Look at the paper that holds these words. What are you holding right now? How is this page related to the one behind it? They were made at the same factory; they probably came from the same tree, or at least the same forest. They both came from the same printer, and they both bear the words of the same author. Examine them further, and you will find that the paper is reasonably dense and thin. But what is the paper itself? Look at the paper not for what it contains, but for what it is. A thin rectangular white piece of compressed processed wood pulp. I've just put a description to the thing, but what does that description mean? What do the words, themselves mean, and more to the point, what do the thoughts that underlie the words mean? To answer these questions, we cannon simply focus our senses upon the paper, we must instead turn to our thoughts to the question.
Not surprisingly, this question has been answered many ways throughout time, in many interesting and inventive ways. The answers range from "the paper does not exist, and you express you philosophical ignorance by posing the question in the first place" to "what do you mean 'What is the paper?' Is it not obvious? Have you never been afflicted with a paper cut?" We are interested in the question in a somewhat more restricted sense. How do the words (whatever words those might be) and the underlying thoughts have meaning?
Let's examine my someone vague description of the paper: "A thin rectangular white piece of compressed processed wood pulp". What does the term 'rectangular' mean? I obviously mean the mathematical concept of a parallelogram who's angles are all ninety degrees. Unfortunately, the paper isn't. It's angles are almost necessarily not at exactly ninety degrees, and it edges aren't even the same length as each other. Rectangles, by definition, exist in two dimensional space. My piece of paper is most definitely a three dimensional object. So by what right do I call this paper a rectangle? By what what right do I call this paper 'paper' for that matter? How did I make that determination? How can I blithely cast an entire series of objects into the 'paper' class?
Let's start with a nice, solid, palpable theory. This paper is paper because it has some connection with some very real entity that _is_ paper. This entity does not _resemble_ paper, it _is_ paper in every conceivable sense. In fact, all other things in the universe are paper, only in so much as they exemplify this entity. Here, we have the theory called Realism. The idea behind Realism is wonderful in it's apparent simplicity. We simply have this thing. It could be corporal, or it could be non-corporal. This thing forms the basis for an entire class of objects. All other objects that are to be classified at this class must resemble the thing we have. This idea has a sort of earthy palpablity that gives philosophers a warm and fuzzy feeling.
In fact, this idea not only has simplicity working for it, it also has history. History with a big 'h', actually. One of the fundamental versions of Realism is called Platonism; surprisingly, this name is not just a coincidence. This was the theory that Plato developed and passed down to his students. As such, this idea has had a profound impact on the development of western culture, even if western culture didn't realize it. Plato envisioned reality as divided into several fundamental groupings: noesis, pistis, eikasia and dianoa. He called this grouping the 'divided line'. This line encompassed reality at every level. Plato's most base and empty reality was illusion. This included the poems, plays and songs of his time. The next level of reality was not quite as base as the first, but neither was it one of the vaulted types of reality that were to come. This level of reality was merely life itself. The entire perceived universe fit quite nicely into just one of Plato's levels. Next comes the first of the really real stuff. Mathematics and geometry compose the third most real levels of reality. Do you sense a trend here? For the final, most vaulted, truest form of reality, Plato chose 'noesis', or 'the form'.
These are the very stuff of reality itself. All things in the lower levels only really exist to the degree that they are like the forms. Our piece of paper, for instance, is only a piece of paper to the degree that it is like the 'form of the paper'. The fact that we refer to this paltry object that actually takes up space and has mass as paper is, strictly speaking, incorrect. It is really an instantiation of 'the form of the paper' (the only thing that can truly be called paper). Plato's idea of the forms is difficult to dispute. His 'form of the paper' isn't something that anyone is likely to stumble upon in the student store. As such it would be hard to point out that 'the form of the paper' is flawed because it is discolored, or has large wood chips in it. It is, by definition, abstract.
Much of current day Realism is based on Platonism. First, let's do a gratuitous redefinition of terms. The idea of 'the form' is what is currently often called 'a universal'. Plato's divided line drops away entirely (well... mostly, anyway), leaving only what is considered the observable universe (with the minor addition of the actual universals which may or may not be observable). The things that we encounter from day to day are known as 'particulars', that is to say that they are a particular instantiation of a universal. Great fun.
So let's approach an interesting curiosity. This universal, let's say the 'form of the paper' (it's a bit less awkward than saying the paper universal) has many instances of itself. Each piece of paper is a piece of paper because it is related to the 'form of the paper' through the relationship of instantiation; that is to say that each particular bit of paper is paper because it is similar to 'the form of the paper'. Each piece of paper that exists in the universe is actually one of these paper particulars. So, 'the form of the paper' is, to some degree at least, the set of all paper particulars in the universe.
Is the 'form of the paper' itself similar to 'the form of the paper'? Of course, via identity. As this is the case, the form of the paper is itself an instance of itself. This seems odd, but not incongruitous. Well, this means that 'the form of the paper' is itself contained within itself, an unenviable position if there ever was one... (How would _you_ like to both contain and not contain yourself?) Well, this is odd, but one could certainly argue that the property of instantiation is more than simple resemblance; that instantiation also means that the object must exist in reality. That makes the theory a bit more oblique, but still tenable. We've just tried to better define instantiation. That seems to just beg the question 'What else could I do to this property of instantiation?' Well, after a bit of thought, another conundrum presents itself.
