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Understanding the Infinite II: Coalgebra

Corfield, David (2011) Understanding the Infinite II: Coalgebra. Studies in History and Philosophy of Science A, 42 (4). pp. 571-579. (doi:10.1016/j.shpsa.2011.09.013) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:28323)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
Official URL
http://dx.doi.org/10.1016/j.shpsa.2011.09.013

Abstract

In this paper we give an account of the rise and development of coalgebraic thinking in mathematics and

computer science as an illustration of the way mathematical frameworks may be transformed. Originating

in a foundational dispute as to the correct way to characterise sets, logicians and computer scientists

came to see maximizing and minimizing extremal axiomatisations as a dual pair, each necessary to represent

entities of interest. In particular, many important infinitely large entities can be characterised in

terms of such axiomatisations. We consider reasons for the delay in arriving at the coalgebraic framework,

despite many unrecognised manifestations occurring years earlier, and discuss an apparent asymmetry

in the relationship between algebra and coalgebra.

Item Type: Article
DOI/Identification number: 10.1016/j.shpsa.2011.09.013
Subjects: B Philosophy. Psychology. Religion > B Philosophy (General)
Divisions: Divisions > Division of Arts and Humanities > School of Culture and Languages
Depositing User: David Corfield
Date Deposited: 28 Oct 2011 09:38 UTC
Last Modified: 16 Nov 2021 10:06 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/28323 (The current URI for this page, for reference purposes)
Corfield, David: https://orcid.org/0000-0003-0432-3221
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