Meaning theory for absolutely general languages

Logique Et Analyse (forthcoming)

Eric Guindon
Brown University
An “absolutely general” or "unrestricted" language is one the quantifiers and variables of which are meant to range over absolutely everything whatsoever. In recent years, an increasing number of authors have begun to appreciate the limitations of typical model-theoretic resources for metatheoretic reflection on such languages. In response, some have suggested that proper metatheoretic reflection for unrestricted languages needs to be carried out in a metalanguage of greater logical resources. For an unrestricted first-order language, for example, this means a second-order metalanguage. Importantly, second-order quantification must then be understood as an irreducible logical expansion, and not as a restricted form of quantification over a special class of things, such as sets or properties. In this paper, I will argue that the use of second-order resources is also required if we are to give an adequate meaning theory for an unrestricted first-order language. I then go on to show how such a meaning theory can be constructed, and draw some consequences for the individuation of propositional content along the way.
Keywords Absolute generality  Second-order logic  Meaning theory
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