Causal selection : the linguistic take

Causal Selection is a widely discussed topic in philosophy and cognitive science, concerned with characterizing the choice of “the cause” among the many individually necessary and jointly sufficient conditions which any effect depends on. In this paper, we argue for an additional selection process underlying causal statements: Causative Construction Selection (CC-selection), which pertains to the choice of linguistic constructions used to express causal relations. We aim to answer the following question: given that a speaker wishes to describe the relation between one of the conditions and the effect, which linguistic constructions are available? We take CC-selection to underlie causal selection, since the latter is restricted by the linguistic possibilities resulting from the former. Based on a series of experiments, we demonstrate that factors taken previously as contributing to causal selection should, in fact, be considered as the parameters that license the various linguistic constructions under given circumstances, based on previous knowledge about the causal structure of the world (the causal model). These factors are therefore part of the meaning of the causative expressions.


Introduction. The double selection problem.
The occurrence of any event requires many different conditions to hold (Mill 1884, A System of Logic, Volume I, Chapter 5, §3). More precisely, many conditions are individually necessary and only jointly sufficient in order for a target event to take place, with several sets of jointly sufficient conditions relating to any event kind (Mackie 1965). These conditions may include other events, states and constant background conditions, intentional actions or unintentional behaviors by an agent, and/or properties of the patient.
To take a very simple example, the opening of an automatic door may depend on one sufficient set of conditions including electricity, the door being unlocked, and an agent pressing the door-open button. Another sufficient set may include a door handle, the door being unlocked, and an agent pushing the handle. Imagine a situation in which a person walks up to the door, pushes the button and the door opens. An observer, who wishes to describe what happened, is faced with what we call the double selection problem, involving causal selection on the one hand, and causative-construction selection on the other.
The first problem has been widely discussed in philosophy and the cognitive sciences: the observer has to decide which among the many necessary and -in the particular situation -jointly sufficient conditions was the cause of the door opening. Many theoretical accounts have been proposed in the recent years, alongside empirical studies testing how people select the cause from a set of conditions (Cheng & Novick 1991, Hilton 1990 inter alia). Studies show, for example, that an action by an agent that violates social norms is more likely to be considered the cause of an effect than an action which is within normative conventions, even in a situation where both actions are necessary for the effect to take place (Hitchcock & Knobe 2009, Reuter et al. 2014, and Icard, Kominsky & Knobe 2017.
The second problem has attracted far less attention in the cognitive sciences: in order to differentiate between causes, an observer has to describe the causal relations through an available linguistic construction, which involves what we call the Causative Construction Selection (henceforth CCselection). In any causal statement, the speaker selects, along with the cause, a linguistic causative construction which appropriately describes the relation behind the observed course of events. In the above example, an observer may state: the pushing of the button opened the door, or pushing the button caused the door to open, to name just two possibilities. The array of causative constructions available includes connectives like because (of), from, by, overt causative verbs like make and cause, and change-of-state (CoS) verbs such as open and boil, and other options available across languages (see Bar-Asher Siegal & Boneh 2020 for a definition of "causative constructions". For typologies of causative constructions see Shibatani 1976, Comrie 1981and Song 1996. The CC-selection problem can be phrased in different ways. We will treat it as answering the following question: given that a speaker wishes to describe the relation between one of the conditions and the effect, which linguistic constructions are available? Notably, this question does not assume singularity of causes. That is, with respect to each of the causative constructions, it is possible that more than one condition can be described as the cause, and our question aims at discovering the range of linguistic expressions that are available.
