Reflection on the Relative Significance of Rigor of Mathematical Justification

Abstract

The justification of mathematical proposition has presupposition in structure and logical gap exists during its demonstration process, therefore, mathematical inference is not unassailable in its adopted logical tools and methods. What’s more, the incompleteness and non-closure of mathematical formalism make mathematical knowledge not able to obtain reliability to the full extent, no matter in its initial form, forming process or its formation. The appeal of justification theory in meta-level is no exception either. Therefore, the criteria for mathematical justification is a dynamic system with comprehensive evaluation.