Mathematical models and reality: A constructivist perspective
Foundations of Science 15 (1) (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 | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,653 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesFinn Collin (1997). Social Reality. Routledge.
A. Quale (2012). On the Role of Constructivism in Mathematical Epistemology. Constructivist Foundations 7 (2):104-111.
James Franklin (1989). Mathematical Necessity and Reality. Australasian Journal of Philosophy 67 (3):286 – 294.
Robert I. Damper (2001). Programs, Models, Theories, and Reality. Behavioral and Brain Sciences 24 (6):1055-1056.
Michael J. White (1992). The Continuous and the Discrete: Ancient Physical Theories From a Contemporary Perspective. Oxford University Press.
Stewart Shapiro (1983). Mathematics and Reality. Philosophy of Science 50 (4):523-548.
Analytics
Monthly downloads |
Added to index2009-10-24Total downloads24 ( #51,551 of 548,984 )Recent downloads (6 months)1 ( #63,327 of 548,984 )How can I increase my downloads? |
My notes
Discussion
