2.1 In syntactic causative constructions

The French verb laisser, much like its English counterpart let, can realise syntactic causative constructions, i.e. constructions in which both the causing event (e₁) and the caused event (e₂) are projected syntactically. In Romance syntactic causatives, e₁ is canonically expressed through a light verb, while e₂ is encoded by a non-finite clause embedded under said light verb. Those constructions have received a lot of attention in the literature for their idiosyncratic properties; however, much of that work focuses on the light verb faire and its Italian cognate fare, both ‘to make’ (Kayne 1975; Guasti 1996; Folli & Harley 2007; Ciutescu 2019). In Faire-Infinitive constructions (FIs), the light verb combines with the non-finite verb, hence creating a complex predicate. Complex predication occurs when two simplex predicates — one of them a light verb — combine in order to form a single complex one with a single argument structure (Butt 1995; 2010).¹ The complex predicate faire chanter has two arguments: a Causer (the subject of the complex predicate) and a Causee (its object). This differs from their English counterpart, in which the Causee is the subject of the embedded verb.

Surprisingly, let-verbs across Romance have received less attention for their syntactic properties, despite realising (at least) two distinct syntactic causative constructions: one of them of type FI, as in (3a), the other realising an Exceptional Case Marking construction (ECM hereafter).

The existence of these two constructions led authors such as Borel (1972); Kayne (1975); Silva (2012); Enghels & Roegiest (2012; 2014) to assume that each construction possesses distinct semantic properties, potentially related to their (also distinct) morphosyntactic properties. Notably, Kayne (1975: 222) uses the contrast between the pair of sentences below in (4) to propose that the FI construction is unmarked, while the ECM construction would carry an intentional flavour (hence a situation in which the guard acted with ‘complicity, or deliberate neglect’).

On the other hand, Silva (2012), and Enghels & Roegiest (2012; 2014) propose a more fine-grained analysis, in which French laisser, Spanish dejar, and Portuguese deixar can accommodate three main readings: (i) permitting, (ii) not opposing, and (iii) releasing.² As noted by Raffy & Donazzan & von Heusinger (2024), the release reading is not relevant for French laisser, as French possesses another verb, lâcher, with which laisser shares the Latin root verb laxare. Therefore, I will be using the terminology of Raffy (2021): (i) authorise, and (ii) not-intervene, which I discuss in section 2.2.2. These readings need not be tied to a specific structure, but Enghels & Roegiest (2012) do observe that the FI construction is more common than the ECM in the French corpus FRANTEXT. Yet, it appears that the FI is dispreferred with animate Causees. Consequently, if we assume that authorising requires two volitional (hence animate) entities in order to be felicitous, then the authorise reading is likely to be encoded by an ECM construction rather than an FI. While this does not seem to suggest as strong a mapping as that proposed by Borel (1972) or Kayne (1975), it still seems to hint at some degree of preference for one construction over the other for each given reading. I propose that these two readings are both non-interference readings, only with distinct aspectual properties which are due to the properties ascribed to the Causer. These differences are developed in the next section.

2.2 Letting it happen: laisser and causation by omission

3.1 Not an enable verb

While counterfactual approaches to causation view it as a necessary relation between events, force-theoretical approaches to causation view it as a relation between (two or more) entities having intrinsic tendencies; how these entities interact with one another is what defines the causal relation (Talmy 1988). In force theories, letting (as well as related notions such as helping and enabling) is generally defined by opposition with causing. Causing refers to situations in which there is (a) opposition between Causer (Affector) and Causee (Patient) as (b) the Causer has a tendency for p while the Causee has a tendency either for ¬p or for neither p nor ¬p. That tendency of the Causee is then overcome by the Causer’s, hence leading to (c) the occurrence of a result. Letting, on the other hand, is analysed by Talmy (1988) as encoding reverse force interactions in which the Causee has a tendency for p, which is blocked by the Causer’s, who has an tendency towards ¬p. The opposition exerted by the Causer is then removed, hence allowing the result to occur. In a later approach, Wolff & Song (2003); Wolff & Thorstad (2017) propose that the notion of opposition is actually not necessary to the understanding of the notion of enable (under which Talmy’s letting is expected to fall). The characteristics for each causal notions as described in Wolff & Song (2003) are replicated in Table 1 below:

The English verb let, when it enters syntactic causative constructions, is generally understood as encoding relations belonging to the causal notion of enable. For this reason, it is often interchangeable with other enable-verbs like allow.⁷

At first glance, the criteria appear to align well with let: it is reasonable to infer that the art teacher allowed the action because (i) Peter had the intention to paint his own portrait, and (ii) the teacher had no objection to it. Given that both the Causer and the Causee displayed tendencies favourable to the result, the occurrence of the result is a predictable. If laisser-causatives were to be interpreted as enable situations, the three inferences in (17) would be true if (16) were true.

