I noticed something a while ago. I was cleaning at school and came across a table with 3 columns. In the first column were the numerals 1 to 10, in the second column the binary values for 1 to 10 and in the third column the hex values for 1 to 10.
The curious thing I realized as I studied the table arose from the question “What do these symbols stand for?”
If I were to ask you what the binary value 10 stood for you would probably say “That stands for 2” and this wouldn’t give you too much trouble.
But what does 2 stand for? 2 is as much a symbol as 10.
The French word (read: symbol) for pineapple is ananas.
The English word for ananas is pineapple.
Ananas and pineapple are both symbols that mean the same thing as 2 and 10 mean the same thing. The difference is that the referent of the symbols for pineapple can be pointed to.
Say I ask you to point out 2 to me. You may direct my attention to a pair of nuts and say “There’s 2: 2 nuts”. If I subtract from the image everything that belongs to the nuts (shape, colour, size, position etc) then I am left with nothing.
There isn’t some entity I can point to and say “Look, there is 2”
This isn’t so much a problem in reality. It is a problem with a picture of language we have developed called the picture theory of language. That is the theory that states that all words have a meaning or that meaning is defined as being a correspondence between a symbol and what it signifies. Numbers are words, components of language that have no signified.