Philosophy 60 Deductive Logic 1 Spring 2019

Deductive Logic I


Catalog description

An introduction to deductive logic. Topics include: basic concepts of deductive logic; techniques of formal proof in propositional and predicate logic. 3 units.

General education

This course satisfies GE area B-5. The definition and general learning objectives of area B-5 may be reviewed here. The specific learning objectives of Area B-5 covered in this class are:

A. Cite critical observations, underlying assumptions and limitations to explain and apply important ideas and models in one or more of the following: physical science, life science, mathematics, or computer science.

B. Recognize evidence-based conclusions and form reasoned opinions about science-related matters of personal, public and ethical concern.

Informal description

In this course you will learn what it really means to prove something. A real proof is a thing of beauty, but it takes quite a bit of work to appreciate this. If this course is successful, then at least once before the end of the semester, the beauty of a deductive proof will smack you hard right between the eyes. You will shed tears of joy, and you will be forever changed. (Unfortunately, this form of success is difficult to test, and does not guarantee a passing grade.)

Real proofs do not occur anywhere except in logic, mathematics, and geometry. For example, there is no such thing as a scientific proof, in our sense of the term. There are such things as mathematical and geometrical proofs, but that is only because mathematics and geometry can be treated as extensions of logic. There is actually quite a bit more to logic than proof, however. Symbolic logic is the most precise form of notation ever developed, and has been absolutely fundamental to contemporary developments in in mathematics, linguistics, computer science and, yes, philosophy. Simply becoming comfortable with logical notation is an enormous benefit to anyone who would like to do advanced work in these fields. More generally, the course will also develop your ability to think carefully and precisely in an abstract way, which will be useful to you in all future studies.

Learning Objectives

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

(1) explain key concepts such as logical necessity, consistency, contradiction, tautology, validity, and soundness;
(2) Employ the logical connectives in formalizing arguments and write out the truth-tables for all of them;
(3) Employ formation rules to determine whether a propositional logic formula is properly formed;
(4) Use truth-tables to test for contradiction, necessity and validity;
(5) Use refutation trees to test for contradiction, necessity and validity;
(6) Formalize statements in natural language using the propositional calculus;
(7) Perform deductive proofs using the rules of the propositional calculus;
(8) Formalize statements in natural language using the predicate calculus;
(9) Employ formation rules to determine whether a propositional logic formula is properly formed;
(10) Evaluate predicate logic propositions relative to a model;
(11) Perform deductive proofs using the rules of the predicate calculus.

Course Structure

General Structure

This is a conditionally self-paced course. What this means is that generally you will study at your own pace and you will decide when to take or re-take a particular test. However, there are specific dates (see schedule page) at which tests 1-6 will no longer be available in class. If you have not passed a particular test by the time at which it is no longer available, the only way to take it is with the instructor's permission. To get the instructor's permission, you must work with the instructor or a tutor and demonstrate your mastery of the material.

After the first week of the semester it will become possible to take tests during any class meeting. However, it will never be possible to take more than one test per class meeting. Hence, it is extremely important for you to keep yourself on a strict test taking schedule. If you do not do so, there will become a point where it is logically impossible to take enough tests to pass the class. Moreover, you will not be permitted to take a test until you have passed the previous one at a designated level. This level will be high, corresponding to a B+ or A in almost all cases. The reason for this is that the material is progressive. If you do not master the material at a certain level, you will find the subsequent level impossible to understand.

Although this course is self-paced, it will not be possible to complete this course more than two weeks prior to the end of the semester. Tests will be made available as the semester develops.

If you are a self-motivated person who can do steady consistent work, you should succeed in this class. If you tend to procrastinate and base your decisions on unreasonably optimistic calculations, then you need to change these habits or you almost certainly will not succeed.

Class Meetings

All of the lecturing for this course occurs online. It is absolutely essential for you to engage the online instructional videos and to read the instructor's slides as well as the book before coming to class. Class time is devoted entirely to providing individual and small-group tutoring as well as to testing during the final half hour or so of each class. You are free to bring laptops, tablets, etc. and to engage the videos in class, as long as you use earbuds or headphones. While taking tests, you may use none of these.

In sum, class meetings are for doing work, not for listening to the professor talk.



Extensive homework assignments and practice tests will be available for every module of the course. The homework will be available on the schedule page, as will the solutions. You do not submit homework, but you will receive help with troublesome problems in class.


Prior to taking any given test you will be required to take and pass a corresponding quiz on SacCT. You may not take any test prior to passing the corresponding quiz! Doing so is grounds for failing the class. It is permissible to take these quizzes during classtime. Your grades on quizzes do not figure into your overall course grade. It is permissible to collaborate on quiz taking; however, if you are unable to pass a quiz on your own, you will almost certainly not pass the test.


Your grade in this course will be calculated on the basis of 13 possible tests. These are all closed book in-class tests. In order to receive a B or an A in this class you must additionally make yourself available for tutoring other students during class time on material covered in tests that you have already passed. See specific requirements for tutoring below.

In order to take a test, you must have passed the previous test. Passing is indicated by a smiley face on your test. If you do not see a smiley face, you did not pass the test, and must retake it. If you proceed without passing a previous test, your course grade will be indexed to the test immediately before the one you skipped. This means, e.g., that if you failed to pass test 7, but passed 8-10, you will receive a D in the course.

