Purposes

The second experiment was planned because of two main reasons. First of all we wanted to check with respect to passive logical competence some of the results we got in the first (active) experiment. We hoped, on one hand, to confirm some of our results, e.g. the difference between the so-called existential import of “most” and of “all”, and on the other hand to look for plausible divergence between both mechanisms: active and passive. For instance we expected that passive evaluation of some inferences as correct (e.g. implicatures) would appear with much higher frequency than active generation of those inferences.

The second reason for conducting the passive experiment was the relatively weak statistical effect of the first one, which because of small sample sizes and the specificity of the layout (e.g. high variety of tasks in the two-premise part) has to be treated as half-qualitative pilot research. One of the main aims of the high diversity in our first experiment was to check what tendencies in replies for different kinds of tasks would appear, so that we could use the results later for formulating detailed hypotheses for statistical testing. Moreover, the high rate of responses that were difficult to classify and required prior interpretation was an additional reason to categorize the research more as a semi-structured interview rather than a purely quantitative study. Therefore we considered that a clear statistically significant result would be a good completion to our research.

The passive experiment was directed towards checking the following proper- ties:

• Scalar implicatures of “most” and “some”; in the case of “some” – both the weak and the strong implicature (see chapter 1.3), in the case of “most” implicature in the particular and in the universal form.

• So-called existential import of “most” and of the universal quantifier, so the inferences: M ost/Some and All/Some (resp. M ostnot/Somenot and

N o/Somenot).

We have already shown in the first experiment that so-called existential import is not connected with any ontological commitment of quantifiers (the lack of between-group difference with respect to empty versus non- empty terms). It is proposed that these inferences are dependent on scalar properties and not on the alleged existential meaning of “most” or “some”, and the lack of such meaning in the case of “all” (resp. “no”).

• Inferences of the form All/M ost and N o/M ostnot, which we henceforth call “reversed implicatures”.

The below working hypotheses were checked in the experiment:

Working hypotheses:

Hypothesis 5. Scalar implicature of “most” will be evaluated as a correct infer- ence.1

Hypothesis 6. The “weak” scalar implicature of “some” (Some/Somenot and Somenot/Some) will be evaluated as a correct inference.

Hypothesis 7. Inferences of the form M ost/Some (M ostnot/Somenot) will display higher frequency than inferences All/Some(N o/Somenot)(accordingly) (stronger so-called existential import of the quantifier “most” in comparison to the universal quantifier). We expect positive premises to display stronger existential import than negative premises.

Hypothesis 8. The “strong” scalar implicature of “some”: Some/M ostnot and Somenot/M ost will be evaluated as correct, but less frequently than the “weak” implicature.

Hypothesis 9. There may be a difference in the frequency of evaluation scalar implicature of “most” (resp. “mostnot”) as correct depending on the form – particular or universal of this implicature. (For ease of exposition, we will further use the notions of “particular” and “universal” scalar implicature of “most” to name the corresponding forms.) At this point we do not, however, have a clear prediction concerning in which direction a form can affect this frequency.

1_{Which means here and below that it will get “yes” replies. The subjects are not asked}

about correctness of inferences, but whether given conclusions are true in the light of premises. Nonetheless, a “yes” reply is interpreted as acceptance of correctness of an inference.

3.1. Layout of the experiment 69

Hypothesis 10. So-called “reversed implicatures” (All/M ostand N o/M ostnot) will be evaluated as correct inferences significantly less frequently than so-called existential import of the universal quantifier (All/Some resp. N o/Somenot) but with no significant difference to so-called existential import of “most” (M ost/Some resp. M ostnot/Somenot).

Let us say a few words about the theoretical and empirical background of our hypotheses. In the previous experiment (two-premise part) we observed that particular conclusions were suppressed by universal conclusions and by conclu- sions with “most”, however universal conclusions suppressed them much more strongly. We expected that the distance on the implicational scale may play a crucial role in suppressing inferences, so that All/M ost inferences may be much more frequently recognized as correct thanAll/Someand alsoM ost/Somemuch more frequently thanAll/Some, but there should bo no significant difference be- tween All/M ost and M ost/Some. Thus, stronger so-called existential import of “most” in comparison to the universal quantifier should be confirmed but has to be explained by scalar factors, namelyM ost/Somewill be more willingly inferred as a correct inference than All/Some, since “most” and “some are closer on the implicational scale than “all” and “some”. This is also connected with the expected lower frequency of the Some/M ostnot implicature – this lat- ter fact having, however, deeper justification in the plausible vague semantics of both quantifiers: “most” and “some”. If “some” means “at least two but not too many” (or “a small part of the domain”), then it is not clear whether a “small part” cannot be sometimes as big as “most”, whereas it seems quite clear that it should not be as big as the whole set.