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Critical Thinking · Module 6

Paradoxes and Puzzles

The first five modules built the tools of clear thinking: arguments, fallacies, logic, judgement, and how we know. This module puts them to work on the most delightful stress-tests reason has ever faced — paradoxes.

A paradox is where careful reasoning seems to collide with itself. Some are surprising truths; some hide a subtle mistake; a few mark the very edge of a concept. Working through them is the ultimate workout for a careful mind, and, again and again in history, resolving a paradox has driven real progress in logic, mathematics, and science.

Lessons
7 lessons
Estimated time
~6-8 hours
Assessment
Module quiz included

Not started yet

Lessons

Lesson 1 · 16 min

The Art of the Paradox

Lesson 2 · 16 min

Paradoxes of Language and Truth

Lesson 3 · 16 min

Paradoxes of Infinity

Lesson 4 · 16 min

Paradoxes of Identity

Lesson 5 · 16 min

Paradoxes of Rationality

Lesson 6 · 16 min

Paradoxes of Self-Reference and Surprise

Lesson 7 · 16 min

What Paradoxes Teach Us

Check your understanding

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Paradoxes and Puzzles — Module Assessment

14 questions · pass mark 75%

  1. 1.In Quine's terms, a 'veridical' paradox is one that:
  2. 2.Zeno's Achilles-and-the-tortoise argument concludes that Achilles never overtakes the tortoise. This is best classified as which kind of paradox, and why?
  3. 3.What combination of ingredients is needed to generate the Liar paradox?
  4. 4.Russell's paradox concerns the set of all sets that are not members of themselves. Whom did Russell famously notify of it, and roughly when?
  5. 5.What does it mean for an infinite series to 'converge'?
  6. 6.In Hilbert's Grand Hotel, how can a hotel that is already full accommodate one more guest?
  7. 7.The Ship of Theseus paradox mainly shows that:
  8. 8.The sorites paradox (the 'paradox of the heap') is traditionally attributed to which philosopher?
  9. 9.In Newcomb's Problem, why does the dominance argument recommend taking both boxes?
  10. 10.What does Buridan's ass illustrate about rationality?
  11. 11.In the Surprise Examination paradox, why do the students first rule out Friday?
  12. 12.How does the Barber paradox differ from the surprise-examination paradox?
  13. 13.According to the lesson, what is the right first response to a paradox?
  14. 14.How did Russell's paradox affect the foundations of mathematics?
Answer every question to submit.