But, in fact, this is not quite the picture that we get from the interpretation of laisser-causatives. Instead, a sentence like (16) yields two possible sets of inferences: if it is read as an authorise scenario, then it triggers the inferences in (18), and if it is interpreted as a not-intervene situation, we get the inferences in (19).

When comparing (17) with (18) and (19), we can see that the first inference remains the same, therefore enable and let share one core principle. However, the second one already differs: while (17b) indicates that Mar intends for David to sing, (18b) and (19b) make no such claims. Instead, Mar is indifferent to David’s singing; in other words, she does not care whether he sings or not. The non-opposition component remains, but Mar’s influence over David’s singing is to be understood as neither stimulatory nor inhibitory. This means she does not push him (force or encourage) him to sing, and neither does she prevent him from singing. The last point ought to be discussed, as this is where authorise and not-intervene diverge; while (18c) highlights that the result does not necessarily occur in authorise-relations, (19c) shows that the so-called result is already ongoing in not-intervene relations (which seems like it goes without saying, but must be pointed out nonetheless). Thus, the way the would-be prevention is exerted slightly differs. In authorise-contexts, David’s choice to sing or not remains open, because his singing is not influenced by any external force (e.g Mar’s intention). He can either choose to sing or not to sing, depending on his intention at t. On the other hand, the would-be prevention is more subtle in not-intervene relations, as the singing is already occurring. Nevertheless, the fact that the situation is expressed through a laisser-causative in which Mar receives the role of Causer is taken to mean that Mar is perceived as being able to prevent the singing if she were to choose to. Canonical force-theoretical theories such as that of Wolff & Song (2003) do not seem to provide us with an guide for understanding the negation of a concept; and yet, this is what we are interested in here – what does it mean to not prevent? Is it the same as authorising? Apparently not, at least not when lexicalised through a laisser-causative. And since those theories fail to account for situations in which the Causer’s tendency cannot be defined in terms of being for or against the result, then they are too restrictive to include concepts such as let.

The claim that laisser does not encode enable-relations is further supported by the fact that it does not pattern with permettre ‘to allow’ the way their English counterparts do. The contrast is particularly salient when the enabling relation is made explicit, as in (20a):

This inability to encode enable-relations indicates that laisser must have a semantics distinct from that of let. It thus remains challenging to determine precisely what laisser contributes to our ontology of causation. The next section examines the limited involvement of the Causer in laisser-causatives and emphasises the importance of viewing causative constructions as linguistic representations of perceived causal relations, rather than as direct reflections of objective or ‘true’ causation.

3.2 Would-be prevention and causal insufficiency

Although it has now been established that laisser is not quite an enable verb, the question of its definition remains. The previous section introduces the idea that the Causer’s involvement is too minimal to qualify for enable; the logical next step is to define the Causer’s participation to the causal relation. In normality approaches to causation, participants in a causal chain are classified as either causes or enabling conditions, depending on whether they meet criteria of necessity or sufficiency (Mackie 1965; 1974; Hart & Honoré 1985; Cheng & Novick 1991; 1992; Wolff & Song & Driscoll 2002; Nadathur & Lauer 2020). As defined by Verschueren et al. (2004), a necessary condition is one without which the outcome cannot occur, while a sufficient condition guarantees the outcome. Let us consider our example with Mar and David above in (16), repeated below in (21).

If laisser-causatives stood for enable-relations, they would be able to select enabling conditions as Causers. Enabling conditions are causal factors that are insufficient but necessary for the result, they are also considered to be both normal and stable (Cheng & Novick 1991). Is Mar’s letting necessary for David’s singing? When no letting is performed, the result may still occur, as is exemplified by (22), which ought to be interpreted as meaning ‘even though Mar did not explicitly state her agreement for David’s singing, David still sung’.

Additionally, the discussion on causation by omission in section 2.2 highlights that the Causer, being a would-be preventer, fails to act normally. However, Mar’s letting is not sufficient either for the occurrence of the result; in authorise-relations, the Causee is not bound to sing by the letting and she can still choose not to sing if it agrees with her tendency (see discussion about (10) in section 2.2.2). For this reason, let-relations allow for a non-culminating reading of the caused event, as in (23):

In this light, the would-be preventer in cases of omission, such as Mar in the let readings, is minimally involved and appears to satisfy neither necessity nor sufficiency, further complicating its classification within standard causal frameworks. If the Causer of laisser-causatives is both insufficient and unnecessary for the result, how come they can enter causal relations at all? If they had no causal relevance, one could expect (24a) and (24b) to have the same meaning:

