Courses |

Intermediate Logic

Mon, 01 Jan 2024 00:00:00 +0000

We explore the power and limitations of formal systems of reasoning.

Course Description

We will explore traditional and contemporary responses to questions that have kept folks across generations up at night, including: Should you believe what you hear? What do we know (if anything)? What does it mean to have a mind? Are our best scientific theories true descriptionsAfter the crisis in mathematics ushered in by Russell’s paradox, developments in formal logic offered renewed hope for foundational security. This course covers its major success stories—namely, the development of a formal notion of syntax and semantics for which the classical rules of inference are sound (everything they prove is true) and complete (everything true is provable). We also face new problems, like Skolem’s paradox, which notes that many logical theories cannot single out their intended models. We’ll conclude by turning to intuitionistic logic, exploring how these sorts of problems afford opportunities to characterize hidden structure in our reasoning.

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Introduction to (Western) Philosophy

Mon, 01 Jan 2024 00:00:00 +0000

What is philosophy, anyway? In this introductory course, we aim to figure that out by getting our hands dirty and doing it.

Course Description

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Philosophy of Science

Fri, 01 Sep 2023 00:00:00 +0000

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Course Description

Scientific theories are powerful! They make stunningly accurate predictions and offer satisfying explanations of phenomena around us. But what makes these theories so successful? How much do they really tell us about the world? And just what makes an explanation “scientific,” anyhow? We will review historical and contemporary approaches to answering these questions, covering topics such as the reality of unobservable entities, how we choose between competing theories, how old theories reduce to new ones (if they do at all), and the nature of scientific explanation. This course is self-contained; no previous scientific or mathematical training is required.

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Advanced Logic

Sat, 01 Apr 2023 00:00:00 +0000

We explore the limits of what we can know with and about formal systems of reasoning.

Course Description

Folks usually hear about Gödel’s famous incompleteness theorems—slogan-ized as “logic can’t prove its own consistency”—before they ever see them. Some bemoan the results as a fundamental limit on the certainty of our reasoning; others celebrate them as evidence that it’s impossible to reduce human thought to a computer program. We’ll take a close look and decide for ourselves. In addition to building the tools to state and prove Gödel’s theorems, we will assess how second-order logic fares against analogs of Gödel’s arguments.

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