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.
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| 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 Samuel Kuhn - 1962 - Chicago: University of Chicago Press.
The Structure of Scientific Revolutions.David Bohm - 1964 - Philosophical Quarterly 14 (57):377-379.
View all 31 references / Add more references
Citations of this work BETA
Understanding Scientific Study Via Process Modeling.Robert W. P. Luk - 2010 - Foundations of Science 15 (1):49-78.
Social Construction, Mathematics, and the Collective Imposition of Function Onto Reality.Julian C. Cole - 2015 - Erkenntnis 80 (6):1101-1124.
Wigner’s Puzzle on Applicability of Mathematics: On What Table to Assemble It?Cătălin Bărboianu - 2020 - Axiomathes 30 (4):423-452.
Is the New Monetary Consensus Still Alive? A Critical Economic and Philosophical Appraisal.Marc Pilkington - 2021 - Revue de Philosophie Économique 2:7-49.
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