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
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Sorry to re-quote the entire post, but it makes the follow up more coherent.
In some contexts, it seems appropriate to take the position that there is an unknowable noumena and only linguistically mediated phenomena. In other contexts you just have to put that on hold. Consider it a form of suspended dis-belief. After all you can use this position to exclude all knowledge except language. You are then left in a tautological world of discursive forms that issue from whence? This is characterized as the epistemological subject whose ontological foundation is intuition ex nihilo.
What I am interested in is figuring out how various structures or orderings to the physical world have shaped not just perception and thinking, but physiological systems and by extension much of the biological world. I am aware that we configure the physical world according to our language and culture. But that isn't the question. I want to look at this dilemma the other way around. I want to provisionally accept the idea that the physical world and its processes have produced the ground upon which our perceptions of it are based.
Well, in any case, returning to Piaget. Piaget started out as a philosopher of science, then turned to study psychology, and finally child development. He was also a major figure in the structuralist movement along with Levi-Strauss. His structuralism started through a re-examination of Husserl, and in opposition to Husserl's transcendental phenomenonology which he termed the false ideal of a suprascientic knowledge. On the other hand Piaget never really abandoned any of his interests in philosophy, science, psychology or child development, but sought to bring both a philosophical and scientific positions to bare on psychology, in particular the formation of the mind through its origins in child development. So, in effect he is all over the map taking a little here and a little there. He appears in different fields as different personae.
Here is something of Piaget's critique of phenomenology (Insights and Illusion of Philosophy, trans. Mays W, Meridian, NY 1971):
``The interesting feature of intuition according to Husserl, which allows him to believe its components to be indissociable, is that it based on an interaction that is indissociable, that of subject and object, creative of `phenomena.' But, and it is this from which the sophism proceeds, it is one thing to say that the _phenomenon_ results from an indissociable bond between subject and object and another to say that the _intuition_ of the phenomenon and all that one undertakes to find there involves an indissociable bond between the normative elements of the subject and the factual elements relative to the object. In reality the phenomenon `being what it is,' its intuition remains subject to error as to truth, as do all the activities of the subject. And to say that the phenomenon is internal to consciousness, and that it is primitive, immediate, etc., changes nothing at all, for a primitive datum can be less true and more deceptive than an elaborated one, because of the twofold meaning of the term `subjective' (distorting or knowing0. the belief according to which intuition is at one and the same time `contact with the object' and `true,' requires therefore a twofold proof, from fact and normative justification; as soon as one looks for these proofs, intuition separates into experiment and deduction.
Such is equally the fate of other concepts belonging to the phenomenological intuitionism. An `essence' is both a concept of the subject and the phenomenal nucleus of the object. But how are we to know if the essence is `true' without examining separately the experience of the object (while submitting it, of course, to the epistemological critique) and also the logic used by the subject to elaborate his concepts. `Intention' is a directing of the subject's consciousness toward essences and productive of cognitive forms, but if it is necessary to recall constantly the way consciousness is thus directed, intention will not suffice either in spite of Thomism, to ensure a necessary success, and this even on the phenomenal level...
It will be said that by separating intuition into experimental verification and deduction, we dissociate the interaction of the subject and object, acknowledged as indissociable. This not the case: but we replace as the analysis of the phenomenon itself requires, the idea, completely arbitrary today, of an absolute beginning, by the dialectical idea of a constant becoming. The history of science as much as the study of individual development shows that this interaction, while remaining indissociable, passes from an undifferentiated phase to one of coordination. Starting from a state of centration on a self uncognizant of itself and in which the subjective and objective are inextricably intermingled, the progressive decentration of the subject leads to a twofold movement, of externalization, tending to physical objectivity, and internalization tending to logico-mathematical coherence. But physical knowledge remains impossible without the logico-mathematical framework and it is impossible to construct the latter without its being applicable to `any' object whatever. It is this twofold movement that intuitionism neglects, and this is why `intuition' remains an extremely poor method for philosophical knowledge.'' (113-5pp)
Notice in the last section, ``Starting from a state of centration on a self...'' This refers to Piaget's own work and the idea that children begin their formation of language, thought, and reality in a state of centration on self. So, he considers what he mentions here as a twofold movement to be developmentally driven by an internal dialectic of becoming aware first of body, then language and self and then society and the world.
The role that mathematics plays in Piaget's thought is developed in a book whose title I can not remember at the moment. It explicitly sets out a program in which broad categorical constructs form a foundation out of which ever more refined, analytical and applicable forms derive.
Chuck Grimes