Numbers – Do they really “exist” ?


One upon a time humans invented numbers. And since then they see numbers everywhere. But do numbers really “exist” ?

Imagine that number do exist. What would that mean for the Universe? As Leibniz postulated (see La Monadologie), if we try to use numbers and fractions, we would always break our head on unsolved paradoxes related to infinity. If something can be divided with everything, then we would end up with everything being consisted of infinite sums of entities with the value zero… And how can you even “know” there is an infinite number of numbers if you can never have an experience of that infinite? Set theory added to the mystery. If a set (and we must remember that a number, e.g. 3, is the set of all sets which have three entities in them – See Frege) is the basis of so many paradoxes like the ones Russel discovered, then how can we relly trust that numbers actually “are” ?

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But things described by numbers actually work!, someone might argue.

But everything “worked” before we invented numbers!, someone might answer.

What does “1+3 = 4” mean for Nature anyway?

Things we create do not necessarily exist. And if our creation leads to unsolved dead-ends then one might logically conclude that it is not as “self-evident” as one might want to believe…

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