Paradoxes and Infinities
|Sites Offered||ATN, BRI, HKU, SCZ, SUN|
From the CTY Summer Catalog:
The second sentence is true. The first sentence is false. Are these sentences true or false? How is it that observing an orange pumpkin is seemingly evidence for the claim that all ravens are black? Students in this course explore conundrums like these as they analyze a range of mathematical and philosophical paradoxes.
Students begin by considering Zeno’s paradoxes of space and time, such as The Racecourse in which Achilles continually travels half of the remaining distance and so seemingly can never reach the finish line. To address this class of paradoxes, students are introduced to the concepts of infinite series and limits. Students also explore paradoxes of set theory, self-reference, and truth, such as Russell’s Paradox, which asks who shaves a barber who shaves all and only those who do not shave themselves. Students analyze the Paradox of the Ravens as they study paradoxes of probability and inductive reasoning. Finally, they examine the concept of infinity and its paradoxes and demonstrate that some infinities are bigger than others.
Through their investigations, students acquire skills and concepts that are foundational for higher-level mathematics. Students learn and apply the basics of set theory, logic, and mathematical proof. They leave the course with more nuanced problem-solving skills, an enriched mathematical vocabulary, and an appreciation for and insight into some of the most perplexing questions ever posed.