Infinite Types and the Principle of Union

Nicolai and Stern, eds., Modes of Truth. The Unified Approach to Truth, Modalities, and Paradox (Taylor and Francis, 2021)

Abstract: In addition to objects (i.e. entities of type 0) should we also believe in entities of other types? Are there also type 1 entities (e.g. first-level Fregean concepts, pluralities), and type 2 entities (e.g. second-level Fregean concepts, superpluralities), and so on? Øystein Linnebo and Agustín Rayo argue that ‘plausible’ assumptions lead to a surprising conclusion for those who accept that first-order quantifiers may range over absolutely every object: absolutists of this kind should countenance proper-class-many types. This chapter takes up their argument for this thesis—Infinite Types—and argues that one of its assumptions is rather less plausible than Linnebo and Rayo suggest. The problematic assumption is the Principle of Union which states that one should countenance any language which ‘pools together’ the expressive resources drawn from any set of languages already deemed legitimate.

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