Individuals and Modality

Individuals and Modality Hisashi Komatsu* Hiroshima City University School of Information Sciences 151-5 Ozuka, Numata-cho, Asa-minaini-ku, Hiroshima 731-31, Japan Tel.: +81-82-830-1615, 1500 e-mail: komatsu@cs.hiroshima-cu.ac.jp Abstract In this paper, I argue that the modality contained in declarative sentences is heterogeneous by nature, and its indiscernible treatment evoked pardoxical behaviors of individuals in modal contexts. The difficulty is avoided by classifying the modality in two kinds from a normative point of view: 1) modality in a traditinal sense, which is a freedom under a certain convention, and 2) multi-modality which stems from the difference of conventions. The former is treated in the traditional modal logic, but the latter kind of modality which typically appears in belief sentences is captured in another framework called multi-model. This solution deeply concerns the ontology of individuals, therefore the existential presupposition of individuals, too. So, I further propose its treatment by means of a kind of three-valued semantics. 1 Introduction The modality of natural languages has always been one of the main objects of formal semantics. Because declarative sentences of natural languages are analyzed as a predication to individuals, and normally appear with modality, behaviors of individuals in modal contexts inevitably come into question. In fact, the effort to clarify them has been continuing hundred years since Frege[8, 9]. And in the modal logic, researchers succeeded in it to a certain extent, proposed some possible solutions to the problems in the philosophy and ordinary languages. However, such a method is not almighty, suffers from difficulties, e.g. in the interpretation of belief sentences. The reason for the difficulty lies in treating heterogeneous modal phenomena in a homogeneous manner. Therefore, it's necessary to analyze the concept of modality into its parts. They consist of the modality in the narrow sense covered by the traditional modal logic and the modality found in belief sentences. The former is the freedom under the same ontological convention of language, the latter is the freedom under several different conventions. They are called (mere) -modality' and 'multi- modality' respectively. The former can be treated by the traditional modal logic or the possible world semantics, but for the treatment of the latter, I introduce the method called 'multi-model'. 2 Origin of Modality The introduction of possible worlds is motivated by the intuition: "This and this could have been otherwise". E.g., suppose that the following sentence (1) Yamada is a student of Hiroshima City University. is actually true. But Yamada could be a student of the Kyushu University under another circumstance. Or the prime minister of Japan (at the time point July 1995) could be Ozawa, although he's actually *The presentation of this paper is partly supported by Electric Technology Research Foundation of Chugoku. 7 Murayama. Such intuitions can be explained by assuming possible worlds where the set of students of Hiroshima City University or the prime minister of Japan are different from the actual ones. The substitutibility of two terms which actually designate the same thing, and the existential general- ization are used to determine if …

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