The reason why they differ is because the speaker attributes the role of would-be preventer to Mar, because she believes Mar could or should have prevented David from singing, but simply does not because she does not care for the outcome. This raises an issue that cannot be made visible by approaches that do not treat causation by omission: the speaker’s knowledge or evaluation of the properties (or assumed properties) of the Causer and the Causee is relevant in understanding the expression of causal relations in natural languages. In other words, linguistic expressions of causal relations are often more of a reflection of the speaker’s knowledge and beliefs rather than a true representation of actual causes and effects following the laws of physics. One famous example of the way our belief system and moral compass influences our judgment of causal relations is the Knobe effect, or side-effect effect (Knobe 2003; 2004). The Knobe effect shows that the bringing about of side effects of actions considered to be morally bad tend to be perceived as intentional, while the bringing about of side effects of actions considered morally good, or neutral, is generally taken to be unintentional. This appears to be particularly true in cases in which there is a moral judgment as well as a causal one: Knobe & Fraser (2008) show that moral judgments of an event may impact the causal judgment on said event. In the example above, say that David sings every night and wakes up his neighbours every time he does, and Mar is David’s mother. One could thus expect Mar to prevent him from singing at night. But we have seen in section 3.1 Mar does not care whether David sings or not, in other words she is indifferent to the outcome. Since the occurrence of the singing (and its side effect of waking everybody up) is borne out of indifference, people will be likely to judge that what she did was morally reprehensible, considering that she breaks rules of politeness and community. While not being entirely similar to McGrath’s normality, it appears to rely on similar mechanisms: if the speaker has any form of expectation (be it moral or not) with respect to the Causer’s behaviour, and those expectations are not met, she is more likely to judge that the Causer is causally responsible for the result.

Because conceptual indifference shapes how we frame and articulate causal relations, it must be recognised and integrated into existing frameworks. Therefore, indifference must be defined as a causal force that warrants modelling in its own right.

3.3 Indifference: an attitude with causal properties

Intuitively, indifference can be understood as an attitude that is neutral towards a certain result. Put simply, the holder of said attitude has a tendency (in the form of an intention) that is neither for nor against the result. Let us take an example. Say that some people want to set up a small yard sale in their neighbourhood. The mayor could prevent them from doing it: he has authority over what is happening in his town. But it is a small town, and everyone knows everyone, so this should not pose any problem. The mayor will not get anything out of it himself, therefore, he has nothing to gain by allowing it nor by preventing it. In short, he simply does not care whether the yard sale takes place or not. By virtue of being a mayor, he has authority over (i) his constituents and (ii) whether the yard sale occurs or not. This is why his intention towards the yard sale matters: if he is in favour of it, it will take place. If he opposes it, it will not. If he is indifferent to it, the occurrence of the yard sale will depend on some other factor (e.g whether the inhabitants of the neighbourhood intend for it to occur or not). The indifference relation is summed up in Table 2 below:⁸

In short, the two bottom rows can be expressed through a laisser-causative such as the following one:

At first glance, it is unclear why a volitional entity who is indifferent (hence does not position themselves for or against a given result) would be fit to receive the role of Causer in a syntactic causative such as (25). Indeed, Causers of syntactic causatives are taken to have control over both causing and caused event. Therefore, we expect the Causer of a laisser-causative to influence the result, even when she is not directly responsible for it. What is highlighted by the data in Table 2, however, is that entities that are indifferent to the result fail to influence it. This mirrors the discussion in section 3.2 above: the (non-)intervention of the Causer seems to be neither necessary nor sufficient, or, in more trivial terms, “useless”.

What makes the mayor able to receive the role of Causer is his being the holder of preventing properties: he possesses authority over his constituents through his position as mayor. As such, he could prevent the yard sale from occurring, yet he does not. In sum, he acts as a would-be preventer for the occurrence of the yard sale. This example is not an isolated one, and the would-be prevention requirement is not forced by this specific scenario in which there is an authority asymmetry between the mayor and its constituents. In fact, Donazzan & Raffy & von Heusinger (2020); Raffy (2021); Donazzan et al. (2023) all point out that the French verb laisser in syntactic causatives requires for its Causer to be would-be preventer for the event encoded by the embedded verb. Any entity that does not have the relevant preventing properties is infelicitous as a subject of a laisser-causative. Obviously, the notion of would-be preventer can be applied more loosely to volitional entities, as they have free will and can choose to prevent events from occurring or interrupt ongoing events. Therefore, what makes the would-be prevention component salient is indifference: there is an expectation that those entities should act, or could act, to prevent the result, and yet they do not. In the following section, I show that indifference is crucial in order to (i) understand laisser-relations and (ii) define let as a causal notion that is distinct from enable: adding indifference to our causal modelling allows for a more fine-grained categorisation of “permissive verbs”.

