Mathematical symbols as epistemic actions – an extended mind perspective
نویسنده
چکیده
Why are mathematical models so surprisingly efficient in the sciences? In this paper, adopt an extended mind perspective on human mathematical abilities. I review evidence from animal, infant and neuropsychology studies that the human brain contains several specialized neural circuits which can be co-opted to solve complex mathematical problems. However, mathematics has emergent properties which cannot be reduced to these cognitive subsystems. In particular, experimental evidence suggests that our evolved number sense is only capable of representing approximate quantities. Active externalism, a cognitive mechanism proposed by various authors, including Andy Clark and Merlin Donald, allows humans to overcome these cognitive limitations by performing epistemic actions in the world that could not be performed in the mind alone. I discuss the extensive use of external symbols in the history of early modern European mathematics, and demonstrate that this has led to an increasing efficiency of mathematics as epistemic tool in the sciences. This externalization of mathematical symbols can be traced back in the archaeological record to at least 20 000 years ago. Wider implications of externalist and evolutionary approaches to understanding mathematical cognition are discussed.
منابع مشابه
Mathematical symbols as epistemic actions
Recent experimental evidence fromdevelopmental psychology and cognitive neuroscience indicates that humans are equippedwith unlearned elementarymathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the ex...
متن کاملWhat’s in a Diagram? On the Classification of Symbols, Figures and Diagrams
In this paper I analyze the cognitive function of symbols, figures and diagrams. The analysis shows that although all three representational forms serve to externalize mental content, they do so in radically different ways, and consequently they have qualitatively different functions in mathematical cognition. Symbols represent by convention and allow mental computations to be replaced by epist...
متن کاملHuman-information interaction: An emerging focus for educational cognitive tools
Educational cognitive tools are interactive, computer-based tools that augment one’s mind to facilitate learning. Examples of these include interactive mathematical software, interactive physics simulations, and interactive biology visualizations. While using these tools a learner’s mind becomes coupled with the tool, forming a cognitive system, such that cognitive processes are distributed acr...
متن کاملKnowledge and cognitive integration
Cognitive integration is a defining yet overlooked feature of our intellect that may nevertheless have substantial effects on the process of knowledge-acquisition. To bring those effects to the fore, I explore the topic of cognitive integration both from the perspective of virtue reliabilism within externalist epistemology and the perspective of extended cognition within externalist philosophy ...
متن کاملEmotions as pragmatic and epistemic actions
This paper explores the idea that emotions in social contexts and their intentionality may be conceived of as pragmatic or epistemic actions. That is, emotions are often aimed at achieving certain goals within a social context, so that they resemble pragmatic actions; and in other cases emotions can be plausibly construed as acts of probing the social environment so as to extract or uncover imp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005