Derivatives of Aristotle's Categories

Whitehead was a mathematician. When he saw that reality was composed of dynamic processes and not static objects, he looked to mathematics for tools to describe this transformation. Derivatives look at the change that occurs between two states (a before and after snapshot). Look at a moving car and the two sequential snapshots show a instantaneous speed of 50 km/hand 60km/h. A derivative would indicate the change, in this case, acceleration.

This change is an abstraction, a different way of thinking, but one that is more true because it more closely resembles reality where everything is constantly changing.

So this transformation helps to re-frame reality and give us dynamic terms for what we have considered static.

The conventional way of understanding the world of objects is based on Aristotle's categories. These categories are:

1. Substance (ousia, essence or substance).^[4] Substance is that which cannot be predicated of anything or be said to be in anything. Hence, this particular man or that particular tree are substances. Later in the text, Aristotle calls these particulars “primary substances”, to distinguish them from secondary substances, which are universals and can be predicated. Hence, Socrates is a primary substance, while man is a secondary substance. Man is predicated of Socrates, and therefore all that is predicated of man is predicated of Socrates.
2. Quantity (poson, how much). This is the extension of an object, and may be either discrete or continuous. Further, its parts may or may not have relative positions to each other. All medieval discussions about the nature of the continuum, of the infinite and the infinitely divisible, are a long footnote to this text. It is of great importance in the development of mathematical ideas in the medieval and late Scholastic period. Examples: two cubits long, number, space, (length of) time.
3. Quality (poion, of what kind or quality). This determination characterizes the nature of an object. Examples: white, black, grammatical, hot, sweet, curved, straight.
4. Relation (pros ti, toward something). This is the way one object may be related to another. Examples: double, half, large, master, knowledge.
5. Place (pou, where). Position in relation to the surrounding environment. Examples: in a marketplace, in the Lyceum.
6. Time (pote, when). Position in relation to the course of events. Examples: yesterday, last year.
7. Position, posture, attitude (keisthai, to lie). The examples Aristotle gives indicate that he meant a condition of rest resulting from an action: ‘Lying’, ‘sitting’, ‘standing’. Thus position may be taken as the end point for the corresponding action. The term is, however, frequently taken to mean the relative position of the parts of an object (usually a living object), given that the position of the parts is inseparable from the state of rest implied.
8. State, condition (echein, to have or be). The examples Aristotle gives indicate that he meant a condition of rest resulting from an affection (i.e. being acted on): ‘shod’, ‘armed’. The term is, however, frequently taken to mean the determination arising from the physical accoutrements of an object: one's shoes, one's arms, etc. Traditionally, this category is also called a habitus (from Latin habere, to have).
9. Action (poiein, to make or do). The production of change in some other object (or in the agent itself qua other).
10. Affection (paschein, to suffer or undergo). The reception of change from some other object (or from the affected object itself qua other). It is also translated as passion and passivity It is clear from the examples Aristotle gave for action and for affection that action is to affection as the active voice is to the passive. Thus for action he gave the example, ‘to lance’, ‘to cauterize’; for affection, ‘to be lanced’, ‘to be cauterized.’ Aristotle's term in its English translations is frequently misinterpreted to refer only or mainly to some kind of emotion or passion.

In Whitehead's transformations these become dynamic:

1. Substance becomes Actuality
2. Quantity becomes Society
3. Quality becomes Truth
4. Relation becomes Peace
5. Place becomes Nexus
6. Time becomes Duration
7. Position becomes Relation
8. State becomes Process
9. Action becomes Adventure
10. Affection becomes Feeling

 Each one of these terms will be explored...