there are … only countably many names you could give a number.
If we take a name to be any pronounceable string pointing to a specific entity*, then in what way is that set limited? If you construct a list of syllables used for all names, and even limit your search to the items that start “the number”, you can always take an existing number name and append a syllable from that list to create a new name. That’s pretty much how set theory establishes integers, as I understand it.
I think there is a difference between “unnameable” and “unremarkable so far, so nobody’s bothered to name it”, which does describe nearly all numbers.
*This is an extremely narrow definition, but functional for this application. It could be extended to include any reproducible symbol including those that can be pronounced, scribed, or thought.
If we take a name to be any pronounceable string pointing to a specific entity*, then in what way is that set limited? If you construct a list of syllables used for all names, and even limit your search to the items that start “the number”, you can always take an existing number name and append a syllable from that list to create a new name. That’s pretty much how set theory establishes integers, as I understand it.
I think there is a difference between “unnameable” and “unremarkable so far, so nobody’s bothered to name it”, which does describe nearly all numbers.
*This is an extremely narrow definition, but functional for this application. It could be extended to include any reproducible symbol including those that can be pronounced, scribed, or thought.
Countable doesn’t mean finite. See https://en.wikipedia.org/wiki/Countable_set