Chapter 10. Informal Summary

Climb to the top of the tree; enjoy the view.

In this chapter, we present an informal overview of many of the topics discussed so far, and focus on the development of a single individual. To begin at the beginning: when we were new to the world, and the world was new to us, what did the world look and feel like?

In the beginning, there was only our perceptual universe; in it, we perceive various things, but we do not conceive of them.[102] Conceptually, the world is undifferentiated . At this early point in our development, we have undefinable experience. It is a complete experience: there is no alternative to it, and there are no thoughts about it. Talking about it, saying that it is a part or a whole, one or many, is problematic because these words imply a conceptual understanding. Our perceptual mechanisms provide us with various lines, dots, and edges, but we do not conceptually know them as such. The world is unique: it just is what it is. Hence, this experience would be inherently hard, if not impossible, to describe conceptually (even if we were intimately familiar with it). We might say that we have not learned to break our experience apart into its constituents; we simply perceive all of it (which avoids an atomistic understanding of this state of affairs). We may also say that it is particulate; we have not learned to unite our experiences into a whole (which avoids a holistic understanding). We might characterize the subjective universe as follows:

Subjective universe: [All experiences and perceptions within the present moment]

Note that the subjective universe is a referential universe: it reflects (or refers to) various aspects of both self and other in the physical universe (although we do not initially know it as such). The referential mapping from the objective to the subjective preserves something of the metric structure of the world: perception is space-like. In other words, the dimensions of these immediate percepts are space (and possibly time), and all percepts occur within these dimensions.

One of the most significant of the perceptual dichotomies, and perhaps the first, is the self/other dichotomy. At an early age, the distinction is perceptual: we have divided everything into two parts, but we have not understood these two things categorically: there are many percepts of me and many of not-me.[103] We may summarize this dichotomy as follows:

Perceptual universe: ‘me’ * / ‘not-me’ *

Despite the fact that in writing this formula we have given a concise label ( ‘me’ ) to a collection of percepts, we do not intend the symbol “me” . Hence, it is somewhat unfortunate that we have been forced to use a symbol within these quotes: although it is necessary for communication, it can be misleading. Percepts are spatial creatures, and they are relatively rich phenomena, unlike concepts (it may have been better to represent this distinction with pictures instead of words).

Concepts are formed for classes of percepts which are significant to the animal. In other words, there is a conceptual universe which becomes divided into two mutually exclusive elements, one of which corresponds to the self-concept, and another which corresponds to everything else. As the conceptual universe refers to the perceptual universe, the conceptual distinction between “me” / “not-me” corresponds to the previous distinction between percepts. These concepts are representations which refer to the (many) percepts out of which they are formed:

Conceptual universe: “me” / “not-me

In this process, an isomorphism develops between a concept and some number of percepts. Eventually, a number of percepts and concepts are formed, many of which are related to one another hierarchically. The divisions which occur are partially determined by their biological importance (this includes things that are most relevant to the individual, such as hunger and thirst). As our conceptual lives develop, biological importance can even become associated with things such as the formulation of philosophical concepts (if, for example, you are employed as a philosopher). Eventually, numerous concepts such as “food” , “friend” , and “enemy” are created out of the undifferentiated perceptual soup, and figure and ground are separated.

The correlation among the objects in the world induces correlation between the concepts in us (and vice-versa). Some of these relationships are emotionally significant, and concepts co-occur with pleasurable or painful experiences. Concepts may come to be good if they make us or our loved ones happy, or bad if they make us or our loved ones sad: in this way, our world is parceled into desirable and undesirable entities. Objects which occur before others in a fairly consistent fashion, and which are relevant to the organism, cause fairly regular chains of behavior to be formed.

Concepts are internal representations of external stimuli that we learn because they are useful predictors of phenomena that we like or do not like. As we learn more and more concepts, it becomes possible to learn stimulus-response chains: the temporal relationships between concepts comes to approximate the temporal relationships between objects in the world. Because of the isomorphic nature of these relationships, the structure of our concepts comes to mirror the structure of objects (although the choice of the objects that we identify is determined by both us and the world).

The essential thing about the mirroring between a concept and an object is that each stands in the same relationship to its respective context (i.e. its context of concepts or objects): the difference in form between concepts and objects is not significant. The isomorphic structure of things persists through several levels of reference. Symbols reference concepts, which reference percepts, which reference objects. The parts at each level influence one another: for example, although objects to some extent determine which concepts are formed, concepts to some extent determine which objects are perceived. Even to speak of objects as independent of a conceptual understanding may give the wrong impression: if the world is continuous and can be divided in arbitrary ways, then to think of the world as decomposable into (only) one object hierarchy as opposed to another is inherently flawed. The fact that we are prone to do so only indicates that our concepts are less permissive of arbitrary division than the world.

The act of perception (or attention) is one of dichotomization. Within the space of that perception, perceptual parts can be produced, which have the same dimensionality. The act of conceptualization is one of unitization: a single concept can refer to numerous constituent percepts or concepts. Despite these characterizations, however, the reverse is also true: conceptualization simultaneously divides its conceptual domain in two parts, the concept and its complement, just as perception collects perceptual features into percepts.

