Compositionality and Expressive Power: Comments on Pietroski

Paul Pietroski has developed a powerful minimalist and internalist alternative to standard compositional semantics, where meanings are identified with instructions to fetch or assemble human concepts in specific ways. In particular, there appears to be no need for Fregean Function Application, as natural language composition only involves processes of combining monadic or dyadic concepts, and Pietroski’s theory can then, allegedly, avoid both singular reference and truth conditions. He also has a negative agenda, purporting to show, roughly, that the vocabulary of standard truth conditional semantics is far too powerful to plausibly describe the linguistic competence of mere human minds. In this paper, I explain some of the basics of Pietroski’s compositional semantics and argue that his major objection to standard compositionality is inconclusive, because a similar argument can be mounted against his own minimalist theory. I argue that we need a clear distinction between the language of the theorist---theoretical notation---and the language whose nature we are trying to explain. The theoretical notation should in fact be as expressively powerful as possible. It does not follow that the notation cannot be used to explain mere human linguistic competence, even if human minds are limited in various ways.