What is “formal logic”?

Abstract
Many people understand the expression “formal logic” as meaning modern mathematical logic by opposition to traditional logic before the revolution that happened in the second part of the 19th century with Boole, Frege and others. But in fact this expression was created by Kant. Some people like to quote a excerpt of the preface of the second edition of the Critic of pure reason, where Kant says that formal logic is a finished and closed science: “logic … has not been able to advance a single step, and hence is to all appearances closed and complete”. Retrospectively, this remark by Kant seems pretty ridiculous. One may wonder how such a wise man could have been so wrong. On the other hand it is quite ironic that the expression created by this philosopher has turned to be used to name the new logic that he was not able to prophesy. Of course “formal logic” is not the only expression used to denote the new logic but it is quite popular and widely spread, maybe because it means several things at the same time
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