Corfield, D.N. (2011) Understanding the Infinite II: Coalgebra. Studies in History and Philosophy of Science A, 42 (4). pp. 571-579.
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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.
|Subjects:||B Philosophy. Psychology. Religion > B Philosophy (General)|
|Divisions:||Faculties > Humanities > School of European Culture and Languages|
|Depositing User:||David Corfield|
|Date Deposited:||28 Oct 2011 09:38|
|Last Modified:||09 Nov 2011 12:30|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/28323 (The current URI for this page, for reference purposes)|
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