for by equating R not with the marked sentence p but with a contextually salient proposition causally linked to p. Since p is a modalized sentence, a reasonable alternative is to conceive of the relevant facts in the contexts above (an appointment with the doctor, a friendly meeting) as causally generating not only the relevant obligational/bouletic state but also the intention that the obligation/desire is fulfilled. After all, it is expected of human agents having obligations or desires that they intend to satisfy them, and it comes naturally to model our optimal continuations on this ground. If we take the projected satisfaction of the obligation/desire to stand for R, we then generate accessible worlds in which María complies with her obligation/desire of going to Pitril. Then the presupposition clause in the definition in (13) states that the actual world is not optimal in that particular respect – pretty much what these sentences are all about. The interpretation follows the same pattern as unachieved-goal^c readings.

1. (27) Past unachieved obligation/desires

   Frust (p), where p = María had to/wanted to q

   1. (a) Assertion: For all w’∈ f(w), R(w’).

   2. (b) Presupposition: The actual world is not optimal with respect to R

      (where R = q)

Let us now consider the endo-X column in Table 2 (that is, weak necessity and unattainable desires). Without a compositional analysis, most of the fine details will remain unclear. But I would like to assess, at least tentatively, two issues: (i) why a core reading of these statements is not available and (ii) how can we make sense of an alternative interpretative path.

Let us start, then, by showing why the attempt to reduce the endo-X cell to a core reading fails. A non-continuation reading can be immediately discarded for the same reasons exposed above: neither weak necessity nor unattainable desire statements (necessarily) express the non-continuation of a state. On the contrary, when these modal claims convey a present temporal perspective, the assertion is precisely the opposite: that an obligation/desire state obtains.

What about the other core reading: unachieved-goal? Can this be the natural interpretation of endo-X statements? Consider weak necessity first. Two key aspects of these types of statements deserve attention. First, unlike the case of transparent wish, the complement of a weak necessity clause does not denote a counter-to-facts situation. On the contrary, it is arguable that ‘María should/ought to p’ actually presupposes that p is attainable for María. This attainability is made evident by a second related aspect: as has been observed in the literature, an ought p claim promotes p among other alternative competitors (Rubinstein Reference Rubinstein2014). A clear indication of this is that weak necessity statements commonly possess an ‘advisory’ flavour to them: ‘You should go by bus (although you may also take two hours walk to get there)’. And here is the central problematic point: it would certainly be counterintuitive that the construction used by speakers for advisory purposes bears an unachieved-goal interpretation.

What about unattainable desires (=wish)? Can they have an unachieved-goal reading? Since unachieved has an obvious link with unattainable, the question arises as to whether the unattainable desire interpretation (wish) is, simply put, a temporal variant of the past unachieved one (wanted, but).

The problem with the ‘core reading’ of wish, however, is how to model the ideal projection that is characteristic of such readings. As I have shown, one can certainly model an unachieved desire statement (‘María wanted to go to Pitril, but…’) by invoking the idea of a failed intention: insofar as the subject's aim to satisfy the ascribed desire configures an optimal standard, the frustrative can be thought to encode the failure of the actual world with respect to that standard. But in the case of ‘María wishes she had a sister’ in a context in which having a sister is unattainable for María, the subject's relevant beliefs do not only include that she does not have a sister: it is also that she cannot have one. And the crucial point here is that María's belief that having a sister is unattainable impedes any real intention (or expectation) in this respect. In other words, if the subject holds a belief that contradicts the very idea of intending (or expecting), the ‘core model’ does not seem to have a starter. What we need is to reach worlds beyond María's beliefs.

These considerations suggest that neither weak necessity nor unattainable desire statements deliver a core-type interpretation of -fu- clauses. With this possibility out of the way, the hypothesis that endo-X constructions derive their interpretation from the meaning that is attested in conditional environments becomes more plausible. But how to conceive of such a derivation, exactly? Although I cannot offer a complete compositional model at this point, I would like to suggest some basic ideas to develop in future research.

A plausible path to explore would be to assume that the contribution of the morphology that marks endo-X constructions is not linked to the expression of counterfactuality itself, but to a more general meaning that is active in conditional environments.Footnote ¹⁷ This hypothesis comes hand in hand with the fact, verified in some languages, that such morphology does not always convey counterfactuality when occurring in conditional environments. As is well known, so-called ‘Anderson conditionals’ (if Jones had taken arsenic, he would show exactly the symptoms he is in fact showing) provide a clear case in which X-marking does not presuppose the falsity of the antecedent. From here, the reasoning seems to be the following: if the morphology that appears in marked conditionals does not always convey counterfactual meaning, perhaps the semantic contribution of X-marking is not directly related to the falsity of the antecedent, but to something else that is compatible, but not analytically linked, to a counterfactual yield. And it is plausible that it is this meaning (and not counterfactuality) that occurs in endo-X statements.

