(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 (...) and propose that they are caused by hyperconnectivity between col- our and number areas at different stages in processing; lower synaesthetes may have cross-wiring (or cross-activation) within the fusiform gyrus, whereas higher synaesthetes may have cross-activation in the angular gyrus. This hyperconnec- tivity might be caused by a genetic mutation that causes defective pruning of con- nections between brain maps. The mutation may further be expressed selectively (due to transcription factors) in the fusiform or angular gyri, and this may explain the existence of different forms of synaesthesia. If expressed very diffusely, there may be extensive cross-wiring between brain regions that represent abstract concepts, which would explain the link between creativity, metaphor and synaesthesia (and the higher incidence of synaesthesia among artists and poets). Also, hyperconnectivity between the sensory cortex and amygdala would explain the heightened aversion synaesthetes experience when seeing numbers printed in the ‘wrong’ colour. Lastly, kindling (induced hyperconnectivity in the temporal lobes of temporal lobe epilepsy [TLE] patients) may explain the purported higher incidence of synaesthesia in these patients. We conclude with a synaesthesia-based theory. (shrink)

PurposeIn this article, we aim to present and defend a contextual approach to mathematical explanation.MethodTo do this, we introduce an epistemic reading of mathematical explanation.ResultsThe epistemic reading not only clarifies the link between mathematical explanation and mathematical understanding, but also allows us to explicate some contextual factors governing explanation. We then show how several accounts of mathematical explanation can be read in this approach.ConclusionThe contextual approach defended here clears up the notion of explanation and pushes us towards a pluralist vision (...) on mathematical explanation. (shrink)

...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 (...) is taken for granted or because we have become unable to detect what constitutes the very way in which we think. (shrink)

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.

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 (...) neuropsychology) that suggests that the human capacity for mathematics is a category-specific domain of knowledge, hard-wired in the brain, which can be explained as the result of natural selection. (shrink)

“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 (...) society developing sufficient familiarity with the toolkit. Many societies have developed something like logic, and past and present use of logic-like toolkits in learning situations and transmission of skills suggests that many societies will develop something like logic. (shrink)