- An attractive principle about domains of quantification is the analogue of the Separation Axiom in set theory: restricting a domain by an arbitrary predicate yields a domain. In particular, restricting a domain by a predicate that applies to nothing yields a domain. Thus if there is a nonempty domain, there is an empty domain. But semantics for the empty domain involves some neglected subtleties. Untangling them requires us to revise the usual definition of truth in a model, avoiding the detour through Tarski's notion of satisfaction.
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- Peer reviewed
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- Copyright holder:
- Tim Williamson
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- The full-text of this article is not currently available in ORA, but you may be able to access the article via the publisher copy link on this record page. N.B. Tim Williamson is now based at the Faculty of Philosophy, University of Oxford.
A note on satisfaction, truth and the empty domain
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