# Thirdness

John F. Sowa (sowa@west.poly.edu)
Thu, 16 Apr 1998 04:16:01 -0400

When I presented the ontology in Ch. 2 of my forthcoming book, there
were many questions about Peirce's three categories called Firstness,
Secondness, and Thirdness. I have revised my presentation several times
in order to answer various objections and to clarify the definitions and
examples. Enclosed is a newly revised part of Section 2.2 with a new
subsection called Triads followed by a revision of the old subsection
called Peirce's Categories.

Following are the major changes:

1. In Triads, I added another quote from Kant, who commented on the fact
that his categories were divided in four groups of three. I followed
the trend with groups of three, especially Hegel, who pushed triads
to the limit.

2. Then in the discussion of Peirce, I added a quote about what he
thought of Hegel's approach and clarified some of the previous
discussion and examples.

3. The most important change to that section is to call Firstness,
Secondness, and Thirdness "metalevel categories", which can be
applied multiple times to generate new triads of ordinary categories.
In particular, the first application generates three categories,
called Thing, Reaction, and Mediation.

4. Those new names are partly in response to many complaints about the
unusual terms Firstness, Secondness, and Thirdness. It is also in
response to Nicola Guarino's complaint that Firstness, Secondness,
and Thirdness are at a different level from the other categories.
I think that criticism is correct, and that the 1-2-3-ness categories
should be considered metalevel categories for generating other categories.

John Sowa
________________________________________________________________________

TRIADS. The symmetry of Kant's table with four groups of three
categories could have been the result of chance, of his esthetic
preferences, or of some deeper principle. Kant believed that the
triadic pattern resulted from something more fundamental than chance
or taste:

In every group, the number of categories is always the same,
namely, three. That is remarkable because elsewhere all _a
priori_ division of concepts must be by dichotomy. Furthermore,
the third category always arises from a combination (Verbindung)
of the second category with the first. Thus totality is plurality
considered as unity; limitation is reality combined with negation;
community is the causality of substances reciprocally determining
one another; finally, necessity is the existence that is given by
possibility itself. It must not be supposed, however, that the
third category is merely a derivative, and not a primary concept
of the pure understanding. For the combination of the first and
second categories in order to produce the third requires a special
act of the understanding, which is not identical with those which
produce the first and second. (B:110)

This brief comment raises more questions than it answers. For each of
the four triads, Kant suggested a different "act of the understanding"
for combining the first and second categories to produce the third. If
the act is different in every case, then the symmetry of the categorial
system is flawed. But if there is some deeper principle common to all
four triads, then that principle is more fundamental than the categories
themselves.

The German philosophers who followed Kant searched for an explanation
of the triadic patterns. They applied the word _thesis_ to the first
category, _antithesis_ to the second, and _synthesis_ to the third.
Those Greek words sound impressive, but the word _synthesis_ is no more
explicit than Kant's word _Verbindung_, which has several meanings
ranging from connection to combination. In chemistry, both words
_Verbindung_ and _synthesis_ are used to describe how two substances
combine in a chemical reaction. Different molecules combine in
different ways, but in each case, the theories of chemistry predict the
method of combination from the internal structure of the molecules.
A complete theory of categories should likewise show how the internal
structure of the concepts determines their method of combination.

The most ambitious development of the triadic approach was by Georg
Wilhelm Friedrich Hegel (1831), who wrote a mammoth tome divided and
subdivided in patterns of three. In explaining his method of deriving
the third from the first and second, Hegel used the verb _aufheben_,
which literally means to raise up, but with the further implication that
the third supersedes the first two:

_Aufheben_ has a twofold meaning in the language: on the one hand
it means to preserve, to maintain, and equally it also means to
cause to cease, to put an end to. Even _preserve_ includes a
negative element, namely, that something is removed from its
immediacy and so from an existence which is open to external
tendencies, in order to preserve it. Thus what is "aufgehoben" is
at the same time preserved; it has only lost its immediacy, but is
not on that account annihilated.

In continuing this discussion, Hegel took delight in finding ambiguous
words, which "have in themselves a speculative meaning." Throughout his
book, he emphasized the contradictions he found among his categories and
considered them the basis for generating new categories to replace or
"aufheben" the old ones.

