Mathematics, Philosophy, and the “Real World”

Overview

Discover how mathematics helped stimulate the development of Western philosophy and shaped how these fundamental ideas and practices can be applied to a fascinating range of areas and experiences. This course guides learners through the rich interplay of mathematics and philosophy over time.

Course Instructor

Taught by Professor Judith V. Grabiner, this course emphasizes the critical role mathematics plays in philosophical thought and its applications in various domains.

Video Lessons

1. What’s It All About?
   • Duration: 33 min
   • Description: Introduction to the course, highlighting the significance of mathematics in philosophical contexts.

2. You Bet Your Life—Statistics and Medicine
   • Duration: 32 min
   • Description: Explore how statistical reasoning can influence medical decisions, illustrated by real-world examples.

3. You Bet Your Life—Cost-Benefit Analysis
   • Duration: 31 min
   • Description: Examine the application of cost-benefit analysis in decision-making frameworks.

• Popular Statistics—Averages and Base Rates
  • Duration: 30 min
  • Description: Investigate different ways to calculate averages and examine how these measures can mislead.

5. Popular Statistics—Graphs
   • Duration: 32 min
   • Description: Learn how to critically evaluate graphs to discern their accuracy and effectiveness.

• Popular Statistics—Polling and Sampling
  • Duration: 31 min
  • Description: Understand public opinion polling and the importance of accurate sampling methods.

7. The Birth of Social Statistics
   • Duration: 31 min
   • Description: Explore how social statistics emerged through the work of key historical figures.

8. Probability, Multiplication, and Permutations
   • Duration: 31 min
   • Description: Dive into probability concepts and their mathematical applications.

9. Combinations and Probability Graphs
   • Duration: 31 min
   • Description: Examine the relationship between probability and combinatorial concepts through practical examples.

• Probability, Determinism, and Free Will
  • Duration: 31 min
  • Description: Explore philosophical implications surrounding free will in the context of probability.

11. Probability Problems for Fun and Profit
    • Duration: 30 min
    • Description: Engage with various probability problems that relate to real-life situations.

12. Probability and Modern Science
    • Duration: 32 min
    • Description: Investigate the application of probability theory in genetics and social sciences.

13. From Probability to Certainty
    • Duration: 31 min
    • Description: Discuss the distinctions between probabilistic reasoning and absolute logical reasoning.

14. Appearance and Reality—Plato’s Divided Line
    • Duration: 30 min
    • Description: Connect Plato’s philosophical ideas to mathematical thought, particularly in geometry.

15. Plato’s Cave—The Nature of Learning
    • Duration: 30 min
    • Description: Analyze Plato’s allegory of the cave and its implications for knowledge and learning.

• Euclid’s “Elements” – Background and Structure
  • Duration: 30 min
  • Description: Explore Euclid’s influential work and its foundational role in mathematics.

17. Euclid’s “Elements” – A Model of Reasoning
    • Duration: 31 min
    • Description: Examine the logical structure within Euclid’s “Elements” and its significance in mathematics.

• Logic and Logical Fallacies—Why They Matter
  • Duration: 30 min
  • Description: Study the foundations of logic and identify common logical fallacies.

• Plato’s “Meno”—How Learning Is Possible
  • Duration: 29 min
  • Description: Investigate Plato’s theories of learning and knowledge through the lens of number theory.

20. More Euclidean Proofs, Direct and Indirect
    • Duration: 29 min
    • Description: Explore direct and indirect proofs used in Euclidean geometry.

21. Descartes—Method and Mathematics
    • Duration: 30 min
    • Description: Examine Descartes’s influence on modern philosophy and mathematics.

22. Spinoza and Jefferson
    • Duration: 31 min
    • Description: Discuss the philosophical contributions of Spinoza and Jefferson regarding rational discourse.

23. Consensus and Optimism in the 18th Century
    • Duration: 30 min
    • Description: Highlight key ideas of the 18th century that merged mathematics with philosophical thought.

24. Euclid—Parallels, Without Postulate 5
    • Duration: 31 min
    • Description: Investigate Euclid’s fifth postulate concerning parallel lines and its impact on geometry.