1 Introduction

Sometimes we want to explain a phenomenon that is too difficult to understand for our audience. In such a case we can explain the phenomenon fully—being aware that the audience probably would not understand it, not explain anything, or we can explain the material in a simplified way, often by knowingly presenting strictly false information. An example of the latter communicative practice are explanations performed by teachers. Walsh and Currie (2015, p. 424), for instance, say that “The truth, the whole truth and nothing but the truth is no teacher’s maxim.” The use of false information in educational contexts is considered to be justifiable or even judged as praiseworthy. Elgin (2007) calls such explanations felicitous falsehoods. At the same time, however, such explanations have been labelled as caricatures (Walsh & Currie, 2015), disinformation (Fallis, 2015), and even lies. Consider the reasoning behind the last label: “A lie-to-children is a statement that is false, but which nevertheless leads the child’s mind towards a more accurate explanation, one that the child will only be able to appreciate if it has been primed with the lie” (Pratchett et al., 1999, p. 38).

An example of such a lie-to-children can be found in teaching physics, where the Bohr model of an atom—which depicts an atom like a little solar system where electrons travel in circular orbits around the nucleus—is still often taught as representing the atomic structure. We know that atoms do not behave as the Bohr model predicts; nevertheless, this model is still used before more complex models are introduced. Such examples are not rare and peripheral—their usage is widespread, especially when it comes to explicating scientific phenomena.Footnote 1 Thus, an explanation of something false is often done with the promise that it will be corrected in the future. Independently of this promise, this example shows a crucial aspect of explanation, i.e., a good explanation is directed towards and adjusted to the audience. The teacher in a primary school cannot explain what science nowadays says about the structure of an atom—such an explanation would be incomprehensible to the audience due to its complexity.

Are teachers who explain such theories as the Bohr model lying? On the one hand, they follow a curriculum and widespread educational practice; moreover, they do that to spread understanding in their pupils about the structure of an atom, even if it is only a partial understanding. On the other hand, however, they knowingly say something they believe to be false, which by most definitions of lying is sufficient to lie. More precisely, the dominant view nowadays is that lies are insincere assertions.Footnote 2 The consensus is that an intention to deceive is not necessary for lying. Proponents of such a view are called non-deceptionists. Their opponents, the deceptionists, claim that an intention to deceive is a necessary condition in a definition of lying.Footnote 3 The status of an intention to deceive has been a subject of empirical investigation (see Sect. 2.3). However, the debate has been primarily focused on specific cases—the so-called bald-faced lies. Crucially, false explanations have not been empirically tested yet—we aim to bridge this gap. Whether one lies in such cases is an empirical matter and thus we empirically investigate intuitions regarding such explanations.

The aim of this paper is to empirically test whether the speaker making a false explanation, such as the explanation of the Bohr model, is considered by ordinary people to be lying. The central question of our study is the following one: “Does modification of the speaker’s intention (positive/negative) change the lie attribution?” We want to test whether ordinary speakers agree that the speaker with a negative intention (for instance, wants to mislead the audience) lies while the speaker with a positive intention (for instance, presents a simplified material because she believes that presenting a more difficult one would be confusing for the audience) does not lie. Our prediction is that changing the speaker’s intention influences the lie attribution: the speaker with the negative intention will be classified as someone who lies to a significantly higher degree than the speaker with the positive intention. Such a result puts some pressure on non-deceptionist definitions of lying, according to which both speakers lie.

The plan is as follows. In Sect. 2, we present a theoretical part of our work. We make a case for appropriate albeit false explanations and argue that such explanations are not lies. Sections 3–5 report three experiments that focus on empirically testing the relevance of the speaker's intention on lie attributions in false explanations. In Sect. 6, we discuss the results, focusing on their consequences for non-deceptionists.

2 Explanations and lies

2.1 What is an explanation?

The link between explanation and understanding is widely recognized. One plausible way of expressing this relation is that explanations provide understanding (Grimm, 2010; Lipton, 2004). In this section, we argue that some false explanations—such as teaching about the structure of an atom by means of simplifications like the Bohr model—can generate understanding and be considered proper in the presented context.

The notion of understanding can be explicated in many ways; the widespread tradition treats understanding as involving an act of grasping.Footnote 4 One take is, thus, to think about understanding as “… something like grasping systematic connections among elements of a complex whole, or gaining insight into certain relations between items within a larger body of information” (Jäger, 2016, p. 180). Among various types of understanding, we focus on the so-called objectual type, which concerns subject matters or domains of things (Kvanvig, 2003; cf. Wilkenfeld, 2013; Kelp, 2015; Baumberger & Brun, 2017). Furthermore, because our focus will be on scientific explanations, we restrict attention to cases of understanding empirical phenomena, like understanding the structure of the solar system, the phenomenon of evolution, climate change, etc.

Having said that, consider the following case of explanation:

Atom Story (positive intention)

John is a physics teacher at a summer camp for primary school students. One day, he teaches about the structure of an atom. He has some freedom in deciding how he will explain this topic. He explains the Bohr model of an atom, according to which electrons travel in circular orbits around the nucleus. John knows that this is a crude simplification and a false depiction of an atom. He is aware that there are other, more exact but also much more complicated models of an atom. He presents the Bohr model because he thinks that knowing this model is sufficient on this level of education. He thinks that explaining a more complicated model would only confuse his pupils. As a result of the presentation, his pupils acquire some understanding of the structure of an atom.

