Introductory logic course designed for students from a broad range of disciplines, from mathematics and computer science to drama and creative writing.
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Logic & Proofs — Open & Free
- Description
- What students will learn
- Learning objectives by module
- Course outline
- Other course details
- System requirements
- Open & Free features
Description
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.
Who should take this course?
This is an introductory course designed for students from a broad range of disciplines, from mathematics and computer science to drama and creative writing. The highly interactive presentation makes it possible for any student to master the material. Concise multimedia lectures introduce each chapter; they discuss, in detail, the central notions and techniques presented in the text, but also articulate and motivate the learning objectives for each chapter.
Open & Free Version
The Open & Free Logic & Proofs course includes the first five chapters of Logic & Proofs, providing a basic introduction to sentential logic.
Independent Paid Version
A full version of Logic & Proofs, including both sentential and predicate logic, is also available without technical or instructor support to independent users, for a small fee. No credit is awarded for completing either the Open & Free Logic & Proofs course or the full, unsupported, Independent Paid version of the Logic & Proofs course.
Additional Course Details
In-Depth Description
Logic & Proofs is an introduction to modern symbolic logic, covering sentential and predicate logic (with identity). The course is highly interactive and engaging. It brings a fresh perspective to classical material by focusing on developing two crucial logical skills: strategic construction of proofs and the systematic search for counterexamples.
Concise multimedia lectures introduce each chapter of the course and discuss in detail central notions and techniques presented in the text. The introductory lectures articulate and motivate the learning objectives for each chapter.
LAB EXERCISES
The two crucial logical skills are developed via numerous exercises in two lab environments:
In the ProofLab, the main workbench of Logic & Proofs, students practice proof construction in a natural deduction framework. Their learning is supported by an intelligent and dynamic automated tutor. This tutor helps students, in a dialogue, to think through arguments in a strategic and systematic fashion. This Proof Tutor is making use of the automated proof search mechanism AProS; see the AProS site here.
In the TruthLab, the semantic counterpart to the ProofLab, students practice techniques for a semantic analysis of formulae and arguments. They begin with chasing truth up a parse tree, then complete truth-tables, and ultimately learn to build truth-trees for predicate formulae involving identity. The emphasis is on reading off counterexamples to invalid arguments from completed trees.
CONTENT STRUCTURE
Each chapter features both review materials and homework assignments, including quizzes and lab problems. The end-of-chapter quizzes (not included in the Open & Free version) and practice questions provide fully automated feedback to the student; the ample practice lab problems offer tutoring, while the problems in the chapter’s lab assignment do not, providing students with the opportunity to demonstrate mastery of the skills developed in completing the practice problems.
