Foundations of Science 16 (4):337-351 (2011)
|Abstract||In this paper it is argued that the fundamental difference of the formal and the informal position in the philosophy of mathematics results from the collision of an object and a process centric perspective towards mathematics. This collision can be overcome by means of dialectical analysis, which shows that both perspectives essentially depend on each other. This is illustrated by the example of mathematical proof and its formal and informal nature. A short overview of the employed materialist dialectical approach is given that rationalises mathematical development as a process of model production. It aims at placing more emphasis on the application aspects of mathematical results. Moreover, it is shown how such production realises subjective capacities as well as objective conditions, where the latter are mediated by mathematical formalism. The approach is further sustained by Polanyi’s theory of problem solving and Stegmaier’s philosophy of orientation. In particular, the tool and application perspective illuminates which role computer-based proofs can play in mathematics|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Marianna Antonutti Marfori (2010). Informal Proofs and Mathematical Rigour. Studia Logica 96 (2):261-272.
Christian Hennig (2010). Mathematical Models and Reality: A Constructivist Perspective. Foundations of Science 15 (1).
Jessica Carter (2004). Ontology and Mathematical Practice. Philosophia Mathematica 12 (3):244-267.
Davide Rizza (2011). Magicicada, Mathematical Explanation and Mathematical Realism. Erkenntnis 74 (1):101-114.
Stojan Obradović & Slobodan Ninković (2009). The Heuristic Function of Mathematics in Physics and Astronomy. Foundations of Science 14 (4).
Davide Rizza (2010). Mathematical Nominalism and Measurement. Philosophia Mathematica 18 (1):53-73.
Madeline M. Muntersbjorn (1999). Naturalism, Notation, and the Metaphysics of Mathematics. Philosophia Mathematica 7 (2):178-199.
Jean Paul Van Bendegem (2005). Proofs and Arguments: The Special Case of Mathematics. Poznan Studies in the Philosophy of the Sciences and the Humanities 84 (1):157-169.
Mary Leng (2002). Phenomenology and Mathematical Practice. Philosophia Mathematica 10 (1):3-14.
Ian J. Dove (2009). Towards a Theory of Mathematical Argument. Foundations of Science 14 (1-2):136-152.
Carlo Cellucci (2013). Philosophy of Mathematics: Making a Fresh Start. Studies in History and Philosophy of Science Part A 44 (1):32-42.
La´Szlo´ E. Szabo´ (2003). Formal Systems as Physical Objects: A Physicalist Account of Mathematical Truth. International Studies in the Philosophy of Science 17 (2):117-125.
Brendan Larvor (2012). How to Think About Informal Proofs. Synthese 187 (2):715-730.
Charles Parsons (2008). Mathematical Thought and its Objects. Cambridge University Press.
Added to index2010-12-24
Total downloads14 ( #83,010 of 548,984 )
Recent downloads (6 months)0
How can I increase my downloads?