Gaszczyk (2023), proposing a detailed analysis of such cases, argues for a normative account of the speech act of explanation with understanding as its norm. Here we only sketch a plausible take. It is natural to assume that the speaker should understand the subject of explanation, as John does here. Moreover, a good explainer must take the epistemic position of their audience into consideration and adjust their explanation to the audience’s background knowledge and to their capabilities of comprehension. John is aware of the complexity of the phenomenon he wants to explain and for that reason gives an explanation that can be grasped by the audience. Finally, in this context, delivering a more exact explanation would be improper—if John were to do that, he would fail as a teacher since his explanation would not be understood by his audience.

Some could wonder how John’s pupils can acquire an understanding if his explanation is (at least) partially false. Factivists about understanding would deny that there is any transfer of understanding in such a case.Footnote 5 However, such an explanation is compatible with the non-factive notion of understanding.Footnote 6 Non-factivism, among other things, explains the fact that understanding is a gradable notion (Elgin, 2007; Hills, 2016; Khalifa, 2017; Kvanvig, 2003). This correlates with our linguistic practice of attributing understanding—one can understand a particular phenomenon barely or partially, but later, one’s understanding can be improved, and thus, one can understand the same phenomenon fully or completely.

Following non-factivism, we can say that John’s explanation provides at least some genuine understanding. The falsehood that electrons travel in circular orbits around the nucleus allows John’s students to grasp the basic concepts of the structure of an atom and the relationship between them. This is corroborated by McKagan et al.’s (2008) empirical research that concerns teaching the Bohr model. They show that starting education from false but simpler theories may help later in a better understanding of more exact theories. Thinking about such cases, Elgin (2009, p. 325) observes that “… the pattern exhibited in this case is endemic to scientific education. We typically begin with rough characterizations that properly orient us toward the phenomenon, and then refine the characterizations as our understanding of the science advances.”Footnote 7 Thus, by his explanation, John lays the ground for expanding the understanding in the future.

2.2 Lying by explaining

Having established that some false explanations can be considered proper, we turn now to the question concerning the sincerity of such explanations. In this section, we argue that John is insincere, but he is not lying. We motivate this view and put it against the dominant approach to lying.

Let us start with the basic account of insincerity. One influential approach to insincerity proposes that each speech act expresses a distinctive propositional attitude (Bach & Harnish, 1979; Searle, 1969). By expressing an attitude, a speaker represents oneself in a certain way. For instance, an assertion expresses a belief, and thus by asserting that p a speaker represents oneself as believing that p. Crucially, one can express a particular attitude without having that attitude. By extension, if one asserts that p while believing that not p, one misrepresents oneself. By doing that, the speaker is insincere. After all, they violate Grice’s first sub-maxim of quality (Grice, 1989, p. 27), i.e., they say something they believe to be false.Footnote 8

Explanations are standardly treated as assertions.Footnote 9 Following this view, by explaining p one represents oneself as believing p. Since this standard of sincerity is most widespread, we will also use it throughout the paper.Footnote 10

Let us return to John. He explains something he believes to be false, and because of that, he is insincere. His good intentions or the fact that he follows the curriculum does not change this. Nevertheless, intuitions regarding such cases vary in two opposite directions, i.e., some argue that he is not insincere, and some that he is not only insincere but that he lies. The rest of this section is devoted to arguing against these proposals.

One strategy that is supposed to show that John is not insincere rests on the premise that his explanation is somehow hedged. Gaszczyk (2023) discusses several variants of this strategy. According to one of them, when John in the classroom says p (for instance, “Electrons travel in circular orbits around the nucleus”), he uses a covert hedge and really means something like “According to the Bohr model, p,” or “According to the textbook, p.”Footnote 11 Thus, John is not making a flat-out assertion that p and thus he does not commit to the truth of p, but rather to the hedged claim that he knows is true. Following this proposal, John’s explanation is sincere because he says something he believes to be true.

There are, however, several problems with this proposal. Firstly, it does not deliver any criteria for determining when John explains the hedged content and when he speaks for himself. Consider that in the presented story it is explicitly stipulated that John has some freedom in deciding how he will introduce the material and how deep into the topic he will dive. It is hard to maintain that John is merely reporting what the textbook says since there is no curriculum or textbook to follow—he gives an explanation that he himself decides is proper for his audience. Secondly, there is no criterion for what kind of hedging John is supposed to use. Since there are many possibilities that differ significantly from each other (e.g., “According to one atomic model, p,” “According to the textbook that I prefer, p,” or “According to my experience as a teacher in how to introduce this topic, p”), this is a major deficiency of this strategy. Finally, even if we would agree that John covertly hedges his explanation, his audience does not know that. Consider that the standard questions that they can ask, such as “How do you know that?,” or “What makes you believe that?,” show that they presuppose that he believes in what he says. This indicates that he is in the context in which the Gricean maxims, particularly the maxim of quality, are in force. After being challenged, he can say that he was covertly hedging his explanation, but this would rather generate confusion and create a sense of insincerity. Thus, we do not find the proposal that John covertly hedged his explanation to be promising.Footnote 12

Others argue that John is not only insincere but that he is lying. This conclusion can be derived from non-deceptionist definitions of lying. All of them are assertion-based definitions, i.e., argue that insincerely asserting is sufficient for lying; they differ in how they define the notion of assertion. We briefly consider two types of such definitions.

