Embodied approaches to cognition see abstract thought and language as grounded in interactions between mind, body, and world. A particularly important challenge for embodied approaches to cognition is mathematics, perhaps the most abstract domain of human knowledge. Conceptual metaphor theory, a branch of cognitive linguistics, describes how abstract mathematical concepts are grounded in concrete physical representations. In this paper, we consider the implications of this research for the metaphysics and epistemology of mathematics. In the case of metaphysics, we argue that (...) embodied mathematics is neutral in the sense of being compatible with all existing accounts of what mathematical entities really are. However, embodied mathematics may be able to revive an older position known as psychologism and overcome the difficulties it faces. In the case of epistemology, we argue that the evidence collected in the embodied mathematics literature is inconclusive: It does not show that abstract mathematical thinking is constituted by metaphor; it may simply show that abstract thinking is facilitated by metaphor. Our arguments suggest that closer interaction between the philosophy and cognitive science of mathematics could yield a more precise, empirically informed account of what mathematics is and how we come to have knowledge of it. (shrink)

The intuition of clarity-valence association seems to be pervasive in daily life, however, whether there exists a potential association between clarity (i.e., operationalized as visual resolution) and affect in human cognition remains unknown. The present study conducted five experiments, and demonstrated the clarity-valence congruency effect, that is, the evaluations showed performance advantage in the congruent conditions (clear-positive, blurry-negative). Experiment 1 through 3 demonstrated the influence of the perception of clarity on the conceptualization of affective valence, while Experiment 4 & 5 (...) verified the absence of the influence of conceptualization on perception, thus the unidirectionality of clarity-valence association in cognition is confirmed. The findings extend the affective perceptual-conceptual associations into the dimension of clarity, thus providing support for the ideas of embodied cognition as well as implications for our preference for clarity and aversion to blur. (shrink)