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Single Idea 15364

[from 'The Tarskian Turn' by Leon Horsten, in 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers ]

Full Idea

The number of English expressions is denumerably infinite. But Cantor's theorem can be used to show that there are nondenumerably many real numbers. So not every real number has a (simple or complex name in English).

Gist of Idea

English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable

Source

Leon Horsten (The Tarskian Turn [2011], 06.3)

Book Reference

Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.73


A Reaction

This really bothers me. Are we supposed to be committed to the existence of entities which are beyond our powers of naming? How precise must naming be? If I say 'pick a random real number', might that potentially name all of them?