Axiomathes 12 (1-2):151-155 (2001)

John L. Bell
University of Western Ontario
is a presentation of mathematics in terms of the fundamental concepts of transformation, and composition of transformations. While the importance of these concepts had long been recognized in algebra (for example, by Galois through the idea of a group of permutations) and in geometry (for example, by Klein in his Erlanger Programm), the truly universal role they play in mathematics did not really begin to be appreciated until the rise of abstract algebra in the 1930s. In abstract algebra the idea of transformation of structure (homomorphism) was central from the beginning, and it soon became apparent to algebraists that its most important concepts and constructions were in fact formulable in terms of that idea alone. Thus emerged the view that the essence of a mathematical structure is to be sought not in its internal constitution, but rather in the nature of its relationships with other structures of the same kind, as manifested through the network of transformations. This idea has achieved its fullest expression in category theory, an axiomatic framework within which the notions of transformation (as morphism or arrow) and composition (and also structure, as object) are fundamental, that is, are not defined in terms of anything else.
Keywords Philosophy   Philosophy   Logic   Ontology   Linguistics   Cognitive Psychology
Categories (categorize this paper)
Reprint years 2004
DOI 10.1023/A:1012766204615
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 50,241
Through your library

References found in this work BETA

A Primer of Infinitesimal Analysis.John L. Bell - 1998 - Cambridge University Press.
The Ghost of Modality.Herman Weyl - 1940 - In Marvin Farber & Edmund Husserl (eds.), Philosophical Essays in Memory of Edmund Husserl. Cambridge: Mass., Published for the University of Buffalo by the Harvard University Press. pp. 278--303.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles


Added to PP index

Total views
151 ( #57,287 of 2,325,387 )

Recent downloads (6 months)
3 ( #298,641 of 2,325,387 )

How can I increase my downloads?


My notes