To make a long story short, we applied the test from reinforceability to specific links and observed that they are not reinforceable, that is, ordinary users of language found reaffirmations of these links redundant to a much greater extent than for conversational implicatures. Below we present the experiment and its results.
Experimental strategy and hypotheses
We focused on three kinds of specific links in our case study: the causal, deductive, and abductive inferential relation.Footnote 12 So, we investigated the cases where someone made a conditional statement ‘If p, q’ conveying that p is a cause of q, or p entails q, or p is evidence for (i.e., best explains) q, and then the speaker reinforced the link by adding explicitly ‘(And) p results in q’, ‘(And) p entails q’, etcetera. Our general aim was to test whether the second part of the statement sounded redundant to a significant degree to the study participants. In order to establish meaningful thresholds for the redundancy rates, we investigated (non)reinforceability of conversational implicatures and broadly conceived semantics entailments at the same time. Our strategy was to compare the level of redundancy of reaffirmed specific links to the levels of redundancy of reaffirmed implicatures on one hand, and reaffirmed semantic entailments on the other hand. This approach enabled us to assess to what kind of phenomena specific links are closer to, according to the reinforceability test.
A possible concern in constructing the reinforceability test for conditionals was that the participants may find the second sentence redundant not because the link has already been expressed by the first one, but because the sentence constituents have been repeated in the second statement (in order to indicate the nature of the link between them). As we have just said, the utterances to be evaluated had a form of, e.g., ‘If p, q. (And) p results in q’. It could then happen that the bare word like ‘results in’ would drown in the sea of information that is literally repeated, i.e., the contents of p and q.Footnote 13
In order to overcome this potential problem, we employed two independent strategies. The first one was not to repeat all the information contained in the conditional’s clauses and use some anaphoric devices instead (e.g., ‘If you press the button with a lollipop, then a lollipop falls out. Pressing the button will result in this.’) The fact that not every clause was explicitly rephrased in the second sentence emphasized that the aim of the second sentence was primarily to indicate the link between the two contents. The second strategy was to repeat the contents of a conditional’s clauses in a somehow different way, not mirroring the structure they had in the first sentence; for example: ‘If there are no sweets on the plate, the dog must have eaten them. The empty plate means that the dog wolfed down the sweets.’ At the same time, we tried to apply close synonyms, or repeat the relevant elements but in a different configuration. This was to avoid situations where a subject’s potential skepticism about redundancy would be related to the fact that he or she interprets the clauses repeated in the second statement as saying something different than in the first statement.
Let us now present our research hypotheses. In line with the theoretical considerations, we predicted that implicatures are reinforceable while semantic entailments are not. That is, we formulated the following hypotheses:
A reinforced semantic entailment is taken to be redundant.
A reinforced conversational implicature is taken to be definitely less redundant than a reinforced semantic entailment.
As far as conditionals and specific links are concerned, our prediction was that the patterns of responses for all three kinds of links would be more similar to the pattern of responses for the semantic entailments than for the implicatures. Crucially, we predicted that specific links are generally much less reinforceable than conversational implicatures. Thus we formulated two basic hypotheses:
A reinforced causal/deductive/abductive link is taken to be redundant.
A reinforced causal/deductive/abductive link is taken to be definitely more redundant than a reinforced implicature.
Our experiment consisted of an online questionnaire prepared on the platform LimeSurvey and spread via Mechanical Turk. It involved 76 participants altogether; the responses of 18 of them were excluded from our analysis, as the respondents did not report English as their first language or failed to correctly answer the attention-check question. Our final sample consisted of 28 females and 40 males (average age: 39.91, SD = 12.84). All participants were recruited via Mechanical Turk and paid for their participation $2.00 each.
Our study employed a simple design with five experimental conditions that were compared within participants: reinforcement of a semantic entailment, conversational implicature, and three others concerning the selected specific links (causal, deductive, and abductive). We will henceforth refer to these conditions as: SE, IM, C-link, D-link, and A-link, respectively. As we have said, the purpose of this manipulation was to establish how the type of a content (i.e., semantic vs pragmatic) affects redundancy judgements and what degrees of reinforceability specific links exhibit in comparison to these two general types of content.
Materials and procedure
All materials were in English and contained short fictional stories with a question at the end of each scenario. These stories (‘contexts’) presented some characters engaged in conversational situations and one of the characters made an utterance of two statements in such a way that the second one was a reinforcement of the content conveyed by the first one. We used ten different contexts per condition, which yielded 50 (10 × 5) target vignettes in total. In addition, we introduced five filler items which resembled the target vignettes in an appropriate way: they presented short stories where a character made two statements, and the participants had to evaluate the second one in terms of redundancy. Two of the fillers contained conditionals as first statements. Since we predicted that all experimental conditions except for one will get high redundancy rates, most of the fillers we created were such that the second statement uttered by a character was weakly– if at all––implied by the first one. Furthermore, the survey was constructed in such a way that fillers appeared as one-third of all questions. This altogether provided a counterbalanced design.