The commitment-based definitions of lying (Marsili, 2020; Viebahn, 2020, 2021; cf. García-Carpintero, 2021) maintain that one lies only if one undertakes a proper commitment. For instance, by committing to p one is responsible to defend p if challenged (cf. Carson, 2006, 2010; Saul, 2012)—John is responsible for doing that. Viebahn (2020, 2021) emphasises the fact that liars do not retain deniability, i.e., when accused of lying about p, liars cannot sincerely and consistently deny saying that p. Consider John: when accused of lying, he cannot sincerely and consistently deny that he ever said that electrons travel in circular orbits.Footnote 13

Another view characterises lying in terms of updating the common ground (cf. Stalnaker, 1978). Stokke (2018) argues that one lies only if one proposes to make something common ground while believing that it is false. Looking at John, his explanation of the Bohr model counts as a proposal to add this information to the common ground; importantly, he believes that it is false.

Thus, most non-deceptionists agree that John is lying.Footnote 14 One strategy to resist this conclusion would be to deny that John is making an assertion in a relevant for lying sense. We think that any such attempts would be unsatisfactory. Any definition of lying that would deny that John makes an assertion would be too narrow and thus wrongly exclude many intuitive cases of lies. For instance, consider this variation of Atom Story:

Atom Story (negative intention)

John is a physics teacher at a summer camp for primary school students. One day, he teaches about the structure of an atom. He has some freedom in deciding how he will explain this topic. He explains the Bohr model of an atom, according to which electrons travel in circular orbits around the nucleus. John knows that this is a crude simplification and a false depiction of an atom. He is aware that there are other, more exact but also much more complicated models of an atom. He presents the Bohr model because he wants to deceive his pupils about the real structure of an atom. He is also aware that explaining a more complicated model would demand from him much more work. As a result of the presentation, his pupils acquire some understanding of the structure of an atom.

This is a clear case of lying.Footnote 15 The only difference with the previous version of the story is in John’s intention—here, he aims to deceive his audience. If someone claims that John is not making an assertion in the first case, it follows that he is also not lying here. This is not plausible. Non-deceptionists classify both versions of Atom Story as lies. However, intuitively at least, there is a striking difference between them. We argue that a proper definition of lying should distinguish between these cases—with only the latter one being classified as a lie.

2.3 Previous studies

There is a general agreement that a proper definition of lying should track how this term is used by ordinary language speakers (e.g. Carson, 2006; Fallis, 2009). Recent experimental studies have been testing ordinary speakers’ intuitions regarding various features of lying; such as whether an intention to deceive or actual falsity is necessary for lying, or whether we can lie with speech acts beyond assertions.Footnote 16 The results of these experiments influenced how lying is nowadays defined.

Non-deceptionist definitions of lying have been greatly impacted by cases of the so-called bald-faced lies, i.e., lies arguably made without an intention to deceive (e.g. Sorensen, 2007; Carson, 2010; Fallis, 2009, 2013, 2015; Saul, 2012; Stokke, 2018; cf. Krstić, 2019). The experimental studies that are supposed to show that an intention to deceive is not necessary for lying concentrate on testing bald-faced lies. However, these studies deliver mostly mixed results.Footnote 17 Some studies suggest that lay people agree that some bald-faced lies do not involve deception (Arico & Fallis, 2013; Krstić & Wiegmann, 2022; cf. Coleman & Kay, 1981; Taylor et al., 2003). Other studies, however, deny that (Meibauer, 2016; Rutschmann & Wiegmann, 2017).Footnote 18 The question regarding an intention to deceive is crucial for our study which presents a pair of cases which differ only in the speaker’s intention.

The empirical work on the notions of explanation and understanding corroborates their close relationship. Recent studies show that scientists and lay people alike consider a speech act to be an explanation when it provides an understanding to the audience (Waskan et al., 2014; Wilkenfeld & Lombrozo, 2020). Wilkenfeld and Lombrozo (2020, p. 2590) argue that “… there is strong reason to believe not only that explanations are judged by the extent to which they produce some mental state (namely understanding), but that understanding is sufficient to play this mental state role.” This is consistent with accounts of explanations that argue that the aim of explanation is to generate understanding in the audience (see e.g. Achinstein, 1983; Wilkenfeld, 2014; Gaszczyk, 2023). Nevertheless, some questions remain unanswered. One of them concerns determining the minimal threshold for understanding. Some studies indicate that the threshold for understanding, in some respects, may be stronger than that for knowledge (Wilkenfeld et al., 2018). Yet, the exact way in which the notion of understanding should be elucidated remains open. In our study, we test stories in which it is explicitly stipulated that the given explanation is false. This is consistent with the assessment of such explanations in the literature (as discussed in Sect. 2.1). If the aim of explanation is to generate understanding, the question is whether the understanding in question can be non-factive. Our study can contribute towards answering this question.

