ADVANCED LOGIC
Offered Spring 2001
Tuesdays and Thursday 11:00 AM - 12:15 PM
503 Main Building


Professor Kit Fine
kf14@nyu.edu
Office hours: Tuesdays at 12:15 PM

TA: Joshua Schechter
js665@nyu.edu
Exercise sessions: Thursdays at 5:00 PM
Offices hours: by appointment


Assignments

Thursday, January 18th:

Read the Appendix sections here. Complete the six exercises on number induction.

Tuesday, January 23th:

Read Chapter I.1. Please complete all of the drill problems for Chapter I.1 (those with a [d] after the number). It is highly recommended that you try several of the exercise problems (those with an [e]), as well.

Thursday, January 25th:

Read Chapter I.2. Complete the four exercises on formula induction in the Appendix. These will be collected in class. (In 3, occurrences of "of" should be replaced by "or". In 4(ii), exercise 9 refers to exercise 3. You may ignore 4(i).)

Tuesday, January 30th:

Read Chapter I.3.

Thursday, February 1st:

Read Chapter I.4. Please complete the drill and exercise problems for Chapter I.2 (and for Chapter I.1 if you have not already done so).

Tuesday, February 6th:

Read Chapter I.5.

Thursday, February 8th:

Complete exercises 1 through 3 of Chapter I.4. These will be collected in class.

Tuesday, February 13th:

Read Chapter I.6.

Thursday, February 15th:

Complete these exercises (for Chapter I.5).

Tuesday, February 27th:

Read Chapter I.7. Complete these exercises (for Chapters I.5 and I.6). These will be collected in class.

Thursday, March 1st:

Read Chapter I.8 and Chapter I.9.

Tuesday, March 6th:

We are now in Part II of the text. Read Chapter II.1 and Chapter II.2.

Thursday, March 8th:

Try the Practice Midterm. (Recall that the midterm will be a closed book, one hour and fifteen minute exam.) It is highly recommended that you complete all of the problems. They will be discussed in class after break.

Here is a solution for problem three, part iii of the last set of exercises.

Tuesday, March 20th:

Re-read Chapter II.1 and Chapter II.2.

Thursday, March 22nd:

Complete questions 1, 2, and 4 from Chapter II.1. These will be collected in classs.

Thursday, March 29th:

Read Chapter II.3 and Chapter II.4. Try problem 0 of chapter II.2.

Thursday, April 5th:

Complete these exercises (for Chapter II.2). These will be collected in class.

Thursday, April 12th:

Read Chapter II.5. Complete these exercises (for Chapter II.4). These will not be collected.

Tuesday, April 24th:

Complete these exercises (for Chapter II.5). These will be collected in class.

Here is the Mock Final.

Here is a short proof of the existence of nonstandard models for arithmetic.

Book Sections

Note: Sections of the book are available on this page in PDF format. If your web browser cannot handle this, download the free Adobe Acrobat Reader. A paper copy of each section is also available in the Philosophy Department library for Xeroxing.


Course Description

We shall cover basic metatheory for sentence and predicate logic (up to the completeness theorem). There will be some discussion of philosophical issues though the main emphasis will be on the technical material. The only required text is the book by Fine and Kuhn. It will be available on this web page in installments. A paper copy will also be available in the Philosophy Department library for Xeroxing.

The following topics will be covered in the metatheory of sentence and predicate logic: syntax (substitution, unique readability and abbreviation); semantics (formal and informal concepts of truth and validity); axiomatics (proofs, derivations, the deduction theorem and other basic metalogical results), completeness (and its consequences, such as compactness, decidability for sentence logic, the Skolem-Lowenheim theorem).


Prerequisites

It is important to have done some previous logic and to be comfortable with abstract mathematical reasoning.


Course Format

We will systematically go through the text in class. It is very important for students to do the reading in advance and to do the weekly assignments. Half of these will be handed in for grading.


Evaluation

Evaluation will be based upon the mid-term (15%), the final (35%) and the assignments to be set throughout the term (50%).




updated 4/20/01
philo.web@nyu.edu