Mathematical Models and Reality: A Constructivist Perspective |
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Authors: | Christian Hennig |
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Institution: | 1.Department of Statistical Science,University College London,London,UK |
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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. |
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