2.4 The aim of the experimental studies

We conducted three experiments in which we presented to the participants two stories with false explanations. In each story, we have a teacher who tries to explain a complex phenomenon (for instance, the structure of an atom) to her students on a theory or a model that simplifies the phenomenon in question so that she knows that what she says is false. The vignettes have two conditions—positive intention and negative intention—that differ only in the speaker’s intention. In the positive intention condition, the speaker makes a false explanation because she does not want to overwhelm her pupils or because she believes that it is pedagogically better to explain something that will be easier to understand. In the negative intention condition, the speaker gives a simplified (i.e., false) explanation because she wants to mislead the audience. The participants’ task was to assess whether the speaker lied by making a false explanation.

Our prediction is that changing the speaker’s intention influences the lie attribution. Namely, participants in the negative intention condition should more frequently claim that the speaker is lying than in the positive intention condition. The additional goal of our study is to test whether, depending on the speaker's intention, people would assess differently the degree to which the speaker explained a given phenomenon. Our prediction is that participants would be more inclined to agree that the speaker explained something in the positive intention condition than in the negative intention condition, even though in both conditions the explanation is the same.

3 Experiment 1

3.1 Method

3.1.1 Participants

One hundred and twenty U.S. and UK residents were tested, aged between 20 and 79 (M = 44.32, SD = 14.88); all with English as a native language; 54 male, 65 female; 1 prefer not to say). Because, according to our knowledge, this study is the first that tests experimentally lie attributions in false explanations, we decided to recruit a similar number of participants as in other studies in experimental philosophy using analogous tasks (e.g., Turri, 2015a, 2015b). In all experiments, participants were recruited and tested online using Qualtrics on Prolific Platform (Palan & Schitter, 2018) and compensated £ 0.54 for about 4 min of their time. Repetitive participation was prevented. In all experiments, participation was voluntary, and participants were informed explicitly that they could withdraw their consent at any point during the study without any adverse consequences, and that their data would be anonymised. All participants signed the informed consent form before the start of the experimental procedures. The experiments were reviewed and approved by the University of Groningen Research Ethics Review Committee (CETO ID 91217593).

3.1.2 Design, materials and procedure

Participants first read general instructions that familiarised them with the task. They were then randomly assigned to one of two conditions: positive intention (n = 60) versus negative intention (n = 60). In both conditions, participants were presented with two stories; one with a simplified explanation of the structure of an atom (Atom Story) and the other an explanation of a basic tenet of the theory of evolution (Evolution Story). Thus, experimental conditions (positive intentions vs. negative intentions) were manipulated between-subject and the topics of story were manipulated within-subject. Atom Story has already been introduced above, i.e., Atom Story (positive intention) and Atom Story (negative intention). All other experimental materials are presented in Appendix. After reading each story, participants needed to assess the following statements: “X is lying,” “X knows that his explanation is false,” and “X explained Y” on a 6-point Likert scale (1–strongly agree, 2–agree, 3–somewhat agree, 4–somewhat disagree, 5–disagree, 6–strongly disagree).Footnote 19 There was no time limit for reading stories and assessing statements. Because each story contains information that the speaker was aware that their explanation is false, the second statement performs a function of manipulation check.

3.2 Results

First, we checked participants’ lie attribution depending on the described speaker’s intention (see Fig. 1). These were analysed as a function of experimental condition (positive intention vs. negative intention) and story (Atom Story vs. Evolution Story), using a two-factor mixed ANOVA. The main effect of the experimental condition proved to be significant, F(1, 118) = 39.55, MSE = 1.95, p < 0.001, \({\eta }_{p}^{2}\) = 0.251. On average, participants were more inclined to claim that the speaker is lying in the negative intention condition (M = 2.69, SD = 1.00) than in the positive intention condition (M = 3.83, SD = 0.97).Footnote 20 A main effect of the story was also significant, F(1, 118) = 4.38, MSE = 0.86, p = 0.038, \({\eta }_{p}^{2}\) = 0.036. Participants were more inclined to agree that the speaker is lying in the case of Evolution Story (M = 3.13, SD = 1.32) than Atom Story (M = 3.38, SD = 1.30). The interaction between experimental conditions were insignificant, F(1, 118) = 0.312, MSE = 0.86, p = 0.578, \({\eta }_{p}^{2}\) = 0.003.

Fig. 1
figure 1

Note Error bars represent standard errors. The numbers indicate how strongly participants disagree that the speaker lied

The degree to which participants attribute lying to the speaker.

Full size image

We also compared the number of participants who agree with the claim that the speaker is lying (i.e., who chose responses from 1–strongly agree to 3–somewhat agree) with the number of participants who disagree with this claim (i.e., who chose responses from 4–somewhat disagree to 6–strongly disagree). Significantly more participants claim that the speaker is lying in the negative intention condition than in the positive intention condition for both Atom Story: 70.0% vs 31.7%, χ2(1) = 17.64, p < 0.001, and Evolution Story: 78.3% vs 43.3%, χ2(1) = 15.42, p < 0.001.

