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 (to which there is no direct access), 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.
Keywords Radical constructivism  Social constructivism  Scientific agreement  History of mathematical modelling  Modelling in practice
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    References found in this work BETA
    Thomas Heath (1923). A History of Greek Mathematics. Journal of Hellenic Studies 43:81.

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