Completeness of first-order logic shows poverty of aspiration rather than fulness of achievement. Implausible to maintain that truths of second-order logic are all analytic. But they are a priori . If synthetic a priori propositions are possible, Empiricism wrong. To be reasonable is not merely to follow a rule.
Reason can be creative and original.
Not out of the question to rely on other people being reasonable. Rules will still be important, but not all important. In history or literary criticism it may be right to recognise the authority of great historians or sensitive critics without being able to reduce their reasoning to explicit syllogistic form. It is difficult to see how there could be a model of Peano's postulates other than the standard one, which we pictured as the boy's railway track starting with some buffers and extending indefinitely far in one direction. This indeed is how the non-standard model starts too.