Arthur M. Young

Categories of knowing

What are the elements of an act of knowing?

At least two are immediately obvious: that which is known, and the consciousness which knows it. The knower's status is at least as important as that of the known, a point which modern physics has been forced to recognize in the uncertainty principle, which reveals the fact that, in order to know something about it, an observer must act upon, and thus disturb, an object. The act of knowing is thus a transaction between the object and the knower which involves physical exchanges of energy. Thus the concept of pure "parallelism" a reflection within the knower of the known - is not tenable. We cannot think of the known as pure reflection within the knower, like the image of a flying swan on the smooth surface of a pond. When the swan lights on the water, its pure image is shattered by the broken surface.

Between observer and observed, then, there exists more than a simple duality. The complete description includes not only the actual physical impingements, the so-called sense data, of the known upon the observer, but also the projections of the observer upon the object. These projections are the source of error, and without them there would be no problem of correct knowledge. But they are not always erroneous. If I recognize a friend by the sound of his voice, I evoke an image of him that is substantially correct. We continually project properties on people and objects that we have learned to expect in them. It requires great mental effort to divest the world we experience of preconceptions and associations, if indeed it is possible at all.

The dynamic confrontation between knower and known, with the addition of the two kinds of relation between them - the objective information (sense data) coming from the object, and the nonobjective qualities projected by the knower upon the object - may be represented diagrammatically:

At least four kinds of relationship are involved:

1. AA - The relationships contained within the object itself: that it is, for example, an equilateral triangle, having three equal angles and sides. Such interrelationship provides the definition of the object. It holds for all equilateral triangles.

2. AB - The data which the knower receives from the object as sensations: its weight, color, texture, etc. This is factual, and concerns the particular object. It tells us that one particular triangle is dented, or broken, or that another triangle is blue.

3. BA - The qualities which the knower projects upon the object: that the triangle is beautiful or ugly, good or bad. This includes characteristics like solidity because such qualities are in part projected by the knower. Solidity is not entirely objective since atomic structure is thought to be ninety-nine percent pure space.

4. BB- The function of the object for the knower: he uses the triangle for a watch fob or to illustrate an argument. This category consists essentially of relations of the knower to himself which he creates for the object, and would include his purpose in making it.

While there is no assurance that this approach will solve all problems, it has the merit of including all possible permutations of the relations between knower and object.

Only the first category (AA) is considered valid and useful in the scientific view. I propose that a complete description necessarily includes the three alternatives to this view.

The first category, that of the relationships contained within the object, conforms to the scientific requirement for a valid description; i.e., one to which all observers agree: a square has four sides, etc. The second category, sense perception of the object, while also objective and the basis for all scientific experiments, provides only a transition to scientific knowledge. It comprises the immediate data obtained from a particular object or experiment and, before it is applicable to new situations, must be formulated and generalized.

Hence, scientific knowledge is derived from observations, but is different from them. The observations consist of particulars, while scientific knowledge is general and belongs in the first category, not the second.

Thus we may describe the objectivity of the first category as general, that of the second category as particular.

The third category consists of values projected upon the object; for instance, its beauty or ugliness. When Hamlet says, "There is nothing good or bad but thinking makes it so," the implication is that value is not inherent in the object itself. This is the usual view, which I do not contest. But the further implication that value, because it is not inherent in the object, is subjective, or limited to the particular consciousness of a particular knower, deserves closer scrutiny. For the moment, I will simply point out that I am replacing "subjective" with the more accurate word "projective" for reasons that will shortly develop.

The fourth category, the function of the object, we also refer to as projective. An alternative key word is orientation, which may be interpreted both metaphorically and literally. It refers not only to the function of the object, which we described as a relation projected for the object rather than upon it, but also to the way in which the object relates to a larger context. It concerns "which way up" the carburetor is installed in the engine or the key is inserted in the lock. This aspect of the object is not objective. We cannot determine it by inspection of the object alone, but only by an awareness of the larger context of which the object is a part.

Such reasoning indicates the appropriateness of supplanting the word "subjective" by "projective." "Subjective" implies a personal description, with the possibility of illusion, while "projective" implies only that which is not objective, and leaves aside the question of reality.

Thus we say that an image is projected on a screen, or that the earnings of a corporation are projected for the year to come. The projective aspect can be of very practical significance. When Thiokol, a synthetic rubber intended for tires, was proposed as rocket fuel (changing its projective aspect), the price of stock in the company soared.

The distinction between general and particular, demonstrated for the first two categories, also applies to the third and fourth. We may call the third projective and general, the fourth projective and particular.

In the third category, valid projections, such as "Where there's smoke there's fire," are possible only because such projection is general. The generality of projections also causes illusion. I see the beautiful tulips and imagine their smell and texture, only to discover that they are wax.

