Hello dumber:
(points on originality)
Welcome to philosophy where you may find that being a know it all entails only that you admit how you don’t know a thing-- so again, points for a great philosophical name!
Anyway to your question: “trying to figure out what principle governs the reduction of something’s parts while the thing remains what it is…i.e., what principle describes the ability to suffer the loss of certain components while remaining the same essential thing.”
The two that immediately come to mind are Holism, which means that: “The whole is more than the sum of its parts.”; and Platonism, in a way, with his attention to Forms and Ideas. What you seek is really early philosophy, that begins with Thales, and tries to discover what is the principle, or thing, which all other things derrive from. It was believed by some that there was this “essense”, this blue-print that was only poorly represented in matter. This is Plato. Aristotle took it further and “was the first to use the terms hyle and morphe. According to his explanation, all entities have two aspects, “matter” and “form.” It is the particular form imposed that gives some matter its identity.” (from Wiki)
Based on this hypothesis (which echoes Parmeneides’ monism in some respects), if I interpret it succesfully, matter is very much the same in-itself-- reduced to it’s most simple components, all things, including you, me, sticks and rocks etc, are made of the same stuff- elements which are given in the periodic table. Yet, our form is different that sticks and stones. So, is there a blue-print that nature follows in our seeds, so that a tree becomes a tree and not a cat, even though, reducibly, materialy, there should be no reason why the seed of a tree should become necessarly a tree and not a cat?
Now, there is Heraclitus. He may have said that you can never step in the same river again. This is what is in your mind, in whatever incarnation it is, and there have been many. “For example, I understand that skin cells die at a rate by which the entire skin of a human being can be said to be totally replaced in seven years.” If we take that as true then, supposing that you are 40-42 years old, then you are on the seventh object under the colloquial “dumbernmud” (You should know that I mean what you consider your self). It is posited worse than that in Hume and in Russell. Logically, even if your cells remain eternally, you yourself should be different at any given moment. This is clearly proven by the fact that you don’t remember many things from childhood, and the fact that from childhood to now, you have changed many views so that you might not be said to be the same…that you have changed. The river flows and does not stop, so that at a given time, though we say it is the same river, new waters now fill the banks. The question for the philosopher is if this habit of still calling a river or a person by name but a means of short-hand language, or is it because the name of something designated it’s essense as well. Is the river more than just the waters that fill a bank? Are you more than a loose collection of inaccurate memories or cells? What is in a name?
More interesting than the principle is the ethical or moral implications of each view. Here is a bit of sci-fi:
Suppose you meet a very nice girl, hot bod, intelligent, like sports, talks to a minimun and never about gossip. You date for few months and sure enough, such a woman, you end up asking in marriage. At your wedding, the priest goes through the usual wedding sermons and declarations and then he gets to the part that he asks those present if there is some reason why they should not be together. Someone steps up and says: He cannot marry Susan because Susan is a robot! Susan does not exist. Susan is not a woman that you can take in marriage!
Here are your options as a philosopher. You could say that “Susan” is the name of that which is in front of you, that is, the stimuli of your impression. From that point of view, you cannot even know if the person who spoke against Susan is a robot himself. Susan simply denotes the surface of things and makes no speculation as to what is it’s essense, so let the wedding continue.
Or you could feel that Susan had lied to you because in some way, what now stands as Susan fails to meet some quality you’ve associated with her name…say her mortality, because you had an idea with her form of humans and as you know, humans are mortal. She looked human, spoke like a human and therefore you assumed she was a human being. To you, Susan implied human, not robot.
Now think this. If I took a human being and “reduce” it to parts, I would have killed it. That means that would have removed an essential characteristic from it that I could not reinstate…no Frankenstein.
But if I take Susan apart, since she is but servos and gaskets etc, I could still put her back together and make her function as before without fail.
I believe that we are more than the sum of our parts, perhaps not to say that we have an essense that is absolute and impertubable, but that we certainly have a pattern in our cells.
This is very interesting stuff and worthy of an initial study because it permeates philosophy from beginning to what you read now.