Below we present three samples of our vignettes: one with a conditional, one with a conversational implicature, and a filler:
[Context “Party organizing”, C-link]
Jessica and Jim are discussing whom they are going to invite to their party next Saturday. Jim does not like Mr. and Mrs. Smith who are Jessica’s colleagues, so he does not want to invite them. However, Jessica is trying to persuade Jim that they should invite the Smiths and during the conversation she says: “If we don’t invite the Smiths, they will feel insulted. Not inviting them will result in this.”
Does the second sentence uttered by Jessica is redundant/unnecessary as it repeats the information from the first one?
[Context “Cider”, IM]
Mary wants to make cider using apples she has in the pantry, but only under the condition that all apples in the pantry are ripe. She asks her husband John to check the apples. John starts checking them and, so far, they are all ripe. But he hasn’t finished checking all of them when Mary asks whether the apples are ripe. John replies: “Well, some apples are ripe. I don’t know yet whether all of them are ripe.”
Does the second sentence uttered by John is redundant/unnecessary as it repeats the information from the first one?
Jane and Jeremy are playing tennis on a Saturday afternoon. Since it is quite hot, after an intensive match Jane proposes that she will go and buy some cold drinks and snacks. She asks Jeremy what he would like to get and he says: “If they have cold blackcurrant juice, you can buy me one. Also, buy me a tuna sandwich, please.”
We made sure to provide a diversity of the examples used in our materials, in order to have a representative sample of a given category/condition. In SE, we included the cases of presuppositions and proper entailments where the second sentence either repeated the whole information from the first one, or only a part of it. In IM, we used examples of both PCI and GCI, including scalar implicatures and unfamiliarity implicatures related to indefinite descriptions, among others.Footnote 14 In the remaining conditions—C-link, D-link, and A-link—we used conditionals of different grammatical forms (i.e., different moods and tenses). All materials are contained in the “Appendix”.
At the beginning of the survey, the participants were briefly informed about the topic of the survey and conditions of participation. Next, they were asked to complete a short demographic survey (age, education, exposure to philosophy and first language). Following a simple attention-check, a question was asked in order to filter out MTurkers who do not treat taking part in surveys seriously.
Next, after a short instruction, each participants got one of five blocks of vignettes (randomly assigned). Each block consisted of 15 vignettes: 10 target items and 5 fillers.Footnote 15 All vignettes were presented separately and their order was randomized within a block. The task for participants was to read the story and evaluate the character’s second statement in terms of redundancy. Each vignette ended with the question of the form: ‘Does the second sentence uttered by X is redundant/unnecessary as it repeats the information from the first one?’. The participants expressed their level of agreement that the statement is redundant by choosing one answer from five options presented as a five-degree Likert-like scale: ‘definitely no’, ‘rather no’, ‘hard to say’, ‘rather yes’, ‘definitely yes’.
At this point, let us stress that our experimental materials did not contain the problematic constructions considered in Sect. 3, so we ensured that our application of the reinforceability test is valid. Crucially, we did not include any example in which the first and the second sentence are contrastive. The reaffirmed content was either stated without any linking word to the previous sentence, or we sometimes used ‘and’ at the beginning of the second sentence. Furthermore, as we will see, we treated the study results as diagnostic in one direction—that is, as indicating whether the contents at issue are semantic or not.
We will now present the results of our experiment. Figure 1 shows the distributions of responses in the non-conditional cases, that is, conditions SE and IM.
Unsurprisingly, most participants found the reinforced semantic entailments redundant (47.8% answered ‘rather yes’ and 27.9% ‘definitely yes’). In order to facilitate a statistical analysis, we coded answers as numbers from 1 (‘definitely no’) to 5 (‘definitely yes’). We obtained the mean of 3.97 (SD = 1.01) which indicates a high level of redundancy judgments among the participants. Next, we conducted the one-sample Wilcoxon signed-rank test in order to check whether the answers differed significantly from the midpoint of the scale (3) and we obtained a statistically significant result (W = 1651, p < 0.001).Footnote 16 So hypothesis (H1) has been confirmed. As expected, the results for implicatures were much different. Only a minority of the respondents gave affirmative answers to the question on redundancy of a reinforced implicature (19.9% ‘rather yes’ and 8.1% ‘definitely yes’, M = 2.46, SD = 1.14, W = 556.5, p = 0.003). Accordingly, conversational implicatures were treated as much less redundant than semantic entailments. To test this prediction, we compared distributions of answers using the paired Mann–Whitney U test and we observed statistically significant differences (IM vs SE: U = 172, p < 0.001). Thus hypothesis (H2) has been confirmed, too.
