The Logic of the Development of Space

Dissertation, York University (Canada) (1995)

Carmel Forde
Saint Mary's University
This dissertation is comprised of three parts. The first part is an intellectual historical thesis, regarding the place of Jean Piaget in philosophic thought. In Chapter One I outline the differences between my thesis and Piaget's position on the development of spatial concepts. My second chapter places his theory within the context of congruent accounts from the philosophy of nature, neurophysiology, and philosophy of psychology. Chapter Three situates him in relation to a selection of philosophers in the history of western philosophy, through a metapsychology. ;In Part II I provide a dynamic account of the order of conceptual development, and clarification of the concepts of topological space, projective space, and euclidean or metric space.$\sp1$ In three chapters I outline a systematic analysis of the genetic development of the concepts based on an analysis and critique of Piaget's observations. The emergence of each concept is shown to be a result of the experience of some incongruity between the concept immediately preceding, and experience. The order I outline differs in some specifics from that suggested by Piaget's broad outline, and I explain the differences as they occur. ;The third part of this dissertation is the most tentative. Chapter Nine discusses the kind of testing I will employ when I test the logical order of concepts. There are four kinds of modes which I use to test each concept. This is followed by Chapter Ten, which tests the dynamic development of concepts of space. In this I attempt to confirm those changes in the development of the concepts, as well as Piaget's overall framework, through the use of Piaget's pre-logical modes as well as others I have extracted from the dynamic development of concepts. ftn $\sp1$ I note here that Piaget means, by euclidean geometry, metric geometry. The distinction between geometry with a euclidean and a non-euclidean metric is not crucial for the purpose of this thesis
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