*Why do numbers exist?*

*The reason numbers exist is to make life simpler and explain our universe.*

So the better you understand numbers, the better your life can be.

That's a pretty good reason to like mathematics.

Apart from the answers to the question "Why do numbers exist?" posted below, you can also read answers at

https://www.linkedin.com/groups/Why-do-numbers-exist-1872005.S.5943156302690656257

Numbers exist in the human mind. All mathematics has been invented by humans so it has no objective existence.

But why have we invented these non-existing abstract numbers? To be able to more easily compare piles of items or groups of things? To more easily keep track of our possessions? Or maybe to be able to order the siblings in a family?

The first numbers developped were the natural numbers, and they exist because nature offered us sufficiently similar things to count with. Nuts, apples, fingers, legs, fishes of a given species but also stones of given kind are so similar, that one had to invent numerals in order to describe quantities of similar items. Similar things originate in similar condition of genesis, see also the property of the Universe to repeat itself (an experiment can be repeated in the same conditions to get the same results). This was predictable aspect of the Universe caused the apparition of numbers and later, stepwise, the development of more complicated mathematics and natural sciences.

Yes, we created names for numerical relationships but the question remains --- why? Numerical concepts exist rudimentarily in other species (conures, apes, etc.) in the ability to detect differences in two or more visible piles of stuff. They don 't have out linguistic tools but perceive neric distinctions. Although this innate-in-multiple-species ability can be honed through appropriate education (remember Mr. WhatsHisFace in the third grade math class), it exists before education.

I argue that numerical and other set-to-set relationships exist outside our minds and concede to Goedel that although unprovable, they exist.

"Classes and concepts may be conceived as real objects , namely 'pluralities of things' orcas structures consisting of a plurality of things and concepts as the properties and relations of things existing independently of our definitions and constructions". Godel quoted in Benacerraf and Putnam, Philosophy of Mathematics (Englewood Cliffs, 1964), p.220.

Fun 🙂

I completely agree with Albert Villasenor. Numbers were invented by humans as tools to make sense of the world. They do not have any objective existence. Just as Euclidean geometry is useful in describing a certain sub-set of the world and non-Euclidean geometry in describing other sub-sets, our everyday arithmetic is useful in describing certain sub-sets of the world. I have written more about it at http://www.philipji.com/item/2014-08-19/on-the-common-belief-that-one-plus-one-equals-2

Given several "definite and separate" (Cantor) objects, the multitude or plurality of those objects is of a determinate cardinality. Multitudes are equinumerous when in one-one correspondence. Abstracting under the equivalence of equinumerosity gives us the multitude's cardinality of number. Treating those abstractions as if they are objects we find nice relationships among "them". But there are no such objects as numbers, it's just that we can treat the numerical relations among multitudes efficiently by speaking and writing as if there were. Numbers are what Leibniz called "well-founded fictions".

Elsewhere, John Kormylo answered my question this way.

When applying for the job of shepherd, the first question is "Can you count?"