We can study logic in many different ways: Formal and informal, theoretical and applied. Very roughly speaking, critical thinking is applied informal logic ... we use it to learn how to reason better in real life.
Formal logic involves the study of abstract reasoning patterns whose validity is independent of the particular subject matter. It's abstract rigor and symbolic precision even provide the basis for mathematics and computer science.
Future posts will delve into each of these branches of logic in much more depth.
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