## syllabus

- Instructor: Dr. Max Weiss
- Instructor email:
`max@whythis.net`

- Class Meetings: TTh 12:00-1:15, Stokes n209
- Office hours: TTh 1:30-3:00
- Office location: Stokes n326

### Overview

The systematic study of valid reasoning is an ancient endeavor, dating back at least to the works of Aristotle (ca 350BC). Indeed, for two millennia after Aristotle logic developed little, so that in 1787 Kant could write: "Since Aristotle... logic has not been able to advance a single step, and is thus to all appearance a closed and completed doctrine".

In the late 19th century, modern logic arose from a crisis. Puzzled by paradoxes in the foundations of calculus, mathematicians became entangled with the analysis of infinity. This, in turn, led mathematicians to try to determine general standards of correct reasoning.

This course is an introduction to modern logic. We will study several logical systems, including propositional logic, modal logic, and first-order predicate logic. We will also carefully develop the theoretical apparatus which surrounds them. In each case, the apparatus includes a recursive specificaiton of syntax, semantic definitions of possible world, of truth, and of validity, and complete codification of valid inference in a system of natural deduction. As time and interest permit, we will also explore the philosophical significance of the various steps in this program.

### Website

The course website is at

`http://whythis.net/logic`

.

Essential resources, including all due dates, readings, assignments, and solutions, will be posted here. You will find your marks there too.

To reach these materials you'll need to sign up at the site, like this:

- load
`http://whythis.net/logic`

, and click`/signin`

- click
`google`

, and select your Boston College email address - at the ensuing
`affiliate`

page, enter the code [redacted for public circulation!]

To sign in from another device, simply repeat steps 1 and 2 above.

### Coursework

For the sake of evaluation, coursework will broken into these components, and weighted by units as follows.

- Twelve homework assignments (two units)
- Two midterms (two units)
- Final exam (two units)
- Attendance and participation (one unit)

You will receive a single letter grade for each component. Your final grade will be the average of your highest six marks on these seven units.

### Reading

All reading assignments will be posted on the course website. The readings will in general be short by number of pages—perhaps six to ten pages per week—but you should expect to spend some time with them. Some concepts in the course will be subtle. You will be expected to master all details of the content of the readings assigned.

### Homework

Studying logic is like learning a musical instrument: you learn by doing. Although we'll work through material together in class, the homework is intended to be the crucial means by which you make progress in this course. Note, also, that the material is cumulative: so keep with it!

As an academic discipline, logic is highly collaborative. People benefit by talking through problems together, until everyone reaches a satisfactory understanding. Naturally, submitted coursework should reflect the understanding reached by you, since if it reflects another student's understanding instead, then the instructor's feedback will be misdirected.

Homework solutions will be posted shortly after the due date. Late assigments will not be accepted.

### Midterms and exam

Midterm and exam questions will in general resemble questions from preceding homework assignments.

So that everyone is on the same page, the instructor will answer questions of the form "what will be on the quiz/exam" only to the entire class.

The midterms are scheduled for the Thursdays of October 12th and November 16th.

The final exam will be given on Wednesday, December 13th, in the same place as the usual class meetings.

### Attendance and participation

Your mark on this component depends partly on attendance and partly on contributing to class discussion. It will equal the average of your marks on the other components, unless your attendance and participation are exemplary.

### Schedule

Here is a tentative schedule of topics, readings and assignments. I may adjust the dosage as we go along. As noted above, the `/schedule`

page of the course website presents ultimate version.

#### Unit 1, weeks 1-2: Deduction and validity

What is valid reasoning? We'll start with examples, a bunch of puzzles to be solved using only rigorous deductive argumentation.

This will motivate the question: when is a deductive argument correct, or logically valid? An intuitive, but only provisional, answer to this question will be given. The provisional answer invokes the notions of "truth" and of "possible world". Clarifying these informal notions, and so making the concept of validity scientifically acceptable, will be a primary goal of the rest of the course.

#### Unit 2, weeks 3-7: Propositional logic

In this segment, we will introduce an elementary formal system, that of truth-functional logic. The idea of truth-functional logic is that the truth or falsehood of a statement can sometimes be determined by the truth or falsehood of simpler statements from which it is constructed. For example, "it's not raining" is false just in case "it's raining" is true.

The study of truth-functional logic begins by introducing a formal language. This involves two components. A syntax specifies a system of grammatical rules. Then a semantics supplies a notion of 'possible world' which is suitable for the language, and then explains how possible worlds make sentences true or false.

Once the language has been introduced, we can say precisely what counts as a valid argument in the language. We'll then develop a formal method of deductive reasoning for truth-functional logic.

As a dessert topic, we'll briefly consider modal logic, the systematizatin of connectives which are not truth-functional, such as "it will become true that...", "Lucy knows that...", and "it might have happened that...".

#### Unit 3, weeks 8-15: Predicate logic

Although propositional logic is a rich source of puzzles and theoretical insights, its underlying conception of logical structure is severely limited. It cannot explain, for example, the fact that "horses are mammals" logically implies "horses' tails are mammals' tails". Nor, does it help us to see whether "some critics admire all artists who aren't admired universally" implies "some artists are universally admired".

In this segment, we will develop the richer system of first-order predicate logic. Predicate logic breaks down statements into smaller parts, namely terms and predicates. While including the materials of truth-functional logic, it also introduces a new kind of connective, the quantifier, which yields a deep analysis of generality.

We'll conclude this segment too with a dessert topic, TBA.