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> Math is a language. Language is not math, therefore math is not language.

godelski 1y ago
Logic doesn't follow. There is no problem with A -> B ∧ B -/-> A Here's an example. "I live in San Francisco" would imply "I live in the US". But "I live in the US" does not mean "I live in San Francisco". Here's a more formal representation of this: https://en.wikipedia.org/wiki/Bijection,_injection_and_surjection https://en.wikipedia.org/wiki/Bijection,_injection_and_surje...
- seadan83 1y ago
  The word "is", maps to the logical "equals" operator. I agree with the example, but I don't agree it is relevant. There is no implies operator. The statement "Math is Language", where A is Math and B is Language, maps to the logical assertion: "A = B". If we are going to really be kinda twisty and non-standard, we could interpret the english "is" to be "is an equivalence class of". Which would map to your example pretty well: language is indeed an equivalence class of math, but math is not an equivalence class of language. Though, nobody is talking about implies operator or equivalence class here.. It's a "is" relationship, logical *equals*
  - seba_dos1 1y ago
    > The word "is", maps to the logical "equals" operator. It very obviously doesn't. A square is a rectangle. seadan83 is (probably) a mammal. Math is a language.
    - seadan83 1y ago
      You point out the "is a" relationship, not the "is" relationship, they are different. [0] Find examples with two singular nouns and just the word 'is'. The phrase in question: 'Math is language' is an example, or something like 'food is love' is too. I concede you could interpret those last few sentences with poetic license to be read more like: "A is a form of B", or "A is a B" - though that is not what was written and this is not a place to expect that much poetic license. *edit*: a minute later, thought of a good example. "ice is water". True that "ice is a form of water", but strictly speaking no, "ice is not water". I'll concede there could exist an implied "is a", or an implied "is a form of", but that is poetic license IMO. [0] Google AI summarized it pretty well: google "logical "is a" vs logical "is" > In logic, "is" typically represents an equality relation, while "is a" (or "is of the type") represents an inclusion relation. "Is" indicates that two things are the same or identical, while "is a" indicates that one thing is a member of a larger class or set of things
      - seba_dos1 1y ago
        > You point out the "is a" relationship, not the "is" relationship, they are different. Well, what you reacted to was, let me copy'n'paste, "Math is a language". It was you who insisted that "is" in this sentence maps to "equals" relation, so thanks for agreeing that you were wrong.
        godelski 1y ago
        Honestly I don't think his point even stands. We were using English to communicate and English doesn't have the strict rules of mathematics. That's literally why we created math (which I'll gladly call "a class of languages"). He's right, "is" maps to "equivalent" but he's also wrong because "is" also maps to "subset" and several other things. "Is" is a surjection. The problem here all comes down to seadan83 acting in bad faith and using an intentional misinterpretation of my words in order to fit them to their conclusion. I'm not going to entertain them more because I won't play such a pointless game. The ambiguity of written and spoken language always allows for such abuse. So either they are a bad faith actor "having fun" (trolling) finding intentional misinterpretations to frustrate those who wish to act in good faith or they are dumb. Personally, I don't think they're dumb.
        seba_dos1 1y ago
        It's such an absurd thing to argue about that I just assumed that some massive brainfart happened there. It happens to everyone, not everyone doubles down on it though.
        godelski 1y ago
        Oh, they did it much more than twice: https://news.ycombinator.com/item?id=43873381 https://news.ycombinator.com/item?id=43873381 But then again, isn't a good portion of this thread non-mathematicians arguing about what math is? I really thought ndriscoll put it succinctly[0] > It's like trying to argue about the distinction between U(1), the complex numbers with magnitude 1, and the unit circle, and getting upset when the mathematicians say "those are 3 names for the same thing". I fear the day some of these people learn about Topology. [0] https://news.ycombinator.com/item?id=43882197 https://news.ycombinator.com/item?id=43882197

Logic doesn't follow. There is no problem with A -> B ∧ B -/-> A Here's an example. "I live in San Francisco" would imply "I live in the US". But "I live in the US" does not mean "I live in San Francisco". Here's a more formal representation of this: https://en.wikipedia.org/wiki/Bijection,_injection_and_surjection https://en.wikipedia.org/wiki/Bijection,_injection_and_surje...

seadan83 1y ago
The word "is", maps to the logical "equals" operator. I agree with the example, but I don't agree it is relevant. There is no implies operator. The statement "Math is Language", where A is Math and B is Language, maps to the logical assertion: "A = B". If we are going to really be kinda twisty and non-standard, we could interpret the english "is" to be "is an equivalence class of". Which would map to your example pretty well: language is indeed an equivalence class of math, but math is not an equivalence class of language. Though, nobody is talking about implies operator or equivalence class here.. It's a "is" relationship, logical *equals*
- seba_dos1 1y ago
  > The word "is", maps to the logical "equals" operator. It very obviously doesn't. A square is a rectangle. seadan83 is (probably) a mammal. Math is a language.
  - seadan83 1y ago
    You point out the "is a" relationship, not the "is" relationship, they are different. [0] Find examples with two singular nouns and just the word 'is'. The phrase in question: 'Math is language' is an example, or something like 'food is love' is too. I concede you could interpret those last few sentences with poetic license to be read more like: "A is a form of B", or "A is a B" - though that is not what was written and this is not a place to expect that much poetic license. *edit*: a minute later, thought of a good example. "ice is water". True that "ice is a form of water", but strictly speaking no, "ice is not water". I'll concede there could exist an implied "is a", or an implied "is a form of", but that is poetic license IMO. [0] Google AI summarized it pretty well: google "logical "is a" vs logical "is" > In logic, "is" typically represents an equality relation, while "is a" (or "is of the type") represents an inclusion relation. "Is" indicates that two things are the same or identical, while "is a" indicates that one thing is a member of a larger class or set of things
    - seba_dos1 1y ago
      > You point out the "is a" relationship, not the "is" relationship, they are different. Well, what you reacted to was, let me copy'n'paste, "Math is a language". It was you who insisted that "is" in this sentence maps to "equals" relation, so thanks for agreeing that you were wrong.
      - godelski 1y ago
        Honestly I don't think his point even stands. We were using English to communicate and English doesn't have the strict rules of mathematics. That's literally why we created math (which I'll gladly call "a class of languages"). He's right, "is" maps to "equivalent" but he's also wrong because "is" also maps to "subset" and several other things. "Is" is a surjection. The problem here all comes down to seadan83 acting in bad faith and using an intentional misinterpretation of my words in order to fit them to their conclusion. I'm not going to entertain them more because I won't play such a pointless game. The ambiguity of written and spoken language always allows for such abuse. So either they are a bad faith actor "having fun" (trolling) finding intentional misinterpretations to frustrate those who wish to act in good faith or they are dumb. Personally, I don't think they're dumb.
        seba_dos1 1y ago
        It's such an absurd thing to argue about that I just assumed that some massive brainfart happened there. It happens to everyone, not everyone doubles down on it though.
        godelski 1y ago
        Oh, they did it much more than twice: https://news.ycombinator.com/item?id=43873381 https://news.ycombinator.com/item?id=43873381 But then again, isn't a good portion of this thread non-mathematicians arguing about what math is? I really thought ndriscoll put it succinctly[0] > It's like trying to argue about the distinction between U(1), the complex numbers with magnitude 1, and the unit circle, and getting upset when the mathematicians say "those are 3 names for the same thing". I fear the day some of these people learn about Topology. [0] https://news.ycombinator.com/item?id=43882197 https://news.ycombinator.com/item?id=43882197