Assignment 7

for the week of November 1

Instructions

By Wednesday, November 1:

· Read Chapter 9 of TTT, through the end of page 228.

· Read the biography of Kant on page 749 of Kahn.

· From Kant’s Critique of Pure Reason, read:

· Sections I and II of the introduction to the second edition, on pages 764-765.

· Sections IV, V, and VI, from page 767 until the end of page 770.

· Sections I and II of Part I of the Transcendental Doctrine of Elements, on pages 774-776.

By Monday, November 6:

· Finish reading Chapter 9 of TTT.

Turn in the homework assignment at the beginning of class on Wednesday, November 8.

Homework assignment

1. A factory has two machines making widgets. The newer machine, machine A, makes 800 widgets a day, while the older machine, machine B, makes 200 widgets a day. Among the widgets made by the new machine, 1% are defective; among the widgets made by the old machine, 2% are defective. At the end of the day, I randomly pick a widget from the day’s production.

a) Assuming each widget is equally likely to be chosen, what is the probability that the widget came from machine A? What is the probability that the widget did not come from machine A?

b) What is the probability that the widget is defective, given that it was made by machine A? What is the probability that the widget is defective, given that it was not made by machine A?

c) What is the probability that the widget is defective?

d) Now, suppose someone tells you that the widget is defective. Use Bayes’ theorem to calculate the probability that it came from machine A.

2. TTT, study question 2 on page 204.

3. TTT, review question 12 on page 218.

4. Explain Kant’s argument, in the Critique, that mathematical judgements are synthetic. (Use examples and quotes from the reading.)

5. TTT, review question 2 on page 244.