Quantification, Instantiation, and Event Individuation

Abstract

This section describes the theoretical basis of quantification in SMS. SL has a set of terms that serve as quantifiers, but they do so in ways that differ somewhat from the ways quantifiers are used in FOL. In SL quantification is allowed over labels, variables, sentential sequences (see section 10.3), links (see section 10.2.2) and concrete markers (see section 10.4), whereas FOL does not allow quantification over some of these objects. Two general types of quantification are recognized in the system: universal quantification and particular quantification. The term ‘particular’ rather than ‘existential’ is used to describe the second type in order to emphasize the point that it is not absolutely necessary to assign existential import to a quantifier of this type (cf. Orenstein, 1978). In section 7.1, it is mentioned that one may wish to avoid the notion of existence when assertions or questions about existence will not arise or are otherwise unimportant in a particular application or implementation of SMS theory. In such a case, the particular quantifier may be taken to be devoid of existential import, and inferencing over objects can be based on mere occurrence or presence of objects in particular realms or spaces. Alternatively, the meaning of the particular quantifier can be defined in a more conventional mode to enable it to be used to ground inferences about the ‘existence’ of objects. The discussions in this chapter presuppose the adoption of this last mentioned alternative so that the uses of particular quantifiers can be more readily compared with the uses of their counterparts in other languages and systems. Unless otherwise indicated, it is to be assumed that labels have at least one concrete instance in the system.