Philosophy 140A: Metalogic

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Branden Fitelson
Office: 132 Moses Hall
Office Hours: TR

Michael Caie
Office: 301 Moses
Office Hours:
T 11–11:30, W 4:30-5, and R 12–1

110 Wheeler
TR 9:30–11


[ Textbook & Supplemental Materials ] [ What, When, Where, Why? ] [ Grades, etc. ] [ Tentative Schedule ]

Textbook & Supplemental Materials

For Part I (the more technical part) of the course, we will be using Geoffrey Hunter's 1971 UC Press text Metalogic. The text should be available at the campus bookstores by the end of January. Meanwhile, I will be making the first 41 pages of the text (Part I) available online. I urge you to order a copy of the text asap if you cannot find one in Berkeley. Click here for a link to all available online copies of the text. Everyone should buy a copy of our textbook, as soon as possible. For Part II (the more philosophical part) of the course, all readings will be posted here. Stay tuned for those (they will appear here several weeks into the course).

Occasionally, I will supplement Hunter's text with handouts (mostly, taken from Peter Suber's Logical Systems course). I will not distribute paper copies of handouts to the class (except for this syllabus!).  Electronic versions of all handouts are posted on the Philosophy 140A Handouts Page at

The handouts will also be posted in our tentative schedule table, below (they will be linked there from the appropriate day's readings). All handouts will be posted either in HTML format (viewable with any unicode compatible browser – I recommend Firefox, which has been tested) or in Adobe Acrobat PDF format (viewable with Adobe's Reader software -- version 7 or later).

What, When, Where, Why?

Philosophy 140A consists of two 75-minute lectures per week [9:30-11 TR @ 110 Wheeler], and one 50-minute discussion section per week. We will arrange section times, places, and rosters during the first week of class. Keep an eye on our Sections Page for details about discussion section times and places, at

Attendance will not figure explicitly into your final grade. But, I highly recommend attending both lecture and sections regularly. The course will move quickly, and much of the material will likely be new to you (and non-trivial!). So, skipping class would almost surely be a bad idea.

The objective of this course is to learn about the metatheory of first order logic and some of its philosophical ramifications. In this sense, the course is a natural successor to 12A. The course presupposes 12A, and it will involve learning lots of new formal concepts at a rather fast pace (especially at the beginning of the course).

The course has two parts. In Part I, we will follow Hunter's book rather closely. We will go through Parts 1-3 of Hunter's text (skipping a few things along the way). Basically, this takes us up through the Löwenheim-Skolem Theorem. This should take around 11-12 weeks (see the schedule table, below, for details). For Part I of the course, I will (more or less) follow Peter Suber's Logical Systems course plan. I will rely heavily on the exellent online resources Peter has compiled for Hunter's text. Most of the handouts, and other course content that goes beyond Hunter will be adapted from Suber's online course.

In Part II. which should take up the last 3-4 weeks, we will turn to some philosophical ramifications of the metatheoretic results studied in Part I of the course. Among other possible topics, we will focus on the Löwenheim-Skolem Theorem, and some of the philosophical puzzles and arguments it spawned (including some anti-realist arguments). The material for Part II (which will involve readings from Quine, Putnam, and others) will be posted sometime after the mid-term. Say tuned for those…

Grades, Assignments, Exams, and all that...

The Basic Structure of the Course

We will have regular (almost daily) "homework" exercises, relating to each of the course lectures. These exercises will not be graded, but you are strongly encouraged to work all the exercises for each lecture, as we go along. Working these exercises as we go along is crucial for keeping up with the (fast-paced) course (they also provide good material for your discussion sections).