4.1 Causal models: some basic notions

Unlike the theories discussed above, causal models are not part of a particular approach to causation; rather, they are formal representations of causal relations. Causal models, in the framework developed by Judea Pearl (Pearl 2000; Pearl & Mackenzie 2018), consist of structural causal models (SCMs), which combine graphical and functional components to represent how variables influence each other. These models are typically represented as directed acyclic graphs (DAGs) depicting causal influences. The DAG structure is made up of nodes representing variables (each corresponding to a proposition) and edges (or arrows) that express direct causal dependence between variables. In this framework, variables are classified as exogenous or endogenous. Exogenous variables, which have no incoming arrows, are determined by background factors outside the model and are treated as independent. In contrast, the value of endogenous variables depends on the values of other variables: each such variable is associated with a function that determines its value based on those of its parent variables (i.e., the variables with arrows pointing to it, see Halpern & Pearl (2005)). This functional structure captures the underlying causal mechanisms and enables the model to evaluate how the system responds under different conditions. Thus, the values of the nodes are not static but can vary depending on the specific configuration of the model, allowing one to reason about interventions and counterfactual scenarios. Let us take a real-life example to make this clearer. When it is sunny outside, one generally puts their clothes out to dry them faster, because the warmth from the sun causes the moisture from the wash to evaporate. Therefore, if it is sunny (S), my clothes will get dry (C), hence S→C. This causal relation is represented in Figure 1.

Figure 1: A model for sun drying.

S = whether it is sunny

C = whether my clothes get dry

In the model above, the node S is exogenous, since it is not influenced by another variable. Although it is clear that there are causes for sunny weather, these causes are not causally relevant to the situation depicted in the model. Conversely, node C is endogenous: its value is set by that of S, because whether it is sunny or not matters for whether my clothes will get dry. In other words, if S = 1, then C = 1, and if S = 0, then C = 0.

Now that the models have been clearer, and since they are perfect for representing causal concepts, let us apply them to a typical enable situation. Say that I want to represent the sentence in (26) below, which encodes a situation in which users would simply not be able to share their opinions on the platform if this was not an available feature of the website. In order to represent this situation accurately, we need at least three nodes: (i) whether the platform possesses an option to let users post comments, (ii) whether users intend to share their opinions, and (iii) whether users do share their opinions. What we are interested in here is how these nodes interact with each other.

The model in Figure 2 is a collider: the result node C acts as a collider in that it is influenced by at least two other nodes, here P and I_U. In this model, both P and I_U have a stimulatory influence, and both are necessary for the occurrence of the result. If the platform enables comments but users do not intend to comment, then they will not be commenting. Similarly, if users intend to comment but this is not an available option on the platform they are using, then they will not be able to share their opinions on that very platform. As we have seen above, this means that the value of C should depend on that of both P and I_U. This is summed up in the truth-table below in Table 10.

Figure 2: Representing (26).

P = whether platform enables comments

I_U = whether users intend to comment

C = whether users comment

The data in Table 3 actually supports the observations previously made in section 3.1: in enable relations, the intervention of the Causer is necessary for the result. If P = 0, then C = 0, regardless of the value of I_U. This means that, if P is set to 1, it “wins” by setting the value of C to 1. This means that P is efficacious for C (Copley 2005; Copley & Harley 2015). Copley (2021) defines efficacy as follows: “efficacious(A,E) iff A → E is in the model, and the value of $f_{\overrightarrow{\text{AE}}}(A)$ in the model is the value of E in the world”. Therefore, the notion of efficacy can be used to describe the participation of the Causer to the causal relation in enable situations.

Now that the functioning of causal models has been made clearer, and that the different types of influences have been addressed, these devices can be put to work to provide an accurate representation for let.

4.2 Addressing the let issue

4.2.2 Building the model

In this section, I propose a general model for let as a causal notion. In other words, I will not be treating here the subnotions of authorise and not-intervene, considering it has already been established in sections 2.2 and 3.3 that the two construals shared the same core combination of would-be prevention with indifference. Let us use the sentence in (16) (repeated as (29) below) as a basis for the model:

1. (29)

1. Mar
2. Mar
1. a
2. has
1. laissé
2. let
1. David
2. David
1. chanter.
2. sing
1. ‘Mar let David sing.’

Recall that there is an apparent clash between the Prevention criterion and the No-influence criterion: current causal models like Pearl’s cannot represent possible influences. We circle back to our initial conundrum: how do we account for the mismatch between “true” causation and “perceived” (hence expressed) causation? Besides, causal models also lack the tools to represent influences that are neither stimulatory nor inhibitory. Representing the Causer’s “influence” (or lack thereof) is thus going to be the challenge to be tackled.

Here, three possible routes can be taken. The first route, represented below in Table 4, is to treat the variable of the Causer’s tendency as having three possible values: +1 if Mar has a strong intention for David to dance, 0 if she is indifferent, and –1 if she really strongly opposes David’s singing.

