<p>Isaacson’s thesis claims that Peano arithmetic is complete with respect to arithmetical truth as defined by Isaacson. According to this thesis, the incompleteness phenomenon revealed in Gödel’s incompleteness theorems does not pertain to arithmetical incompleteness. In our analysis, we discuss both the advantages and disadvantages of Isaacson’s thesis. Additionally, we propose seven case examples that may pose potential challenges to Isaacson’s thesis. To effectively defend Isaacson’s thesis, one must address these case examples. We conclude that either Isaacson’s notion of arithmetical truth is not right, or that it is difficult to defend Isaacson’s thesis.</p>