Philosophy 240.501-509 — Syllabus
Spring Semester 2024

This primary purpose of this course is to introduce students to formal techniques for evaluating arguments. Our primary focus will be on deductive reasoning, which will consist in the study of three different logical systems: categorical logic, propositional logic, and predicate logic. Categorical logic (a.k.a. syllogistic logic) — which formed the basis of logic for over two thousand years — is the study of arguments whose constituent sentences express certain relations between classes (or categories) of things. Propositional logic (a.k.a. Boolean logic) is the study of arguments that depend on the a number of important sentence-connecting expressions in ordinary language like and, or, and not — expressions whose logic also lies at the foundation of modern computer systems. Predicate logic (a.k.a. first-order logic) extends propositional logic to arguments that depend on the linguistic phenomena of predication (e.g., “Socrates is a philosopher”) and quantification (e.g., “All prime numbers except 2 are odd”). Predicate logic arose in the 19th century originally to aid in the clarification of mathematical arguments but has since extended its reach considerably into the fields of (notably) philosophy, linguistics, and artificial intelligence. To study these various logical systems, we develop in each case an appropriate formal language — a rigorously defined symbolic system — for representing a relevant class of natural language sentences. We then introduce a variety of mathematical methods for evaluating arguments that are formalized in the relevant formal language, notably, Venn diagrams (for categorical logic), truth tables (for propositional logic), and formal deductive systems (for both propositional and predicate logic).

In the final section of the course, we will focus upon the notion of probability, a notion that is at the heart, not only of scientific and statistical reasoning, but of much commonsense reasoning: our decisions are often based on our judgments of how likely certain outcomes are if we choose one way rather than another. In our study, we will first identity the eight basic mathematical axioms, or rules, of the probability calculus, a mathematical theory that enables us to calculate the probabilities of complex propositions in terms of the probabilities of their component parts. We will conclude our overview of probability with the examination of a crucial consequence of the probability calculus known as Bayes’ Theorem. The theorem provides an important insight into how the strength of our belief in a hypothesis should be adjusted in light of the evidence we have for it and, hence, is particularly useful in applied situations like medical diagnosis.

Learning Outcomes

At the end of the course, students will be able to:

1. Represent information in symbolic forms, notably the formal languages of categorical, propositional, and predicate logic.
2. Interpret and evaluate formalized arguments by means of formal semantic and deductive models, notably, Venn diagrams, truth tables, and formal deductive systems.
3. Calculate complex probabilities on the basis of the eight mathematical axioms of the probability calculus and Bayes’ Theorem.
4. Identify and evaluate assumptions in both inductive and deductive reasoning as they appear in our daily experience.
5. Express an understanding of the fundamental concepts of deductive (categorical, propositional, and predicate) logic, inductive logic, and probability theory, including: formal language, Boolean operator, quantification, class, argument, validity, proof, probability, probability calculus, and Bayes’ Theorem.

As described more fully on the course homepage, on Mondays and Wednesdays, I will lecture on the material in the book, and on Wednesday, Thursday, or Friday you will also attend a lab that will feature an online quiz. Note that the labs will all meet in YMCA 114. Lab time can also be used for getting help from your TA, who will be leading the session.

We are fortunate to have a Supplemental Instruction (SI) leader, Ms Maddy Kampes, this semester! (See →HERE← for details about the SI program.) She will be offering two regularly scheduled help sessions each week:

Day	Time	Location
Monday	7:00pm-8:15pm	BLOC 163
Thursday	7:00pm-8:15pm	ILCB 229

Maddy has also created a PHIL 240 SI website that contains her schedule, contact info, and other useful info.

Course Text (required)

D. Howard-Snyder, F. Howard-Snyder, R. Wasserman, The Power of Logic, McGraw-Hill, 2020 (6th Edition — earlier editions are not recommended). As you'll see after clicking the preceding link, you have three options:

• "eBook": An electronic version of the text;
• "Print": A printed text;
• "Connect": An electronic version of the text + the McGraw-Hill Connect site for the text.

