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Good points. I know you know, but it's also worth mentioning that most math symbols don't have a definite meaning. Meaning is defined in the context it is prese

Good points. I know you know, but it's also worth mentioning that most math symbols don't have a definite meaning. Meaning is defined in the context it is presented, in whatever way the author feels makes the most sense. Math is a natural, not a formal language.

WilliamEdward 7y ago
Is that really true though? having precise definitions for symbols is important for proofs
- throwaway_pdp09 7y ago
  Yes, it's true. Please re-read what he said, especially the "in the context of" part.
- reikonomusha 7y ago
  In "proper" mathematics, the symbols are defined precisely in their context. This does not mean that the symbols' meanings are universal. I think this is what GP meant. The lack of universality of meanings of symbols is a feature, not a bug, of math notation.
carapace 7y ago
The messed up thing is that the math notation of computer science is in the same mess. It doesn't even have a name. (There's a talk about it but I can't find the link right now.)
- carapace 7y ago
  Found it! "It's Time for a New Old Language" – Guy Steele [video] (youtube.com) https://news.ycombinator.com/item?id=15473199 https://news.ycombinator.com/item?id=15473199 https://www.youtube.com/watch?v=dCuZkaaou0Q https://www.youtube.com/watch?v=dCuZkaaou0Q
- justinmeiners 7y ago
  This isn't a mess, this is a good thing. Math is a way of talking about ideas, not a formal system for computers.
  - carapace 7y ago
    So what's the difference in your view between math and philosophy?
    - justinmeiners 7y ago
      That's a little complicated as math is intertwined with science. But at the core I only see them as a difference in subject matter. Math is a philosophical study of space, logical structure, quantity, etc. Proofs are just tools for articulating arguments about these subjects. Deduction just tends to work better in math, so the methods are more refined and agreed upon.
    - m463 7y ago
      I took a philosophy course in college to learn symbolic logic

WilliamEdward 7y ago

Is that really true though? having precise definitions for symbols is important for proofs

throwaway_pdp09 7y ago
Yes, it's true. Please re-read what he said, especially the "in the context of" part.
reikonomusha 7y ago
In "proper" mathematics, the symbols are defined precisely in their context. This does not mean that the symbols' meanings are universal. I think this is what GP meant. The lack of universality of meanings of symbols is a feature, not a bug, of math notation.

carapace 7y ago

The messed up thing is that the math notation of computer science is in the same mess. It doesn't even have a name. (There's a talk about it but I can't find the link right now.)

carapace 7y ago
Found it! "It's Time for a New Old Language" – Guy Steele [video] (youtube.com) https://news.ycombinator.com/item?id=15473199 https://news.ycombinator.com/item?id=15473199 https://www.youtube.com/watch?v=dCuZkaaou0Q https://www.youtube.com/watch?v=dCuZkaaou0Q
justinmeiners 7y ago
This isn't a mess, this is a good thing. Math is a way of talking about ideas, not a formal system for computers.
- carapace 7y ago
  So what's the difference in your view between math and philosophy?
  - justinmeiners 7y ago
    That's a little complicated as math is intertwined with science. But at the core I only see them as a difference in subject matter. Math is a philosophical study of space, logical structure, quantity, etc. Proofs are just tools for articulating arguments about these subjects. Deduction just tends to work better in math, so the methods are more refined and agreed upon.
  - m463 7y ago
    I took a philosophy course in college to learn symbolic logic