The Sum Of Its Parts

That something, if applicable, is the sum of its parts or greater than its individual parts is not a mathematical, geometric, or scientific axiom, though it is true of mathematics, geometry, and science.  It is related to a logical axiom, and any particular example that follows from this is not self-evident.  That something is the sum of its parts is a truth about identity when there is this sort of applicable metaphysical constitution--that is, when one thing is made up of others, whether of a set containing multiple individual units of the same kind, a physical object composed of many particles, and so on.  However, it is the abstract truths of reason that are at the very core of reality and on which all else stands, and it is only what might be called the law of identity that is itself axiomatic regarding this issue.

An axiom is a self-evident truth: to fall into this category, it must be relied on even when denied, which makes it unavoidable.  It is not self-evident that grass is green, for perception of color requires a consciousness, which is itself self-evident to someone who makes no assumptions, and then, of course, the color green, like any color, would only be possible if it is consistent with logical axioms.  To doubt one's own conscious mind, one has to exist as a consciousness, and even though this is self-evident, it is only the laws of logic, which would still be true even if false (rendering their falsity an impossibility) that are self-necessary.  One of the axioms of logic is that a thing is what it is.  This is self-evident because if something is that which it is not, then it still is what it is, and thus the law of identity is true regardless.

It and other logical axioms are true independent of matter and would have to be true in order for any composite object to exist (or else it would be impossible beforehand); it is also true in a way that underpins mathematical groupings, such as how 5 is equal to 1 added to 1 added to 1 added to 1 added to 1.  Not even the logical truth as it pertains specifically to mathematics is self-necessary or self-evident, but this hinges on the fact that a thing is what it is independent of and thus metaphysically prior to all examples.  A given number being itself or a given number being reached by the addition of two other numbers depends on the law of identity and that certain things or or do not follow from others.  It is not the other way around so that numeric quantities ground the laws of logic!

The so-called axioms of equality in mathematics are not axioms at all.  They hinge entirely on the real logical axioms, which are more foundational and are what is truly self-evident, along with one's own conscious existence, though the latter still depends metaphysically on the former and is revealed epistemologically by the former.  However, that something is the sum of its parts, or that the whole is greater (literally, larger or more complete) than the individual parts, is still absolutely certain.  It is just not evident in itself.  Without these logically necessary truths, all the same, it would be impossible for anything to be true regarding numbers, which would of course encompass their identity and relations.  Logical axioms are not assumed or arbitrary starting points as other alleged axioms are.  They are things that cannot be false.