
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: 
Reread 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 SkolemLowenheim
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 midterm (15%), the final (35%) and the
assignments to be set throughout the term (50%).
