2. References

References form the basis for points of view.

The introduction of “nothing” into our domain of discourse forces us to take account of references (as “nothing” is such a thing). References are both things in themselves, as well as things which refer to other things. The significance of references most often derives not from what they are, but from what they represent. For example, the firing of a neuron might be an electrical discharge, but it might mean that a cat is rubbing up against our leg. From a subjective viewpoint, the neuronal activity is not merely associated with something else: it is something else.

References depend on interpretation, or the adoption of a certain point of view: although they can be understood in terms of what they are materially, they are references because they can substitute for the thing to which they refer. The semantics of a situation are altered by taking things at face value, as opposed to understanding those things as references to other things. In virtue of this, references form the basis of different points of view of the same phenomena.

In the field of semiotics, two primary kinds of references are distinguished: signs and symbols. Signs are things which point to something else. For example, an arrow painted on the ground points to (signifies) something else; it does not point to itself. Symbols, on the other hand, stand for (or represent) something else. For example, words are in some sense substitutable for the things they reference. In this book, the term “references” encompasses both signs and symbols.

The term “reference” is convenient because of the symmetric notion of dereferencing. If a reference to a thing is dereferenced, the original thing is once again obtained. For example, if x is the name for y, then we may say that x references y, or that x is a reference to y. We might also say that x denotes y, or that y is denoted by x.

References may differ, even though the things they refer to are the same.

In some situations, the hierarchy which is responsible for carving a particular part out of a larger whole is arbitrary. For example, one may wish to identify green tomatoes. Two parthood derivations that identify a thing that is green, which is also a tomato, are depicted in the following two figures. The diagram labeled “Green Tomatoes” illustrates a hierarchy where green/notgreen is ontologically prior to tomato/nottomato, and the diagram labeled “Tomatoes, Green” shows the alternative scenario (where tomato/nottomato is ontologically prior to green/notgreen):

The things identified by the bottom left node in figures 3.1 and 3.2 are the same: greenish tomatoey things , or alternatively, tomatoey greenish things (neglecting the fact that “tomatoey” has somewhat looser membership criteria than “tomatoes” ). In both cases, the referenced concept must be constructed from other words, so it takes at least two hierarchical levels to create (i.e. we do not have a single concept for green tomatoes). From the awkwardness of the latter construction, it seems that most English speakers would derive this thing as in figure 3.2, where the category tomato is prior to color.[32]

The substitutability of the nodes that represent nouns and adjectives is coincident with treating them as similar things on a conceptual level. In particular, nouns and adjectives are both understood as conceptual functions that apply to space. The significant difference is that nouns have already been applied to that spatial thing, while adjectives still require that spatial thing (which is exactly why they require nouns).

Although most people would not be surprised to find such a conceptual simplification, some people might advocate for treating adjectives like nouns ( “green things” ) instead of like functions ( “green” ). This approach, which is the one taken by first order logic, poses a number of problems for natural language. For example, if we treat small as equivalent to the set of small objects, then we must be able to enumerate the set of small objects. However, if we include objects such as small apples in the set of small things, it poses a problem because these objects are huge when compared to large cherries. In other words, treating adjectives as nouns does not account for context sensitivity : sets of small things can be enumerated only after knowing the domain to which they apply.

References encode small amounts of information about the referenced domain.

Evolution rewards animals which can represent and make use of an immense amount of information, as long as the biological cost of this representation is not too great. Hence, the compression of information is of great value. That compression entails the use of references to encode information. References are easy to manipulate as opposed to the things that they reference, so their use is certainly convenient. If we wish to represent the world in a smaller part of itself, the use of concise references is mandatory: otherwise the contained thing would have to be as large as its container. In other words, references (or words) are a means of signal compression. This view of language offers a number of insights into the nature of human language and thought, two of which are briefly explored here.

One insight is that the use of symbols to encode information makes the distribution of the symbols critically important. For example, if there is no snow in the world, then there is little use for words that describe snow. If there are numerous kinds of snow, sleet, and hail, then this variety would entail a large number of symbols to represent it accurately: in practice, this is exactly what happens.[33]

The other significant insight derives from the fact that signal compression is often achieved by means of dimensionality reduction. The key observation behind reducing the number of dimensions in order to compress information is that much of the change in an event happens only in a few of the dimensions which that event occupies. For example, if some object moves from here to there, there are many dimensions of the object which do not change (such as the dimensions which take account of only its internal structure). Because the dimensions of variation are primarily those related to the position of that object, we can represent the change using only those dimensions: the other dimensions are not significant.

By not describing the variation along dimensions which change by relatively insignificant amounts, it is possible to both achieve a great simplicity in representation and also discard very little significant information. Of course, the determination of which information is significant can be difficult: from some points of view the object is changing so much that it does not even make sense to consider it the same object: from other points of view, these same changes can effectively be ignored. In practical terms, although there is some risk in discarding important information, a large amount of compression can be achieved if the dimensions of change are chosen carefully.[34]

[32] This comparison ignores the fact that green and tomato are different parts of speech. However, ontological priority is inextricably connected with creating parts of speech in the first place. For English, one means of codifying ontological priority in language is by making the ontologically-prior thing a noun, and the ontologically-subsequent thing an adjective. Syntactically, this corresponds to the fact that nouns can operate as noun phrases, but adjectives cannot.

[33] The linguist Benjamin Whorf gathered information about this phenomenon: he found that Alaskan natives had seventeen different words for snow, while speakers of most other languages have many fewer. This particular evidence is relatively famous because it is tied to what is called the Sapir-Whorf hypothesis. In a weak formulation, this hypothesis states that language enables thought, so that possessing a rich language about a given subject allows more detailed or precise thought about that subject.

[34] It makes sense to reduce dimensionality for the purposes of conveying an event. However, the listener must not make the assumption that the event itself is a low-dimensional thing; only the characterization of it is of low dimensionality (which is required for symbolic communication).