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Math major here. 'is' is a reflexive relationship. If math is language, therefore language is math. I believe clearly language is not math, therefore math is no

Math major here. 'is' is a reflexive relationship. If math is language, therefore language is math. I believe clearly language is not math, therefore math is not language. Math is described with language, Math itself is not language. It is a 'has-a' relationship vs a 'is-a' relationship.

godelski 1y ago
> Math major here Forgive me if I doubt, but your comment would strongly suggest otherwise, along with this one[0]. The reason for doubt is a failure in fairly basic logic. Your claim is: ¬(A ↦ B) ⟹ ¬(B ↦ A) I'd expect anyone willing to claim the title of "math major" is aware of structures other than bijections and isomorphisms. The mapping operator doesn't form an abelian group. [0] https://news.ycombinator.com/item?id=43873351 https://news.ycombinator.com/item?id=43873351
- seadan83 1y ago
  The word "is", typically refers to the logical equals operator (written as "="). Let A = Math, and let B = Language, the phrase "Math is Language" is therefore "A = B". My claim is that "B != A", which implies "A != B" because "!=" is reflexive. "A != B" then contradicts the claim "A = B". In words: because "language is not math", therefore it cannot be true that "math is language". This is not number theory, not set theory, just logic. I don't see how the properties of Abelian groups applies. I do suspect that non-abelian groups is a case where "¬(A ↦ B) ⟹ ¬(B ↦ A)" is false, and would be a contadiction to my counter claim if "¬(A ↦ B) ⟹ ¬(B ↦ A)" was my counter-claim. No, my counter claim is simply that because "B != A" therefore "A != B" The statement "¬(A ↦ B) ⟹ ¬(B ↦ A)" is quite different, and I'm not 100% sure whether you are mixing set and logic notations? [0][1] It does seem you are bringing in number theory concepts, or we are misunderstanding one another? I assume "↦" is the set mapping operator and "⟹" is logical implies, and "¬" is logical not. "¬(A ↦ B) ⟹ ¬(B ↦ A)" could potentially be phrased as: "If the element A cannot be mapped to B, then the element B cannot be mapped to A". I would agree that statement is not 'generally' true. Could you please clarify so we are not talking past each other. [0] Per google: The symbol "↦" is a mapping symbol, typically used to indicate a function or relationship where one element maps to another. It's not a standard logical operator in the same way that symbols like &&, ||, or ¬ are. Instead, it represents a directional relationship between sets or elements, often seen in set theory and mathematical notations [1] https://simple.wikipedia.org/wiki/Implication_(logic) https://simple.wikipedia.org/wiki/Implication_(logic)
  - thaumasiotes 1y ago
    > This is not number theory, not set theory, just logic. Try that in a philosophy class and you can expect an F. A math class too.
    - seadan83 1y ago
      The proposition was "A = B" (logical equals, A and B are entities) The simple refutation was: because B != A, therefore A != B That WAS the math exam!! No group or set theory needed. It's simple and this is not interesting.
      - thaumasiotes 1y ago
        > The proposition was "A = B" (logical equals, A and B are entities) That's only in your head. Inventing claims so that you can pretend other people are wrong isn't a good move. > That WAS the math exam!! No group or set theory needed. It's simple and this is not interesting. I'm surprised you can pass a math class.