You can either rent or purchase the text, but I would recommend renting unless you think the text will be useful to you in the future (which it well may be, especially if you are pre-law). I would also strongly recommend that you opt for one of the two eBook options. Of the two, I do recommend the McGraw-Hill Connect option ($95) which gives you access to the eBook and a lot of additional study resources that will help you to understand the concepts and methods we will be discussing. The Power of Logic Web Tutor will still be the site you use the most, because you can actually work problems there, but the resources on Connect are in my opinion worth the extra $41. To activate Connect, you will have to “register” for this course at their site. You can do so by clicking →HERE←. Those students who wish to forego the eBook options can rent a hard copy from the Aggie Bookstore or purchase one from McGraw-Hill.

NB: Some of your peers may have told you that you do not need the text for this course, that my slides and the Web Tutor are enough. Do not believe them! Unless you are both extremely gifted and have an incredible work either, the text is absolutely essential to your success in this course! It contains a ton of excellent exposition and, as noted, the Connect version of the text has a bunch of additional study features to help you understand the material.

The Slack Channel

As noted on the course homepage, I will be using Slack as our primary means of communication, so it is important that you join the channel — "#phil240-spring24" — that I have set up for the course in the TAMU Slack workspace to ensure that you won't miss any critical information. This involves one, two, or three (easy) steps.

1. If you haven't yet, claim your TAMU NetID by clicking →HERE←.
2. Click →HERE← to join or (if you've already joined) sign in to the TAMU Slack workspace. You will be redirected to a Microsoft login screen.)
• If you have the Slack app installed, go ahead and let your browser open it.
3. Use your full TAMU email address to sign in! (E.g., I would use "cmenzel@tamu.edu".)
4. You'll be sent a confirmation code via your TAMU email; copy it and enter it into the space provided.
5. You are now in the TAMU Slack workspace. In the maroon-colored column to the left click on "More" and select "All Channels".
6. In the search bar (where your cursor should be) search for "phil240". That should bring up our channel #phil240-spring24. Click the "Join" button over to the right.

That's it! The channel should now appear over in the left column. Once you have joined the channel, please use it exclusively to communicate with me or your TA. In particular, don't use email, as it is too easy for emails to get lost or overlooked and, even more importantly, it is by nature slow and inefficient. By contrast, Slack allows us to communicate in real time, so it is vastly faster and more effective; there is even an option to switch from text to video for direct, face-to-face discussion.

Slack works perfectly well in your browser but there is a dedicated app for Windows and MacOS. I would also recommend that you install it on your Android or Apple mobile devices and turn on notifications so you won't miss any messages. (You can of course silence notifications whenever you like.)

Grading Policy

Exams are designed to test the student’s mastery of the various logics and methods that will be studied in the course. Your final score is determined by your performance on three exams and the weekly quizzes. (Extra credit problems are sometimes announced ad hoc during lectures or via the Slack channel.) Your exam average will count toward 75% of your final score and the average of your weekly quizzes over the semester will count toward 25%. (Any extra credit a student has earned will be added on top of that score.) I throw out your lowest quiz score, so you can afford to have one unexcused absence from the labs without it affecting your average. Your final grade will then be determined by your final score. As a rough rule, 90 and above will be an A, 80 up to 90 will be a B, and so on. I do round scores like 89.5 up to the next whole number, and the cutoff between grades, or for a passing grade, might dip slightly lower.

Concerning the labs. The labs are intended to be low-stress affairs. The quizzes are designed to help you understand the material presented in the lectures for that week and are not particularly difficult. Moreover, You are encouraged to work with a partner, and you can also consult other students in your vicinity. Your TA will also help guide you toward a correct solution. You will be awarded at least 50 (out of 100) points just for showing up and making a reasonable effort to complete the quiz. That said: You must take the weekly quizzes in the logic lab for your assigned section in order to get credit unless other arrangements have been made with your instructor or your TA. Quizzes taken from outside the Logic Lab when without permission will be treated as academic dishonesty.