Second, we investigated to what degree participants are inclined to say that the speaker explained the scientific phenomenon in question (see Fig. 2). A 2 (condition) × 2 (story) ANOVA indicated a significant main effect of the condition, F(1, 118) = 6.980, MSE = 2.01, p = 0.009, \({\eta }_{p}^{2}\) = 0.056. Participants in the positive intention condition were more inclined to claim that the speaker explained given phenomena (M = 3.02, SD = 1.00) than in the negative intention condition (M = 3.50, SD = 1.01). A main effect of the story, F(1, 118) = 3.96, MSE = 0.51, p = 0.049, \({\eta }_{p}^{2}\) = 0.032, and an interaction, F(1, 118) = 5.52, MSE = 0.51, p = 0.020, \({\eta }_{p}^{2}\) = 0.045, also reached statistical significance. Pairwise comparisons with Bonferroni corrections showed that only in the case of the Atom Story there was a significant difference between positive and negative conditions, -0.70, SE = 0.20, p < 0.001. The assessment of the speaker’s explanation in the Evolution Story was similar in positive and negative conditions, − 0.27, SE = 0.21, p = 0.211.

Fig. 2
figure 2

Note Error bars represent standard errors. The numbers indicate how strongly participants disagree that the speaker explained the phenomenon

The degree to which participants agree that the speaker explained a scientific phenomenon.

Full size image

When we grouped responses together, in Atom Story, more participants in the positive intention condition (80.0%) claimed that the speaker explained the phenomenon than in the negative intention condition (61.7%), χ2(1) = 4.88, p = 0.027. There was no such difference for Evolution Story, χ2(1) = 0.33, p = 0.564 (the positive intention condition: 68.3%; the negative intention condition: 63.3%).

Finally, we check the relationship between the lie attribution and the degree to which the participants agree that the speaker explained the phenomenon. The results were similar in both experimental conditions, so we grouped them together. The more participants claimed that the speaker was lying, the more they disagreed that they explained a given scientific phenomenon—moderate correlations: r = − 0.541, p < 0.001, for Atom Story, and r = − 0.375, p < 0.001, for Evolution Story.

3.3 Discussion

Does modification of the speaker’s intention (positive/negative) change the lie attribution in the case of false explanations? The aim of Experiment 1 was to answer this question and, in doing so, test whether all such explanations should be classified as lies, as non-deceptionist definitions of lying predict. Our results go against this prediction. Participants distinguished between two conditions of the same stories—when the speaker’s intention was deceitful, more participants classified the explanation as a lie than when the intention was positive. Moreover, participants attributed lying to a greater degree in the negative intention condition than in the positive intention condition. Still, a substantial number of participants agreed that the speakers were lying in the positive intention condition.

The second question concerned whether the stories are considered to be explanations. Here the results differ between the stories. In the case of Atom Story, participants distinguished between the positive and negative intention conditions—in the former, participants agreed to a greater extent that John explained the structure of an atom than in the latter. This shows that the change in intention influences not only the attribution of lying but also of explanation. The results for Evolution Story are less clear. In both conditions, participants similarly assessed the degree to which the speaker explained the phenomenon of evolution. Many factors may contribute to this result, such as participants’ background knowledge or strong intuitions about the theory of evolution. It may also be important that participants are more eager to claim that the speaker is lying in Evolution Story than in Atom Story. Importantly, in both conditions, a negative correlation was observed between the degree of perceived explanation and lie attribution.

4 Experiment 2

The first aim of Experiment 2 was to test whether we would be able to replicate the observation regarding the lie attribution on new stories. Because the effect of the speaker’s intention on lie attribution was not, according to our knowledge, tested experimentally before, it is of utmost importance to check whether the obtained pattern of results is not material driven. The second aim of Experiment 2 was to test whether we could receive more unequivocal results about the perceived degree of attributed explanation by the speaker.

4.1 Method

4.1.1 Participants

One hundred and twenty U.S. and UK residents aged between 22 and 77 years (M = 41.02, SD = 15.25) were tested; all with English as a native language; 89 female, 30 male). In Experiment 1, the main effect of the condition (positive intention vs. negative intention) on lie attribution had a very large effect size equal \({\eta }_{p}^{2}\) = 0.251. A total sample size equal to 14 participants would be sufficient to obtain a comparable effect with a statistical power of 0.95 and α level at 0.05. However, in Experiments 2 and 3, we decided to test about 60 participants per condition because we used new (Experiment 2) or modified versions (Experiment 3) of the stories and due to inevitably of more potential confounding variables during online testing.

