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pragmatist comments on Help Reform A Philosophy Curriculum - Less Wrong Discussion
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These would be the formal classes in my ideal philosophy curriculum:
Symbolic logic (sentential and predicate logic, some model theory)
Set theory and category theory
Mathematical logic (along the lines of your 454)
Scientific reasoning (elementary statistics, causal inference)
Probability theory and the philosophy of probability
Rational decision-making (decision theory, heuristics and biases)
Formal epistemology (Bayesian epistemology, confirmation theory, computational learning theory)
Some sort of "programming for philosophers" class, teaching basic programming but emphasizing the connections with the material they've learned in their logic classes.
I'm tempted to merge symbolic logic and mathematical logic. I'm not sure how they are different from each other. How would you divide them?
I'd put Probability theory before scientific reasoning, since the latter flows from the former (not historically, but this is a philosophy course, not a history one). The result should naturally include the "Bayesian epistemology" part of your formal epistemology course.
Typically, symbolic logic classes focus on reasoning with formal systems and mathematical logic classes focus more on reasoning about formal systems. So in a symbolic logic class you would mainly learn how to do proofs while in a mathematical logic class you would learn about things like Godel's theorems. Maybe "mathematical logic" is a bit of a misnomer, but it is the traditional title of these classes.