Philosophy 1630: Problem Sets

Some Reminders

It is a requirement of the class that all of the problem sets must be completed and submitted for marking. (I'll let you off once, if you do miss one.) Failure to submit all (but one) of the problem sets will automatically lead to a grade of NC. Please note that the requirement is that the problem sets should be "completed", and by that I mean that one has given them a proper effort. Simply turning in a piece of paper with a few random jottings does not count as completing a problem set

As with any mathematical subject-matter, it is impossible to learn this material without doing a lot of exercises. The book contains many more exercises than are assigned, and students are encouraged to do additional exercises to improve their understanding of the material. Students are also encouraged to work on the problems together—though, of course, submitted material should be a student's own work.

Harder problems are marked with an asterisk and are optional.

Problem Set Grades

Problem sets will be marked on a scale of 1--5, with half points where appropriate. A 4.0 signifies a problem set that meets expectations. That is, it displays a perfectly adequate understanding of the material covered. A 4.5 signifies something beyond that: Problems that were done especially well, for example. A 5.0 is rare and signifies a problem set that displays an especially deep understanding of the material.

Scores below 4.0 signify some inadequacy in the understanding displayed. A 3.5 probably means a few too many mistakes, but nothing to be overly concerned about. A 3.0 means that the understanding of the material displayed is barely adequate. Scores below 3.0 signify increasing difficulties. Since, as with any math class, the material is cumulative, it is recommended that anyone receiving a 3.0 or lower score see the instructor to make sure the student's difficulties are addressed.

The Problem Sets

Problem Set 1

Exercises 1.1.10, 11, and 13; Extra Problem 1

Problem Set 2

Exercises 1.3.15; one of 1.3.17-19; one of 1.3.20-21; 1.3.22; and *1.3.24; Extra Problems 2 and 3
Note: For problem 1.3.22, note that the * translation replaces sentence-letters by their negations, not every sentence. Hint: Use the result of part (i) to do part (ii). Also, try calcuating truth-tables for the translations of a few different formulae.

Problem Set 3

Exercises 1.4.32, 33, 35, 41, *43, *48
Notes: Regarding part (iii) of 1.4.32, note that the set {p, p & q} is equivalent to the set {p, p → p & q}, and the latter is independent.
Problem 1.4.33 should be the same way as Lemma 1.4.28 was, i.e., without appeal to compactness.
The last part of 1.4.16(i), in our notation, is: Cl(Γ) = Th(Mod(Γ)).

Problem Set 4

Exercises 2.1.31-33; Extra Problem 4

Problem Set 5

Exercises 2.2.40, 43 (do three cases), 44, *45, 46, 49, *50; Extra Problem 5

Problem Set 6

Exercises 2.3.65, 67, 70, 72; Extra Problem 6

Problem Set 7

Exercises 3.1.22; Extra Problem 7; 3.2.27-29; *3.2.30

Problem Set 8

Exercises 1.6.20, 21


Richard Heck Department of Philosophy Brown University