Words Are Voids

A mathematical phrase has an interesting property: the meaning is the same under a safe rename. Let's see what that means.

Suppose we have a phrase: (next zero). If we rename next to after, we will have (after zero). The meaning of the phrase is the same - we just renamed a word. Let's translate it into French: (après zéro). The meaning still the same - but notice that the words are meaningless to a non-French speaker. We can replace words with characters: (x y). We can replace characters with numbers: (1 0). The meaning is still the same, so we can conclude:

• The words don't define the meaning of a mathematical phrase.
• The positions of the words define the meaning of a mathematical phrase.