Unfortunately, Hegel chose to call his book _The Science of Logic_.
That title invited scathing criticism from logicians, who seized upon
the contradictions to point out how far from logic it had strayed. At
the end of a 16-page discussion of Hegel, Bertrand Russell (1945)
concluded "the worse your logic, the more interesting the consequences
to which it gives rise." Despite its flaws, what makes Hegel's book
interesting is its wealth of categories based on triads. As a
generative principle, however, the verb _aufheben_ is even more
problematic than _combine_ or _synthesize_.

PEIRCE'S CATEGORIES. Like most logicians, Peirce found Hegel's logic
repugnant, but he was equally intrigued by the patterns underlying
Kant's triads. He said that in his youth he was "a passionate devotee
of Kant":

I believed more implicitly in the two tables of the Functions of
Judgment and the Categories than if they had been brought down
from Sinai.... But Kant, as you may remember, calls attention to
sundry relations between one category and another. I detected
some additional relations between those categories, _all but_
forming a regular system, yet not quite so. Those relations
seemed to point to some larger list of conceptions in which they
might form a regular system of relationship. After puzzling over
these matters very diligently for about two years, I rose at
length from the problem certain that there was something wrong
with Kant's formal logic. (1898, p. 124)

After extensive analysis, Peirce concluded that some, but not all of
Kant's triads reflected three more basic categories, which he called
Firstness, Secondness, and Thirdness:

First is the conception of being or existing independent of
anything else. Second is the conception of being relative to, the
conception of reaction with, something else. Third is the
conception of mediation, whereby a first and a second are brought
into relation. (1891)

In distinguishing his triads from Hegel's, Peirce emphasized the equal
status of all three categories and rejected the idea that "Firstness and
Secondness must somehow be _aufgehoben_" (CP 5.91).

In Kant's system, the clearest illustration of Peirce's principle is
categories under Property in Brentano's tree of Figure 2.3:

1. Inherence (Inhaerenz) characterizes entities by their intrinsic
qualities, independent of anything else. In Brentano's tree, it
includes qualities such as shape and color and quantities such as
size, length, and mass.

2. Causality (Kausalitaet) is defined by dyadic relations directed from
cause (Ursache) to effect (Wirkung). Kant remarked that causality
includes activity and passivity, which are two of the categories that
Brentano placed under Directedness.

3. Community (Gemeinschaft), according to Kant, is the "reciprocity
between agent and patient" (Wechselwirkung zwischen dem Handelnden
und Leidenden). In Peirce's terms, it is the mediation "whereby a
first and a second are brought into relation." Under Containment or
_in-something-ness_, Brentano put Spatiality and Temporality, which
are the two kinds of "something" in which a community is contained.

As Kant observed, most concepts are subdivided by dichotomy. It is
therefore significant that Brentano's only trichotomy corresponds to the
Kantian triad that most clearly illustrates Peirce's principle.

Peirce's triad is a metalevel principle for generating new categories
by viewing entities from different perspectives. A category of
Firstness is determined by the qualities inherent in something,
Secondness by a relation or reaction directed towards something else,
and Thirdness by some mediation that brings multiple entities into
relationship. Formally, the three kinds of categories are characterized
by the minimum number of entities that must be involved in their
definition. The first can be defined by a monadic predicate P(x), which
describes an entity x by its inherent qualities, independent of anything
external to x. The second requires a dyadic relation R(x,y), which
describes some reaction between an entity x and an independent entity y.
The third requires an irreducible triadic relation M(x,y,z), which
describes how an entity x mediates two entities y and z. In Thirdness,
one of the three entities must have a "mind" or mind-like aspect that
determines the intention behind the mediation. Peirce maintained that
it is not necessary to go beyond three, because Fourthness, Fifthness,
and higher-order relations can be defined in terms of triads.

As an example, the type Animal can be defined by qualities inherent
in the individual. The type Pet, however, is defined in relation to
some human being. What makes an animal into a pet is a mediating
relationship that resembles a contract, at least at the level of a
"gentleman's agreement." As the fox said to Saint-Exupe<ry's Little
Prince, "You become responsible, forever, for what you have tamed." The
responsibility on the human's part and the trust on the animal's part
constitute the mediating contract that binds them together. Aspects of
the three categories appear in the vocabulary of every domain:

1. As Firstness, a concept type, such as Woman, represents an individual
characterized by inherent qualities, independent of any particular
relationships. Although no human being can live in a vacuum, an
individual's internal structure and qualities can be described
without mentioning anything external.

