Summary |
Semantic
theories of natural and formal languages often appeal to the notion of domain
of quantification in specifying the interpretations and truth conditions of
sentences of the object language. In natural language, quantificational
expressions, such as ‘every’, ‘some’, ‘most’, are routinely evaluated with
respect to a salient and typically restricted range of entities (e.g. an
ordinary utterance of ‘she knew everything’ can be true despite the fact that
the person referred to is not omniscient). In formal languages, standard model-theoretic
semantics specify the interpretations of the object language by fixing a domain
of quantification and assigning semantic values constructed from that domain to
non-logical expressions of the language. A question
that has received much attention of late is whether there is an unrestricted
domain of quantification, a domain containing absolutely everything there is.
Is there a discourse or inquiry that has absolute generality? Prima facie
examples of sentences that quantify over an all-inclusive domain abound (e.g. 'everything is self-identical' or ‘the empty set contains no element’). However, a
number of philosophical arguments have been offered in support of the view that
absolutely unrestricted quantification cannot be achieved. The growing body of
literature on the issue has ramifications for semantics, metaphysics, and
logic. |