This paper discusses a number of methodological issues with mainstream formal semantics and then investigates whetherWittgenstein’s later work provides an alternative approach that is able to avoid these issues.

The Monist’s call for papers for this issue ended: “If formalism is true, then it must be possible in principle to mechanize meaning in a conscious thinking and language-using machine; if intentionalism is true, no such project is intelligible.”We use the Grelling-Nelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal languages, is not suitable for it. We also point out that object-object mapping theories of semantics, the usual account for the possibility of nonintentional semantics, do not seem able to accountfor the indefinitely extensible productivity of natural language.