CC-selection has largely been ignored in philosophy and psychology, although its relevance has been demonstrated by research inspired by linguistic theories (e.g. Wolff 2003). A parallel question has been raised within theoretical linguistics (cf. Dowty 1979), where various analyses correlate CoS causatives like Mary opened the door with direct rather than indirect causation. An example of the latter would be pushing somebody who accidently fell against the door open button (Fodor 1970, Shibatani 1976, Wolff 2003. Further semantic differences between the various causative constructions have been recently raised by Bar-Asher Siegal & Boneh (2020) (for discussion on differences between specific construction see also Neeleman & van der Koot 2012, Maienborn & Herdtfelder 2017, Bar-Asher Siegal & Boneh 2019, Nadathur & Lauer 2020. We take CC-selection to be more crucial in the choice of a statement than causal selection, due to the fact that causal selection is restricted by the linguistic availabilities resulting from CC-selection. Consider again the door example: determining whether "the cause" of the door to open was electricity, the person or the pushing of the button requires these possibilities to be stated. The relation between causal selection and CC-selection can be observed in experimental studies on causal selection (e.g. Knobe and Fraser 2008): First the participant is confronted with a causal scenario, whose underlying causal structure is known or provided, and in which (usually) two events occur, followed by a target event. The participants are then presented with causal statements, which generally include the phrases Event A caused the target event and Event B caused the target event, and asked to indicate how much they agree with the given statements. In this common experimental paradigm, the researcher pre-selects the causative constructions for the statements they regard as appropriate descriptions. Hence the researcher has made an act of CC-selection, based upon which the participants are asked to make an act of causal selection.
In this paper, we demonstrate that CC-selection affects causal judgements, showing first which causative constructions are available to observers describing the causal dependency between a condition (a member of a sufficient set of conditions) and an effect (Section 2). We explore the semantics of causative verbs based on structural equation models, and propose a respective formal theory. Second, we present a series of experiments (Section 3), in which we investigate CCselection, showing that participants systematically rate the acceptability of certain causative constructions higher under specific conditions. We test how factors that have been shown to affect causal selection (cf. Danks 2017) affect CC-selection, including violation of social norms and foreseeability of the effect by the involved agents. We show that these factors can be considered as the parameters that license the linguistic construction under given circumstances (Section 4). These factors, therefore, become part of the meaning/truth-conditions of the causative expressions.

2.
A theory of the semantics of causative constructions. In linguistics, the object of investigation into casual statements has traditionally been the structural and interpretative properties of causative constructions. Nonetheless, dealing with causation is not trivial within formal approaches to semantics. The challenge has to do with the fact that formal approaches to the semantics of natural languages are truth-conditional and model-theoretic. In such frameworks, the meaning of a sentence is taken to be the proposition which is true or false relative to some model of the world. It is not trivial, however, to model causal statements, as they do not describe simple state-of-affairs in the world, or even in possible worlds.  Over the last decade, several works have explored the approach developed by Judea Pearl (Pearl 2000) in the context of computer science to examine causality through Structural Equation Modeling (SEM), as a way to provide a model for the truth conditions of causal statements (Baglini & Francez 2016, Baglini & Bar-Asher Siegal 2020, Nadathur and Lauer 2020. In SEM, causality is modeled by graphs that fit networks of constructs to data. On this approach dependencies between states of affairs are represented as a set of pairs of propositions and their truth values. Here, we rely on Baglini & Bar-Asher Siegal's (2020) formal definition for causal models. Considering once more the example of the automatic door, we can define the variables (pairs of propositions and truth values) in A-F in Figure 1. The fact that some variables depend on others for their value is represented by structural entailments in G-I. Variables can be classified as belonging to one of two types: Exogenous variables do not depend on any other variable (in the model). The values of the endogenous variables, in contrast, are based on the values of variables on which they depend. In our door example, the exogenous variables are A, B, D and E. The endogenous variables are C and F. Dependencies within the SEM can be represented qualitatively with directed acyclic graphs model (as in Figure 1). Nodes correspond to variables, and arrows