Semiotics

Axiom 1: We are allowed to name a thing.
(1)

EXAMPLE: $a$ names $99$
$a$ is the name. $99$ is the thing. Observe that $1$ and $99$ are themselves names. What thing does $1$ name? Observe that a name is itself a thing, and so may itself be named.

Axiom 2: We are allowed to use a name instead of the thing.
(2)

EXAMPLE: $a$ names $99$
$a$ is the name. $99$ is the thing. If I tell you I have $a$ pencils, how many pencils have I told you that I have? I have 99 pencils.

Axiom 3: We are allowed to name several things with a single name.
(3)

EXAMPLE: 1, 2, 3, ... names the [set of all] natural numbers
'1, 2, 3, ...' is the name. 'the [set of all] natural numbers' are the several things. In fact, '1, 2, 3, ...' is a convention for how to name all the counting numbers from 1 to infinity. How do you say "1, 2, 3 ..."? You may say "one, two, three and so on [forever]", or you may say "the [set of all] natural numbers, or you may say "all the counting numbers from one to infinity". All these are synonymous. Do you see that a name may name another name, that many names may name the same thing (or name), and that many names may name the same [several] things (or names)?