The particular is tied to the universal by property of 'instantiation'. We could, with just a bit more thought, bring this a bit further out. A particular relationship between a particular particular and a a particular universal is itself a relationship. This is an instantiation of an instantiation. Lovely. But wait, there's more! The relationship of the relationship of the relationship is also an instantiation of another universal entirely. And so goes the infinite loop. Now, for whatever reason infinite loops don't put me off, but they are certainly messy...
So with this, we move on to a somewhat more exotic type of realism. What if these 'universal' things didn't exist in the abstract way that Plato envisioned? What if our 'universal paper' was not, in fact this super-papyrus object, rather it was literally all things paper. Let's not confuse this with Nominalism (which we'll get to later). This is a real thing. It just happens to be a spatio-temporally discontinuous thing. Perhaps there is really only _one_ piece of paper, and all those things that we perceive as separate paper-entities are just manifestations of the very same object in multiple places.
Imagine for a moment a finger-less glove. You put your (quite in one piece) hand into it, and all of a sudden, your hand is concealed and all that you are left with is five fingers poking out of the glove. It is still one object, but it appears to be five separate spatially discontinuous object. Now what would happen if you stumbled onto five closely positioned wormholes, and put your fingers through them. Your fingers (which are still attached to your hand) have suddenly become five spatio-temporally discontinuous objects that are, in fact, one object.
Now that you are looking at your nice, spatio-temporally continuous hand again, think about how other objects could be quite similar to your spatio-temporally discontinuous hand. You really have no way of telling that this isn't the case. Unfortunately this idea is somewhat conceptually bulky. Other ideas end up solving the same problems but without nearly as much overhead. Occum's Razor strikes again, and this theory remains in relative obscurity.
Now that you're nice and comfortable with the idea of universals, I'm going to pull a fast one. We're going to talk about Nominalism now, where universals don't exist. Oh sure, people may _think_ they exist, and for that matter, they may think that groupings of all sorts exist, but the Nominalist knows that really, nothing is really a group, they are merely a collection of individuals.
***What?***
Exactly. Groups don't exist. Oh yeah; all those years that you thought that groups did exist: You were wrong. The common conception of the 'group' is merely a odd holdover of human mental sloppiness. Hey: These things happen.
In fact, names don't exist either. Neither do places. These are also examples of human mental sloppiness. People's names are not unique, you see, so they are useless. The real way to identify someone is to list out every single action that person has ever taken, every position in space-time that they have occupied, and lump all this data together into one giant name tag. Hello, I'm ( Born in Santa Cruz May 25, 1975 8:15am, moved my left foot two inches to the right on May 25, 1975 at 8:17, another two inches to the right just a few short seconds later, blinked just a bit after that ... writing an essay for Philosophy 411 right now), pleased to meet you!
The things that we (damn! There's another group!) call paper are really just one of the things that are members of a particular set. We really ought not say 'paper', in fact; we should instead list every instance of what we consider to be paper from the beginning of the universe until its end. This set itself is paper. Every piece of 'paper' is merely a member of that particular set.
This entire scheme is cumbersome to the extreme. The only advantage that I see is that no viable reductio 'ad absurdium has occurred yet, and probably never will for the simple reason that this scheme removes anything even remotely worth arguing about. How can you argue against a system that purports to contain _nothing_ but particulars? Unless the universe is itself disproved (and relatively few people are willing to do that for fear that they might be successful... Think how annoyed people would be if they found out they didn't exist _at_all_. I don't know about you, but I'd be pretty darned pissed!) particulars aren't going away. The primary problem with Nominalism is that it is conceptually difficult in the extreme to justify every day, normal thought processes. They are simply logically flawed. This isn't itself a contradiction (people are wrong all the time, even on a mass scale), but it certainly makes the idea less appealing...
Lastly, I will cover the theory that I like the most. It is, coincidently, also the easiest to explain, and it contains the least baggage while still allowing for normal human thought and reasoning. The theory is conceptualism.
The idea is simple. Universals don't exist, per say. There is no such thing as a 'universal' tromping about. It is extremely unlikely that on your morning run you are going to stumble across 'red'. Not something that _is_ red. Just red. Universals, though they don't _actually_ exists, do offer a wonderfully compact way of expressing a concept. It may very well be that all that 'red' is is the commonality of all objects that reflect or emit about 700 nm light waves, but that's OK. So it's a big group. We can collectively know this group as just 'red' without having to enumerate _all_ members of the group. In fact, we can specify a incredibly small proportion of red things and still get the point across. It is a truly great idea that allows us humans, with out inherently finite brains to gaze into the infinite in many ways.
This could be said to suffer from the same problem as Realism, but that would be wrong for this particular variety of Conceptualism. The entire idea is that the groups (read 'universals') are made up of commonalities of the members, not the opposite. Even if the same argument _could_ be made, I would still make the claim that it didn't matter. Conceptualism is, at its root, a theory of mental convenience. Upon proving that an infinite recursion existed, I would simply shake my head and exclaim "Well, if it is more convenient for you to see it as an infinite recursion, by all means proceed, however I will continue to see it as a simply first order relationship". Conceptualism is not a theory that purports to be completely logically simple, but it is one that can always be _treated_ as completely logically simple. And that is it's power.
So, that is the 'universal'. It is, depending on your point of view and your mental rigidity either a profoundly interesting area of study, or a profoundly frustrating one. I hope to have, at least, demonstrated that with a certain amount of flexibility, the entire issue can be resolved in one of several ways. Which way is, of course, a personal choice (as it is with all philosophy, really). I personally choose the theory that makes my day to day thought processes rational, because being rational pleases me.