indicate the direction of dependency: the value of an originating node dictates the value of nodes it points to. Sufficient sets are circled (cf. VanderWeele & Robins (2009). H I Following Mackie (1965), we treat the nodes in the causal model as INUS conditions: a variable or a set of variables which are Insufficient but Necessary alone, but together Unnecessary but Sufficient. In our example, when the door is unlocked, a closed circuit with electricity supplied constitutes a set which is sufficient but not necessary (since the pair of conditions Unlocked and Handle together are also sufficient for opening the door). We follow Baglini & Bar-Asher Siegal's (2020) formal system for the definitions of necessary conditions, a sufficient set of conditions and situations within the SEM framework. (A situation is defined as a set of pairs of propositions S in a language P and their values.) In this approach, the SEM encodes speakers' knowledge of the causal structure. Moreover, formal definitions of various types of nodes/conditions (such as INUS), can be used to capture the requirements for licensing linguistic judgments, or in our terms -for defining CC-selection. Following Baglini & Bar-Asher Siegal (2020), we take a CoS verb applied to a certain condition Q representing the cause in the model ("The pushing of the button opened the door"), 1 which is part of a situation S, to yield an acceptable causal statements under the conditions in (1). Similarly, (2) captures the licensing conditions when Q is the subject of an overt causative cause ("Pushing the button caused the door the open"): The function SUFF(icient) takes a situation (S) -a set of pairs of propositions and their valuesand returns 1 if it is a sufficient set in the model for a specific result (R). The formula amounts to a description of a completion event. Thus, in this line of analysis, lexical causatives select the temporally last condition to complete the sufficient set of conditions as its subject (1), while the periphrastic causative "cause" selects any condition in the set (2) (i.e., any INUS condition). Baglini & Bar-Asher Siegal (2020) demonstrate that these formal descriptions capture previous observations regarding "direct causation" in the literature. The next section presents an investigation of the claims represented by (1)-(2), in a variety of experiments, showing that while it holds to a large degree, it must be slightly modified.

Experiments
3.1 AIM AND HYPOTHESES. We report on a series of 3 experiments aiming to empirically investigate CC-selection, by measuring the effect of the semantics of causative constructions on the acceptance of causal statements. Based on the theory described in the previous section, we hypothesized that (1) statements with CoS verbs will be more accepted for conditions completing a sufficient set of (preexisting) conditions; (2) sentences with an overt cause to construction will only be sensitive to whether their subject is an INUS condition for the effect to take place.
3.2 OVERVIEW. We confronted participants with a common effect structure in which two conditions conjunctively generated the target effect. Hence, the two conditions were INUS conditions in the terms of Mackie (1965). Participants were presented with various scenarios, in which two conditions were generated independently one after the other before the effect took place. We manipulated the temporal order such that both conditions were equally necessary for the effect, but only the condition occurring second completed a sufficient set. Participants were asked to rate causal statements referring to each condition individually. One type of statement used a lexical, CoS causative (e.g., Suzan opened the window), the second type a periphrastic, overt causative (Suzan caused the window to open). Experiment 1 was designed to show that observers prefer certain causative constructions to describe what happened (i.e. CC-selection). Experiment 2 explored how the violation of social norms affects CC-selection. Experiment 3 did the same with respect to foreseeability.
3.3. EXPERIMENT 1. DESIGN. The study had a 2 (order of causes) x 2 (causative construction) x 4 (scenario) design. All three factors were manipulated within subjects. The study was run anonymously online using limesurvey (limesurvey.org). According to regulations at the University of Goettingen, no clearance by an ethics committee was required. PARTICIPANTS. We collected data of 35 participants, 32 of which passed the comprehension test. Adult participants were recruited from prolific (prolific.org). English had to be their first language. MATERIALS AND PROCEDURE. First, participants were informed that we are interested in how people use and understand language and that they would be presented with various scenarios and asked several questions examining their understanding of the scenario. Then, participants were explicitly asked to indicate their informed consent to participate. Next participants were presented with the first of four scenarios (Expose/drawings, Flood/land, Open/door, or Set off/alarm). (3) presents the the Set off/alarm scenario. The participants were asked to rate four statements according to their compatibility with the facts presented in the scenario, as in (4).