        seadan83 1y ago
        > That's only in your head. Inventing claims so that you can pretend other people are wrong isn't a good move. I'm not the only one that interprets a statement as "Math is Language" to be of the form "A = B" where "math" is A, "language" is B, and "is" is the equals operator, see: https://news.ycombinator.com/item?id=43874322 https://news.ycombinator.com/item?id=43874322 Seems kinda simple.. You're engaging in a almost pure personal attacks. Care to address the substance of how the 3 word long statement is not of the form "A = B", but is of some other different form? In which case, perhaps you can guide the conversation for why it is an interesting statement or not? If you want to change all the givens and use your own definitions, please provide those. Without common ground, this remains uninteresting.
        thaumasiotes 1y ago
        > I'm not the only one that interprets a statement as "Math is Language" to be of the form "A = B" where "math" is A, "language" is B, and "is" is the equals operator, see: https://news.ycombinator.com/item?id=43874322 https://news.ycombinator.com/item?id=43874322 This appears to be a link that contains zero support for your sentence. Neither the comment you linked nor the response below it features such an interpretation. > Seems kinda simple.. You're engaging in a almost pure personal attacks. Care to address the substance of how the 3 word long statement is not of the form "A = B", but is of some other different form? You're in luck! I've already provided that material, and you responded to it. For further discussion, you'd need to have a better working understanding of English.
thaumasiotes 1y ago
> Math major here. You say that like you think it's a qualification? You're not making it look good. A common use of be is to express set membership rather than identity. For example, "two is an even number" or "tigers are cats". We may hope that one day you'll come to realize that set membership is not reflexive, and - more to the point - also not symmetric.
- seadan83 1y ago
  You're saying that "Math" and "Language" are 'sets'? And that the phrase "Math is Language" should be interpreted as expressing the relationship between sets? If we do want to talk sets, that seems far more interesting. The statements like "Math is a language", or "Math has equivalence classes within languages", or "Mathematics are a Language" are slightly more interesting to consider IMO. >> Math major here. > You say that like you think it's a qualification? Agree, appeal to authority fallacy. I take that over mis-framing any day though. Any old-timers might appreciate that we're arguing over the meaning of the word "is" =D
- seadan83 1y ago
  > A common use of be is to express set membership rather than identity Google for "logical "is a" vs logical "is"". Google AI answers this: > "is" typically represents an equality relation Rest is from the AI response: 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. Logical "is" (equality): Meaning: "A is B" means that A and B are the same thing, or have the same properties. Example: "The Eiffel Tower is in Paris" (the Eiffel Tower and the thing in Paris are the same thing). Logical "is a" (inclusion or type): Meaning: "A is a B" means that A belongs to the category or class of things that are B. Example: "A dog is an animal" (dogs are a type of animal).
  - thaumasiotes 1y ago
    Try applying some thought. You asked a stupid question and you got a stupid answer. What conclusions do you think that supports? What does "silk is cloth" mean?

