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)

An ideography is a general-purpose code made of pictures that do not encode language, which can be used autonomously – not just as a mnemonic prop – to encode information on a broad range of topics. Why are viable ideographies so hard to find? I contend that self-sufficient graphic codes need to be narrowly specialized. Writing systems are only an apparent exception: At their core, they are notations of a spoken language. Even if they also encode nonlinguistic information, they are (...) useless to someone who lacks linguistic competence in the encoded language or a related one. The versatility of writing is thus vicarious: Writing borrows it from spoken language. Why is it so difficult to build a fully generalist graphic code? The most widespread answer points to a learnability problem. We possess specialized cognitive resources for learning spoken language, but lack them for graphic codes. I argue in favor of a different account: What is difficult about graphic codes is not so much learning or teaching them as getting every user to learn and teach the same code. This standardization problem does not affect spoken or signed languages as much. Those are based on cheap and transient signals, allowing for easy online repairing of miscommunication, and require face-to-face interactions where the advantages of common ground are maximized. Graphic codes lack these advantages, which makes them smaller in size and more specialized. (shrink)