Review Comment

[PHIL GU4802] Math Logic II

May 19, 2017

Gaifman, Haim
[PHIL GU4802] Math Logic II

The other reviews are fairly critical of Gaifman in one of two contexts: teaching an introductory logic class with insufficient pity or teaching a more subjective class with insufficient structure. Perhaps he is not the right professor to take in those contexts; however, in an upper level formal logic (think mathematics) course like this, his style of instruction is a bit more palatable. Though he still struggled with pacing, he typed up well-structured notes for us. And his explanations and proofs were always thorough enough. Though he moved between levels of abstraction, for the more advanced audience, this was not a big issue. I enjoyed this class and learned from Gaifman.

In terms of material, we covered self-reference and fixed-points, Gödel's first incompleteness theorem, Peano's and Robinson's theories of arithmetic, computability and undecidability in these theories, the Rosser trick, Gödel's second incompleteness theorem, and a bit more on provability logic. Some of the topics require a lot of thought to understand even the theorem statements, though the proof techniques were always straightforward. Gaifman made a very nice presentation of the basic material, leading us into it in a very natural way. Instead of proving the theorems very formally, he provided good intuition about what we were doing. This totaled around 50 pages in his typed notes, and to me, it felt a bit light. We spent more time reviewing than I felt was needed, which might explain why the semester felt a little light.

This course definitely requires a very good grounding in first order logic. It is the second course in the math logic sequence, and understandably, people who did not take the first struggled. Though Gaifman never dives into the details of the FOL deductive system, I used it to complete the exercises.

I will not complain about Gaifman's personality. He called out students a bit more than most professors, though never maliciously. Coming from a mathematical background, I did not find him too abstract. He may struggle to explain the fine-grained details on occasion, but, at this level, the student should be able to do this for himself. Gaifman is easily reachable by telephone, and holds office hours regularly. He did not give a lot of feedback, leaving students in the dark about their potential grades.


The only work in this class was exercises; some were assigned week-to-week, others comprised a take-home midterm and final. We were not required to do them all, but I managed to. Some of the exercises took more effort to parse than to solve, though I am not sure if that was due to how meta the topics are or a flaw in how they were posed. Some of the proofs and deductions were kind of tedious when done to a sufficient level of rigor, and others were amazingly insightful and only a few lines. Really a mixed bag.

I'm not sure exactly how the problems were graded, though I think I got the final grade I deserved. According to the syllabus, the grade is 10% participation, 20% exercises throughout the semester, and 70% exam. However, I never received grades for these individual components.

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