Phil 100G 02 : Logic and Critical Analysis (Spring 07)

Course Description:

This course is an introduction to logic for students with no previous experience with the subject. Logic is the formal study of arguments, where argument is intended in a very specific sense. Whenever anyone puts forward a set of reasons for accepting a sentence, e.g.:

Most scientists are alarmists, so gobal warming is not a serious problem.

Or,

If Israel goes into the war, then the casualties will be much higher. But Israel will not go into the war, so casualty levels will be low.

they are providing an argument. An argument in our sense is a sequence of statements, one of which is supposed to follow from, or be supported by, the others. In logic we are interested in characterising what makes an argument a good argument.

In this course we will study the semantics and proof theory for truth-functional (or propositional) logic and first order predicate logic with quantifiers, concluding with soundness and completeness proofs.

Syllabus

Sections marked "optional" on the book's content's page are not required reading unless I explicitly say that they are to be read (below or in class.)

Week 1 (beginning Tues 16th January)

Reading: Introduction (LPL)
Software Manual (LPL cd)

Week 2 (23nd of January)

Chapter 1 : Atomic Sentences
Chapter 2 : The Logic of Atomic Sentences

Week 3 (30th January)

Chapter 3 : The Boolean Connectives - including section 3.8
Chapter 4 : The Logic of Boolean Connectives - including sections 4.5 and 4.6

Week 4 (6th February)

Chapter 5 : Methods of Proof for Boolean Logic

Week 5 (13th February)

Chapter 6 : Formal Proofs and Boolean Logic - including section 6.6 on proofs without premises

Week 6 (20th February)

Chapter 7 : Conditionals
Chapter 8 : The Logic of Conditionals

Week 7 (27th February)

(No extra reading)

Week 8 (6th March)

Tues 6th March: Review session for the midterm

Thursday 8th March: Midterm Examination

Week 9 (12th March)

SPRING BREAK

Week 10 (20th March)

Chapter 9 : Introduction to Quantifiers
Chapter 10 : The Logic of Quantifiers

Week 11 (27th March)

Chapter 11: Mutiple Quantifiers
Chapter 12: Methods of Proof for Quantifiers

Week 12 (3rd April)

Chapter 13: Formal Proofs and Quantifiers

Week 13 (10th April)

Chapter 14: More about Quantification

Week 14 (17th April)

Chapter 16: Mathematical Induction
Chapter 17: Advanced Topics in Propositional Logic

Week 15 (24th April)

Chapter 18 : Advanced Topics in FOL (18.1-18.3 only)
Chapter 19: Soundness and Completeness (19.1 only)

Assessment

The subject is largely mathematical in nature and assessment in this course will be by way of 6 problem sets to be done at home (60%), and midterm (20%) and final (20%) examinations. Problem sets should be turned in to your TA (Ben, if your surname starts with an A, a K, or some letter in between, David, for everyone else). If you have any doubts about who your TA is, drop me an email and I'll tell you.

Assignments for this course can be downloaded as .pdf files from the table below.

Policy on Late Work

As of 27th February 2007, the class policy on late homework assignments will be as follows:

Late work will not be accepted except in cases of medical or family emergency--that is, work turned in late will receive no credit. Late work being computer files turned in after midnight (as measured by the time-stamp on the email sent to us by the Grade Grinder), or written work turned in after the Philosophy Department has closed on the day the assignment is due. As far as excuses go, this rules out computer or email failure as well as work handed in to David or Ben's department mailboxes, the TA office, and work accidentally placed in the wrong hanging folder of the file cabinet--these have been common excuses. We know this might seem harsh, but we think that the number and variety of unverifiable cover-stories offered so far makes it necessary.

Since the late policy has been unclear up to this point, we're going to handle late work on assignments 1 and 2 on a case by case basis.

Academic Misconduct

It is very important that you understand the rules for collaboration on this course. You may work with other students in order to solve the problems in your take-home problem sets, in fact, this is encouraged. However each student must write up his or her own solutions. You may not do it with another student looking over your shoulder to correct you. You may not do this from notes which another student has made, nor may you make notes on another student's written solutions. You may not lend or copy digital or paper homework solutions - at any stage of completion. Collaboration is, of course, completely forbidden during the midterm and final examinations. Sometimes it is unclear whether a hypothetical case of collaboration is permissible according to these rules, or whether it counts as misconduct, but it is your duty to ensure that ALL your collaborations are clearly permissible. One good way to do this is not to take any written notes whilst working with other students: use a chalk board or white board to work out ideas, or, if you use paper, dispose of the written solutions before you separate to write up your individual homeworks alone. The Grade Grinder incorporates sophisticated mechanisms for detecting plagiarism and I suggest you read about these mechanisms on the LPL website and in the LPL book. Students suspected of plagiarism or any other form of academic dishonesty or misconduct will be reported to the academic integrity officer for Arts and Sciences (currently Dean Killen), so that the incident may be handled in a consistent, fair manner, and so that substantiated charges of misconduct may be noted in students' records.

Related Links

The website for the book is here: http://www-csli.stanford.edu/LPL/

Richard Zach's guide to the LPL celebrities: Who are Fitch, Boole and Tarski?

Greg Restall's Great Moments in Logic

For those students who wish to take the class pass/fail, final grades for the course of C- or above will constitute a pass.