Philosophy of Science

Meta-Methodology of Resolving the Dispute of Mathematical Proof

Document Type : Research Paper

Authors

Hossein Bayat 1
musa akrami 2

1 . Ph.D Student, Department of Philosophy of Science, Faculty of Theology and Philosophy, Islamic Azad University, Science and Research Branch of Tehran

2 Associate Professor of Philosophy of Science Department, Faculty of Theology and Philosophy

Abstract
The extension of the mathematical argumentation methods, in recent decades, has led to an essential critique of classic definition of mathematical proof. The critics often have suggested alternative definitions, which have different and sometimes incompatible presuppositions and implications. Such a situation has exposed mathematics to relativism.
The problem of multiplicity of definitions, therefore, can be considered as one of the most important epistemological issues in mathematics. In this paper, we try, from third order or meta-methodological position, to answer this question: ‘what is the meta-criterion for choosing the best definition of mathematical proof?’ by answering this question we will be one step closer to a justified definition of mathematical proof.
The authors will show that the explanatory power meta-criterion, compared to the two other rivals, i.e. the equivalence meta-criterion and the consensus meta-criterion, is more tenable.

Keywords

: meta-theory of definition
theory of mathematical proof
explanatory power
proof facts
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