4.1.2 Design, materials and procedure

The procedures were exactly the same as in Experiment 1. The difference was in the tested stories, i.e., Solar System Story and Laws of Motion Story, which can be found in the Appendix. To give the gist of the stories, in the former, the speaker explains the heliocentric model, by saying that the planets in our solar system move around the Sun in circular, instead of elliptical, orbits, even though he knows that this is a false depiction of our solar system. In the latter story, the speaker explains the laws of motion on the basis of Newton’s laws, knowing that they are false and that we have much more accurate theories at our disposal.Footnote 21

4.2 Results

We excluded one participant from the following analyses because their experimental data did not save due to a technical problem. We conducted 2 (condition) × 2 (story) mixed ANOVA to check participants’ lie attribution (see Fig. 3). There was a significant effect of condition, F(1, 117) = 38.36, MSE = 1.79, p < 0.001, \({\eta }_{p}^{2}\) = 0.247. Participants were more inclined to claim that the speaker is lying in the negative intention condition (M = 2.51, SD = 1.01) than in the positive intention condition (M = 3.58, SD = 0.88). The main effect of the story was also significant, F(1, 117) = 11.52, MSE = 0.71, p < 0.001, \({\eta }_{p}^{2}\) = 0.090. Participants were more eager to agree that the speaker is lying in Solar System Story (M = 2.87, SD = 1.21) than Laws of Motion Story (M = 3.24, SD = 1.26). The interaction was not significant, F(1, 117) = 0.11, MSE = 0.71, p = 0.737, \({\eta }_{p}^{2}\) = 0.001.

Fig. 3
figure 3

Note Error bars represent standard errors. The numbers indicate how strongly participants disagree that the speaker lied

The degree to which participants attribute lying to the speaker.

Full size image

A binary comparison shows that significantly more participants agree that the speaker is lying in the negative intention condition than in the positive intention condition for both Solar System Story: 89.8% vs 56.7%, χ2(1) = 16.64, p < 0.001, and Laws of Motion Story: 78.0% vs 36.7%, χ2(1) = 20.72, p < 0.001.

Next, we performed a 2 (condition) × 2 (story) ANOVA on participants’ assessment of explanations provided by the speakers (see Fig. 4). The ANOVA showed a significant main effect of the condition, F(1, 117) = 15.93, MSE = 1.76, p < 0.001, \({\eta }_{p}^{2}\) = 0.120 and the story, F(1, 117) = 4.91, MSE = 0.68, p = 0.029, \({\eta }_{p}^{2}\) = 0.040. In the positive intention condition, participants were more inclined to claim that the speaker explained the given phenomenon (M = 2.53, SD = 0.84) than in the negative intention condition (M = 3.27, SD = 1.02). Moreover, reading the Laws of Motion Story (M = 2.74, SD = 1.13), participants claimed to a greater degree that the speaker explained the scientific phenomenon than when reading Solar System Story (M = 2.97, SD = 1.18). The interaction was not significant, F(1, 117) = 0.93, MSE = 0.68, p < 0.337, \({\eta }_{p}^{2}\) = 0.008. These results are consistent also with χ2 analysis when we combined agree/disagree responses. More participants agree that the speaker explained the scientific phenomenon in the positive intention condition than in the negative intention condition, for both Solar System Story: 90.0% vs 66.1%, χ2(1) = 9.95, p = 0.002, and Laws of Motion Story: 86.7% vs 74.6%, χ2(1) = 2.79, p = 0.095. However, in the latter case, the difference was only numerical.

Fig. 4
figure 4

Note Error bars represent standard errors. The numbers indicate how strongly participants disagree that the speaker explained the phenomenon

The degree to which participants agree that the speaker explained a scientific phenomenon.

Full size image

Finally, as in Experiment 1, we checked the relationship between lie attribution and explanation attribution. Again, the more participants claimed that the speaker was lying, the more they disagreed that the speaker explained the scientific phenomenon—moderate correlations: r = − 0.317, p < 0.001, for Solar System Story, and r = − 0.474, p < 0.001, for Laws of Motion Story.

4.3 Discussion

The results replicated the main findings from Experiment 1. When the speaker intended to mislead the audience, participants to a greater degree classified the explanation as a lie than when the speaker’s intention was positive. This difference between the conditions is hard to explain by non-deceptionists. Simultaneously, again, a substantial number of participants, especially in Solar System Story, agreed that the speakers were lying in the positive intention condition. When it comes to the judgments of whether the stories are considered to be explanations, this time in both stories, participants distinguished between the positive and negative intention conditions—in the positive intention conditions, participants were more inclined to agree that the speakers explained the phenomena than in the negative intention conditions. Again, there was a negative correlation between the perceived degree of explanation and lying.

It is worth noting that participants were more willing to agree that the speaker is lying and disagree that the speaker explained the given phenomenon while reading Solar System Story than Law of Motion Story. These differences may stem from story-specific qualities. For example, participants may have assumed that it would be relatively easy to provide the correct explanation (use elliptical orbits instead of circular ones) in the case of Solar System Story.

5 Experiment 3

The aim of Experiment 3 was to extend the observations from Experiments 1 and 2 in two important aspects. Firstly, we added a new experimental condition, in which the speaker’s intention was unspecified, to test whether there was any difference between the negative intention and the lack of intention in educational contexts. It is possible that in such contexts, lay people assume the positive intention of the teacher. If so, we would observe no difference between the positive intention and the lack of intention conditions. At the same time, participants would be more inclined to claim that the speaker is lying in the negative intention than in the lack of intention condition.

