Indexed definiteness

Iterating Definiteness

A central concept in the study of vagueness is the concept of a borderline case. This concept has its most basic application when we are faced with a question of the form ‘Is x F?’, but are unwilling to answer ‘Yes’ or ‘No’ for a certain distinctive kind of reason. Wanting to be co-operative, we need to say something; by saying ‘It’s a borderline case’, we excuse our failure to give a straightf...

Definiteness and Indefiniteness *

The prototypes of definiteness and indefiniteness in English are the definite article the and the indefinite article a/an, and singular noun phrases (NPs) determined by them. That being the case it is not to be predicted that the concepts, whatever their content, will extend satisfactorily to other determiners or NP types. However it has become standard to extend these notions. Of the two categ...

Extending Positive Definiteness

The main result of this paper gives criteria for extendibility of mappings defined on symmetric subsets of ∗-semigroups to positive definite ones. By specifying the mappings in question we obtain new solutions of relevant issues in harmonic analysis concerning truncations of some important multivariate moment problems, like complex, two-sided complex and multidimensional trigonometric moment pr...

Exclusivity, uniqueness, and definiteness

An utterance of (2a) means of course that there is only one author of Waverley – indeed, that is most likely one’s point when one uses (2a). But (2b) can mean that there is strictly more than one author of Waverley, on the reading that can be paraphrased, ‘It’s not the case that only Scott is an author of Waverley’. In (2c) the question may concern the number of authors; if the answer is no, th...

Double definiteness in Scandinavian