PHI 201: Introductory Logic

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Logic is the oldest and most foundational of the university disciplines — having been taught every year for at least a thousand years. The goal is to equip you with most general possible framework for sound and rigorous reasoning — one that will support you in any intellectual activity you pursue (e.g. mathematics, politics, chemistry, English literature, law, religion, etc.). What’s more, logic aspires to be independent of the quirks of a particular natural language, programming language, or mathematical system. In this sense, logic aims to to capture that which is universally rational. (We might argue later about the extent to which logic is universal, but we will have to use logic to do that!)

Instructors

• Quanzhi: Wednesday 10:40-12:00, 1:20-2:40
• Ludovica: Wednesday 1:20-2:40, 2:55-4:15
• Pacy: Wednesday 9:00-10:20, 10:40-12:00
• Chris: Wednesday 9:00-10:20, 10:40-12:00
• Junyan: Wednesday 9:00-10:20, 10:40-12:00
• Jake: Wednesday 9:00-10:20, 10:40-12:00
• Jaehyun: Wednesday 9:00-10:20 and Thursday 1:20-2:40
• Hans: Wednesday 1:20-2:40

Course format

• One 80 minute lecture, and one 80 minute “workshop” (i.e. precept) each week
• Problem sets approximately every week (50% of grade). Drafts of all psets are linked to this page. However, the official pset is not released until seven days before the due date. One pset may be dropped.
• In class midterm exam (15% of grade)
• In class final exam (30% of grade)
• Engagement and participation (5% of grade)

Late policy

We are unable to accept late homework, except in case of a documented medical or family emergency.

Recommended work protocol

1. Weekend before lecture
   1. Look over next problem set
   2. Skim relevant section of text
2. Monday: Attend lecture and take notes
3. Between lecture and precept
   1. Read text more closely
   2. Work on pset
   3. Look at feedback on previous week’s pset
4. Wednesday: Attend precept
   1. Review previous week’s pset
   2. Work on this week’s pset
5. Optionally: visit preceptor’s office hours
6. Friday: submit pset

Academic integrity

The policy for this course is that collaboration between students is encouraged, but in no case should one student copy another’s work. That is hardly a precise criterion, but the spirit of the law is that you need to understand what you write down on your paper. If you fail to do that, then your lack of understanding will most likely reveal itself on the exam. As a general rule, we would suggest that you put away any notes from joint brainstorming sessions before writing your final answers.

Please note that ChatGPT is far from logically careful, which is precisely the skill that we are teaching (and testing) in this class.

Resources

• How Logic Works can be accessed via Princeton library jstor. You can purchase your own copy from Princeton University Press or your favorite retailer.
• Online tools: https://lemmon-checker.onrender.com
  
• The LaTeX files for the textbook can be accessed here: hhalvors/logic-works

Subject matter

While this subject has been taught for over a millenium, the content got an overhaul in the mid 1900s, when modern symbolic logic was consolidated. (The content has been stable since the 1950s.) Since then, the standard format for an introductory logic class has been to learn the “predicate calculus” in three steps: propositional logic, monadic predicate logic, polyadic predicate logic. We follow this same outline, but with a few twists.

1. We emphasize reasoning techniques (natural deduction) over calculational techniques (truth tables or trees).
2. We teach proofs before truth tables. It’s harder, but makes your brain stronger.
3. We incorporate more analysis of arguments in natural language (e.g. argument mapping).
4. We illustrate logical concepts, when helpful, by displaying them concretely in the general framework of functional programming languages. However, this course presupposes no background in programming, nor does it presuppose that students are interested in programming.

Schedule

Week 1

pset1 is due on the first Friday of classes. It covers basic concepts, some translation, and some simple proofs.

Reading: Chapters 1 and 2

Week 2

pset2 covers proofs with dependency numbers (conditional proof and $\vee$ elimination)

Reading: Chapter 3

Week 3

pset3 covers more proofs ($\vee$ elimination and RAA)

Reading: Chapter 3

Here’s a draft of the lecture notes: lecture3

Week 4

pset4 covers truth-table problems

Reading: Chapter 5 (note that we are skipping over Ch 4 for now)