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Unfortunately, it often seems like "low barrier to entry" means "no prior effort invested" even if it means knowing basic logic notation which is taught in gymn

Unfortunately, it often seems like "low barrier to entry" means "no prior effort invested" even if it means knowing basic logic notation which is taught in gymnasiums

Gravityloss 6y ago
Hmm, is that symbol basic logic notation, and were you taught that symbol in high school? Which one of these? Do you type it often? https://en.wikipedia.org/wiki/Turnstile_(symbol) https://en.wikipedia.org/wiki/Turnstile_(symbol)
nyanpasu64 6y ago
Is a gymnasium a school in Europe? It's an exercise facility in the USA. I've gone through high school and taken CS (and a bit of discrete math and logic) in college, and never seen the ⊢ symbol before.
- mcaruso 6y ago
  > Is a gymnasium a school in Europe? It's an exercise facility in the USA. https://en.wikipedia.org/wiki/Gymnasium_(school) https://en.wikipedia.org/wiki/Gymnasium_(school) > I've gone through high school and taken CS (and a bit of discrete math and logic) in college, and never seen the ⊢ symbol before. Interesting. I was taught ⊢ first semester in CS in Logic class. Along with most other common logic notation.
- throwawaygh 6y ago
  > Is a gymnasium a school in Europe? It's an exercise facility in the USA. https://en.wikipedia.org/wiki/Gymnasium_(Germany) https://en.wikipedia.org/wiki/Gymnasium_(Germany) And yes, teaching basic notation from mathematical logic is pretty standard in Gymnasium's. I've taught sequent calculi at US high school enrichment programs; honestly, the students get it perfectly fine. The notation is no more difficult to understand than a two column proof. It's always the teachers who struggle. Every attempt at math ed reform in the US meets that crux -- the teachers' and parents' willingness/ability to learn anything new is always massively over-estimated. The only way to teach real mathematics in US high schools is to smuggle it in through "enrichment" programs. > I've gone through high school and taken CS (and a bit of discrete math and logic) in college, and never seen the ⊢ symbol before. Discrete math courses are different from university to university; sometimes formal logic is covered, and sometimes it's more of an "introduction to basic proof techniques and combinatorics" course. A university course in logic should certainly have shown you a sequent calculus at some point. I'm actually confused about how you would fill a semester-long course on logic without a turnstile ever showing up. What notation were you using to write down your derivations? They used to say "the US has the best high schools in the world; unfortunately, they're called universities". But the universities have become so watered down that many Americans get university degrees without ever passing through an institution at the level of a good gymnasium.
  - nyanpasu64 6y ago
    It was not strictly a logic class, but more of an overview course of discrete math, logic and proofs, and some statistics. They taught -> I think. I've never heard of "sequent calculus" before, and I don't expect anyone I know to have heard it. Apparently it's not calculus. > They used to say "the US has the best high schools in the world; unfortunately, they're called universities". But the universities have become so watered down that many Americans get university degrees without ever passing through an institution at the level of a good gymnasium. I don't think universities are watered down because they don't teach notation that most people don't know and find obscure. My university is famous for a difficult admissions process, tough courses that most people only learn 2/3 of the material, and grading curves calibrated so getting 60% on exams is enough for a B or A. ---- https://en.wikipedia.org/wiki/Sequent_calculus https://en.wikipedia.org/wiki/Sequent_calculus Wikipedia says "Sequent calculus is one of several extant styles of proof calculus for expressing line-by-line logical arguments." I didn't learn "every statement is conditional" logic involving turnstiles, I learned something where the assumptions were given in the problem, and each line was proven based on the previous lines, which boiled down to the initial givens.

Unfortunately, it often seems like "low barrier to entry" means "no prior effort invested" even if it means knowing basic logic notation which is taught in gymnasiums

Gravityloss 6y ago

Hmm, is that symbol basic logic notation, and were you taught that symbol in high school? Which one of these? Do you type it often? https://en.wikipedia.org/wiki/Turnstile_(symbol) https://en.wikipedia.org/wiki/Turnstile_(symbol)

nyanpasu64 6y ago

Is a gymnasium a school in Europe? It's an exercise facility in the USA. I've gone through high school and taken CS (and a bit of discrete math and logic) in college, and never seen the ⊢ symbol before.

mcaruso 6y ago
> Is a gymnasium a school in Europe? It's an exercise facility in the USA. https://en.wikipedia.org/wiki/Gymnasium_(school) https://en.wikipedia.org/wiki/Gymnasium_(school) > I've gone through high school and taken CS (and a bit of discrete math and logic) in college, and never seen the ⊢ symbol before. Interesting. I was taught ⊢ first semester in CS in Logic class. Along with most other common logic notation.
throwawaygh 6y ago
> Is a gymnasium a school in Europe? It's an exercise facility in the USA. https://en.wikipedia.org/wiki/Gymnasium_(Germany) https://en.wikipedia.org/wiki/Gymnasium_(Germany) And yes, teaching basic notation from mathematical logic is pretty standard in Gymnasium's. I've taught sequent calculi at US high school enrichment programs; honestly, the students get it perfectly fine. The notation is no more difficult to understand than a two column proof. It's always the teachers who struggle. Every attempt at math ed reform in the US meets that crux -- the teachers' and parents' willingness/ability to learn anything new is always massively over-estimated. The only way to teach real mathematics in US high schools is to smuggle it in through "enrichment" programs. > I've gone through high school and taken CS (and a bit of discrete math and logic) in college, and never seen the ⊢ symbol before. Discrete math courses are different from university to university; sometimes formal logic is covered, and sometimes it's more of an "introduction to basic proof techniques and combinatorics" course. A university course in logic should certainly have shown you a sequent calculus at some point. I'm actually confused about how you would fill a semester-long course on logic without a turnstile ever showing up. What notation were you using to write down your derivations? They used to say "the US has the best high schools in the world; unfortunately, they're called universities". But the universities have become so watered down that many Americans get university degrees without ever passing through an institution at the level of a good gymnasium.
- nyanpasu64 6y ago
  It was not strictly a logic class, but more of an overview course of discrete math, logic and proofs, and some statistics. They taught -> I think. I've never heard of "sequent calculus" before, and I don't expect anyone I know to have heard it. Apparently it's not calculus. > They used to say "the US has the best high schools in the world; unfortunately, they're called universities". But the universities have become so watered down that many Americans get university degrees without ever passing through an institution at the level of a good gymnasium. I don't think universities are watered down because they don't teach notation that most people don't know and find obscure. My university is famous for a difficult admissions process, tough courses that most people only learn 2/3 of the material, and grading curves calibrated so getting 60% on exams is enough for a B or A. ---- https://en.wikipedia.org/wiki/Sequent_calculus https://en.wikipedia.org/wiki/Sequent_calculus Wikipedia says "Sequent calculus is one of several extant styles of proof calculus for expressing line-by-line logical arguments." I didn't learn "every statement is conditional" logic involving turnstiles, I learned something where the assumptions were given in the problem, and each line was proven based on the previous lines, which boiled down to the initial givens.