Imagine learning the first-order concept “apple” . Having experienced visual percepts corresponding to several different apples ( ‘apple1 ’ , ‘apple2 ’ , ... ‘appleN ’ ), it is possible to form the concept “apple” . Initially, when the level of conceptual differentiation is relatively crude, the apple may be recognized as an instance of the (more generic) “food” concept, as opposed to an “apple” . Eventually, by acquiring a sufficient amount of experience with different food objects, certain of them are categorized as apples. As our experience increases still further, we learn to recognize specific types of apples, or even particular apples.

All animals have these first-order concepts, which are references to percepts that in turn refer to objects. For most animals, the conceptual universe encompasses only these first-order concepts: as symbols are not formed, higher-order concepts are not possible. However, this is where the conceptual universe of human beings is just getting started: humans learn words, or symbols, which are labels for these first-order concepts. This process, whereby we learn words and associate them with objects, is called naming:

me’ = “me

The creation of symbols, in virtue of the ability to form percepts from concepts, allows a referential loop. This cycle allows the formation of higher-order concepts (or metaconcepts). For example, a second-order concept is a concept which refers to a symbol (or percept) that refers to a first-order concept (which, again, is a concept which refers to a percept which refers to an object). There is obviously a lot of referencing to keep track of, but this bookkeeping is rarely explicit. [104]

After a sufficient number of first-order concepts are learned using physical references (percepts), second-order concepts can be learned directly from those concepts. It is at this point that a dictionary first becomes useful. For example, if you know the words “apple” and “juice” , you can learn the concept of “cider” without having to drink it: the concepts of “apple” and “juice” can be combined (although to do so requires casting them into a perceptual space). This is a form of thought which involves refining concepts with other concepts. In virtue of this thought (or conceptualization), the direct perception of cider is not necessary (which is necessary for the formation of a first-order concept). This abstraction is the basis of imagination, through which it is possible to construct objects which do not have referents in the physical world.

This conceptual manipulation presupposes the ability to dereference the symbols which we form, or to activate the concepts which those symbols represent. Although it is possible to treat symbols as merely percepts, such as running in response to hearing the speech utterance ‘run’ , it is also possible to treat percepts as symbols , which allows the retrieval of the original concept. In the first situation, which is representative of animal cognition, the word ‘run’ is a stimulus to which an animal may or may not respond: animals form a concept which references that stimulus, just as we might form a concept of a stick (i.e. an object). They do not dereference this percept to retrieve the underlying concept; hence, they do not derive its meaning . For humans, the symbol run is understood (dereferenced): it triggers the activation of a concept, “run” (which does not derive its meaning from the utterance), but rather from the percepts which were used to create its associated concept.

The use of mathematical notions of space to describe perception and cognition is tremendously useful (not to mention somewhat ironic, since mathematical and logical laws themselves spring fairly directly from basic mental principles). Two of the most significant of these notions for our purposes are space and dimensionality . The dimensionality of percepts is taken as a phenomenological given: percepts occur with a particular dimensionality (e.g. they are often one-dimensional or two-dimensional). As concepts are references to percepts, their dimensionality when dereferenced is equivalent to these percepts. For example, suppose that binocular vision gives rise to three-dimensional percepts. Concepts which aggregate those percepts are therefore four-dimensional.

By forming a collection of concepts, we are effectively adding a dimension which spans them. Language and syntax rely heavily on this process of abstraction, although their use of dimensionality is rarely explicit. Count nouns, for example, require this additional dimensionality; they are constructed as collections of proper nouns, each of which is a lower-order concept. In this sense, discontiguous entities (e.g. “cats” ) are not nebulous concepts: they are singular, contiguous entities of a high dimensionality.[105] The syntactic role of various parts of speech, and the division of the sentence into a noun phrase and a verb phrase, is directly related to this notion of dimensionality.

As a final and somewhat Platonic note, although ontological development forms concepts which are increasingly abstract (or which have an increasingly high-order), it may be the case that these high-dimensional concepts are a better fit for reality than their lower-dimensional counterparts. In other words, although more concrete concepts correspond better to low-dimensional perceptions, it may be that more abstract (higher-dimensional) concepts correspond better to the objects which they are intended to reference.

[102] I am unfortunately speculating here, as I am hardly ever without one concept or another, and my memory is not that good.

[103] It may be that perception cannot be divided without the top-down aid of conception. In that case, this process should be considered as more of a simultaneous process.

[104] For simplicity, it is desirable to talk about the order of a percept or concept (where percepts of objects are first order, as are the concepts corresponding to these first-order percepts). There is an implicit assumption here that all objects are first-order, which is done as a matter of convenience. It may not be valid: some people may believe that objects in the objective world are higher than first-order. This belief might correspond to whether an individual found the world (objectively) meaningless or meaningful.

[105] Although these statements are to some extent equivalent, the former has connotations of imprecision which are unnecessary.