Negation in Negationless Intuitionistic Mathematics

0570227 - FLÚ 2024 RIV GB eng J - Článek v odborném periodiku
Ferguson, Thomas
Negation in Negationless Intuitionistic Mathematics.
Philosophia Mathematica. Roč. 31, č. 1 (2023), s. 29-55. ISSN 0031-8019. E-ISSN 1744-6406
Institucionální podpora: RVO:67985955
Klíčová slova: G.F.C Griss * D. Nelson * negation * intuitionistic mathematics
Obor OECD: Philosophy, History and Philosophy of science and technology
Impakt faktor: 1.1, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1093/philmat/nkac026

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.
Trvalý link: https://hdl.handle.net/11104/0346060