The second objective of Experiment 3 was to give participants an option to withhold the decision of whether they agree/disagree with the assessed statements. To this end, we added the option “neither agree nor disagree” to the Likert scale. We wanted to preclude the possibility that the pattern of results in the previous experiments emerged mostly because the participants were forced to agree or disagree. Thus, we wanted to see whether we were able to replicate the previous results on the modified scale.Footnote 22

5.1 Method

5.1.1 Participants

In total, 179 participants aged between 20 and 79 (M = 40.70, SD = 13.13) were tested; (125 females, 3 non-binary or gender diverse, 50 males, 1 prefer not to say).

5.1.2 Design, materials and procedure

In Experiment 3, the design and procedure were similar to those in Experiments 1 and 2. However, compared to the procedure in the previous experiments, this time participants were randomly assigned to one of three conditions: positive intention (n = 59), negative intention (n = 61), or lack of intention (n = 58). In all conditions, participants were presented with two stories—one from each of the previous experiments: Atom Story and Laws of Motion Story.Footnote 23 Participants assess the same statements as in the previous experiments, but this time using a 7-point Likert scale (1—strongly agree, 2—agree, 3—somewhat agree, 4—neither agree or disagree, 5—somewhat disagree, 6—disagree, 7—strongly disagree).

5.2 Results

As in previous experiments, we checked participants’ lie attribution (see Fig. 5). These were analysed in the 3 (condition) × 2 (story) mixed ANOVA. Again, the ANOVA yielded a significant effect of condition, F(2, 176) = 17.39, MSE = 4.03, p < 0.001, \({\eta }_{p}^{2}\) = 0.165. Pairwise comparisons with Bonferroni corrections showed that, as in previous experiments, participants were more inclined to claim that the speaker is lying in the negative intention condition (M = 2.88, SD = 1.29) than in the positive intention condition (M = 4.08, SD = 1.54), -1.21, p < 0.001. Similarly, more participants were willing to attribute lying to the speaker in the negative than neutral condition (M = 4.29, SD = 1.42), -1.41, p < 0.001. However, the positive and neutral conditions did not differ in that regard, -0.20, p = 1.00. As in Experiment 2, the main effect of the story was also significant, F(1, 176) = 8.63, MSE = 0.79, p = 0.004, \({\eta }_{p}^{2}\) = 0.047. This time, participants were more eager to agree that the speaker is lying in Atom Story (M = 3.60, SD = 1.70) than in Laws of Motion Story (M = 3.88, SD = 1.64). The interaction was not significant, F(2, 176) = 1.57, MSE = 0.79, p = 0.211, \({\eta }_{p}^{2}\) = 0.08.

Fig. 5
figure 5

Note Error bars represent standard errors. The numbers indicate how strongly participants disagree that the speaker lied

The degree to which participants attribute lying to the speaker.

Full size image

Participants’ agreement that the speaker explained the scientific phenomena indicated a marginally significant main effect of the story, F(1, 176) = 3.26, MSE = 0.85, p = 0.073, \({\eta }_{p}^{2}\) = 0.018; participants were slightly more inclined to claim that the speaker explained the scientific phenomena in the case of Laws of Motion Story (M = 2.89, SD = 1.32) than in Atom Story (M = 3.07, SD = 1.28). The main effect of the condition, F(2, 176) = 1.01, MSE = 2.51, p = 0.365, \({\eta }_{p}^{2}\) = 0.011, and the interaction were insignificant, F(2, 176) = 1.86, MSE = 0.85, p = 0.159, \({\eta }_{p}^{2}\) = 0.021 (Fig. 6).

Fig. 6
figure 6

Note Error bars represent standard errors. The numbers indicate how strongly participants disagree that the speaker explained the phenomenon

The degree to which participants agree that the speaker explained a scientific phenomenon.

Full size image

As in previous experiments we observed significant and negative correlations between lie attribution and explanation attribution: r = -0.381, p < 0.001, for Atom Story, and r = -0.437, p < 0.001, for Laws of Motion Story.

5.3 Discussion

In Experiment 3, participants claimed to a greater degree that the speaker is lying in the negative intention condition than in both the positive intention condition and the lack of intention condition. Moreover, the last two conditions did not differ in terms of lying assessment. Thus, we not only replicated the results observed in Experiments 2 and 3 but also extended these observations to the condition where the intention was not provided. It seems that providing information about a positive intention in an educational domain is not necessary because teachers’ trustworthiness is assessed similarly regardless of knowing their positive intentions or not. This changes when the speaker’s intention is deceptive.

In all experimental conditions, participants’ assessment of whether the speaker explained the scientific phenomena was similar. This result is in contrast with observations from Experiment 2 (and partially with Experiment 1) where the participants claimed that the speaker explained a scientific phenomenon to a greater degree in the positive intention condition than in the negative intention condition. When we combined responses “strongly agree,” “agree” and “slightly agree” together, about 80% of participants in each condition chose one of these options.Footnote 24 In the previous experiments, it was approximately 65%. Thus, the observed lack of difference between the conditions may stem from the fact that the participants generally claimed that the speaker explained the scientific phenomenon.

