Relevant Arithmetic and Mathematical Pluralism

In The Consistency of Arithmetic and elsewhere, Meyer claims to “repeal” Goedel’s second incompleteness theorem. this paper, I review his argument, then consider two ways understanding it: from the perspective mathematical pluralism monism, respectively. Is relevant arithmetic just another legitimate practice among many, or is it a rival its classical counterpart—a corrective Goedel, setting us back on path (One) True Arithmetic? To help answer, sketch few worked examples mathematics, see what non-classical (re)formulation mathematics might look like in practice. conclude that, while unlikely that describes past present practice, so be most acceptable as pluralist enterprise, may yet prescribe more monistic future venture.