A Theory of Freedom
by John Valley
Standish, Michigan
April 01, 2008
Chapter 4. Representation
In the last chapter, it was suggested that the concept of representation would form the foundation of intentionality. In this chapter, we want to draw more clearly how representation is at the center of intentionality, to connect representation to language, linguistic forms, semantics, meanings of all kinds, and the elementary principles of structure, form, and organization. It would be remiss to let this subject go by without addressing the physicalist belief that these kinds of entities are only a way of thinking about properties of matter, and not real in themselves.
The defining property of a representation is that it sets out a sign and pairs something else with it. The sign is always a physical entity of some sort: a mark, a fragment of speech, a piece of paper stuck on a door, or even an event, such as an alarm going off, a starter’s gun shooting, or a light switching on. The signified, however, that which the sign represents, is not physical. The entity paired with the sign is called its meaning. An extremely extended kind of representation can be found in the arts such as oil painting, where a hodgepodge of colored oils smeared on a canvas is supposed to represent the Last Supper; a form of representation which a blind man would have no means of understanding. But regardless of how simple or extended the representation, it can always be reduced to two basic elements, thus:
R: s → m
In other words, a representation is composed of a sign and a meaning.
This sort of structure is very plainly illustrated by the contents of an english-language dictionary. The term to be defined–a word– is set off on the left side of an entry. To help the reader, some sort of mark is inserted to separate the term from what follows: its definition. But in fact, no such separator is needed. The entire semantic form of a dictionary entry is encapsulated by the form
ab
where a is the term to be defined and b are the words of the definition. These two objects aren’t even of different kind: they are both words or strings of words.
A symbol has the same form as a dictionary entry. It is also a pairing, between the sign and whatever the symbol is supposed to represent. So, at once, we see that the basic concept of representation is equivalent to the concept of the symbol, and they differ in practical usage only by the types of signs. Symbols are usually understood to be words or written marks (although not necessarily, and no doubt the usage of “symbol” and of “representation” do cross over). Representations are usually more complex objects, like the case of the painting mentioned earlier. But the underlying structure is the same.
R1: The form of a symbol is an intention. The intention of the symbol is to represent its meaning.
R2: Intentionality exists as representation.
This is how representation relates to the subject of intention in the previous chapter. We were talking about intentionality, but it wasn’t made clear how intentionality actually exists. Intentionality is instantiated by the symbol. When intentionality is made manifest, it takes the form of a representation. A representation implies an intention to represent, and the representation is understood in terms of what is represented. In other words, the meaning of the representation is not its sign; such a case would be called a literal statement of the sign, and a sign taken literally is just the sign, without any meaning.
Because intentionality is manifest as a symbol or representation, this implies that free will and choice are abstract objects and necessarily obey rules of the sort that logic takes. In any further discussion of how physical law constrains choice and intention by causality, we have to look at how physical law constrains symbol and representation, because that’s what intention is.
Before going on, I should explain how an ordinary intention, such as a man's intention to go grocery shopping this afternoon, exists as a symbol. The most trivial example would be in the form of a note in his calendar: "Go shopping." The note is linguistic. It need not be. He could tie a string around his finger, using a convention that it means, "Go shopping this afternoon." The written note is a bit superior, of course, because it's more explicit about the intention, but even so, the note is not very exact. It doesn't say who should go shopping, when they should go shopping, where they should go shopping, or what they should get. More likely, the man will make no note at all, and simply remember his intention. In this case, something about the state of cells in his brain will signify the intention; that is, some of his brain cells will serve as the s-part. And this is the conventional view about how mental functions are instantiated: they take some physical form in the brain.
This is all well and good except for one thing: If the brain cells only contain the s-part, where is the m-part? The sign is no good without its meaning, but by pressing the brain into service as the token of the intention, we've run out of places to put the meaning.
Let’s set that question aside for the time being and go back to the first fundamental proposition again, R1, and amplify on what is meant by “the form of a symbol.”