(3) The Kagan family has a motion-sensitive security system, which they switch on when they leave the house. Last Monday, Mary switched the system on, not knowing that her daughter, Emily, was staying at home. When Emily woke up, she passed in front of one of the motion sensors and activated it. The alarm went off. The rating scale ranged from 1 (least compatible) to 7 (perfectly compatible). After their answer, participants were queried about the order of events to check whether they correctly grasped the given information. Participants continued to the next scenario without receiving any feedback. The order of the scenarios and the order of the presented statements was randomized. STATISTICAL ANALYSIS. In all experiments we used a multilevel model to analyze the data, taking into account the design of the study. Factors (here order, causative construction, scenario, and the interaction of order and causative construction) were entered as fixed effects. RESULTS. Figure 2 displays the mean ratings depending on order and causative construction for the four scenarios. Across all scenarios, ratings of statements with CoS causatives were highly sensitive to order. Ratings were much higher when the condition completed the sufficient set. Ratings for statements involving overt causatives were less sensitive to order. Statements with the first causal condition being the subject were rated higher when an overt causative construction was used than when a CoS causative was. For the Set off/alarm scenario this means that they rated the statement "Mary set off the alarm" as less acceptable than "Mary caused the alarm to go off". There was no difference for statements referring to the second cause, which completed the sufficient set. This pattern was confirmed by the statistical analysis. The multilevel model allowed to predict participants' ratings, LogLik = -41.9, Chi 2 = 83.7, p < .0001, R 2 = .15. The main effect contrast of order was significant, t(474) = 9.45, p <.0001, as was the main effect contrast of causative, t(474) = 3.32, p = .001, and their interaction, t(474) = 3.66, p =.0003.
DISCUSSION. The findings provide evidence for CC-selection: participants rated the acceptance of causative constructions differently depending on which causal condition the statement referred to. When the causal condition completed the sufficient set, overt and CoS causatives were considered appropriate. By contrast, CoS causatives were considered less appropriate than overt causatives for a necessary condition that did not complete the sufficient set. These findings support our first hypothesis: participants were highly sensitive to the completion of a sufficient set when CoS verbs were used. Regarding the second hypothesis, we found that participants were less sensitive to a completion of a sufficient set for overt causatives.
3.4 EXPERIMENT 2. In this experiment, we investigated the interaction between CC-selection and violation of social norms, which has been shown to strongly affect causal selection (cf. Knobe & Fraser 2008, Icard et al. 2017. We hypothesized that a violation would have a stronger impact on the acceptance of statements when the subject represents the first condition with overt causatives than with CoS causatives. DESIGN. The study had a 2 (order of causes) x 2 (causative construction) x 3 (scenario) 2 x 2 (first agent violates norm vs. second agent violates norm) design. While the first three factors were manipulated within participants, the last factor (violation) was manipulated between participants. Again, the study was run anonymously online. PARTICIPANTS. Seventy-four people participated (37 per violation condition). Five participants were excluded, because they failed the comprehension test. Recruitment and selection criteria were the same as in Experiment 1. MATERIALS AND PROCEDURE. Instructions and the procedure were the same as in Experiment 1. Three new scenarios involving two agents were presented (Lock/computer, Set off/alarm, Burst/ tank). The lock/computer scenario is presented in (5), with two possible continuations in (a-b).
Participants were asked to rate the statements in (6) on a scale from 1 (do not agree at all) to 7 (completely agree). After providing ratings, participants' understanding of the scenarios was tested. The order of the scenarios and the order of the presented statements was randomized.

