Open Access. Powered by Scholars. Published by Universities.®
Logic and Foundations of Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Publication Type
Articles 1 - 2 of 2
Full-Text Articles in Logic and Foundations of Mathematics
Recognizing Mathematics Students As Creative: Mathematical Creativity As Community-Based And Possibility-Expanding, Meghan Riling
Recognizing Mathematics Students As Creative: Mathematical Creativity As Community-Based And Possibility-Expanding, Meghan Riling
Journal of Humanistic Mathematics
Although much creativity research has suggested that creativity is influenced by cultural and social factors, these have been minimally explored in the context of mathematics and mathematics learning. This problematically limits who is seen as mathematically creative and who can enter the discipline of mathematics. This paper proposes a framework of creativity that is based in what it means to know or do mathematics and accepts that creativity is something that can be nurtured in all students. Prominent mathematical epistemologies held since the beginning of the twentieth century in the Western mathematics tradition have different implications for promoting creativity in …
Three Essays In Intuitionistic Epistemology, Tudor Protopopescu
Three Essays In Intuitionistic Epistemology, Tudor Protopopescu
Dissertations, Theses, and Capstone Projects
We present three papers studying knowledge and its logic from an intuitionistic viewpoint.
An Arithmetic Interpretation of Intuitionistic Verification
Intuitionistic epistemic logic introduces an epistemic operator to intuitionistic logic which reflects the intended BHK semantics of intuitionism. The fundamental assumption concerning intuitionistic knowledge and belief is that it is the product of verification. The BHK interpretation of intuitionistic logic has a precise formulation in the Logic of Proofs and its arithmetical semantics. We show here that this interpretation can be extended to the notion of verification upon which intuitionistic knowledge is based. This provides the systems of intuitionistic epistemic logic …