Minimalism, supervaluations and fixed points

Abstract

In this paper I introduce Horwich's deflationary theory of truth, called 'Minimalism', and I present his proposal of how to cope with the Liar Paradox. The proposal proceeds by restricting the T-schema and, as a consequence of that, it needs a constructive specification of which instances of the T-schema are to be excluded from Minimalism. Horwich has presented, in an informal way, one construction that specifies the Minimalist theory. The main aim of the paper is to present and scrutinize some formal versions of Horwich's construction.

Inferential Deflationism

“…In response, Horwich (2010) proposed an iterative construction that determines a maximal set of ground truths for which one can accept material disquotation. A recent result by Sergi Oms (2020), adapting a formalization of Horwich's strategy by Thomas Schindler (2020), shows that the set of truths obtained by iteratively taking ground instances is exactly σ vF , the set of truths defined by the van Fraassen hierarchy. Our result that QWBL ω T axiomatizes the internal logic of σ vF independently confirms a close relationship between this hierarchy and deflationism.…”

“…This hierarchy is sometimes defined in different, non-equivalent ways Field (2008). andMeadows (2015) supervaluate at the successor step over all τ ⊇ σ α with condition (i), whereasOms (2020) supervaluates over all τ ⊇ σ α with condition (ii). These are not equivalent.…”