Plato's Heaven
A User's Guide with Professor James Robert Brown of the University of Toronto

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Logic and Mathematics
See how all that you have learned in the course relates to mathematics--and vice versa. Trace the origin of deductive logic to the ancient geometrician Euclid. Then consider the development of non-Euclidean geometries in the 19th century and the puzzle this posed for mathematicians.
An Introduction to Formal Logic
Logic is intellectual self-defense against such assaults on reason and also a method of quality control for checking the validity of your own views. But beyond these very practical benefits, informal logic--the kind we apply in daily life--is the gateway to an elegant and fascinating branch of philosophy known as…
Solving Sudoku
What's the key to solving Sudoku problems when you're at your wits' end? Training your mind to look for patterns and to use careful logic, just like mathematicians. This episode is packed with helpful techniques and strategies for overcoming even the most difficult Sudoku grids. Among those you'll learn about:…
Letters for Sojourners
[Hebrews, James, 1 Peter] Paul wasn't the only letter writer in the New Testament. Join Professor Koester for a discussion of the books of Hebrews, James, and 1 Peter, which sought to comfort and inspire early Christian outsiders through keeping the faith, focusing on integrity, and questioning what it means…
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Enter the fray with philosophers John Rawls and Robert Nozick, who reached different conclusions about what would constitute a just society. Begin with a thought experiment based on Christopher Nolan's movie Interstellar, pondering how you might start civilization from scratch in the fairest possible way.
Proofs and Proof Writing
Episode 8 of Geometry
The beauty of geometry is that each result logically builds on the others. Mathematicians demonstrate this chain of deduction using proofs. Learn this step-by-step process of logic and see how to construct your own proofs.
Reading Biblical Literature: Genesis to Revelation
Rightly recognized as one of the world's most important spiritual texts, the Bible has shaped thousands of years of faith, art, and human history. Yet for all its importance to believers and nonbelievers alike, we rarely engage with the Bible as a collection of unique narratives that were only later…
The Geometry of a Circle
Episode 19 of Geometry
Explore the world of circles! Learn the definition of a circle as well as what mathematicians mean when they say things like radius, chord, diameter, secant, tangent, and arc. See how these interact, and use that knowledge to prove the inscribed angle theorem and Thales' theorem.
The Classification of Triangles
Episode 15 of Geometry
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During his reign, Herod also built Greco-Roman style cities in his non-Jewish territories. Here, Professor Magness guides you through the most famous of these: the port city of Caesarea Maritima (where Paul was imprisoned, according to Acts 23-24). Comb through the ruins of the city's harbor, hippodrome, aqueducts, and more.
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See what happens if we deny the central claim of classical logic, that a proposition is either true or false. This step leads to new and useful types of reasoning called multi-valued logic and fuzzy logic. Wind up the course by considering where you've been and what logic is ultimately…
Modal Logic
Add two new operators to your first-order predicate vocabulary: a symbol for possibility and another for necessity. These allow you to deal with modal concepts, which are contingent or necessary truths. See how philosophers have used modal logic to investigate ethical obligations.