Table 4: Three-valued logic for Causer’s intention in (16).

I_J = whether Mar intends for David to sing

I_M = whether David intends to sing

R = whether David sings

IM	ID	S
+1	1	1
+1	0	0
0	0	0
–1	1	{0,1}
–1	0	0

Creating a third value that is different from +1 for enable and –1 for prevent allows the integration of the notion of indifference, encoded by let. However, this does not provide any help with how this node, when set to 0, interacts with the other nodes (which is shown by the similarity between the three sets of rows). Additionally, it does not allow us to represent would-be prevention: the variable being set to 0 does not by default entail that the Causer possesses preventing properties. This route is therefore ruled out.

The second route arises from the observation that the Causee can still pick a different course of action in laisser-relations, even when the Causer appears to be exerting a prevention, as examplified in (30) below. Conversely, such an option does not seem to be available for the relation(s) encoded by the causative verb empêcher ‘to prevent’, as in (31). This could be taken as a hint that the negation of laisser encodes some form of weaker prevention.

1. (30)

1.    Jean
2.    Jean
1. ne
2. neg
1. laisse
2. lets
1. pas
2. neg
1. Marie
2. Marie
1. danser,
2. dance
1. alors
2. so
1. elle
2. she
1. le
2. it
1. fait
2. does
1. en
2. in
1. cachette.
2. hiding
1.    ‘Jean does not let Mary dance, so she does it on the sly.’

1. (31)

1. ??Jean
2.    Jean
1. empêche
2. prevents
1. Marie
2. Marie
1. de
2. to
1. danser,
2. dance
1. alors
2. so
1. elle
2. she
1. le
2. it
1. fait
2. does
1. en
2. in
1. cachette.
2. hiding
1.    ‘Jean prevents Marie from dancing, so she does it on the sly.’

If Jean decides to reward Marie by giving him permission to dance at t₀, then the permission must still be standing at t₁ when Marie starts dancing, else she will be misbehaving (which, as a reminder, she can still choose to do). If we assume that Marie is generally honest and will respect Jean’s decision either way, then Marie dancing is more likely to happen with Jean’s permission than it is without it.

As seen in section 3.2 above, some previous approaches to causation have attempted to categorise causes in terms of sufficiency and necessity (Mackie 1965; Lauer & Nadathur 2018; Baglini & Siegal 2020; 2021). As a reminder, these terms fail to describe accurately the Causer’s force in laisser-relations, as it would be categorised as both insufficient and unnecessary. Fischer (2005: 284) proposes that “an unnecessary and insufficient force or condition is a cause of an injury if it joins with other forces or conditions to cause an injury.” While he is talking about law and the justice system, perhaps his proposal can be adapted to our laisser cases. The approach taken by Baglini & Siegal (2020; 2021) is to treat periphrastic causatives using Mackie’s (1965) INUS condition: Insufficient but Necessary part of an Unnecessary but Sufficient set. They propose that causal sufficiency is a property of sets conditions rather than of individual conditions. If we assume a joint set that contains Marie’s intention to read and Jean’s lack of a prevention (intention not to prevent?), then this set is sufficient for the occurrence of the reading event. I will not be pursuing this approach here, as I do not think it will fully allow us (or at least, not as far as I know) to represent the notion of indifference that, I believe, is crucial to letting.

The last route is inspired by Talmy’s representation of onset letting (Talmy 1988), which he defines as a situation of cessation of impingement, or, in other words, removal of a blocking. In such a situation, the Causer’s (or Antagonist’s) force is removed, which allows the Causee (Agonist) to proceed with her tendency. Talmy illustrates it with the following sentence, which is pictured in the diagram in Figure 3.

Figure 3: Onset letting for Talmy (1988: 57).

When examplifying his diagrams, Talmy (1988) did not use sentient entities, as they are presumably harder to deal with. However, many of his diagrams can be used with a few small amendments to describe causal relations between Agents. Based on Talmy’s insight for cessation of impingement, we can now represent let. In his diagram, Talmy shows that the blocking (what I have referred to as a prevention) is being removed. The blocking and the removal can be operated by the same entity (in cases of intra-psychological causation, for instance) or by two separate entities, it does not matter for Talmy. In our laisser-cases, the removal of the blocking is done by the Causer. The prevention, however, might be a pre-existing one (e.g the law) or can have been exerted by the Causer himself up until the letting started (mostly true in authorise cases). Therefore, one node representing the standing prevention must be added, in order to account for cases in which they are embodied by two distinct entities. The Causer removes the standing prevention, which erases the arrow from the node representing the prevention to the Causee’s node. This means that the Causee’s node is now independent, and the result node depends only on the value of the Causee’s node.

