4 ms·

You're using "being named" in a very unusual sense. Most people would consider you not to have named something if you're literally never allowed to stop speakin

You're using "being named" in a very unusual sense. Most people would consider you not to have named something if you're literally never allowed to stop speaking (or writing) the name. Most reals "have infinitely long names" under your definition, and there is no finite time at which you've distinguished between reals with the same initial segment of "name", so really what's the use of the naming scheme at all? (For a more compelling argument, the equality of real numbers is uncomputable, so it must be impossible to name them. If we could name them usefully, then we could determine equality by asking which ones had different names.)

thaumasiotes 4y ago
> You're using "being named" in a very unusual sense. No, I'm not. > Most people would consider you not to have named something if you're literally never allowed to stop speaking (or writing) the name. What's the connection? Names do not completely describe their referent. They're names. I know someone named Ko. Given that name, what can you tell me about Ko?
- jiggawatts 4y ago
  Naming a number in mathematics has different rules to assigning names to objects in the physical world. You can "name" a number such as: "a positive number, that when multiplied by itself, the result is 2". This is a finite statement that requires only a handful of 'bits' to represent, but it exactly and uniquely identifies the square root of two. If written with decimal digits, then the square root of two would require an infinite number of digits, but it can be defined ('named') with a finite number of bits. It turns out that this is a rare property for real numbers. The vast majority do not have a shorthand name like this, only the infinitely long description exists.
  - riversflow 4y ago
    What does naming have to do with AC though? This seems completely tangential to the axiom. It’s about the nature of sets, not the semantics of how you make the selection and reference it. AC says: if there is a set of non-empty sets y with length x, I can construct a new set z of length x by taking a member from each set in y. How does being able to name the constituents z or any member of y matter to the logic of the axiom?
    - Smaug123 4y ago
      This is all in response to a comment which basically said "why do people think AC is obvious - if you can't even name all elements of the set, why would you expect to be able to choose them". (Which is handwavy, of course, and leads to the wrong intuition about uncountable-but-well-ordered sets, and depending on how you look at it it may even lead you to conclude that you can't ever choose even a single element from an uncountable set.)
- Smaug123 4y ago
  Honestly, I really am trying, but as far as I can see you are using the word "named" in a sense that allows most numbers to be called "0". I really can't see how your words make sense given any other definition. Is that correct?
  - thaumasiotes 4y ago
    That is essentially correct, and we actually do call many different numbers "0" in different contexts, but it's not necessary for any two numbers to share a name this way. You can give them all unique finite names with an infinitely large alphabet if you prefer. You might consider that in the existing Chinese writing system, 口 and 囗 are distinct symbols.

thaumasiotes 4y ago

> You're using "being named" in a very unusual sense. No, I'm not. > Most people would consider you not to have named something if you're literally never allowed to stop speaking (or writing) the name. What's the connection? Names do not completely describe their referent. They're names. I know someone named Ko. Given that name, what can you tell me about Ko?

jiggawatts 4y ago
Naming a number in mathematics has different rules to assigning names to objects in the physical world. You can "name" a number such as: "a positive number, that when multiplied by itself, the result is 2". This is a finite statement that requires only a handful of 'bits' to represent, but it exactly and uniquely identifies the square root of two. If written with decimal digits, then the square root of two would require an infinite number of digits, but it can be defined ('named') with a finite number of bits. It turns out that this is a rare property for real numbers. The vast majority do not have a shorthand name like this, only the infinitely long description exists.
- riversflow 4y ago
  What does naming have to do with AC though? This seems completely tangential to the axiom. It’s about the nature of sets, not the semantics of how you make the selection and reference it. AC says: if there is a set of non-empty sets y with length x, I can construct a new set z of length x by taking a member from each set in y. How does being able to name the constituents z or any member of y matter to the logic of the axiom?
  - Smaug123 4y ago
    This is all in response to a comment which basically said "why do people think AC is obvious - if you can't even name all elements of the set, why would you expect to be able to choose them". (Which is handwavy, of course, and leads to the wrong intuition about uncountable-but-well-ordered sets, and depending on how you look at it it may even lead you to conclude that you can't ever choose even a single element from an uncountable set.)
Smaug123 4y ago
Honestly, I really am trying, but as far as I can see you are using the word "named" in a sense that allows most numbers to be called "0". I really can't see how your words make sense given any other definition. Is that correct?
- thaumasiotes 4y ago
  That is essentially correct, and we actually do call many different numbers "0" in different contexts, but it's not necessary for any two numbers to share a name this way. You can give them all unique finite names with an infinitely large alphabet if you prefer. You might consider that in the existing Chinese writing system, 口 and 囗 are distinct symbols.