godelski 1y ago

> Math major here Forgive me if I doubt, but your comment would strongly suggest otherwise, along with this one[0]. The reason for doubt is a failure in fairly basic logic. Your claim is: ¬(A ↦ B) ⟹ ¬(B ↦ A) I'd expect anyone willing to claim the title of "math major" is aware of structures other than bijections and isomorphisms. The mapping operator doesn't form an abelian group. [0] https://news.ycombinator.com/item?id=43873351 https://news.ycombinator.com/item?id=43873351

seadan83 1y ago
The word "is", typically refers to the logical equals operator (written as "="). Let A = Math, and let B = Language, the phrase "Math is Language" is therefore "A = B". My claim is that "B != A", which implies "A != B" because "!=" is reflexive. "A != B" then contradicts the claim "A = B". In words: because "language is not math", therefore it cannot be true that "math is language". This is not number theory, not set theory, just logic. I don't see how the properties of Abelian groups applies. I do suspect that non-abelian groups is a case where "¬(A ↦ B) ⟹ ¬(B ↦ A)" is false, and would be a contadiction to my counter claim if "¬(A ↦ B) ⟹ ¬(B ↦ A)" was my counter-claim. No, my counter claim is simply that because "B != A" therefore "A != B" The statement "¬(A ↦ B) ⟹ ¬(B ↦ A)" is quite different, and I'm not 100% sure whether you are mixing set and logic notations? [0][1] It does seem you are bringing in number theory concepts, or we are misunderstanding one another? I assume "↦" is the set mapping operator and "⟹" is logical implies, and "¬" is logical not. "¬(A ↦ B) ⟹ ¬(B ↦ A)" could potentially be phrased as: "If the element A cannot be mapped to B, then the element B cannot be mapped to A". I would agree that statement is not 'generally' true. Could you please clarify so we are not talking past each other. [0] Per google: The symbol "↦" is a mapping symbol, typically used to indicate a function or relationship where one element maps to another. It's not a standard logical operator in the same way that symbols like &&, ||, or ¬ are. Instead, it represents a directional relationship between sets or elements, often seen in set theory and mathematical notations [1] https://simple.wikipedia.org/wiki/Implication_(logic) https://simple.wikipedia.org/wiki/Implication_(logic)
- thaumasiotes 1y ago
  > This is not number theory, not set theory, just logic. Try that in a philosophy class and you can expect an F. A math class too.
  - seadan83 1y ago
    The proposition was "A = B" (logical equals, A and B are entities) The simple refutation was: because B != A, therefore A != B That WAS the math exam!! No group or set theory needed. It's simple and this is not interesting.
    - thaumasiotes 1y ago
      > The proposition was "A = B" (logical equals, A and B are entities) That's only in your head. Inventing claims so that you can pretend other people are wrong isn't a good move. > That WAS the math exam!! No group or set theory needed. It's simple and this is not interesting. I'm surprised you can pass a math class.
      - seadan83 1y ago
        > That's only in your head. Inventing claims so that you can pretend other people are wrong isn't a good move. I'm not the only one that interprets a statement as "Math is Language" to be of the form "A = B" where "math" is A, "language" is B, and "is" is the equals operator, see: https://news.ycombinator.com/item?id=43874322 https://news.ycombinator.com/item?id=43874322 Seems kinda simple.. You're engaging in a almost pure personal attacks. Care to address the substance of how the 3 word long statement is not of the form "A = B", but is of some other different form? In which case, perhaps you can guide the conversation for why it is an interesting statement or not? If you want to change all the givens and use your own definitions, please provide those. Without common ground, this remains uninteresting.
        thaumasiotes 1y ago
        > I'm not the only one that interprets a statement as "Math is Language" to be of the form "A = B" where "math" is A, "language" is B, and "is" is the equals operator, see: https://news.ycombinator.com/item?id=43874322 https://news.ycombinator.com/item?id=43874322 This appears to be a link that contains zero support for your sentence. Neither the comment you linked nor the response below it features such an interpretation. > Seems kinda simple.. You're engaging in a almost pure personal attacks. Care to address the substance of how the 3 word long statement is not of the form "A = B", but is of some other different form? You're in luck! I've already provided that material, and you responded to it. For further discussion, you'd need to have a better working understanding of English.

thaumasiotes 1y ago

> Math major here. You say that like you think it's a qualification? You're not making it look good. A common use of be is to express set membership rather than identity. For example, "two is an even number" or "tigers are cats". We may hope that one day you'll come to realize that set membership is not reflexive, and - more to the point - also not symmetric.

seadan83 1y ago
You're saying that "Math" and "Language" are 'sets'? And that the phrase "Math is Language" should be interpreted as expressing the relationship between sets? If we do want to talk sets, that seems far more interesting. The statements like "Math is a language", or "Math has equivalence classes within languages", or "Mathematics are a Language" are slightly more interesting to consider IMO. >> Math major here. > You say that like you think it's a qualification? Agree, appeal to authority fallacy. I take that over mis-framing any day though. Any old-timers might appreciate that we're arguing over the meaning of the word "is" =D
seadan83 1y ago
> A common use of be is to express set membership rather than identity Google for "logical "is a" vs logical "is"". Google AI answers this: > "is" typically represents an equality relation Rest is from the AI response: 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. Logical "is" (equality): Meaning: "A is B" means that A and B are the same thing, or have the same properties. Example: "The Eiffel Tower is in Paris" (the Eiffel Tower and the thing in Paris are the same thing). Logical "is a" (inclusion or type): Meaning: "A is a B" means that A belongs to the category or class of things that are B. Example: "A dog is an animal" (dogs are a type of animal).
- thaumasiotes 1y ago
  Try applying some thought. You asked a stupid question and you got a stupid answer. What conclusions do you think that supports? What does "silk is cloth" mean?