This appears to be the right thing to do: (i) all the nodes are present, and I_C influences R through P (in an indirect way, since the arrow is erased), which satisfies the Fidelity criterion, (ii) the prevention is represented by the node P, so the Prevention criterion is met, and (iii) I_M is independent, R is freed from the direct influence of I_C, which both solves the influence asymmetry issue and fulfills the No-Influence criterion.

But if we were to do this, we would be rushing into things and forgetting the basic rules of causal modelling. Indeed, in a situation in which Mar lets David sing, the model in Figure 4 could potentially work. As there is no law in France against singing, it is clear that the “standing prevention” would be a rule in Mar’s household, hence created and enforced by Mar herself. Therefore, one could argue that Mar being indifferent to whether David sings or not is her cancelling her standing rule. But it is not quite so. Instead, she is overruling it through her letting, not discarding it. In order to make this clearer, let us take a look at an example from Raffy (2021), in which the prevention and the Causer are two separate entities:

Figure 4: Representing (16) – take 1.

P = whether a standing prevention is exerted

I_C = whether Mar removes the prevention

I_e = whether David intends to sing

E = whether David sings

1. (32)

1. Le
2. The
1. patron
2. boss
1. a
2. has
1. laissé
2. let
1. ses
2. his
1. employés
2. employees
1. fumer
2. smoke
1. à
2. at
1. l’intérieur
2. the-inside
1. du
2. of-the
1. batiment.
2. building
1. ‘The boss let his employees smoke inside the building.’

Here, it is common knowledge that there is a law in the European Union that prevents people from smoking inside in public spaces. Therefore, the prevention is this European law. The Causer, on the other hand, is the boss. Say that the boss is indifferent to his employees smoking or not, and, as such, he suspends the standing prevention. His letting his employees smoke will not make the law against smoking disappear. Therefore, there cannot be an arrow from the Causer’s node to the prevention node, because the value of the Causer’s node simply cannot set that of the prevention node. The Causer’s action is to be understood as removing (or at least strongly lessening) the influence the prevention has on the whether the result occurs or not. Therefore, the Causer’s influence is not on the prevention, but on the influence the prevention has on the result. The resulting model, which I adopt in this paper, is the following in Figure 5:

Figure 5: Causal model for x laisse y p.

P_C = whether Causer holds preventing properties

P = whether a standing prevention is exerted

P_c = whether Causee holds properties to bring about result

R = whether the result occurs

The indifference of the Causer is highly relevant in such situations: by being the holder of such an attitude, she frees the Causee from any existing inhibitory influence. She is able to perform this removal of influences through her own preventing properties. As noted by Donazzan et al. (2023), this is particularly evident when the Causer is an authority figure and there is an authority imbalance between Causer and Causee. The term would-be preventer ought to be understood in two ways: not only can the Causer prevent the result from occurring by upholding the standing prevention (which is done through authority or abilities for an Agent, through preventing properties like dispositions in an inanimate object), but she can also prevent the standing prevention from applying. What this means for our model is that if the value of P_C is 0 (meaning that she is indifferent), then the arrow from P to R will be erased. If the value of P_C is set to 1 (i.e the Causer exerts a prevention), then the arrow remains, setting the values of R to 0, given that the Causee behaves. Table 5 shows that all three criteria are satisfied.

Table 5: Testing Figure 4 against the three criteria.

	Fidelity	Prevention	No-Influence
Figure 4	✓	✓	✓

These functions (or the ensuing relation) do not exist in traditional causal modelling, edges cannot generally point at other edges. We proceed somewhat in the spirit of Pearl (1993; 2009: 70–73) by treating “influencing an influence” as altering the function that corresponds to the arrow between P (the prevention node) and R (the result node). As a reminder, each arrow between two nodes is associated with a corresponding function. For instance, the arrow from P to R is associated with the function $f_{\overrightarrow{\text{PR}}}$ , which is (without the intervention of P_C, the node representing the Causer’s preventing properties) an inhibitory function, marked f–, and defined in Table 6 below. In turn, this means that the arrow from P_C is a function that takes as arguments the value of P_C and the function $f_{\overrightarrow{\text{PR}}}$ . Instead of giving out a value, it yields a relation, marked R_indep.

Table 6: Influence of P on R in the absence of P_C.

f–
P	R
1	0
0	1

Recall that the brackets in the second table mean that the two values are still available for R, they are used as an abbreviation for or. The relation R_indep should remind the reader of the “indifference influence” in Table 2. In short, what the data in Table 7 tells us is that P does not influence the value of R anymore because R is made independent from P by the intervention of P_C. As such, the value of R does not depend on that of P anymore, which explains the curly-bracket notation: both values might be available for R, depending on the value of the other variables it depends on (in Figure 5, that would be P_c). While it is likely that P would be efficacious for R in the absence of P_C, the influence of P_C has made P unable to prevent. Because the two variables are now independent from one another (and there is no remaining arrow between them), the relation between them cannot be treated as a function anymore. Even though it it still a relation, I will refer to the relation between P and R (noted PR) in the presence of P_C as R_indep: the independence relation. I make this explicit below in Table 8:

Table 7: Influence of P on R in the presence of P_C.

