AGAINST CUMULATIVE TYPE THEORY

Abstract Standard Type Theory, ${\textrm {STT}}$ , tells us that $b^n(a^m)$ is well-formed iff $n=m+1$ . However, Linnebo and Rayo [23] have advocated the use of Cumulative $\textrm {CTT}$ which has more relaxed type-restrictions: according to $b^\beta (a^\alpha )$ $\beta>\alpha $ In this paper, we set ourselves against We begin our case by arguing Rayo’s claim sheds new philosophical light on theory. then argue that, while ’s type-restrictions are unjustifiable, imposed justified a Fregean semantics. What more, semantics provides with principled way resist Semantic Argument for end examining an alternative approach cumulative types due Florio Jones [10]; their theory best seen as misleadingly formulated version