Mathematical models and reality: A constructivist perspective [Book Review]
Foundations of Science 15 (1):29-48 (2010)
Abstract
To explore the relation between mathematical models and reality, four different domains of reality are distinguished: observer-independent reality, personal reality, social reality and mathematical/formal reality. The concepts of personal and social reality are strongly inspired by constructivist ideas. Mathematical reality is social as well, but constructed as an autonomous system in order to make absolute agreement possible. The essential problem of mathematical modelling is that within mathematics there is agreement about ‘truth’, but the assignment of mathematics to informal reality is not itself formally analysable, and it is dependent on social and personal construction processes. On these levels, absolute agreement cannot be expected. Starting from this point of view, repercussion of mathematical on social and personal reality, the historical development of mathematical modelling, and the role, use and interpretation of mathematical models in scientific practice are discussed.Author's Profile
DOI
10.1007/s10699-009-9167-x
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Citations of this work
Social Construction, Mathematics, and the Collective Imposition of Function onto Reality.Julian C. Cole - 2015 - Erkenntnis 80 (6):1101-1124.
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Should causal models always be Markovian? The case of multi-causal forks in medicine.Donald Gillies & Aidan Sudbury - 2013 - European Journal for Philosophy of Science 3 (3):275-308.
Wigner’s Puzzle on Applicability of Mathematics: On What Table to Assemble It?Cătălin Bărboianu - 2019 - Axiomathes 1:1-30.
References found in this work
The Structure of Scientific Revolutions.Thomas Samuel Kuhn - 1962 - Chicago: University of Chicago Press.
The Structure of Scientific Revolutions.David Bohm - 1964 - Philosophical Quarterly 14 (57):377-379.