2. The same individual could be classified relative to or in reaction
with many other things, as in the concept types Mother, Attorney,
Wife, Pilot, Employee, or Pedestrian. Such concepts are defined by
Secondness. They represent the individual in relation to another
type, such as Child, Client, Husband, Airplane, Employer, or Traffic.

3. Thirdness focuses on the mediating intention that brings the first
and second into relation. Motherhood, which comprises the act of
giving birth and the subsequent period of nurturing, relates the
mother and the child. The legal system gives rise to the roles of
attorney and client. Marriage relates the wife and the husband.
Aviation relates the pilot to the airplane. The business enterprise
relates the employee to the employer. And the activity of walking on
a street that is dominated by vehicles relates the pedestrian to the
ongoing traffic.

Peirce's principle is used throughout this book to generate triads of
categories: in Section 2.7, it is used to distinguish three kinds of
_granularity_ for describing or measuring objects; in Section 5.4, to
classify contexts as actual, modal, or intentional; and in Section 6.6,
to classify signs in nine categories generated by the product of two

MORE EXERCISES

As a further illustration of Peirce's approach, I added the following
two exercises at the end of Chapter 2 and included brief answers at the
back of the book.

EXERCISE 2.5. The criteria for classifying entities may be based on
Firstness, Secondness, or Thirdness. As an example, consider the
following list of items: eraser, pencil, toothbrush, bar of soap,
razor, pocket calculator, apple, sandwich, roll of toilet paper, rubber
ducky, book, three-ring binder, towel.

1. By Firstness, the items in that list have little in common. Yet they
all share at least one common property. What inherent property of
the items was used to sort them in the order listed?

2. By Secondness, the items could be partitioned in two groups according
to some external relationships. Make such a grouping.

3. An arbitrary grouping by Secondness could be purely accidental. A
grouping by Thirdness, however, must be based on some reason that
explains why these groups were selected rather than any others.
State the reasons for the grouping in part two.

Make similar lists of your own that illustrate the principles of
classification by Firstness, Secondness, or Thirdness.

1. Weight is a common property of all the items in the list. They are
sorted in order of increasing weight.

2. Items found in a bathroom: toothbrush, bar of soap, razor, roll of
toilet paper, rubber ducky, towel. Items found in a book bag:
eraser, pencil, pocket calculator, apple, sandwich, book, three-ring
binder.

3. Explanation: Items in the bathroom are used in water-based
activities for personal hygiene. Items in the book bag are used
during a student's day at school.

EXERCISE 2.7. In applying Hegel's categories to the analysis of
economic systems, Karl Marx classified feudalism as the first or
_thesis_, capitalism as the second or _antithesis_, and socialism as the
third or _synthesis_. Using Hegel's idea that the third somehow
supersedes the first and second, Marx concluded that the natural
progress of history would cause socialism to replace capitalism, which
replaced feudalism. If Marx had adopted a Peircean view of the three
categories instead of a Hegelian view, would his analysis of history
have changed? How?

Cooperation. All three concepts involve Thirdness, since they express
the mediation x that relates someone y to something z. The difference
lies in the nature of z:

1. Ownership is Thirdness relating Firstness: x relates an owner y to
an actuality z (P1).

2. Competition is Thirdness relating Secondness: x relates two or more
potential owners y&sub1., y&sub2., ..., to a possible prehension z
(P2) of an actuality (P1).

3. Cooperation is Thirdness relating Thirdness: x relates two or more
potential competitors y&sub1., y&sub2., ..., to a nexus z (P3) in
which they adopt compatible goals (P3O) with regard to some actuality
(P1).

Unlike Hegel's view of a historical progression from the first to the
third, Peirce would insist that all economic systems at all times
involve aspects of all three. As the environment and technology change,
the emphasis and balance of the three aspects may change, but none of
them completely replaces the others.

Note that the categories Competition and Cooperation illustrate
Peirce's observation that all higher-order relations can be generated by
combinations of triads. Competition is an example of Fourthness since
it relates x, y, and z to some actuality (fourth); Cooperation is an
example of Fifthness since it relates the first three to some goal
(fourth) and some actuality (fifth). Peirce's theory of semiotics,
which is discussed in Section 6.6, has more examples of such
combinations.