The AskPhilosophers logo.

Language

There is an infinite number of words - "ONE", "TWO", "THREE"... etc. Every word has a definition. Every definition consists of letters. There is a finite number of arrangement of letters; thus there is a finite number of definitions. Thus there is at least one word that doesn't have a definition. Paradox?
Accepted:
November 17, 2020

Comments

There is a finite number of

Stephen Maitzen
November 19, 2020 (changed November 19, 2020) Permalink

There is a finite number of arrangements of letters; thus there is a finite number of definitions.

Is that true if we're allowed to use each letter an increasing number of times? If our stock of letter tokens increases without limit, then can't the number (and length) of our definitions also increase without limit? Certainly the names of the numbers will tend to get longer as the numbers they name increase, and those names will reuse letters to an ever-increasing degree.

  • Log in to post comments

Why do you say that the

Jonathan Westphal
November 10, 2024 (changed November 10, 2024) Permalink

Why do you say that the number of words is infinite? The OED has only about 600,000, and the number of languages around the world is finite.

  • Log in to post comments
Source URL: https://askphilosophers.org/question/28644
© 2005-2025 AskPhilosophers.org