Hacker News new | past | comments | ask | show | jobs | submit login

What is meant here is an ordinary empirical claim that is false, which is unsurprising because it is made independently of any empirical investigation into how we form our notion of space.

Observational studies in developmental psychology--which didn't exist in Poincare's day, much less Kant's--tell us that our notions of space are developed interactively, not observationally. We are not passive recipients of sensation trapped in Plato's cave, but active intervenors in the world who learn about the universe by being causes.

"According to Piaget, the origin of spatial representation coincides with the origin of drawing, language and representational thinking in general. In spite of their common development, drawing soon falls behind the mental conception of space (especially in the case of complex and three-dimensional constructions). Yet, in its simplest and earliest appearances, drawing should be conceived as the representation or even the motor of spatial conception, because—here Piaget quotes his teacher, the philosopher of mathematics Léon Brunschvicg—drawing is not founded on geometry, but on the contrary, geometry is founded on the practice of drawing. If one explains the origins of geometry as arising from drawing, the child’s drawing can indeed be operationalized as a reconstruction apparatus of the psychogenesis of space. If one understands drawing in this way, it does not record an independent process of development, rather it documents and reflects its own developmental conditions—and thereby furthers mental ontogeny. Children’s drawings are able to visualize geometric conceptions because they are one of its main motors. The drawing child constitutes a veritable machine that works on the production of a Euclidean future, because—as Piaget detected in his experiments—it helps to complete and partly to conceal the infant’s older tacit topological knowledge." (emphasis added) -- http://www.mpiwg-berlin.mpg.de/en/news/features/feature11

I am not in any sense a strict Piagetian, and I realized there has been a lot of work done on this topic since, but I use this as an example simply because his empirical investigations were foundational and should have brought us to the point where everyone recognizes that philosophical imaginings are not a useful way to approach any question whatsoever regarding the development of ideas, even when they are the imaginings of someone as clever as Kant, whom as others here have pointed out, Poincare' was channeling.

The imagination is a terrible guide to what is real: we can imagine all kinds of things that can't exist (the god of the Bible, for example) and can't imagine all kinds of things that do exist (whatever lies behind quantum phenomena, say).

Philosophers (and at times mathematicians) like to sweep away the messy empirical realities that actually give rise to our ideas of geometry and everything else. It's a fun game to play. It just tells us far more about the human imagination than the rest of reality.




Guidelines | FAQ | Lists | API | Security | Legal | Apply to YC | Contact

Search: