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Cnossen, A.

Auteur: A. Cnossen
Afstudeerjaar: 2010
Vakgroep: Theoretische filosofie

Titel: Vagueness, A logic for non-precise models


The predicate `tall' is what we call a vague predicate. Paradigm examples of vague predicates are a dime a dozen. Bald, child, man, red, cloud, house are all vague to some extent. The reader can easily spend the rest of his day expanding on this list. These predicates share the feature that it is not clear for all things whether or not that predicate applies. Some things are tall and some things are not. There are, however, also things which are neither really tall nor really not tall.
Most literature on the subject takes vagueness to be the existence of borderline cases. As a definition however, this notion is to broad. Predicates, both artificial and real, can have borderline cases without being vague. Additionally, it is to narrow as well. The notion of borderline case is only applicable to predicates. Other terms of a language, however, can be vague as well. A definition which only aims to capture predicate vagueness only captures a small area in which the phenomenon is to be found. The situation is akin to providing a theory of gravity which is only applicable to gravity on earth. It might work locally, but far more interesting is a theory which works everywhere. For vagueness, this means that when identifying the phenomenon we cannot solely focus on predicates. Object vagueness, for instance, cannot be ignored. The prime candidates for the title of vague object are things like clouds and geographical areas like Mount Everest. For any cloud it can be reasonably argued that there are drops of water, those on the edge of the cloud, for which it is not entirely clear whether or not they are part of the cloud. The same goes for the Mount Everest. The bits of rock and snow that constitute the top of Mount Everest are clearly part of it. But for those at the start of the slope it is less clear. We cannot really say there is a single grain of sand, or a single snowflake, which marks the beginning of Mount Everest.

Current efforts to provide a theory and logic of predicate vagueness do not seem to provide much hope for a better understanding of object vagueness. In my thesis I provide a logic, using predicate abstraction, for vague objects and predicates. There is a strong sense in which predicates have borderline cases because they are vague. Whereas objects seem to be vague because they have borderline parts.
Laatst gewijzigd:01 november 2013 14:01