*Vico’s Ring*

89

*morphisms*

are the

*changes*

or

*transitions*

in temperature readings

173

.

Such complexes of entities/objects with their capacity or affinity

of being altered, metamorphosed in some way function thus as

the “primitives” of category theory. In this language, the three

spheres of Vico’s grand explanatory project, the trichotomy of

“philosophy”, “philology”, and the actual historical world, are

epistemologically equivalent to three categories

*sui generis,*

and any

of the descriptions made regarding them so far pertained only to

their internal structure, considered individually

*.*

However, this

aspect of category theory obviously does not go far enough to

throw light on the crucial question of the relationships

*between*

them, separately from the morphisms

*within*

them.

Conceptually, this necessitates moving the category concept

to the next higher level: taking individual categories themselves

as the objects, and allowing for morphisms between them also.

These higher-level morphisms have been given the special no-

menclature of

*functors*

174

*.*

This is, in fact, the level at which Vico’s

trichotomy is being considered. However, merely exchanging

nomenclature, that is,

*functors*

for different metaphors, accom-

plishes little, if anything. The value of functors stems from the

fact that they come, and act, in multiple forms and ways, and

thus enable bringing to the surface features that would not come

into view otherwise. For our present purposes, two types of

functors are particularly relevant: (1) the “forgetful functor”, and

(2) the “contravariant functor”.

In mathematics, the somewhat quaint term “forgetful func-

tor” describes a specific process of abstraction, as when a “set

with structure” of group theory is subsequently viewed without

the “structural” properties, the formalized group-theoretic opera-

tions and relationships, resulting in a mere underlying un-

structured “set”

175

. Usually, in mathematics, “forgetting” certain

important properties of complex entities has far-reaching impli-

cations, such as turning geometry into topology by factoring out

metrics (distance, angle). The example of a temperature scale,