After the third  or fourth week of class it will become possible to get extra tutoring and test outside of class with a student assistant during specified times. Testing will only be available for students who are behind the cut-off date.  You may take no more than one test per tutoring session.


   Your grade in this course is a function of the last test that you pass, as follows.

Final test passed 1 2 3 4 5 6 7 8 9 10* 11* 12* 13*
Course grade F F F FF D CB- B B+A- A

*Requires tutoring service as described below.

However, there are further requirements that must be met as described immediately below.


In order to receive a B, B+, A- or or A in this class you must help other students learn by spending time in class tutoring. Testing will start during the second week and in class tutoring will start during the third week. This means that there are 24 class periods available for tutoring. There are a limited number of tutoring opportunities available for each session.  If you wish to tutor on a given day,  you should plan to be there at the beginning of the period.  If, on a given day, more students wish to tutor than there are spots available, preference will be given to those who did not do it the previous class meeting. and for at least the first 30 minutes of it. (This will allow time for you to take a test at the end of this period if you wish.) There will be a limited number of spots available each day, so you are not guaranteed of being able to tutor on any given today. When supply exceeds demand, preference will typically be given to those who did not tutor during the previous session. You will get credit for your tutoring time whether or not students come to you for help. Other details of the tutoring procedure will be provided in class. The minimum total contributions for each grade level are as follows:
Grade Sessions
B  5
A- 7

The highest grade you can achieve without tutoring is a B-. If you fall short of the tutoring requirements associated with your grade level, you will receive the grade associated with the number of sessions you have tutored. For example, if you pass test 12, but only tutor 6 sessions, you will receive a B+ rather than an A-.

In order to be a peer tutor you must be achieving at least a B at the time. This means that you must be on the  B track as defined in the schedule.

Please note that peer tutoring is not a way of achieving extra credit. Students who engage in tutoring but do not meet the testing standards required to achieve a B or an A do not receive credit for it.


The attendance policy for this class is unusual so be sure to take time to understand its justification. Each course grade is indexed to a required level of attendance, as represented (together with the above requirement) in the table below. You will notice that the higher the grade, the lower the attendance requirement and vice versa. The reason for this is as follows. Students who are doing well on their own are demonstrating that they need less additional help in class and are therefore given greater discretion regarding where and how to study. Alternatively, students who are struggling, are demonstrating the opposite, and must be in class for tutoring on a regular basis.

If you fall short of the attendance requirements associated with your grade level, you will receive the next lowest grade. For example, if you pass test 10, but do not have at least 15 record attendances and 5 peer tutoring sessions then you will receive a B-.

Advice: Do not fall prey to optimism bias! Plan to attend class regularly at least during the first part of the semester so that you can develop a reasonable sense of how the class is going for you.

Grade Last test passedMinimum attendancePeer tutoring
F <7NA 0
D 720 0
C- 7*18 0
C 819  0
C+* 8*17 0 
B- 916 0
B   1015 5
B+ 1114 6
A-  1213 7
A 1312 8

*C- and C+ are not grades available on the testing rubric, but they may be assigned as a final grade if a student achieves the requisite attendance and a strong but not quite passing performance on Test 8 or 9 respectively.

Regarding the above, please note the following:
  • Note that even at the D level, this is a very light attendance policy. Everyone is encouraged to attend far more frequently than required, both to help others and to receive help.
  • In order to receive attendance credit for a particular day you must be present for at least the first 30 minutes of class until the testing session begins.
  • You do not accrue points or credit of any kind simply for attending class.

Test grading and return

Due to the size of this class and the number of tests being taken, physical copies of graded tests will not be returned. (You may pick them up during office hours if you like.) Rather, they will be scanned and returned digitally. To receive digital copies of your test you must establish a Gmail account (which is an email account through Google) or register a different email with Google. This will allow me to share a folder with you in Google Drive where I may return digital copies of your tests to you. This also allows for the shortest possible return time.

Never simply assume you have passed a test. Always check your folder. If you have passed, you will see a smiley face on your test. If you do not see a smiley, you must retake the test.

Re-take policy

All tests can be retaken without a definite limit on the number of retakes. You are limited only by the fact that you may only take one test per class meeting.

Final Exam

There is no final exam for this class. However, we will meet during the scheduled final exam period so that students may take one remaining test.


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. It is also not possible to do well on tests administered later in the course if you have not learned the material covered in earlier ones.

Academic honesty

Collaborative learning will be emphasized in class. You are also 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. Note especially the requirement to have passed the relevant online quizzes prior to take a test. Taking a test prior to passing the online quiz constitutes cheating in this course.

Course materials

Textbook: Schaum's Easy Outline of Logic, Crash Course. by Nolt, Rohatyn, and Varzi.

Recommended Supplementary Text: Schaum's Outline of Logic, by Nolt, Rohatyn, and Varzi. (This is a more complete version of the easy outline and provides you with more solved problems.)

Instructional videos, problem sets, and solutions distributed on instructor's website. (See schedule.)

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.

Student resources

Do not hesitate to contact either of the following resources if you are experiencing serious distress.

Communicating with instructor

By far the most effective means of communicating with the instructor is by e-mail. Unless you send an email late at night, you will normally receive a reply within a few hours at the most. 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.