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.
Keywords Radical constructivism  Social constructivism  Scientific agreement  History of mathematical modelling  Modelling in practice
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DOI 10.1007/s10699-009-9167-x
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References found in this work BETA

The Structure of Scientific Revolutions.Thomas S. Kuhn - 1962 - University of Chicago Press.
The Structure of Scientific Revolutions.Thomas Samuel Kuhn - 1962 - Chicago: University of Chicago Press.
The Social Construction of What?Ian Hacking - 1999 - Harvard University Press.
Against Method.Paul Feyerabend - 1975 - London: New Left Books.
The Structure of Scientific Revolutions.David Bohm - 1964 - Philosophical Quarterly 14 (57):377-379.

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Citations of this work BETA

A Theory of Scientific Study.Robert Luk - 2017 - Foundations of Science 22 (1):11-38.
Understanding Scientific Study Via Process Modeling.Robert W. P. Luk - 2010 - Foundations of Science 15 (1):49-78.

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