A classic formal representation of this alternative meaning can be summarized in the two clauses below:Footnote ¹⁸

1. (28) Bare conditional: p$\;\cap $ f(w) ⊆ q.

2. (29) Added presupposition of marked conditionals: p$\;\cap $ C $ = \emptyset .$

According to the traditional view sketched in (28), bare conditionals of the form if p, then q express that all the worlds in the intersection of f(w) and p are worlds in which q obtains, where f is the modal function that assigns a set of accessible worlds to the evaluation world w. This view is supplemented with (29): marked conditionals add a presupposition to (28), namely, that the context set C (the set of the common ground beliefs shared by participants in conversation) contains no p-worlds. This basically means that marked conditionals presuppose that the antecedent p is false.

This view is of course challenged by Anderson conditionals, precisely because the utility of such constructions is to argue for the truth of the antecedent p. Thus, the added presupposition cannot be that p is false. Granted that some marked conditionals do not add the presupposition in (29), then, the challenge is to (re)define the contribution of X-morphology so as to account for the possibility of a non-counterfactual yield. According to von Fintel (Reference von Fintel, Sauerland and Percus1998), an appealing way to do this is by assuming that the presupposition at play in marked conditionals does not concern the falsity of the antecedent, but the domain of quantification f(w). More concretely, the basic idea is that the relevant morphology indicates that “the domain of quantification is partly outside the context set” (von Fintel and Iatridou Reference von Fintel, Sauerland and Percus1998:7), as stipulated in (30):

1. (30) X-marking: f(w) ⊈ C

The proposal relies on some ideas originally presented in the philosophical work of Stalnaker (Reference Stalnaker1975, Reference Stalnaker2014). Note that the presupposition of marked conditionals thus conceived does not make any claim about the truth-value of the antecedent p. Crucially, this omission results in a more general meaning that can account for both counterfactual and non-counterfactual interpretations of marked conditionals. In effect, every time the antecedent is false (as in strictly counterfactual conditionals), we will need to access worlds beyond C to find the p-worlds. If, on the other hand, p is (possibly) true (as in Anderson conditionals), p-worlds may all be located within C, but the access to non-actual worlds beyond the C is motivated for some other reason (according to von Fintel, to deal with the triviality of the conditional in its indicative form; see von Fintel Reference von Fintel, Sauerland and Percus1998: 9).

The basic claim, then, is that the morphology that appears in the consequent of a marked conditional signals that the domain the modal operator quantifies over is not entirely contained within the common ground beliefs shared by participants. In a more recent contribution, von Fintel and Iatridou (Reference von Fintel and Iatridou2023: 39) admit the difficulties this idea faces when one attempts to account for endo-X meanings in a unified way: “The only way towards unification that we see is to recast what X-marking signals to encompass both domain widening (in conditionals and desires) and ordering source addition (in necessity constructions). The common denominator is that in all three cases, there is a certain kind of departure from a default setting.”

How to understand the away-from-default meaning referred to in the passage above with respect to weak necessity? To recall, one crucial aspect of weak necessity is that it does not seem to convey a counter-to-facts meaning. On the contrary, the advisory aspect commonly attested in these statements runs against the supposition that the promoted event has no possibilities of being materialized in the actual world. More concretely, the speaker of a statement like ‘Pedro should/ought to go to a Mapuche school’ can be described as promoting a non-compulsory course of action that fulfils a salient ideal among many other competing and attainable possibilities. That is to say, instead of ascribing an inflexible duty (‘attending primary school’) derived from a non-negotiable ideal (‘obeying the law’), weak necessity statements promote one negotiable ideal (‘attending a bilingual primary school’) that competes with others (‘attending the school that is closer to home’). Consider:Footnote ¹⁹

How is the data in (31) linked to an away-from-default meaning? Consider what the speaker acknowledges as normative ideals and possible courses of action. According to one plausible characterization of the situation, by asserting ‘Pedro should go to the Mapuche school’ (instead of ‘Pedro must go to the Mapuche school’) the speaker implicitly acknowledges (not one but) a bundle of salient competing ideals (‘going to the school closer to home’, ‘prioritize Spanish over Mapudungun’, ‘learning the language of one's ancestors’, etc.), to then promote one of them (‘learning the language of one's ancestors’). One way to understand this (although, perhaps, not the only one) is to conceive of weak necessity statements as qualifying a seemingly undisputed background ideal (‘providing the best for Pedro's upbringing’) with some secondary considerations (‘attending the school closer to home’, ‘speaking the language of one's ancestors’, ‘learning exclusively Spanish’, etc.). As the relevant context reveals potential conflicts of opinion about which ideal best fulfils the default ideal (that is why Victoria asks for advice), ‘speaking the language of one's ancestors’ operates only as a secondary standard of what is optimal in the speaker's opinion. Crucially, the speaker does not impose his standard as an undisputed default ideal but acknowledges other potential perspectives on the issue.

