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.

中文翻译：

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无否定直觉数学中的否定

数学家 GFC Griss 以他的无否定直觉数学程序而闻名。尽管格里斯拒绝否定被认为是他哲学的特征，但这是可执行性要求的结果，即心理构造以主体执行相应的心理活动为前提。将格里斯的可执行性要求恢复到核心角色允许对否定的拒绝进行更微妙的表征，根据这一点，D. 纳尔逊的强可构造否定与格里斯的原则是相容的。这揭示了无否定数学中否定的“全息”理论，其中完整的否定理论在假定的无否定环境中被“扁平化”。