LA PERSONALIDAD JURIDICA I NOCIONES GENERALES
IV. TIPOS DE ESTADO
3. Una sana reacción contra esos procedimientos se ha producido en las últimas décadas.
for this quantifier lying outside the default denotation. This results in All/M ost
inferences being more frequent thanAll/Some inferences.
Hypothesis 8
Inferences Some/M ostnot are less frequent than Some/Somenot inferences be- cause of vagueness of the default denotation of “some”, in other words, the case “most” belongs to the default denotation of “some” but with lower degree than e.g. the case “less than half”, whilst the case “all” is outside the default denota- tion. This explains subjects uncertainty about Some/M ostnot inferences.
3.6
Summary and further research
We presented passive versions of experiments concerning scalar implicatures and the so-called existential import of the considered quantifiers. Based on our results we proposed how scalar implicatures of quantifiers “some” and “most” can be modeled with the use of fuzzy semantics. We describe these quantifiers as fuzzy with flexible default denotations. Those default denotations are further defined as not including the whole domain as an element. Therefore, the implicature “not all” is a part of the default meaning of both “some” and “most”. Since the denotations are flexible, both considered quantifiers are extendable to the case “all”, however such extension is more natural in the case of “most”, since the whole domain is the only witness set for this quantifier lying outside the default denotation. In the case of “some” such extension is more difficult, since its default denotation is itself vague, which results also in people’s indecisiveness about so-called strong scalar implicature of this quantifier.
As further research concerning vagueness and flexibility of quantifiers we plan the following:
• Estimation of the cardinality dependence of “some”: approximating the borders of the default denotation
• Differentiation between the two mechanisms: suspension of implicature and extension of quantifiers
As an especially important completion to the above research we would con- sider the within-subject comparison of all the relevant inferences: All/Some,
All/M ost, Some/Somenot, Some/M ostnot both in the context (textual rea- soning tasks) and with the use of pictures; for passive and active competence. Additionally, subjects should be asked to evaluate the certainty with which they infer their conclusions.
Chapter 4
What can fictitious discourse tell us
about existence?
4.1
Introduction:
what to do with empirical
data?
This thesis began as a study of existential import, developed as a study of scalar implicatures of quantifiers and came back to the initial point. In our experiments we showed how all the inference relations between categorial sentences1, includ- ing inferences that are traditionally said to invoke existential import (thus the inferences All/Some and N o/Somenot), are dependent on scalar properties of the considered quantifiers. Moreover, we claimed that it is only scalar properties that matter here and that the considered quantifiers are free of any ontologi- cal commitment. Thus, the truth-value of categorial sentences does not depend on the ontological status of the entities referred to, so on the emptiness or non- emptiness of the domain. Whereas the first part of our claim was widely motivated on many pages of the previous chapters, the second one still needs analysis and justification. The problem yet remains and we are left with the question of how to interpret categorial sentences in predicate logic, since even if “some” has the suggested scalar implicature and vague denotation, it still has, in contrast to the universal quantifier, existential meaning.
Let us briefly recall from chapter 1, that the relationship between the onto- logical category of existence and the particular categorial sentence “Some A’s are B’s” results from how this sentence is represented in predicate calculus, namely as an existentially quantified sentence ∃x(A(x)∧B(x)). The further transfer of the existential commitment to the universal categorial sentence follows from what is traditionally understood by existential import, and is described as “subalter- nation” in the Aristotelian Square of Opposition. We mean here inferences:
1here – sentences of a formQ(A, B), whereQ∈ {All, N o, Some, Somenot, M ost, M ostnot}
(A/S) All(A, B)
Some(A, B) (N/SN)
N o(A, B)
Somenot(A, B)
2,
which in the present study are described as “so-called existential import”. However, since the universal categorial sentence is contemporarily represented as ∀x(A(x) → B(x)) and thus can be vacuously satisfied (in contrast to the particular sentence), then if we want to preserve this kind of inference, we need to find some better logical model. 3
The empirical evidence for the ontological independence of A/S and N/SN
inferences consist in the lack of any between-group difference with respect to empty resp. non-empty domains. In our experiments the subjects’ readiness to inferSome(A, B)fromAll(A, B)(orSomenot(A, B)fromN o(A, B)) did not dif- fer with respect to emptiness of domains. (Similarly for conclusions with “most” inferred from universal premises.) In general, even if we observed any between- group differences, they were of such a kind that cannot be connected with the presumed existential load of the quantifier “some” (and the lack of such a load in the case of the universal quantifier). Let us recall that in the direct inferences part of the first experiment, so-called existential import was even stronger in the empty-terms group than in the control group. This effect was explained by such factors as:
• differences in logical background of subjects in both groups,
• stronger context-dependence of reasoning with non-empty terms than with empty terms, namely that in the case of reasoning with the use of terms referring to entities that are familiar to us, it is difficult to abstract from factual knowledge about world.