As for unattainable desires, the away-from-default model can be implemented in a more obvious way. To recall, we are considering actual desires for unattainable prejacents. For concreteness, consider a current desire for something strictly counterfactual:

The context makes clear that: (i) María's desire is actual and (ii) that María's beliefs include that she cannot have a sister. Since intentions and expectations are realistically linked to beliefs, there are no possible intentions or expectations in the topic situation (Maria's beliefs simply impede any real intention or expectation of having a sister). This gives us a clear indication of what -fu- expresses in these types of contexts: that the modal quantification reaches beyond the default domain, which in the case of bouletic expressions coincides with the agent's doxastic set (see Heim Reference Heim1992, von Fintel Reference von Fintel1999, Villalta Reference Villalta2008, Rubinstein Reference Rubinstein2017). Very schematically, then, the claim is that the domain expands beyond the agent's beliefs so as to include (some) p-world(s), where p is the (presumably unattainable) desired proposition. Under a best worlds analysis, the semantics of a wish statement says that the best worlds in this expanded domain are all p-worlds.Footnote ²⁰

If this descriptive overview is on the right track, the frustrative-modal interactions open three possible paths: core readings (for unachieved obligations/desires), endo-X readings (for weak necessity and unattainable desires) and exo-X readings (for counterfactual obligations and desires). While the first of these paths conveys a meaning that mirrors the unachieved-goal interpretation described in section 3.1, the exo-X path can be reduced to the strictly counterfactual interpretation described in section 3.2. As for Mapudungun endo-X statements (ought and wish), this section suggests that they do not seem reducible to either core or exo-X readings. The suggestion is that an away-from-default analysis may be a reasonable idea to explore in future research. Table 3 summarizes these results.

Table 3: Mapudungun frustrative-modal interactions

As a concluding remark, I would like to point out a (perhaps too) obvious theoretical concern, one related to the unifying potential of the away-from-default view that seems to be dismissed in Table 3. In effect, von Fintel and Iatridou's away-from-default view seems to be a working proposal for a unifying account of the semantic contribution of the X-morphology in three different environments: conditionals, endo-X and exo-X. To stress, the away-from-default view is not circumscribed, in the authors’ view, to endo-X environments, but applies to conditionals (including exo-X constructions). In the view sketched in Table 3, however, the away-from-default interpretation is circumscribed to endo-X constructions, while exo-X (on a par with the Mapudungun marked conditionals examined in section 3.2) are classed as ‘strictly counterfactual’ interpretations.

For the purpose of reaching a unifying account of -fu-, this may seem a dubious strategy. A more integrating option would be to reduce the contribution of -fu- in the three environments (conditionals, endo-X and exo-X) to the same meaning (away-from-default), leaving only core readings as a different interpretative path.

The reason for the mosaic-like (instead of unifying) overview of Mapudungun frustrative semantics is very simple: as shown in section 3.2, counterfactuality is strictly derived from the semantics of -fu- in conditional environments, leaving no apparent space for ‘marked-yet-not-counterfactual’ readings. This has been confirmed for me by the fact that my consultants have systematically rejected Anderson conditionals. I have tried different variants and the result is recurring: the construction does not seem to overcome its contradictory flavour.Footnote ²¹

These results, although preliminary, delineate an interesting case: the X-morphology that surfaces in Mapudungun marked conditionals is neither dedicated (as in languages like Hungarian; see von Fintel and Iatridou Reference von Fintel and Iatridou2023 for data) nor ‘fake’ (as in English). Rather, the same ‘authentic’ frustrative semantics that is operative in (core) -fu- clauses conveys counterfactuality in conditional environments. From here, one would expect that the morpheme could not occur in modal environments in which, crosslinguistically, no counterfactual meaning is attested (namely, endo-X statements). This is not the case, however. As the data examined in this article show, Mapudungun is a transparent language in a quite systematic way: weak necessity and unattainable desires are expressed with modal clauses marked with -fu-. This suggests that transparency constitutes a morphosemantic pattern that surfaces even in languages wherein counterfactuality is necessarily derived by the occurrence of X-morphology in conditional environments. Whether this is a pattern that can be confirmed for other frustrative languages is an interesting empirical question. Further research is needed.