Complexity and Hierarchy in Truth Predicates∗

Since seminal work of Tarski (e.g. Tarski, 1935), hierarchies have been much discussed in the literature on truth and paradox. Especially in recent years, this discussion has been decidedly negative. Tarski’s hierarchy of languages is sometimes described as the “orthodox” response to the Liar paradox (e.g. Kripke, 1975), but it is an orthodoxy many authors have gone to great lengths to avoid. Frequently, the unpalatability of hierarchies is taken for granted, and the main task is taken to be developing theories of truth that avoid them. In this paper, I shall speak in favor of hierarchies. I shall argue that hierarchies are more well-motivated and can provide better and more workable theories than is often assumed. I shall not argue here that hierarchies are inevitable (though I have argued that elsewhere); rather, I shall argue that if we wind up with one, that is not by itself a bad result. Along the way, I shall sketch the sort of hierarchy I believe is plausible and defensible, which is different in important respects from the orthodox Tarskian one. My defense of hierarchies will assume a particular view of the nature of truth that is fundamentally ‘inflationary’ and sees truth as a substantial semantic concept. My main thesis will be that if one adopts this view of truth, hierarchies arise naturally. In contrast, if you adopt a deflationist line, hierarchies are much less plausible, and certainly lack motivation. As a corollary of these claims, we will see an important way in which theorizing