In addition to the ungraded "homeworks", there will be one (1) in-class quiz, one (1) project, two (2) in-class exams (including the final), and one (1) take-home exam. The final exam will be a cumulative, in-class exam (with a combination of technical and philosophical questions). See our assignments & exams page for details on the schedule of assignments and exams:

Your final grade in the course will be calculated according to the following weighted average:

See our Assignments & Exams page for all of the details about (including the schedule of) assignments and exams. We will be grading ``on a curve'' which means that a 65 might end-up being a ``B,'' depending on how the class does (statistically). After each grading episode, I will try to give you a rough idea of where ``A''s, ``B''s, etc. fall on our numerical scale (cumulatively).

Group Work

We urge people to work in groups on the "homeworks", the project, and on the take-home exam (basically, on anything in the "Take-Home" category). In fact, we will award bonus points for group work. See the "Working in Groups" handout

for all of the rules, regulations, and details concerning group work. Make sure to read that document carefully. Failure to conform to these rules could result in a charge of plagiarism.

Tentative Course Schedule

For the first 11-12 weeks, we will be following the Hunter text pretty closely. Keep a close eye on the course Home Page and the schedule table below for announcements about changes/updates to the course schedule (and other developments pertinent to the course). Aside from making announcements in lectures, the Home Page and the schedule table below will be the main mechanisms by which I will keep you informed about developments in the course (administrative or otherwise).

In the last few weeks, we will move on to philosophical readings concerning the ramifications and implications of the metatheoretical material convered in Part I of the course. These materials (which will include readings from Quine, and others) are posted on our handouts page.

The following table gives an outline of what we will be doing on each day of the course. The required readings for each day are listed, along with recommended readings and supplementary materials for that day. Be sure to carefully go over the required readings (including exercises!) before each lecture. I also encourage you to work through as much of the other recommended material as possible for each day of the course. This will help you to stay on top of things. The table also includes the timeline for "homeworks", exams, and the project. Keep a close eye on this table as we go along -- it is the main source of information for the course. This schedule is subject to change.

Week 1, January 15-19 (pp. 3-10 of Hunter)
Tu (1/16)
First class; Administrative stuff, brief introduction to the course, and pp. xi-xiii of Hunter [available online here]
Recommended: Map of Some Logical Systems, How to read proofs, Formal system assignment
Th (1/18)
Hunter Day 1, pp. 3-15 [available online here]
Recommended: Exercises for week 1 (Set 1), Sample formal system, The shadow problem
Week 2, Janurary 22-26 (pp. 16-41 of Hunter)
Tu (1/23)
Hunter Day 2, pp. 16-28 [available online here]
Recommended: A Crash Course on Infinite Sets, Exercises for week 2 (Sets 2-4)
Th (1/25)
Hunter Day 3, pp. 28-41 [available online here]
Recommended: A Crash Course on Infinite Sets, Exercises for week 2 (Sets 2-4)
Week 3, Janurary 29 - February 2 (pp. 45–62 of Hunter)
Tu (1/30)
45-minute Quiz (on infinite sets). Then, pp. 46–54 of Hunter (Michael).
Recommended: Exercises for week 3 (Sets 5 & 6)
In-class Quiz – through Day 3.
Th (2/1)
Hunter, Day 4, pp. 54-62 [available online here]
Recommended: Terms and Symbols of Propositional Logic, My Handout on the Interpolation Theorem, Exercises for week 3 (Sets 5 & 6)
Week 4, February 5-9 (pp. 62–83 of Hunter)
Tu (2/6)
Hunter Day 5, pp. 62-72
Recommended: Forbes's discussion of expressive completeness, Exercises for week 4 (Sets 7–9)
Th (2/8)

Hunter Day 6, pp. 72-83
Recommended: My Handout on the History of (PS), Exercises for week 4 (Sets 7–9)

Week 5, February 12-16 (pp. 84 – 107 of Hunter / omitting sections 30–31)
Tu (2/13)
Hunter Day 7, pp. 84-91 [last day of material on mid-term]
Recommended: My Handout on the DT for PS, Mathematical induction, more induction links: #1, #2, #3, #4, #5, Exercises for week 5 (Set 10)
Tu (2/20)

Hunter Day 8, pp. 91–95 & 105-107 [skipping sections 30 and 31]
Recommended: My Handout on (a) of Henkin's Proof, Exercises for week 6 (Sets 11&12)

Week 6, February 19-23 (pp. 107 –116 of Hunter)
Tu (2/20)

No lecture. In-class Mid-term (through Day 7).