Rindep
P	R
1	{0,1}
0	{0,1}

Table 8: The independence relation.

PC	PR
1	Rindep
0	f–

What we have in Table 8 is the function that laisser encodes. The inhibitory function from the node representing the properties of the Causer to that representing the event description is erased through the influence of a third variable.

5.1 Authorise

My approach to authorise is based around the analysis made for authorise-laisser in Donazzan et al. (2023), discussed above in section 2.2. As a brief reminder, the authors propose that the Causer in authorise-laisser has authority over the Causee’s set of alternatives; she could restrict that set but does not. I have argued above that the reason that she does not act on that set is because she is indifferent to the outcome. Nevertheless, what this entails is that the Causee has free choice over her alternatives: she is not made to pick one or the other and can act according to her own tendencies (desires, beliefs, intentions, abilities). Therefore, an additional criterion must be added in order to represent authorise-laisser: the Choice criterion.

• Fidelity criterion: the model should remain faithful to the syntax, as far as possible: it ought to contain at least three nodes: one for the Causer’s force, another for the Causee’s, and one for the result.

• Prevention criterion: the notion of prevention (or possible prevention) must be included and visible in the model.

• No-influence criterion: the model must represent the lack of influence the Causer has on both the Causee and on the result, in order to represent indifference.

• Choice criterion: free choice and free will must be represented in the model for authorise.

We find that the model above in Figure 5 perfectly fits these requirements without any need for further modification (see Table 9): the Causee’s node, I_D, is completely exogenous, which means it is independent from any influence. Therefore, the Choice criterion is met. The authority of the Causer is represented by (i) the arrow coming out of P_J and pointing at the edge from P to S and (ii) the edge being made dashed by the Causer’s indifference (i.e. P_J being set at 1). The (amended) Prevention criterion is therefore met as well.

Figure 6: Causal model for authorise-laisser.

P_J = whether the judge holds authority

P = whether a prevention is actually exerted

I_D = whether the defendant intends to speak

S = whether the defendant speaks

5.2 Not-intervene

Let us turn to not-intervene. Recall that not-intervene refers to situations in which there is an ongoing event performed by the Causee that is not being interrupted by the Causer; in those cases, no alternative set is introduced, as the event is ongoing. This means that, while the question of free choice is not relevant for not-intervene (Donazzan et al. 2023), the issue here is that of the ongoingness of the caused event. Say that I utter the sentence in (34) with a not-intervene reading – the sentence can be paraphrased as (35), in which we find the periphrastic construction en train de, which encodes the progressive aspect.

The event encoded by the embedded predicate is already ongoing at t when the letting starts: they appear to be co-temporal rather than successive, unlike in authorise relations. In turn, this entails that the event cannot be prevented from happening but can be prevented from reaching its endpoint or culmination. Therefore, ongoingness must be added to the model.

• Fidelity criterion: the model should remain faithful to the syntax, as far as possible: it ought to contain at least three nodes: one for the Causer’s force, another for the Causee’s, and one for the result.

• Prevention criterion: the notion of prevention (or possible prevention) must be included and visible in the model.

• No-influence criterion: the model must represent the lack of influence the Causer has on both the Causee and on the result, in order to represent indifference.

• Ongoingness criterion: the model must represent the result node as encoding an ongoing event.

Applying the model for let from Figure 5 above to our configuration in Figure 7 causes us to run into a problem with respect to the Ongoingness criterion. This problem arises because the most basic causal models we have been using do not represent time; therefore causal modelling cannot represent aspect. For that reason, they can simply never satisfy the Ongoingness criterion. The most obvious way to go about representing scenario like that of (34) and (35) is to actually represent it as in Figure 8 below, by treating the node as a constituent that is large enough to include aspect. In short, F is simply to be treated as F = whether my cousin is picking fruits.

Figure 7: Tentative causal model for not-intervene-laisser.

P_M = whether I hold preventing properties

P = whether a prevention is actually exerted

I_C = whether my cousin intends to pick fruits

F = whether my cousin picks fruits in my garden

Figure 8: Final causal model for not-intervene-laisser.

P_M = whether I hold preventing properties

P = whether a prevention is actually exerted

I_C = whether my cousin intends to pick fruits in my garden

F = whether my cousin is picking fruits in my garden

This slight modification immediately repairs the model, which is now well-fitted for not-intervene.