A few other things to note:

• All exams, including the final, are in CHEM 100.
• Bring a blue book to your exams unless instructed otherwise.
• Midterm dates will be confirmed with at least 7 days notice.

Attendance Policy

The university views class attendance and participation as an individual student responsibility. Students are expected to attend class and to complete all assignments. Please refer to Student Rule 7 in its entirety for information about excused absences, including definitions, and related documentation and timelines.

Make-up Policy and Procedures

Students will be excused from attending class on the day of an exam or quiz for the reasons stated in Student Rule 7. I am also willing to excuse students who are participating in some Rec Sports club competitions, notably (among others) collegiate cycling and triathlon races. Please contact me well in advance to see whether I will allow you to make up an exam that conflicts with an event you would like to participate in.) In any case, written documentation from an appropriate figure is required. In the case of illness or other medical issues, the figure in question must be a doctor or other qualified and appropriate medical professional. The note must be on official stationery and must include full contact information. If you need to make up an exam or quiz, arrange a time to do so with your TA and be sure to either email your documentation to him or her ahead of time or (if you do your make-up in person) bring your documentation with you; you will not be permitted to make up your exam without it. NB: Exams/quizzes must be made up by the end of the week following the day of the scheduled exam/quiz unless circumstances do not permit it. In such cases, your instructor must be notified as soon as circumstances permit to discuss your situation. Please refer to Student Rule 7 in its entirety for information about makeup work, including definitions, and related documentation and timelines.

Absences related to Title IX of the Education Amendments of 1972 may necessitate a period of more than 30 days for make-up work, and the timeframe for make-up work should be agreed upon by the student and instructor” (Student Rule 7, Section 7.4.1).

“The instructor is under no obligation to provide an opportunity for the student to make up work missed because of an unexcused absence.” (Student Rule 7, Section 7.4.2) Students who request an excused absence are expected to uphold the Aggie Honor Code and Student Conduct Code. (See Student Rule 24.)

Lecture and Exam Schedule

Here follows the lecture and exam schedule for the course. Clicking on any of the section numbers below will download the PDF containing the slides for my lecture for that section. Prior to each lecture, you should download the PDF for that lecture and load it into your favorite PDF app on your computer or tablet (or print it out) so that you can add my annotations and/or your own in class. Because I review the slides for each lecture a few days ahead of time and often make small changes, do not download them all at once. Rather, wait until the day before, or if possible the day of, class to download the relevant PDF.

NB: Labs meet every week unless explicitly noted on the syllabus! Week # Dates Topics Sections CATEGORICAL LOGIC 1 15 Jan 17 Jan Martin Luther King Day! Introduction and Logistics No labs this week! 1.1 2 22 Jan 24 Jan Standard Forms of Categorical Statements Mood and Figure; Venn Diagrams 5.1 6.1, 6.3 3 29 Jan 31 Jan Venn Diagrams (continued) Rules for Evaluating Syllogisms 6.3 6.5     STATEMENT LOGIC   4 05 Feb 07 Feb Symbolizing the Logical Form of Arguments Truth Tables for Boolean Connectives 7.1 7.2 5 12 Feb 14 Feb Evaluating Validity: The Truth Table Method The Abbreviated Truth Table Method 7.3 7.4 6 19 Feb Review 21 Feb EXAM 1 No labs this week! 7 26 Feb 28 Feb Implicational Rules of Inference Equivalence Rules I 8.1 8.2 8 04 Mar 06 Mar Equivalence Rules II Conditional Proof 8.3 8.4 9 11 Mar 13 Mar SPRING BREAK 10 18 Mar 20 Mar Reductio ad Absurdum (RAA) Theorems 8.5 8.6 11 25 Mar Review 27 Mar Exam 2 No labs this week!     PREDICATE LOGIC   12 01 Apr 03 Apr The Formal Language of Predicate Logic Universal Instantiation; Existential Generalization 9.1 9.3 13 08 Apr 10 Apr Existential Instantiation; Universal Generalization Quantifier Negation, RAA, and CP 9.3 9.4 14 15 Apr 17 Apr The Logic of Relations: Symbolization The Logic of Relations: Proofs 9.5 9.6     PROBABILITY THEORY   15 22 Apr 24 Apr The Probability Calculus: Rules 1-5 The Probability Calculus: Rules 6-8 10.4 10.4 16 29 Apr Bayes’ Theorem 10.4 07 May FINAL EXAM — 10:30am-12:30pm!

