If unicorns exist, but humans can never observe them do you really care whether they exist or not?
I generally am reducing questions that are only relevant to philosophy such as "Do real numbers exist?" to questions which you can actually answer.
To make something clear, rationals have a finite description. If you allow infinite descriptions, all real numbers can be described by Cauchy sequences. When I talk about countably many names, I am talking about the set of finite names humans use for numbers. You cannot meaningfully have infinitely many sets of finite names that humans agree on so you cannot cover the real numbers with names.
The interesting number paradox only works for countable sets unless I am mistaken. You can have "interesting" real numbers.
I generally am reducing questions that are only relevant to philosophy such as "Do real numbers exist?" to questions which you can actually answer.
To make something clear, rationals have a finite description. If you allow infinite descriptions, all real numbers can be described by Cauchy sequences. When I talk about countably many names, I am talking about the set of finite names humans use for numbers. You cannot meaningfully have infinitely many sets of finite names that humans agree on so you cannot cover the real numbers with names.
The interesting number paradox only works for countable sets unless I am mistaken. You can have "interesting" real numbers.