As for the fourth category, since function or purpose is an individual matter (my friend uses parking tickets to light the fire), the projection is particular. The word "orientation" implies this particularity; an orientation is by its very nature particular.

To illustrate the categories of knowing, let us use the example of an elephant:

1. The formal description. The structure of the elephant. The elephant as an object of scientific study. His anatomy, biology, behavior. Objective general.

2. The sense data which we experience by direct encounter with an elephant. The smell, the hairiness, the warm breath through the trunk. Objective particular.

3. The values we project on the elephant. How big he is! He seems kind, or patient, or terrifying, as the case may be. Projective general.

4. The function. The knower's interest in the elephant, what use he will make of him, as a circus attraction, a beast of burden, a zoological specimen, a source of meat or ivory. Projective particular.


The four aspects of a situation

In extending the method to deal with situations as well as objects, we must use more complicated examples. Suppose that a person is lost, but has a map. What kinds of information does he need to find his way?

1. The map itself. This, like the scientific description of the elephant, is an objective statement of the relationship of the distance between cities, of the location of roads, rivers, etc. The map is general and objective.

2. Where he is on the map. This information is different from the preceding. The person's position is particular as to place and time. It changes as he moves about. It is objective information but, unlike the map as a whole, it is particular and objective.

3. The scale of the map. Again, a different kind of information. It involves not just the scale in miles per inch on the map but the means of travel at the person's disposal. It is general and projective.

4. Orientation of the map. This different kind of information must be supplied by a compass. It also changes as the traveler moves about and is therefore particular. Note that it is an orientation, a direction, and that the direction of north and the direction in which the traveler wants to go are not necessarily the same. But in order to know in which direction to go, one must know how to orient the map. It is a relation of the map to the larger context. It is particular and projective.

In this example, there are again four aspects which correlate with four kinds of relationship:

Form correlates with the interrelationship of the parts of the known to one another.

Position correlates with the relationship of the traveler to points on the map.

Scale correlates with the relationship between a distance on the map and the effort the traveler is called upon to make.

Orientation correlates with the relationship of the traveler to a more ultimate reference which is not objective, his goal. This relationship is particular and projective.


Aristotle's causes

The concept of four basic categories of knowing, or four aspects of a situation, is not new - as is evident by reference to the famous four causes of Aristotle. Aristotle described an object (for example, a table) as having:

1. A formal cause. The blueprint or concept of the table, its shape and proportion. Corresponds to the objective general.

2. An efficient cause. The work of the carpenter in making the table. Corresponds to the objective particular. His particular work produced this particular table.

3. A material cause. The wood or other raw substance of which the table is made. The projective general. Wood is general because it can make many things besides tables. There is some ambiguity here since one might choose a particular piece of wood to make a table. However, both the work and the wood have general and particular aspects.

4. A final cause. The purpose of the table. Its function of holding things. The projective particular.

Whether we refer to them as causes, categories, or kinds of relationships between an observer and an object, we can recognize that the examples we have listed all involve an observer and an object or situation.

We need not expect exact correspondences between the different examples, but notice only that they are all subject to analysis in terms of the particular-general and objective-projective dichotomies, and demonstrate the sufficiency of a fourfold analysis.

The next step is to display the four categories graphically. If, in fact, we call the categories aspects, the graphic portrayal is almost mandatory, since the word "aspect" implies a direction from which something is viewed. The apparent sufficiency of exactly four categories suggests representing them as pairs of opposites on a cross axis. But before we attempt this, we must decide which categories should be considered opposites. For instance, should the formal cause be opposite the material cause, or the final cause? Other alternatives, such as in what direction to have each aspect face, or in what order to have the aspects, are arbitrary.

To decide which pairs are opposite, we shall refer to the two dichotomies of general versus particular, and projective versus objective. Since formal cause is objective and general, and final cause is projective and particular, they are doubly opposite and hence their relationship should be represented by the maximum angle, a full diameter of difference. Thus we have:

Several important properties of the four categories are made apparent by this graphic representation which, by correlating the aspects with directions in space, permits us to say:

1. Four aspects are sufficient for the analysis of a situation. If there were a fifth, it would be compounded of two others.

2. Four aspects are necessary to a situation. If, for example, we know of three, we should expect to be able to find a fourth.

3. Aspects can be formally related. Aspects 90 degrees apart are independent of one another. On the other hand, aspects at opposite ends of an axis are mutually opposed. This idea can be illustrated by reference to the four directions. We can move due east without moving north or south, but not without moving away from, or negating, west.

To illustrate the first point, we may refer again to the map. One could say, "In addition to the four aspects of the map already given, there is a fifth, the direction in which the traveler wants to go." But this direction is like a compass reading. It is an orientation, hence it is not a new category.

The second and third points will be illustrated later.


The Geometry of Meaning