What do we mean when we talk about the meanings of words? What should linguists mean? The dominant view in natural language semantics is that a good account of the meanings of words will be a specification of their (compositionally-determined) truth conditions. I argue that, even if words have truth conditions, this is not yet the right characterization of meaning from the perspective of human psychology. Hilary Putnam famously argued that the truth-conditional approach to word meanings as intensions, i.e. functions that determine extensions, cannot be a psychological theory. Yet, meanings might be intensions in quite another sense. Alonzo Church understood intensions as procedures (algorithms) that compute functions (sets of input-output pairs), a distinction perfectly mirrored in David Marr's discussion of Level 2 versus Level 1 study of the visual system. Making Church's distinction in the language domain leads to a very different way of thinking about the study of meaning as a part of linguistics. I present evidence from a number of experiments with children and adults in support of the view advanced most prominently by Paul Pietroski, in which meanings are psychological procedures that direct the construction of complex concepts.