Academic Integrity Statement and Policy

An Aggie does not lie, cheat or steal, or tolerate those who do.

Texas A&M University students are responsible for authenticating all work submitted to an instructor. If asked, students must be able to produce proof that the item submitted is indeed the work of that student. Students must keep appropriate records at all times. The inability to authenticate one’s work, should the instructor request it, may be sufficient grounds to initiate an academic misconduct case (Section 20.1.2.3, Student Rule 20). You can learn more about the Aggie Honor System Office Rules and Procedures, academic integrity, and your rights and responsibilities at the Aggie Honor System Office website.

Americans with Disabilities Act (ADA) Policy Statement

Texas A&M University is committed to providing equitable access to learning opportunities for all students. If you experience barriers to your education due to a disability or think you may have a disability, please contact Disability Resources in the Student Services Building or at (979) 845-1637 or visit the TAMU Disability Resources website. Disabilities may include, but are not limited, to attentional, learning, mental health, sensory, physical, or chronic health conditions. All students are encouraged to discuss their disability related needs with Disability Resources and their instructors as soon as possible.

Title IX and Statement on Limits to Confidentiality

Texas A&M University is committed to fostering a learning environment that is safe and productive for all. University policies and federal and state laws prohibit gender-based discrimination and sexual harassment, including sexual assault, sexual exploitation, domestic violence, dating violence, and stalking.

With the exception of some medical and mental health providers, all university employees (including full and part-time faculty, staff, paid graduate assistants, student workers, etc.) are Mandatory Reporters and must report to the Title IX Office if the employee experiences, observes, or becomes aware of an incident that meets the following conditions (see University Rule 08.01.01.M1):

• The incident is reasonably believed to be discrimination or harassment.
• The incident is alleged to have been committed by or against a person who, at the time of the incident, was (1) a student enrolled at the University or (2) an employee of the University.

Mandatory Reporters must file a report regardless of how the information comes to their attention – including but not limited to face-to-face conversations, a written class assignment or paper, class discussion, email, text, or social media post. Although Mandatory Reporters must file a report, in most instances, you will be able to control how the report is handled, including whether or not to pursue a formal investigation. The University’s goal is to make sure you are aware of the range of options available to you and to ensure access to the resources you need. Students wishing to discuss concerns in a confidential setting are encouraged to make an appointment with Counseling and Psychological Services (CAPS).

Students can learn more about filing a report, accessing supportive resources, and navigating the Title IX investigation and resolution process on the University’s Title IX webpage.

Statement on Mental Health and Wellness

Texas A&M University recognizes that mental health and wellness are critical factors that influence a student’s academic success and overall wellbeing. Students are encouraged to engage in healthy self-care by utilizing the resources and services available from Counseling and Psychological Services (CAPS). Students who need someone to talk to can CAPS or the TAMU Helpline (979-845-2700) from 4:00 p.m. to 8:00 a.m. weekdays and 24 hours on weekends. 24-hour emergency help is also available through the 988 Suicide & Crisis Lifeline (Dial 988) or at 988lifeline.org.