The philosophy of one.

There is only one of me. Half of me or even 0.1 of me is no longer me. There cannot be two of me because then the one of me can no longer be. There cannot be many **of** me but there can be many **like** me. But me, together with one more like me, could only be one of something else, which would still not be me. Identity and existence go hand-in-hand. The essence of identity lies in oneness. There can only be one of any **thing** once that thing has identity. Once a thing is a thing there is only one of it. Half that thing is no longer that thing. There can be many **of** such things but every other such thing is still something else.

Numbers are abstract and do not exist in the physical world. They are objects (“words”) within the invented language of mathematics to help us describe the physical world. They enable counting and measuring. The logical *one* or the philosophical *one* or the mathematical *one* all emerge from existence and identity. Neither logic nor philosophy nor mathematics can explain what *one* is, except that it is. Every explanation or definition attempted ends up being circular. It is what it is. Mathematics presupposes that one exists but can only assume what it is.

The properties of one are prescribed by the assumptions (the “grammar”) of the language. One (1,unity), by this “grammar” of mathematics is the first non-zero natural number. It is the integer which follows zero. It precedes the number two by the same “mathematical distance” by which it follows zero. It is the “purest” number. Any number multiplied by one or divided by one remains that number. It is its own factorial. It is its own square or square root; cube or cube root; *ad infinitum. *One is enabled by existence and identity but thereafter its properties are defined, not discovered.

Stanford Encyclopedia of Philosophy

Numerical identity requires absolute, or total, qualitative identity, and can only hold between a thing and itself. ……. Numerical identity can be characterised, as just done, as the relation everything has to itself and to nothing else. But this is circular, since “nothing else” just means “no numerically non-identical thing”. It can be defined, equally circularly (because quantifying over all equivalence relations including itself), as the smallest equivalence relation (an equivalence relation being one which is reflexive, symmetric and transitive, for example, having the same shape).

What existence is the answer to is anybody’s guess. From existence emerges the identity of our universe as a smooth, homogeneous soup of energies and matter, spiced by waves and particles and flavoured both light and dark. Interspersed in this nebulous, existential soup are croutons of hard, firm, observable things. From identity emerges oneness. Every atom of the 10^{80} atoms thought to be in our universe is separate and distinct in its existence from every other atom at *any given instant*; and there is only one of each. And if we could assign identity to each of the particles making up these atoms, then each of those particles would be separate and distinct at *any given instant*, with only one of each such particle.

Each a crouton in the soup of existence.