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Logic & Proofs

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Logic & Proofs

Carnegie Mellon @OLI
Class Start: always available
Certificate: No
Level: beginner
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Logic is a remarkable discipline. It is deeply tied to mathematics and philosophy, as correctness of argumentation is particularly crucial for these abstract disciplines. Logic systematizes and analyzes steps in reasoning: correct steps guarantee the truth of their conclusion given the truth of their premise(s); incorrect steps allow the formulation of counterexamples, i.e., of situations in which the premises are true, but the conclusion is false. Recognizing (and having conceptual tools for recognizing) the correctness or incorrectness of steps is crucial in order to critically evaluate arguments, not just in philosophy and mathematics, but also in ordinary life. This skill is honed by working in two virtual labs. In the ProofLab you learn to construct complex arguments in a strategically guided way, whereas in the TruthLab the emphasis is on finding counterexamples systematically. Topics Covered: The notions of statement and argument; Logical analysis of informal arguments; Syntax and semantics of: sentential logic, predicate logic, and identity; Natural deduction-style proofs, with an emphasis on effective and strategic proof construction; and Truth-trees, with an emphasis on systematic construction of counterexamples from completed trees.
Categories: [Mathematics]

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