<HTML>Chuck Grimes writes: << But it is space, the external form of physical reality independent of any mental construct that is the ground of these symmetries. They are not an artifact of human perception and cognition. The empirical proof of this is found in crystallography where spatial symmetries are expressed physically as chemically formed atomic lattice structures. In other words there is structure to physical reality, and our constructs of the world are formed through our interaction with these structures, which exist apriori to our mental formulation of them. >> Linguistics is an area where my curiosity far outstrips my knowledge, so I more inclined to ask questions than stake out positions. I know a bit more about Piaget, given his role in education theory. I think Chuck's account of his work is generally on target, although I do not remember mathematics being as central to the theory as Chuck's suggests. Spatial organization, yes; mathematics, not so much. My question relates to the way in which Chuck (or is it the voice of Piaget?) presents spatial organization, as external and prior to human perception and organization. I am skeptical of this claim. To begin with, I think it is clear that human beings have not simply understood the organization of space differently at different times, but also organized space in some quite different ways throughout their history. In this respect, it is instructive to look at the form of maps in different historical periods -- cartographers talk about maps embodying a cosmology. Now, clearly there is a materiality of space which precedes human organization of it; it would be absurd to deny otherwise. But the concept of 'space' is somewhat like the concept of 'nature': the very notion of nature (of a living, material world, with its own 'laws', separate and distinct from human beings) is a product of a human discursive organization which establishes 'nature' as something outside of us. Thus, the opposition of 'nature' and 'culture'/'history'. Many human cultures do not recognize or see this separation and opposition, and have no concept of nature as such. One can say, therefore, that for human beings, there is no 'nature' other than that we appropriate through our discourse. Similarly, one could make the case that for human beings, there is no 'space' outside of our discursive organization of the world around us. To use Kantian language, it is impossible to "know" nature or space [the thing in itself]; our knowledge is always mediated by our discursive construction of the object we are studying. Thus, insofar as Piaget sees "space" as a purely or solely 'pre-given,' he fails to grasp the element of human subjectivity -- and the role of human history -- in the constitution of that "space." Like Freud, therefore, he mistakes stages of human development which are culturally and historically specific, as universal. Does this make sense to those of us who know linguistics a whole lot better than I? Leo Casey United Federation of Teachers 260 Park Avenue South New York, New York 10010-7272 (212-598-6869) Power concedes nothing without a demand. It never has, and it never will. If there is no struggle, there is no progress. Those who profess to favor freedom, and yet deprecate agitation are men who want crops without plowing the ground. They want rain without thunder and lightning. They want the ocean without the awful roar of its waters. -- Frederick Douglass --</HTML>