Do numbers exist?

This seems like a bit of an odd topic for a maths fanatic to discuss, and really it isn't very mathematical to even think about it, as you will you soon find out it is more philosophical.


You'd think it is obvious that the answer is "yes, they do exist", but it really isn't that simple. The fundamental idea of numbers started with counting a number of items, animals, children, etc. and from there it spiralled off. In fact the definition of a number is: "an arithmetical value, expressed as a word or symbol representing a particular quantity".


So numbers 'exist' to serve a purpose for counting, arithmetic and calculations. So if we have 'two' dogs, do we count the number of hairs they have as being them? Do we count the number of bugs on them? Do we need to count the number of atoms in the dog towards the 'two'? So is it really 'two' or is it some uncountable number of atoms? Or quarks? But just because we can not clearly state what two is in real life, it does not mean they do not exist.


Numbers do make interpreting what is happening an awful lot easier, but that doesn't mean they 'exist'. They easily could have been created by man to help with problems, the problem arises when you need to define what 'existing' is. To 'exist' you need to have reality or being, do numbers really have this? They are not a physical, touchable thing and could anyone really argue the case of a number having a reality to it?


You could then argue that nothing really, truly exists, as what is reality? But that is a completely different tangent for a future post. I mean, do thoughts really exist? Do words that are spoke? But anyway, I digress...


Numbers can be thought of as tools developed by us a civilization to help understand the world we live in. But if there was a race of intelligent aliens there is almost no doubt that they would have a form of maths, they may work in a different base (in fact the Aztec's worked in base 6, opposed to our base 10), or some of their basic principles may be different (a negative times a negative could still be a negative, for example). But there is almost no doubt that basic principles of maths will be there. And once they are in place more advanced concepts start to develop like how are these numbers distributed? What about a number between 1 and 2? How do we add numbers? How do we multiply numbers? And so on.


So whether they are invented or they exist, they are a necessity. It takes away the "what if?" factor from so many elements and provides concrete and quantifies otherwise incomprehensible things and data. Numbers are so useful for everything, so really it doesn't matter if they exist or not because what they accomplish is real, the data, the facts and the information they provide about the world we live in is real, they have a real impact.


So rather than getting bogged down in the semantics of whether numbers 'exist' or not should not detract from the joy and beauty of mathematics. Maths is fun, do not let your philosophical stand point alter any of that.