Let us now focus on our main findings, namely, the redundancy rates for conditionals. Figure 2 shows the distributions of responses in the C-link, D-link and A-link conditions.
The results clearly show that all three types of links in conditionals are taken to be redundant when reaffirmed. In other words, hypothesis (H3) has been confirmed, since most of the respondents responded ‘rather yes’ or ‘definitely yes’ to the question on redundancy (C-link: 30.1% ‘rather yes’ and 41.2% ‘definitely yes’, M = 3.86, SD = 1.03, W = 1669.5, p < 0.001; D-link: 28.7% ‘rather yes’ and 40.4% ‘definitely yes’, M = 3.88, SD = 1.03, W = 1606, p < 0.001; A-link: 34.6% ‘rather yes’ and 34.6% ‘definitely yes’, M = 3.71, SD = 1.06, W = 1356, p < 0.001, all tests Wilcoxon for H0: μ = 3). Furthermore, the pattern of results for conditionals is far different from the one concerning implicatures (IM vs C-link: U = 1830, p < 0.001; IM vs D-link: U = 1765, p < 0.001; IM vs A-link: U = 1836.5, p < 0.001, all tests paired Mann–Whitney U). In short, causal, deductive, and abductive specific links are definitely less reinforceable than conversational implicatures. Thus hypothesis (H4) has been confirmed.
Figures 3 and 4 show the results of all conditions giving a general comparison between specific links, implicatures, and semantic entailments.
A visual inspection already indicates that specific links—while being obviously much less reinforceable than implicatures—are non-reinforceable to the extent typical for semantic entailments. Although the number of ‘definitely-yes’ responses to the question on redundancy was greater in SE than in any of the conditions: C-link, D-link, A-link, the statistical analysis did not detect a significant difference between the mean levels of redundancy evaluation across all four conditions.
Finally, we can note that slightly fewer people chose the ‘definitely-yes’ answer in A-link than in C-link and D-link. This observation holds with respect to every of the two versions of our study that we conducted earlier. It suggests that causal and deductive entailments are more strongly associated by people with the semantic meaning of ‘if-then’ than the abductive relation. However, the observed difference never reached any statistical significance.Footnote 17
The results of our experiment bring the following conclusions. Firstly, semantic entailments are non-reinforceable, as expected, while implicatures are reinforceable as their reaffirmation does not sound redundant to ordinary speakers. Secondly, the results suggest that causal, deductive and abductive links expressed by conditionals are not reinforceable. Furthermore, these types of links are almost similar to semantic entailments in the size of redundancy effects under reaffirmation.
Thus the test from reinforceability indicates that specific links are semantically expressed by a conditional statement. This outcome nicely corresponds to the other recent results of experimental research on conditionals discussed in Sect. 3 (e.g., Douven et al., 2018; Krzyżanowska & Douven, 2018; Skovgaard-Olsen, Collins, et al., 2019) and may be viewed as a development or another step of the project pursued by these authors. Not only the general inferential link, but also a more specific form of this link is a part of what is semantically expressed by a conditional utterance in a context. Our findings, in turn, point in a different direction than the one suggested by the earlier-mentioned studies which reported little effect, if any, of the connection between a conditional’s subclauses to its acceptability (e.g., Oberauer et al., 2007). The results of those studies seemed to provide support for a theory saying that the link between a conditional’s subclauses is not a part of its truth-conditional content. Our experiment provides a challenge for such a theory, which is to explain why specific links are nonetheless treated as a part of the truth-conditions of a conditional in a context.
Based on our findings, one may be tempted to say that they, in fact, provide evidence against those theories which deny that the link requirement is a part of the lexical meaning of conditionals (such as, for instance, the truth-functionalist view or the suppositional theory). However, we should be careful with such conclusions. Firstly, our results suggest that specific links do not arise in the way characteristic for conversational implicatures. But conversational implicatures may not be the only candidate for a pragmatic account of the links and perhaps the right pragmatic account has not been found as yet. Secondly, in order to establish the conclusion that specific links are semantic in a decisive way, one needs to conduct more linguistic tests of various kinds which would likewise confirm their semantic character. Finally, as we have already noted, our results pose a challenge to Gricean account of specific links and, in general, to the approaches which attempt to derive these links from conversational principles. Hence, the presented data—even if valid—may not refute the aforementioned theories of conditionals themselves, but only suggests that any such theory should incorporate essentially different mechanisms from the Gricean ones in order to account for specific links. In the next section, we will show how specific links can be accounted for as semantically relevant without abandoning standard semantic analyses of ‘if-then’ and this proposal will appeal to an important contemporary view of the boundary between semantics and pragmatics.