
The author offers ``a defence of free logic, specifically a free logic admitting both empty names and empty definite descriptions as genuine singular terms''. He presents an interpreted first-order language containing both its own denotation predicate and the definite description operator, and argues that (1) such languages provide a positive support for a free logic, (2) a free logic admitting definite descriptions as genuine terms needs something like the constructions involved. Guided by \textit{S. Kripke's} ``Outline of a theory of truth'' [J. Philos. 72, 690-716 (1975)], he describes a least fixed-point construction for a class of partial free structures appropriate to the language mentioned above; the resulting structure possesses several desired properties. The construction leans upon the technique derived by \textit{S. Feferman} [J. Symb. Logic 49, 75-111 (1984; Zbl 0574.03043)] and is, for the most part, routine. The author distinguishes carefully between the terms having the empty value in a structure and those undefined in the sense that (the facts described by) the structure do not determine whether they are empty or non-empty. The presentation is preceded by a short general discussion on arguments for free logic against classical logic. The approach taken up in the paper has already been sketched by the author [Theoria 50, 178-211 (1984; Zbl 0581.03002)].
Logic with extra quantifiers and operators, empty definite descriptions, Other model constructions, partial structure, Philosophical and critical aspects of logic and foundations, Other nonclassical logic, least fixed-point construction, free logic, denotation predicate, empty names
Logic with extra quantifiers and operators, empty definite descriptions, Other model constructions, partial structure, Philosophical and critical aspects of logic and foundations, Other nonclassical logic, least fixed-point construction, free logic, denotation predicate, empty names
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