P310 Valid Reasoning II

Professor: Craig DeLancey

Office: CC212A

Email: craig.delancey@oswego.edu

**Current Assignments**

**14 May**
Sorry, I don't think I can get practice problems up in time.
I'm struggling to get my finals written and accomplish all
the other end-of-semester things I have to do before Wednesday.
But your book is FULL of practice problems, many with solutions
in the back. Also, try proving some of the theorems that are
proved in the chapters themselves, and then check your proof
after against the book's.

**15 May**
Final exam in class, 10:30 a.m. -- 12:30 p.m. Study questions
include:
- How do we define completeness for L?
- What is a tautology?
- How do we define completeness for K?
- What is a logically valid sentence or logical valid formula?
- Is L complete? Is K?
- Given the main required theorems, explain why K is complete.
- What is Cantor's Theorem? Prove it.
- What does Cantor's Theorem tell us about the maximal size of sets?
- What do we mean when we say the axioms of NBG or ZFC
(appear) adequate? Or when we say this of Peano's axioms
(revised into S)? [Several of you asked about this. The
issue is, why do with think S is good? It can't be that S is
complete, since we know arithmetic is not complete. But,
consider instead: what would happen if we got rid of axioms
S5-S9, and just kept S1-S4? You are likely to say, we won't
be able to do _____, and fill in the blank with something from
your experience with arithmetic you know is essential to
arithmetic. The issue here is that we have as a standard all
the things we do in naive or natural arithmetic. Similarly,
we don't add axioms to Peano/S presumably because they've
proved to be enough to do what we expect of natural
arithmetic.]
- Compare and contrast a Leibniz modal versus a Kripke model
for modal propositional logic.
- Basic proofs in L and K.
- Basic proofs in set theory.
- Basic proofs in Peano Arithmetic.
- Basic proofs in modal logic.

**Tentative assignments**

**16 May**
Think logically all summer.