Deductive Logic II
Catalog DescriptionFurther 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 reacquainting ourselves with the tree method of proof as well as natural deduction. We will then learn to do mathematical induction and go on to prove some of the basic metalogical properties of propositional logic, including its completeness, soundness and decidability. We will then (re)acquaint ourselves with natural deduction and trees in predicate logic, and extensions of predicate logic to identity, functions and membership (i.e., set theory.), followed by an examination of the basic metalogical properties of predicate logic, including completeness, soundness and undecidability. We will examine Cantor's settheoretic development of infinity and an outline of Gödel's incompleteness theorems. We will examine the basic nature of higherorder logics. We will finish by learning some systems of modal logic and nonclassical logics.
By the end of the course you will be able to:
(1) Do proofs in propositional and predicate logic.
(2) Do proofs by induction.
(3) Summarize the basic significant metalogical properties of propositional logic.
(4) Summarize the basic significant metalogical properties of predicate logic.
(5) Prove basic properties of finite sets and related concepts.
(6) Explain basic properties of infinite sets and related concepts.
(7) Summarize the structure and implications of Gödel's first incompleteness theorem. (8) Summarize the nature of higher order logics and perform simple proofs.
(9) Summarize the significance of modal logic and related concepts.
(10) Do proofs in propositional modal logic.
(11) Summarize the motivation of nonclassical logics.
(12) Do basic proofs in some types of nonclassical logic.
Course RequirementsTests
There will be three inclass tests worth 25 points each. The third test occurs during the final exam period. It will be somewhat 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.
Homework
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. (See grading rubric below.) 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. Clarifications: (1) If homework is not assigned for a given day then you will receive 1 point for simply attending class. (2) Homework will not be assigned for the day of a test, so you will get 1 homework point for showing up to take the test.
Besides the extra credit possibility noted in the Homework section above, there will be 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.
Grading
Including extra credit there are 110 points possible, but your grade is calculated on the basis of 100.
 Quantity  Value  Max Possible  Tests  3  25  75  Homework  28  1  28  Course evaluations  1  2  2  Total points possible    105  Total basis    100

Sample calculation 
 Tests  65  Homework  15  Course evaluations  1.4  Total points  81.4  Grade  B 
Final letter grades are assigned on a standard scale. 92% and above = A, 9091% = A, 8889% = B+, 82 87% = B, 8081% = 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 policyNo assignments may be submitted late. Under extreme documented circumstances you may arrange to take a test early.
Keep up in this course yo! 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.
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.
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 in Canvas. It is possible to rent or purchase used hard copies of this book on Amazon. All other materials will be provided online or in Canvas. The material from the first 34 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 coauthored by John Nolt and employs the notation and proof procedures employed in Logics.
A note on systems and notationsSome 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)
2786955 with appropriate documentation. This is the link to the SacState SSWD page.
Communicating with instructorBy far the most effective means of communicating with the instructor outside of class is by email. Unless you send an email late at night, you will normally receive an answer within a few hours. Resend your email if you do not. When communicating with instructor by email, observe the guidelines at this link.
Caveat
Minor changes in dates, times and the schedule of
readings are subject to revision at the discretion of the instructor.