In-class Mid-Term – through Day 7.
Th (2/22)

Hunter Day 9, pp. 107-116
Recommended: My Handout on (d) of Henkin's Proof, Exercises for week 6 (Sets 11&12)

Week 7, February 26 - March 2 (pp. 11–125 of Hunter)
Tu (2/27)

Hunter Day 10, pp. 116-125
Recommended: Exercises for week 7 (Sets 13-15), My Handout on Hiz's System,

Th (3/1)

Hunter Day 11, pp. 116-125
Day 11 is the last day of TFPL.
Recommended: Massey on Independence and Consistency in Propositional Logic, Exercises for week 7 (Sets 13-15), Review

Core/preview of formal system due.
Week 8, March 5-9 (pp. 137–152 of Hunter)
Tu (3/6)
Hunter Day 12, pp. 137-152
Recommended: Exercises for Week 8 (Sets 16-17), Terms and symbols of predicate logic
Th (3/8)
Hunter Day 13, pp. 137-152
Recommended: Exercises for Week 8 (Sets 16-17), Satisfaction, Three levels of truth
Week 9, March 12-16 (pp. 152–160 of Hunter)
Tu (3/13)

Hunter Day 14, pp. 152-160
Recommended: Exercises for Week 9 (Set 18)

Th (3/15)
Hunter Day 15, pp. 152-160
Recommended: Exercises for Week 9 (Set 18)
Week 10, March 19-23 (pp. 166–180 of Hunter)
Mon (3/20)

Hunter Day 16, pp. 166-173
Recommended: Exercises for Week 10 (Set 19)

Take-Home Mid-Term assigned.
Wed (3/22)

Hunter Day 17, pp. 173-180
Recommended: Exercises for Week 10 (Set 19)

Week 11, March 26 - 30 (SPRING BREAK)
Tu (3/27)




Th (3/29)
Week 12, April 2-6 (pp. 173–190 of Hunter)
Tu (4/3)

Hunter Day 18, pp. 173-180 (cont'd)
Recommended: Exercises for Week 12 (Set 20)

Th (4/5)

Hunter Day 19, pp. 180-190 [skipping 190-194]
Recommended: My Handout on 45.12, Exercises for Week 12 (Set 20)

Week 13, April 9-13 (pp. 180–190 of Hunter)
Tu (4/10)
Hunter Day 20, pp. 180-190
Recommended: My Handout on 45.14, Exercises for Week 13 (Set 21)
Take-Home Mid-Term due.
Th (4/12)
Hunter Day 21, pp. 180-190
Recommended: My Handout on 45.17, Exercises for Week 13 (Set 21), Löwenheim-Skolem theorem (sections 1-5)
Week 14, April 16-20 (pp. 195–205 of Hunter)
Tu (4/17)
Hunter Day 22, pp. 195-200
Recommended: Exercises for Week 14 (Set 22)
Th (4/19)
Week 15, April 23-27
Tu (4/24)
Hunter Day 24, pp. 205-208: Philosophical Ramifications 1
Recommended: Löwenheim-Skolem theorem (section 8)
Th (4/26)
Philosophical Ramifications 2
Readings TBA
Complete formal system due.
Week 16, April 30 - May 4
Tu (4/29)
Philosophical Ramifications 3
Readings TBA
Th (5/3)
Philosophical Ramifications 4 (Michael?)
Readings TBA
Week 17, May 7-9
Tu (5/8)
Review for Final Exam (Michael).

Final Exam: Tuesday, May 15, 8–11am (room TBA)