(5)
The cyber defense company iForce has a secured server which allows only one user to be logged into its system at a time. If a second user tries to log in, the system locks itself. According to schedule the senior developer Beth works on the system every day between 7:00 and 13:00. Her team-mate Frank is scheduled to work on the same system from 13:15 until 19:00. RESULTS. The results are depicted in Figure 3. When the second agent violated the norm (lower row in Figure 3), the first cause received very low ratings. The second cause (completing the sufficient set) received high ratings regardless of the causative construction. By contrast, when the first agent violated the norm (upper row in Figure 3), ratings were sensitive to order and causative construction. 3 Statements referring to the second cause were rated similarly in the respective scenario given both causative constructions. Statements referring to the first cause, however, were accepted more when an overt causative was used. The latter findings replicate the findings of Experiment 1. We also replicated the findings that overt causative statements referring to agents violating norms are rated higher than those referring to agents not violating norms (Hitchcock & Knobe 2009, Reuter et al. 2014and Icard, Kominsky & Knobe 2017. Importantly, our findings show that there is an interaction of causative construction, order, and norm violation. DISCUSSION. These findings again show the significance of CC-selection: participants rated different causative constructions differently with respect to the causal condition (here, an agent) the statement referred to. They also indicated a subtle interaction of norm violation, order, and causative construction. Preferences for a specific construction was strongest when the statement referred to an agent acting first and violating a norm. In this case, an overt causative was clearly preferred over a CoS causative. The fact that participants sometimes preferred a CoS causative for the first cause (not completing the sufficient set) over a CoS causative for the second effect (completing the sufficient set) indicates that our hypotheses need to be modified. A violation of norms affected CC-selection beyond the completion of a sufficient set.
3.5 EXPERIMENT 3. In Experiment 2, the norm violator could have foreseen the action of the other agent, but the agent conforming to the norm could not. Foreseeability has been shown to moderate the effect of norm violation in causal selection (Reuter et al. 2014). Therefore, the aim of Experiment 3 was to explore the effect of foreseeability on CC-selection. DESIGN. The study had a 2 (order of causes) x 2 (causative construction) x 4 (scenario) x 2 (first agent foresees action of second agent vs. first agent does not foresee action of second agent) mixed design. While the first three factors were manipulated within participants, foreseeability was manipulated between participants. PARTICIPANTS. Ninety-four people participated (47 per violation condition). Three participants failed the comprehension test and were excluded from the analysis. Recruitment and selection criteria were the same as in Experiment 1. MATERIALS AND PROCEDURE. Instructions and procedure were the same as in the previous experiments. Four scenarios were presented to participants (Lock/computer, Stop/elevator, Set off/alarm, Open/door). The Lock/computer scenario is given in (7), with two possible continuations in (a-b). Note that there was no explicit social norm that forbade the first agent to act. Participants were asked to rate on a scale from 1 to 7 how much they agreed with the statements in (8).
(7) The cyber defense company iForce has a secured server "F1", which allows only one user to be logged into its operation system at the same time. If a second user tries to log in, the system locks itself. Frank is the programmer responsible for performing daily checks on the F1 system, every day at 2pm.  Figure 4. On the left-hand side, the results for the individual scenarios are shown, on the right-hand side the averages across scenarios. As in the previous two experiments, participants preferred statements with an overt causative over a statement with a CoS causative when the statement referred to the first necessary but not sufficient cause. Across scenarios, there was no clear preference for a particular causative construction for statements referring to the second cause. Note that there was an effect of foreseeability for overt and for the CoS constructions. The difference between ratings for the first and the second agent was smaller, when the first agent could foresee the action of the second agent (see Figure 4 right hand side). DISCUSSION. Again, we found CC-selection to be crucial. When the first agent was the subject of the sentence, participants preferred a statement with an overt causative over a lexical causative regardless of whether the first agent could foresee the action of the second agent. When the statement referred to the second agent, there was no clear preference for a particular causative construction. Foreseeability affected the acceptance with respect to the first agent for overt causatives and CoS verbs, the latter to a lower degree.

RESULTS. Results are displayed in
There is an important limitation to the experiments: We manipulated the completion of a sufficient set through temporal order. Therefore, one might argue that the results show that CoS causatives are merely sensitive to order (see Einhorn & Hogarth 1986 the effect of order on causal judgments). An ongoing trial tests this possibility. However, note that there is a theoretical motivation for why CoS causatives should be sensitive to a completion of the sufficient set (Baglini & Bar-Asher Siegal 2020), and notably, sensitivity to the completion of a sufficient set entails sensitivity to temporal order.
linguistic constructions under given circumstances. Accordingly, these factors are taken as part of the meaning/truth conditions of the linguistic expressions.
