It is difficult to eexplain our everyday and scientific use of natural language without endorsing in some form or another properties, relations and propositions. Yet, any attempt to formulate an explicit theory about the nature of such entities (property theory) must confront difficult conundrums such as Russell’s paradox and other paradoxes of predication, the paradox of analysis, or Frege’s puzzle about reference and identity. This book proposes a preperty theory that circumvents the paradoxes of predication by relyin on Gupta’s and Belnap’s account of circular definitions. This yields a distinctive approach to analysis and a type-free version of Montague’s treatment of natural language determiners. By building on this, a theory of singular reference is offered, one that is in sharp contrast with the currently dominant theory of direct reference, championed by Kripke and Kaplan.
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