6 General discussion

The aim of the experiments was to test the judgements of ordinary speakers regarding lie attributions in false explanations. Our prediction was that changing the speaker’s intention would influence the lie attribution in such explanations. Simultaneously, the prediction of non-deceptionists, the dominant way of defining lying, is that the speaker lies by making such explanations, independently of her intention. The results challenged this prediction. The experiments demonstrated that the speaker’s intention matters to lay people. Across four different scenarios, participants agreed to a higher degree that the speaker lies in the negative intention condition than in the positive intention condition.

Our prediction was also that participants would be more inclined to agree that the speaker explained something in the positive intention condition than in the negative intention condition, even though in both conditions the explanation was the same. We suspected that the speaker’s intention matters not only for lie attribution but influences also other factors. In Experiments 1 and 2, in all cases except Evolution Story, participants were more inclined to attribute explanation in the positive intention condition than in the negative intention condition. In the theoretical part, we proposed that such false explanations should be considered genuine explanations and that they involve non-factive understanding. Still, some participants assessed that the speaker did not perform an explanation (although it was only around 20% in Experiment 3). Previous studies (e.g. Wilkenfeld et al., 2018) indicated that lay people’s notions of explanation and understanding have minimal thresholds, however, so far, these thresholds have not been specified. If the speakers do not explain something, some may wonder, what kind of speech acts they are performing. One possibility is that lay people’s notion of explanation is more exclusive, and thus false explanations belong to a different, broader category, like teaching something. However, in a study that directly addresses the question of what kind of speech acts false explanations are, it may turn out that lay people do classify them as genuine explanations.Footnote 25 Nevertheless, our main question did not consider the nature of explanation and understanding, rather we focused only on explanations in relation to the lie attribution. Thus, we leave this topic for further research in the future.

Non-deceptionists fail to distinguish between two conditions (positive intention vs. negative intention) of the stories and thus they incorrectly classify both conditions as lies (the same concerns the lack of intention condition). Our stance is the following: non-deceptionists are on the right track in defining lying as insincerely asserting, however, at least in some cases, there is a need for a further criterion in the definition of lying.

One way out is reintroducing, appropriately modified, an intention to deceive in a definition of lying.Footnote 26 Consider, for instance, Lackey’s (2013) deceptionist definition of lying. She argues that lying involves intending to be deceptive, which she understands as aiming to conceal information from the audience.Footnote 27 John in Atom Story (positive intention) has no intention to be deceptive in this sense, even though he says something he believes to be false; in contrast, in Atom Story (negative intention) he intends to deceive his audience. Thus, it seems that Lackey’s definition delivers a desirable result. Accepting a deceptionist definition—due to bald-faced lies—is very controversial, however.Footnote 28 Another option is to propose a definition of lying that is not formulated in a deceptionist way but would simultaneously allow us to make correct predictions. Peet’s (2021) definition seems to do the job here and can be seen as a compromise between deceptionists and non-deceptionists. For Peet, lying involves displaying poor testimonial worth in one’s insincere assertion, where ‘testimonial worth’ is understood as “… a reflection of the quality of character a speaker displays in asserting” (2021, p. 2392). A poor testimonial worth does not necessarily mean that one’s assertion is false, rather it involves the assessment of the general character of the speaker as a testifier. Looking at John, in Atom Story (positive intention) he displays good testimonial worth since he makes a false explanation to not confuse and overwhelm his audience. By contrast, in Atom Story (negative intention) he gives the same explanation to deceive his audience, and thus displays poor testimonial worth. These two definitions are only examples of the recent accounts of lying that distinguish between both conditions. Our aim in this paper was not to provide a definition of lying but to present new data that need to be taken under consideration. More work must be done to propose a definition of lying that will be able to correctly capture these and all other cases.

Nevertheless, one may think of construing a non-deceptionist definition of lying that could, at least for some cases, deliver correct predictions.Footnote 29 However, such a definition cannot merely say that lies are insincere assertions. Rather, it should employ some additional resources. Here are two possibilities. Firstly, a non-deceptionist could try to explicate the analysed explanations as cases of loose talk, or employ a scalar notion of sincerity.Footnote 30 Thus, for instance, one could argue that the explanation in the positive intention condition is sincere because it is true enough or it meets a certain threshold on a sincerity scale, while the explanation in the negative intention condition does not satisfy these standards and so it is insincere. Secondly, a non-deceptionist could propose that there are two standards of sincerity for explanations—one should not only believe (or express one’s belief) that p but also understand p.Footnote 31 Here, some could argue that while the speaker in the positive intention condition is violating the belief standard but complies with the understanding standard, the speaker in the negative intention condition is violating both standards of sincerity. However, these two proposals need to be fully developed to see whether they can satisfactorily address the tested cases.

As a final note, we want to point to two potential directions for future research. Both concern the ideas mentioned above. Firstly, we only tested vignettes that explicitly stated that the explanations were false. However, it is worth checking if the participants’ judgments change when alternative formulations are used, such as saying that the explanation is true enough, is a simplification, or is a case of loose talk. Secondly, we focused on the belief standard of sincerity, however, there may also be an additional sincerity standard, one based on understanding. It would be worth investigating how these two relate to each other, whether the speaker can violate one without the other, or whether such violations result in insincerity or lying. We hope that our study can be seen as a stepping-stone in researching the relationship between the concepts of lying and sincerity, on the one hand, and explanation and understanding, on the other.