The naturalization of logic aims at a revision of mainstream logic. In this article, I contend it is an urgent task to be completed. This new project will permit a new collaboration between logic and cognitive science. This can be accomplished doing for logic what many decades ago Quine and other philosophers undertook in the case of epistemology. First of all, this article analyzes how the naturalization can be achieved thanks to some insights provided by the recent John Woods’ book Errors of Reasoning: Naturalizing the Logic of Inference; important concepts that regard a naturalized logic are synthetically analyzed: errors (and the problem of fallacies), paradigm creep, third-way reasoning, consequence-having and consequence drawing...