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LING 1050 - Language and Formal Reasoning

People talk. People think. Other creatures also think, though not so well as people, but they don’t talk. These two facts—that only people talk and that people think better than other creatures—are related facts. This course is about why and how these facts are related. The kind of thinking we study in the course is called reasoning: transitions in thought where some thoughts (or beliefs) provide the grounds for arriving at other thoughts (or beliefs). Our central question is this: Why and how does having the ability to talk improve the ability to reason? Our answer to this question has two parts: (1) understanding that “having the ability to talk” requires “knowing a language” (including Sign languages that aren’t spoken) and (2) uncovering (some of) what we know when we know a language. We use set theory to develop a formal model that uncovers the parts of language that help to explain human reasoning abilities. Using the set theoretic formal system, students do proofs of arguments that have long been studied (syllogisms), and we also analyze other reasoning patterns and language phenomena. Ultimately, we discover that an appropriately developed formal system provides us with a remarkable tool for our explicitly thinking and talking about our talking and thinking.
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