Negation in Negationless Intuitionistic Mathematics. Issue 1 (21st October 2022)

• Record Type: Journal Article
• Authors: Ferguson, Thomas Macaulay
• Is Part Of: Philosophia Mathematica. Volume 31:Issue 1(2023)
• Page Start: 29
• Page End: 55
• Publication Date: 2022-10-21
• Subjects: Mathematics -- Philosophy -- Periodicals; Wiskunde; Filosofische aspecten; Mathematics -- Philosophy; Periodicals; 510.105
• DOI: 10.1093/philmat/nkac026
• Languages: English
• ISSNs: 0031-8019

Abstract

Abstract: The mathematician G.F.C. Griss is known for his program of negationless intuitionistic mathematics . Although Griss's rejection of negation is regarded as characteristic of his philosophy, this is a consequence of an executability requirement that mental constructions presuppose agents' executing corresponding mental activity. Restoring Griss's executability requirement to a central role permits a more subtle characterization of the rejection of negation, according to which D. Nelson's strong constructible negation is compatible with Griss's principles. This exposes a 'holographic' theory of negation in negationless mathematics, in which a full theory of negation is 'flattened' in a putatively negationless setting.