Philosophy 310: Valid Reasoning II
Professor: Craig DeLancey
Office: Campus Center 212A
Office Hours: MF 3:00 - 4:00 p.m., most Ws 3:00-4:00pm, and by appointment


In advanced logic, we ask a range of fascinating questions. What is logic? What is reasoning? How can we study the limits and abilities of logic (that is, how can we study the logic of logic)? Are there infinities? How can we study them? What are possibility and necessity? What is the logic of ethics?

Our answers to these questions matter not just to logic and metaphysics, but to nearly all other disciplines. For example, we are now seeing the development of self-driving cars; these will need to be programmed with an ethical logic to manage crash situations. What should that logic be?

This class develops the skills and knowledge from PHL111, Valid Reasoning, to ask more radical questions about logic and its applications. Topics covered will include: first order logic with multiple quantifiers and identity; set theory; mathematical induction; axiomatic approaches to propositional logic, and the completeness of propositional logic; axiomatic approaches to first order logic, and the semantics of first order logic; modal logic and applications and interpretations of modality.


We'll be picking an choosing from many texts, most of which will be in eReserves. However, the text from which we will draw the most, and which is available at the bookstore, is
Mendelson, Elliot. Introduction to Mathematical Logic. New York: Oxford University Press.
But you don't need to buy that unless you are a logic maniac and want to have the book available as a resource in the future (90% of it we will not discuss in class). Also available to you for free will be:
DeLancey, A Concise Introduction to Logic.

Assignments and exams

You will have three exams, and also frequent (ideally, weekly) homework assignments.

Logic is a discipline that requires practice. Homeworks will be graded strictly, in order to make clear what you have done correctly and what not; but your overall homework grade will be curved. Also, note that I will sometimes give you questions about material we have not discussed in class yet. This is a way to get you to think about the material before the lecture, so that you are better aware of what the lecture is about, what you need to understand from the lecture, what you may be failing to understand, and so on.

You can work together, but you must write up your homeworks by yourself. This means that you will not get credit for identifiably identical homeworks.

If you have a disabling condition which may interfere with your ability to successfully complete this course, please contact the Disability Services Office.


The raw grade will be determined in the following way:
Homework assignments: 40%
Class exams: 35% (15%, then 20%)
Comprehensive final exam: 25%
Note that the exams count more as the class progresses. This means that you always have an opportunity in this class to catch up and do significantly better. This also accommodates that some people learn at different rates.

See my grading policy for a brief note on how I turn the raw grade into a final grade.

Homeworks will sometimes be reviewed in the class period where they are due. For this reason, late homeworks will not be accepted for credit.

I regret that I cannot accept homework by email. Also, I delete all the following emails unanswered: "I missed class today, can you tell me everything you said?" "I don't have the book, can you type up the problems and email them to me?" "I know you don't accept homework by email, but can I email my homework to you until I come to class sometime and give you the hardcopy then?"

If you miss an exam and have an excused absence for the day you miss the exam, you may make it up, by special appointment with me, when you are able to come back to class. It is your responsibility to arrange any make-up exams as soon as you know you are going to miss the exam. Otherwise you may lose the opportunity to take the test, since I cannot give make-up exams after the class has gone over the answers.

Here is how you secure an excused absence: Only prior notification with credibly documented or easily verifiable reasons (e.g., medical visits to Mary Walker, documented participation in official sporting events, etc.) will result in excused absences. You must notify in writing, call, or email me prior to your absence from class. You must notify the Philosophy Dept. secretary, Pat Meleski, before you are going to be absent, via email at, or by phone at x2249. However, you must make sure she knows your name, the number of the course, the date, and your easily verifiable reason, along with a request to forward the information to me. It is better to give your information to me, except when you are unable to communicate with my phone or email for some reason.

Please hold onto all of your assignments and exams. Sometime before the end of the semester I recommend that you ask me to review the grades that I have recorded to make sure that I have not made any mistakes. I'm only human and can make typos in recording grades!

Any forms of cheating will earn a zero grade, and will be reported to the Dean.


I am asking that no one use a computer or cell phone in class. I know that this is a catastrophe of some kind, but I have found that they always become terrible distractions. If you must use Snapchat or watch Netflix, just skip class.

College Policy on Intellectual Integrity

Intellectual integrity on the part of all students is basic to individual growth and development through college course work. When academic dishonesty occurs, the teaching/learning climate is seriously undermined and student growth and development are impeded. For these reasons, any form of intellectual dishonesty is a serious concern and is therefore prohibited.

The full intellectual integrity policy can be found at

Office Hours

In addition to the listed office hours, I encourage you to make appointments. I am available quite a bit. Please try to come to office hours with specific questions in mind. You can of course come with a general request for help, but it is always helpful if you spend a little time thinking about how I can best help you out.


I will frequently update an online schedule of readings and yassignments. It is your responsibility to check the www pages for the class at least every other day!


We have 14 weeks together. I'd like to cover approximately the following material:
  1. Review natural deduction. Introduction to set theory.
  2. Natural deduction with several quantifiers. More set theory.
  3. Introduce an axiomatic system. The propositional logic.
  4. Proofs with the natural deduction system. Mathematical induction.
  5. Proving stengthening. Proving completeness.
  6. Propositional logic axiom system.
  7. Completeness of propositional logic.
  8. Peano axioms.
  9. Proving things with the Peano axioms.
  10. Recursion theory from 10,000 feet.
  11. Modal logic. Basic systems.
  12. Modal logic: Kripke semantics.
  13. Applying modal logic to some philosophical problems.
  14. Other philosophical applications, such as deontic and temporal logics.