Horst Steinke

90

above, is a concrete, real world, case of the outcome of a forget-

ful functor in the form of the thermometer: the temperature

readings produced by the thermometer are mere

*numbers*

,

stripped of the physical content with which the thermometer in-

teracted

176

. Nevertheless, the purely numerical entities constitute

a new epistemic domain (category) of undeniable value and

meaningfulness.

In certain ways, “contravariant functors” are the opposite of

forgetful functors

177

. They take the entities of a category and

“use” them as the starting point for a process of transformation

such that the resultant target category acquires “richer” cardinali-

ty, properties, and structure

178

. Appropriately, the contravariant

functor can also be termed “enriched functor”

179

. However, re-

versing the “direction” of functors is not the same, or as simple,

as a reciprocal operation like multiplication and division (in

standard algebra)

180

.

With these brief comments on category theory, and before

proceeding with the narrative, we will attempt to depict Vico’s

trichotomy in relationship to each other by means of following

schematic:

Fig. 2. Vico’s Trichotomy with its Interactions.