Phil 100G 02 : Logic and Critical Analysis (Fall 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 - Thursday 30th August

Reading: Introduction (LPL)
Software Manual (LPL cd)
You should use this time to familiarize yourself with the computer software, sorting out technical problems so that you know what you are doing when it is time to submit the first homework assignment. There will be an (optional) practice assignment and we reccommend that you complete this as a way of familiarising yourself with the submission process.

Week 2 - 4th and 6th September

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

Week 3 - 11th and 13th Septermber

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 - 18th and 20th September

Chapter 5 : Methods of Proof for Boolean Logic

Week 5 - 25th and 27th September

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

Week 6 - 2nd and 4th October

Chapter 7 : Conditionals
Chapter 8 : The Logic of Conditionals

Week 7 - 9th and 11th October

Thursday 11th October: Review session for the midterm

Week 8 - 16th and 18th October

Tuesday 16th October: Midterm Examination

Thursday 18th October: Soundness and Completeness

Week 9 - 23rd and 25th October

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

Week 10 - 30th October and 1st November

Chapter 11: Mutiple Quantifiers

Week 11 - 6th and 8th November

Chapter 12: Methods of Proof for Quantifiers

Week 12 - 13th and 15th November

Chapter 13: Formal Proofs and Quantifiers

Week 13 - 20th November

Chapter 14: More about Quantification

No class on Thursday 22nd November (thanksgiving break)

Week 14 - 27th and 29th November

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

Week 15 - 4th and 6th December

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

Thursday 6th December: Review session for the final

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. If you have any doubts about who your TA is when it is time to submit your homework, 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

Late work will incur a penalty at a rate of 20 percent of the total possible grade every 24 hours.

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 alone. 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.

Homework Assignments

Homework assignments may be downloaded from this table.

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.