In this paper, we focus on the development of geometric cognition. We argue that to understand how geometric cognition has been constituted, one must appreciate not only individual cognitive factors, such as phylogenetically ancient and ontogenetically early core cognitive systems, but also the social history of the spread and use of cognitive artifacts. In particular, we show that the development of Greek mathematics, enshrined in Euclid’s Elements, was driven by the use of two tightly intertwined cognitive artifacts: the use of (...) lettered diagrams; and the creation of linguistic formulae. Together, these artifacts formed the professional language of geometry. In this respect, the case of Greek geometry clearly shows that explanations of geometric reasoning have to go beyond the confines of methodological individualism to account for how the distributed practice of artifact use has stabilized over time. This practice, as we suggest, has also contributed heavily to the understanding of what mathematical proof is; classically, it has been assumed that proofs are not merely deductively correct but also remain invariant over various individuals sharing the same cognitive practice. Cognitive artifacts in Greek geometry constrained the repertoire of admissible inferential operations, which made these proofs inter-subjectively testable and compelling. By focusing on the cognitive operations on artifacts, we also stress that mental mechanisms that contribute to these operations are still poorly understood, in contrast to those mechanisms which drive symbolic logical inference. (shrink)

For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for (...) representing the shapes of large-scale, navigable surface layouts and of small-scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems. (shrink)

Heuristics are often invoked in the philosophical, psychological, and cognitive science literatures to describe or explain methodological techniques or "shortcut" mental operations that help in inference, decision-making, and problem-solving. Yet there has been surprisingly little philosophical work done on the nature of heuristics and heuristic reasoning, and a close inspection of the way(s) in which "heuristic" is used throughout the literature reveals a vagueness and uncertainty with respect to what heuristics are and their role in cognition. This dissertation seeks to (...) remedy this situation by motivating philosophical inquiry into heuristics and heuristic reasoning, and then advancing a theory of how heuristics operate in cognition. I develop a positive working characterization of heuristics that is coherent and robust enough to account for a broad range of phenomena in reasoning and inference, and makes sense of empirical data in a systematic way. I then illustrate the work this characterization does by considering the sorts of problems that many philosophers believe heuristics solve, namely those resulting from the so-called frame problem. Considering the frame problem motivates the need to gain a better understanding of how heuristics work and the cognitive structures over which they operate. I develop a general theory of cognition which I argue underwrites the heuristic operations that concern this dissertation. I argue that heuristics operate over highly organized systems of knowledge, and I offer a cognitive architecture to accommodate this view. I then provide an account of the systems of knowledge that heuristics are supposed to operate over, in which I suggest that such systems of knowledge are concepts. The upshot, then, is that heuristics operate over concepts. I argue, however, that heuristics do not operate over conceptual content, but over metainformational relations between activated and primed concepts and their contents. Finally, to show that my thesis is empirically adequate, I consider empirical evidence on heuristic reasoning and argue that my account of heuristics explains the data. (shrink)