The Problem of Disagreement in Mathematical Philosophy: How Far Can It Go?

This article stresses the need for accurate interpretation of mathematical results in meta-language, e.g., in English, by philosophers of mathematics. When we try to interpret, or unfold, mathematical statements in a compact and coherent manner in meta-language, then we often produce oversimplified statements which give us nothing but anxiety. The article exposes one path, among the many possible, through sources in the philosophy of mathematics that seems to exhibit a possibility of crucial doubt related to the truths of the Standard model of arithmetic and, implied by this doubt, disagreement among mathematicians. As a result, the flawed reasoning underlying such doubt is exposed.