Nonetheless, the experiments clearly showed that people’s readiness to produce inferences of the formA/S orN/SN was not dependent on the ontological status of the objects referred to. This suggests that both quantifiers indeed have similar truth-value conditions in empty and non-empty domains. The question is, how- ever, whether they are both existentially loaded (and hence both false in empty domains) or rather both free of any existential burden.
In this last chapter, we propose how to solve this puzzle. Let us introduce briefly what are our main assumptions:
1. Categorial sentences such as “All A’s are B” or “Some A’s are B” (among others) can be true or false independently of the ontological status of the
2Actually the latter inference (N/SN) in the Aristotelian Square of Opposition is not depen-
dent on granting existential import to the negative universal categorial sentence (since “some not” lacks such import), but it requires additional assumption of non-emptiness of domains in modern logic.
3For a discussion of possible strategies of dealing with this problem – other than the one
4.1. Introduction: what to do with empirical data? 103 domain. This assumption is the result of the following conviction. We believe that there is an essential difference in truth-value between the two sentences: “Zeus lived on Mount Olympus” and that “Zeus lived on Mount Tabor”, namely the first one is true and the latter is false. Similarly “All elves have pointed ears” is in our opinion a true sentence, and not just because we believe that the universally quantified sentence can be vacuously satisfied. It is true since, indeed, according to what we know about elves their ears are pointed. On the contrary, a sentence “All elves have four legs” is clearly false, because elves are two-legged beings.
2. There is a crucial difference between so-called empty and non-empty terms. Let us make it clear. We do not claim that all terms are non-empty and hence that all objects are existent. Elves can be two-legged beings with pointed ears, and Zeus can be a Greek god, whose seat is Mount Olympus, but neither elves nor Zeus exist, at least not in the same world as ourselves. Therefore “Zeus” and “elves” are empty terms, namely terms non-referring to anything in the real, actual world. What is even more, elves inhabit different worlds than are ruled by Greek gods.
It follows that “A’s exists” is an ambiguous sentence, or rather it can have different presuppositions concerning the world or sets of worlds to which it applies. “Elves exist” is a false sentence if we are referring to the actual world (or if we refer to the world of Greek mythology), but it can be true, when understood as “In some fairy-tale worlds (e.g. Tolkien’s world), i.e. some possible worlds, elves exist”.
3. Existence indexes possible worlds, which are dynamic constructions. While under traditional approaches, possible worlds are treated as static ob- jects and their internal structure is rarely examined, we take an approach in which possible worlds are dynamic mental constructions providing (possibly incomplete) descriptions of certain world-states (called world-descriptions
orworlds from now). Neither objects nor worlds are primitive, thus worlds can be constructed of objects and objects can be also constructed within worlds if enforced by some world-laws defining them. Sentences about the real world are special only in the respect that the description of a world- state which is (often implicitly) conveyed in them is one of the real world (the world in which the sentence-using individual lives). Thus, existence is treated as amodal index, assigning objects to a certain world-state descrip- tion. The most common natural-language use of the word “exists” is now treated as an implicit assignment of objects to the description of the real world.
In what follows, we develop each of these points, giving also some justification for our assumptions. Finally we will describe in more detail how our proposal solves the problem of existence and existential import.