CuthbertJ - 08 June 2012 01:28 PM
What’s the difference between you and the Universe?
If we looked down to the atomic level it’d be hard to tell the difference between where your finger, say, ended and the air around it started. So what’s the difference between the thing we call the universe and the thing we call you and me? Is the relationship one of Whole to Whole, Whole to Part?
Intuitively, it seems obvious at the macro level that you, as a sentient entity on the earth, is part of the earth, the earth is part of the solar system, the solar system is part of the milky way galaxy, the milky way galaxy is part of all the galaxies and the galaxies are parts of the universe.
So, you are one miniscule part of the universe. But, is it so?
However, at the quantum level, it is not so obvious as quantum objects are vague objects. That quantum objects are indiscernibles which can exhibit superposition and entanglement seems to imply that they, you and the universe (both of which consist of quantum objects) is one indivisible whole.
This leads us to mereology, the study of parts and wholes.
From the wiki on mereology
Axiomatizations:
Mereology has been axiomatized in various ways as applications of predicate logic to formal ontology, of which mereology is an important part. A common element of such axiomatizations is the assumption, shared with inclusion, that the part-whole relation orders its universe, meaning that everything is a part of itself (reflexivity), that a part of a part of a whole is itself a part of that whole (transitivity), and that two distinct entities cannot each be a part of the other (antisymmetry). A variant of this axiomatization denies that anything is ever part of itself (irreflexive) while accepting transitivity, from which antisymmetry follows automatically.
The “assumption that the part-whole relation orders its universe” makes sense at the macro level but it is only an assumption and as such, it could be wrong.
OTOH, there are other philosophical perspectives to consider.
From the wiki on gunk (mereology)
In mereology, an area of philosophical logic, the term gunk applies to any whole whose parts all have further proper parts. That is, a gunky object is not made of indivisible atoms:
If something is made of atomless gunk then it divides forever into smaller and smaller parts—it is infinitely divisible. However, a line segment is infinitely divisible, and yet has atomic parts: the points. A hunk of gunk does not even have atomic parts ‘at infinity’; all parts of such an object have proper parts.
—Ted Sider
From the wiki on mereological nihilism
Mereological nihilism (also called compositional nihilism, or rarely simply nihilism) is the position that objects with proper parts do not exist (not only objects in space, but also objects existing in time do not have any temporal parts), and only basic building blocks without parts exist. Or, more succinctly, “nothing is a proper part of anything.”
Explanation:
A number of philosophers have argued that objects that have parts do not exist. The basis of their argument consists in claiming that our senses give us only foggy information about reality and thus they cannot be trusted; and for example, we fail to see the smallest building blocks that make up anything, and these smallest building blocks are individual and separate items that do not ever unify or come together into being non-individual. Thus they never compose anything. So, according to the concept of mereological nihilism, if the building blocks of reality never compose any whole items, then all of reality does not involve any whole items, even though we may think it does.
From the wiki on mereological essentialism
Mereological essentialism is a philosophical thesis about the relationship between wholes and its parts, and the conditions for their persistence. It holds the view that objects have their parts essentially, implying that if an object were to lose or gain a part, it would cease to exist—that is, it would no longer be the original object but a new, different one.
So, what about quantum objects? Do they have parts? Are they discernible objects?
From this article at the SEP on The Identity of Indecernibles
The Identity of Indiscernibles is a principle of analytic ontology first explicitly formulated by Wilhelm Gottfried Leibniz in his Discourse on Metaphysics, Section 9 (Loemker 1969: 308). It states that no two distinct things exactly resemble each other. This is often referred to as ‘Leibniz’s Law’ and is typically understood to mean that no two objects have exactly the same properties. The Identity of Indiscernibles is of interest because it raises questions about the factors which individuate qualitatively identical objects. Recent work on the interpretation of quantum mechanics suggests that the principle fails in the quantum domain (see French 2006).
So, what is a whole and what is a part? 