Our results show that temporal order, and thereby the completion of a sufficient set, had an effect on both types of constructions, contra to our second hypothesis, and against the common claim relating direct causation with CoS causatives and not with overt ones. In other words, while the findings are in line with the "direct causation" analysis of lexical causatives, the effect of temporal order on the overt causative is unexpected. Norm violation and foreseeability showed interactions with construction and order, which means that these factors affect the acceptance of causative constructions differentially. Table 1 summarizes the interactions of order, norm violation and foreseeability with linguistic construction. It reveals variation between scenarios (always/sometimes) and also relative influence between the two constuctions. The results show that speakers' evaluations of the adequacy of different causal statements vis à vis a particular state of affairs vary systematically, depending on the type of linguistic expression employed to describe them. This variation indicates that we must treat CCselection independently, and that causal selection depends on linguistic facts (i.e. the choice of constructions) and not merely on the metaphysical or cognitive characteristics of the relata.

Relative influence
Overt cause to Order (completion of a sufficient set) Always a factor > Always a factor Violation of Norms Sometimes a factor < Always a factor Foreseeability Always a factor < Always a factor Following these results, we suggest to revise the proposal of Baglini & Bar-Asher Siegal (2020) reviewed in Section 2, regarding the selection constraints for both types of constructions. While being an INUS condition is probably the basic semantic requirement for using the construction with cause to, it is not enough. While it is possible that there are various factors that license the use of this construction, it is possible to offer one systematic principle, for the licensing of the cause to constructions. The higher sensitivity to norm-violation (Experiment 2) and to the ability of agents to foresee the effect (Experiment 3) both pertain to the degree of responsibility attributed to the condition with respect to the effect (see Sytsma et al. 2012 andSamland andWaldmann 2016 for the notions of moral responsibility and blame in the context of causal selection). We propose that in assigning the role of the cause in the causative construction (i.e., the subject of the sentence), speakers seek to blame the specific condition for the occurrence of the effect. Blame can be naturally assigned due to responsibility, but also as a result of a completion of a sufficient set. Accordingly, an event is perceived as more "responsible", or "blameworthy", for an effect if it is the last to complete the set of sufficient conditions (see Henne et al. 2021 regarding the notion of "recency"). If this proposal is on the right track, all factors are criteria for the same constraint: the condition represented by the subject of the cause-construction must be perceived as the one which is more responsible than the other according to at least one parameter. We therefore suggest (9) as a representation of an additional constraint to that in (2) on the choice of condition (Q) among all Conditions (Cs): (9) ∀c∈S (C≠Q Responsibility (Q) > Responsibility (C)) With respect to the CoS construction, we see that the requirement that the condition represented by the subject completes the sufficient set is stronger with this construction. However, we must account for two additional facts: in Experiment 2, norm violation was a factor for accepting this construction, and in Experiment 3 we found that, when the agent in the first condition could foresee the effect, this condition received a higher rating. In light of this, we wish to make the following preliminary proposal according to which foreseeability is also related to the notion of completion of the sufficient set. Thus, there are two modes of completion of a sufficient set: An objective take: the last event which completes a sufficient set (then only time order matters); and a subjective take: the last condition that the agent didn't know would be fulfilled (hence foreseeability matters). This difference is formally captured between (10), which repeats (1), and (11), in which the model is indexed with a perspective of a certain individual (I below). According to this, when the agent forsees that the second condition will take place, his own action is the last condition that he cannot know would be fulfilled. Therefore, his action subjectively completes the sufficient set. In this way we can explain the results from Experiment 3. In Experiment 2, the agent violating the norm could expect the occurence of the other condition, therefore it might also be a case of a subjective completion of a sufficent set.

Conclusion.
Three experiments demonstrated the significance of CC-selection, by showing that the acceptance of a causal statement was affected by the choice of the causative construction. Consequently, we took the factors affecting the acceptance of the various constructions to be parameters that license the linguistic construction under given circumstances. We propose that they are components in the meaning of the causative expressions. An important ramification from these results is that future studies in cognitive science on causal selection must control for the linguistic construction used to express causative relations, thus accounting also for CC-selection.