The form of the symbol is its structure. In other words: s → m. The left side of the symbol is the “token.” The token is all we encounter in any use of the symbol, but it always forms a paired structure in our understanding, so a symbol is a unique kind of entity in that it never occurs in its entirety in any usage of it. Physical objects aren’t like this. Where they occur, they occur completely. There is no part of the object that isn’t part of the object. With a symbol, however, even when, as in a dictionary, the symbol appears together with its definition, the definition of the symbol is not the words of the definition. In fact, you can define the symbol with any sequence of words that means the same thing; translations are possible, and this is important in writing books such as English-German translation dictionaries. The term on the left is in English, and the list of German words on the right is its definition–but this doesn’t mean the word becomes German by virtue of this. On the contrary, the only part of the definition that matters is its meaning, not its words.
Let’s say that again.
A symbol consists of two parts, only one of which exists in the world. The token of the symbol is the sign itself. The meaning of the symbol is what makes it a symbol, but it isn’t present. This is the case even when the meaning of the symbol refers to an explicit object. For example, the meaning of the word “Plato” is a man, but clearly the meaning doesn’t depend on the actual existence of Plato. Plato can die, decompose, and vanish, and this has no reciprocal effect on the symbol “Plato;” it still means what it did. In other words, a reference to an object is a reference to the idea of the object.
So we have an apparent contradiction: the symbol is not a symbol without a meaning, but the meaning is not present in the world, therefore the symbol is not a symbol because it has no meaning. This contradiction must be resolved, but the most obvious resolution, to suppose that meanings exist in brains, is incoherent. As noted above, the brain has to contain the s-part of thoughts, meanings, and representations. The meaning can't be there because meanings aren't explicit, and if they were (as with the definition part of a dictionary entry), you'd still have to say what it means.
To this point, the reader may think we are only talking about language, and language, while interesting, is an imaginary object and nothing real, so if there’s any purpose here, on my part, to cast all this linguistic analysis as some sort of challenge to physics, we are all just wasting our time.
On the contrary, there can be no physics without form and structure. Physics is relational. Its mathematics focuses on the relationships between masses, energies, forces, and interval and duration, and all the possible constructs of those elements. In other words, a physical object cannot exist by itself. That is, a physical entity is an incomplete entity. An attempt to depict the world in purely physical terms would fail, because such a depiction isn’t possible. Yet the study of physics seems to do this, so how does it do it?
Let’s consider a simple physical system consisting of two particles, thus:
Fig. 1
This is just about the simplest physical system you can have. The two particles each have a location. In figure 1, they are shown relative to an arbitrary origin, but it would be just as easy to make the point of reference coincide with either one of the two particles.
Notice all the structural relationships in this system. Each dimensionless point particle has two co-ordinates (x1 and y1, or x2 and y2) which specify the relative distance the particle lies along the two axes. In fact, we can form a pairing of coordinates to yield a position P:
P: (x,y)
Finally, the distance between the two particles s is a function of the positions of the two particles:
s = ƒ(P1,P2).
These descriptions of the physical system use the particles as tokens of a representation: the positions of the particles are given in terms of coordinate axes which don’t actually exist; the distance between the particles is described by a line which isn’t there. In other words, the only way to understand the system of particles is through its relationships to abstract entities. What is represented by the particles is the two-particle system (and its geometry).
While this may seem harmless at first glance, it should be clear that if we consider the representation to be imaginary (in the same sense that a description is not the thing it describes), then, in effect, we’re saying the distance between the two particles doesn’t exist. And this is true, if ‘exists’ has to mean in the sense that each of the particles exists–as points of matter. The two particles exist, but the distance, shown in Fig. 1 as a line, isn’t actually there, and if there’s any question about that, try photographing the system. Where the distance is supposed to be, there will only be a gap on the photograph.
To conclude this section on representation, it can be said that any physical system is a token which forms the s-part of an R, where the m-part (its meaning) is the structure of the system, and by the very nature of symbols and representations, the meaning is not explicitly present in the system itself. In other words, the structure of the system is not the particles that comprise it.
In the next chapter, we’ll want to look more closely at this extension of the concept of representaiton: Form and Structure. If all goes to plan, it will show that form and structure, so important to all descriptions of things, is an elaborated construct of representations, and so, not physical.