= 27d567bc2d48d9f40e9ccc20ea370b15)
bryjnar comments on Proofs, Implications, and Models - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (209)
My data point: as an undergraduate mathematician at Oxford, the mathematical logic course was one of the most popular, and certainly covered most of this material. I guess I haven't talked a huge number of mathematicians about logic, but I'd be pretty shocked if they didn't know the difference between syntax and semantics. YMMV.
It terrifies me that I seem to be unique in having had pretty much all of this covered in my high school's standard math curriculum (not even an advanced or optional class). Eliezer's method of "find the point where it becomes untrue" wasn't standard, but I think (p ~0.5) that my teacher went over it when I wrote a proof of 2=1 on the board. I knew he was a cool math teacher who made a point of tutoring flagging students, but I hadn't realized he was this exceptional.
Judging just from your description, he's probably more than two standard deviations of abnormal.
Your curriculum sounds at least a good deal above average, but the core problem is that most "curricula" are effectively nothing more than a list of things that teachers should make sure to mention, along with a separate, disjoint, often not correlated list of things that will be "tested" in an exam.
I expect many curricula would contain a good deal of the good parts of traditional rationality and mathematics, but there are many steps between a list on one sheet of paper that each teacher must read once a year and actual non-password understanding becoming commonplace among students.
I still have a copy of my Secondary 4 (US 10th / high school sophomore) curriculum somewhere, which my math teacher gave me secretly back then despite the threat of severe reprimand (our teachers were not even allowed to disclose the actual curriculum - that's how bad things often are). We both verified back then that not even half of what's supposed to be covered according to this piece of paper ever actually gets taught in most classes. That teacher really was that exceptional, but he only had so much time, split across several hundred students.
Another data point: in Cambridge the first course in logic done by mathematics undergraduates is in third year. It covers completeness and soundness of propositional and predicate logic and is quite popular. But in third year people are already so specialised that probably way less than half of us take it.