5.3 Discussion

Such an approach allows us to account for any type of situation involving a would-be preventer. While I have exclusively spoken of volitional entities in this article, they are not the only ones that can enter laisser-causatives as Causers. Non-volitional, non-force-generating Causers are perfectly felicitous (exclusively) when the Causee is also non-volitional and non-force-generating.⁹ Since the notion of indifference is restricted to agentive entities who can choose to act or not, it is obviously impossible to make it apply to constructions in which the Causer is not an Agent. The two questions that arise from this minor obstacle are the following: (i) do these constructions behave in the same way as their agentive counterparts, and (ii) if they do, how can we account for them without using the notion of indifference?

Let us consider the relation encoded by the sentence in (37) below, taken from Donazzan et al. (2020: 67).

The involvement of Causers of non-agentive laisser-relations is the same as that of agentive ones. The curtains are not necessary for the light to enter the room, a window with no curtain would have yielded the exact same result. They are also not sufficient for the light to enter the room, as the light would have failed to filter through if the window was tinted, for instance. Therefore, we observe the same “uselessness” of the Causer in non-agentive laisser-causatives.¹⁰ This fact leads us to expect that this apparent uselessness is actually a case of would-be prevention: the Causer possesses properties (that are not actualised) that are relevant for preventing the result. This leads us to our second question: what is encoded by the sentence in (37) is not that these curtains have the property to let light through. Instead, what is implied is that those curtains should not let light through, and yet they do. This is possible strictly because curtains are artefacts, and there are given expectations on artefact kinds. According to Thomasson (2003), artefacts, being man-made, come with built-in intentions. In other words, all objects of the same kind are expected to serve the same purpose since they were produced with the same intention in mind. In order to serve this purpose, they are created with a given set of properties relevant to their kind, which Thomasson calls ‘K-relevant properties’ (2003: 600). Curtains may typically serve two purposes: they may be decorative, or they can be used to block light. If the curtains are designed with the built-in intention for them to be decorative, then the only K-relevant properties that they may have are for them to be pretty or trendy (which is overall fairly subjective). On the other hand, if they are meant to block light, then the main property that they should possess is that of being opaque. It is clear that the curtains in (37) are not the decorative kind, as there is no sort of connection between being pretty and letting light through. Conversely, their opacity (or lack thereof) is what is at stake here: there is an expectation that they ought to block light, and yet they fail to do so.

What is being expressed here through the laisser-construction is a mismatch between an ideal world in which artefacts are perfect instances of the kind that they belong to and the real world in which artefacts can be defective. The expectation of the speaker with respect to the Causer is just not met; as such, Causers of non-agentive laisser-causatives are not would-be preventers, they are should-be preventers. They nevertheless fit the definition for normality in McGrath (2005), as one can consider that it would be normal for curtains to block light (since it is a K-relevant property of the kind curtain), and this specific curtain acts abnormally.

Therefore, I believe this model can be used to represent any situation of causation by omission. Let us conclude by revisiting our roast example from the introduction in (1), repeated below in (38):

I have treated let as encoding situations introducing a comparison between the actual world and an ideal world in which entities behaved according to the speaker’s expectations. What laisser does is underline the mismatch between these two worlds. This mirrors the notion of normality as defined by McGrath (2005): there are expectations for entities to behave a given way, which is what she calls normally. If they stray from such expectations, they become Causers because they are abnormal.

The function from A_f to the (non-)function from E_f to B represents this mismatch between the ideal world and the actual world. By making B independent from E_f, A_f sets it to be influenced solely by H. In other words, the only “real” reason why my food is burning is because heat is being applied to it even though it is already cooked. If heat was no longer applied to it (say, because my oven broke in the middle of cooking it), then my friend’s forgetting would not matter anymore because there would be no result.

Let us take a closer look at Table 10: the two rows in which B is receives no value (marked ×) are rows in which there is no expectation for on my friend to turn off the oven: a sentence like (38) simply cannot be true if such an expectation did not exist. The results for the two remaining rows are explained easily using the data for the influence relation from Table 8. When my friend does not forget to turn the oven off (A_f = 0), then the inhibitory function f– from E_f to B applies: my friend turns the oven off as expected and the roast does not burn. On the other hand, when my friend does forget to turn the oven off even though it would be normal for him to do so, then the independence relation R_indep applies; whether the burning of the roast occurs or not is now solely dependent on an outside factor (here, whether heat is applied to my roast or not). This means that causation by omission and let as a causal notion are actually one and the same.

Figure 9: A general model for causation by omission.

A_f = whether my friend prevents the roast from burning

E_f = whether it is normal for my friend to turn the oven off

I_C = whether heat is applied to the roast

B = whether the roast burns