عنوان مقاله [English]
We first look at some controversial issues in mathematical logic. These issues are often confused by non-specialists. The main topics that we will address in this regard are: Tarski's definition of truth, Tarski's theorem on undefinability of truth, Gödel's completeness theorem and Gödel's incompleteness theorems, and first and second-order logic. Next, we will introduce some non-classical logics and their place in philosophical logic as well as logic in computer science. In addition, we discuss some philosophical issues related to logic. Among the issues we discuss are the definition of logic, the difference between logic and logical system, and the challenge of monism versus pluralism in the choice of logic. By separating logic from logical systems, we will defend the view that mathematical logic, as part of mathematics, should only be committed to the standards of mathematics. In this regard, any non-classical logic system that meets these standards will have legitimacy.