A note on Horwich’s notion of grounding

25 Apr 2018

Horwich (Deflationism and paradox, Oxford University Press, Oxford, pp 75–84, 2005) proposes a solution to the liar paradox that relies on a particular notion of grounding—one that, unlike Kripke’s (J Philos 72:690–716, 1975) notion of grounding, does not invoke any “Tarski-style compositional principles”. In this short note, we will formalize Horwich’s construction and argue that his solution to the liar paradox does not justify certain generalizations about truth that he endorses. We argue that this situation is not resolved even if one appeals to the ω-rule. In the final section, we briefly discuss how Horwich might respond to the situation.