Models of memory in cognitive science and philosophy have traditionally explained human remembering in terms of storage and retrieval. This tendency has been entrenched by reliance on computationalist explanations over the course of the twentieth century; even research programs that eschew computationalism in name, or attempt the revision of traditional models, demonstrate tacit commitment to computationalist assumptions. It is assumed that memory must be stored by means of an isomorphic trace, that memory processes must divide into conceptually distinct systems and (...) phases, and that human remembering consists in inner, cognitive processes that are implemented by distinct neural processes. This dissertation draws on recent empirical work, and on philosophical arguments from Ludwig Wittgenstein and others, to demonstrate that this latent computationalism in the study of memory is problematic, and that it can and should be eliminated. Cognitive psychologists studying memory have encountered numerous data in recent decades that belie archival models. In cognitive neuroscience, establishing the neural basis of storage and retrieval processes has proven elusive. A number of revised models on offer in memory science, that have taken these issues into account, fail to sufficiently extricate the archival framework. Several impasses in memory science are products of these underlying computationalist assumptions. Wittgenstein and other philosophers offer a number of arguments against the need for, and the efficacy of, the storage and retrieval of traces in human remembering. A study of these arguments clarifies the ways that these computationalist assumptions are presently impeding the science of memory, and provides ways forward in removing them. We can and should characterize and model human memory without invoking the storage and retrieval of traces. A range of work in connectionism, dynamical systems theory, and recent philosophical accounts of memory demonstrate how the science of memory can proceed without these assumptions, toward non-archival models of remembering. (shrink)