Syllabus Philosophy 60 Fall 2017

Deductive Logic II


Catalog Description

Further study of deductive logic. Topics include: principles of inference for quantified predicate logic; connectives; quantifiers; relations; sets; modality; properties of formal logical systems, e.g. consistency and completeness; and interpretations of deductive systems in mathematics, science, and ordinary language. Prerequisite: CSC 28 or PHIL 60 or instructor permission. Units: 3.0

Informal Description

In this course we will begin with methods of proof in propositional logic, quickly (re)acquainting ourselves with the semantic tree method of proof as well as natural deduction.  We will then extend our system of propositional logic to include predicate logic, identity, and functions. We will develop two systems of modal logic (Leibnizian and Free Logic) and learn to do natural deduction proofs in these systems.  In the foregoing we will develop a strong understanding of the difference between the semantics of  a system and its system of deduction. We will then introduce the relation of membership to predicate logic, see how this provides the basis of set theoretic concepts and learn to do both formal and informal proofs in set theory.  We will then learn to do strong mathematical induction and develop an understanding of the basics of recursion. We will finish the semester  by examining  Cantor's set-theoretic development of infinity, Church's theorem on the undecidability of predicate logic and an outline of Gödel's incompleteness theorems.

By the end of the course you will be able to:

(1) Do semantic proofs and natural deduction in propositional and predicate logic.
(2) Do semantic proofs and natural deduction in modal logic and free logic.
(3) Do natural deduction and informal proofs in set theory.
(4) Explain the nature of and do proofs in strong mathematical induction.
(5) Explain the nature of recursively defined functions and sets.
(6) Explain basic properties and paradoxes of infinite sets and related concepts.
(7) Explain the meaning and significance of un(soundness), (in)completeness and (un)decidability. 
(8) Summarize the structure and implications of Gödel's first incompleteness theorem

Course Requirements


There will be three in-class tests worth 25 points each. The third test occurs during the final exam period. It will be  comprehensive and will be designed to take the entire period. If you perform better on the third test than on one of the previous two tests, the grade on the lowest of the two previous tests will be raised to the grade you received on the final. This is true even if the previous lowest grade is a zero due to missing the test.


There will be homework assigned for each class meeting after the first week. Homework is assigned at the What's Up link. Each homework will identify specific problems and/or questions that must be submitted at the beginning  of class.  You may not turn in homework if you do not come to class. Homework receives a grade between 0 and 1 inclusive.  As there will be 28 homework assignments, you may accrue up to 28 points. However, your final grade is assigned on the basis of a 25 point maximum for homework. This means that you can miss 3 homeworks (and therefore be absent 3 times) and still accrue the maximum grade on homework.  If you receive more than 25 points on homework it will count as extra credit. If no homework is assigned for the date of an exam, you will get homework credit for taking the exam.

Course evaluations

There are two points of extra credit available for doing course evaluations at the end of the semester. This works as follows: The percentage of students in the class who complete the course evaluation will be multiplied by 2. The product will be added to every students point total. For example, if 80% of students do the evaluations then 1.6 points will be added to every student's final grade.


 Including extra credit there are 110 points possible, but your grade is calculated on the basis of 100.

 QuantityValueMax Possible
Tests 3 25 75
Homework 28 1 28
Course evaluations 1 2 2
Total points possible  105
Total basis  100

Sample calculation for Logan
Tests 65
Homework 15
Course evaluations 1.4
Total points81.4 

Final letter grades are assigned on a standard scale. 92% and above = A, 90-91% = A-, 88-89% = B+, 82- 87% = B, 80-81% = B-, etc. Fractional point totals are rounded up from .5 and down from < .5 You and only you are responsible for monitoring your performance in this course.  Be sure to pay close attention to the drop and withdrawal deadlines in the second page of this document.

Late policy

No assignments may be submitted  late. Under extreme documented  circumstances you may arrange to take a test early. 


 Keep up in this course! Logic is a skill.  Learning it is similar to learning math or a foreign language in that it is cumulative and that it requires you to work steadily.  For the vast majority of students it is not possible to do well on logic tests  by cramming.  

Academic honesty

You are free and encouraged to study together outside of class.  However, testing is non collaborative and subject to the CSUS academic honesty policy, which you may read at:  Academic Honesty Policy & Procedures.   Students caught cheating during any test will be failed in the course and referred to Student Affairs for disciplinary action.  

Course materials

You are not required to purchase any reading materials for this course. The primary text for this course is Logics, by John Nolt.  An electronic copy will be available free on Blackboard. It is possible to rent or purchase used hard copies of this book on Amazon. All other materials will be provided online or in Blackboard. The material from the first 3 weeks of the semester will be drawn from the instructor's Philosophy 60 course, which uses the Schaum's Easy Outline of Logic as the primary text. This book is co-authored by John Nolt and employs the notation and proof procedures employed in Logics.

A note on systems and notations

Some of you will have learned introductory symbolic logic elsewhere, and will more than likely have learned different notations and slightly different systems of proof.  It will be necessary for you to use the notations and proof procedures employed in this course.  The first three weeks of the course is dedicated to review partly for this purpose.

Students with special needs

Students who have special learning or testing needs must notify the instructor  by the end of the second week of the semester.  Students who fall into this category must visit SSWD Lassen Hall 1008 (916) 278-6955 with appropriate   documentation. This is the link to the SacState SSWD page.

Communicating with instructor

By far the most effective means of communicating with the instructor outside of class is by e-mail.  Unless you send an email late at night, you will normally receive an answer within a few hours. Re-send your e-mail if you do not.  When communicating  with  instructor by e-mail, observe the guidelines at this link.


    Minor changes in dates, times and the schedule of readings are subject to revision at the discretion of the instructor.