Hierarchies Ontological and Ideological

Author: Linnebo ystein   Rayo Agustn  

Publisher: Oxford University Press

ISSN: 1460-2113

Source: Mind, Vol.121, Iss.482, 2012-04, pp. : 269-308

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Abstract

Gdel claimed that Zermelo-Fraenkel set theory is what becomes of the theory of types if certain superfluous restrictions are removed. The aim of this paper is to develop a clearer understanding of Gdel's remark, and of the surrounding philosophical terrain. In connection with this, we discuss some technical issues concerning infinitary type theories and the programme of developing the semantics for higher-order languages in other higher-order languages.