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In the past decades, recent paradigm shifts in ethology, psychology, and the social sciences have given rise to various new disciplines like cognitive ethology and evolutionary psychology. These disciplines use concepts and theories of evolutionary biology to understand and explain the design, function and origin of the brain. I shall argue that there are several good reasons why this approach could also apply to human mathematical abilities. I will review evidence from various disciplines (cognitive ethology, cognitive psychology, cognitive archaeology and (...) |
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“Logic” entails both a toolkit for dealing with situations requiring precision, and a prescription for a type of public reasoning. A sufficiently extended society facing a stream of genuinely novel opportunities and challenges will benefit from an ability to generate and encourage the use of such reasoning systems to deal with these opportunities and challenges. The study of “logic” is the result of using the toolkit on itself, which would appear to be a necessary and not unnatural step for a (...) |
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Recent years have seen a growing acknowledgement within the mathematical community that mathematics is cognitively/socially constructed. Yet to anyone doing mathematics, it seems totally objective. The sensation in pursuing mathematical research is of discovering prior (eternal) truths about an external (abstract) world. Although the community can and does decide which topics to pursue and which axioms to adopt, neither an individual mathematician nor the entire community can choose whether a particular mathematical statement is true or false, based on the given (...) |
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When Ken Malone investigates a case of something causing mental static across the United States, he is teleported to a world that doesn't exist. |
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(1) The induced colours led to perceptual grouping and pop-out, (2) a grapheme rendered invisible through ‘crowding’ or lateral masking induced synaesthetic colours — a form of blindsight — and (3) peripherally presented graphemes did not induce colours even when they were clearly visible. Taken collectively, these and other experiments prove conclusively that synaesthesia is a genuine percep- tual phenomenon, not an effect based on memory associations from childhood or on vague metaphorical speech. We identify different subtypes of number–colour synaesthesia (...) |
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...that is, “Let no-one without knowledge of geometry enter:” the inscription displayed on the entrance to Plato’s Academy reminds us how close the relationships between mathematics1 and philosophy used to be. In this perspective, when we approach the issue of how philosophical inquiry can further maths’ teaching/learning, a sort of archaeological attitude is in order, which delves into the layers of a long history, plumbs the recondite depths of Western thought, and unearths what remains too often concealed either because it (...) |
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