From the Tree to the Labyrinth (4 page)

But these are not the bases which allow us to understand expressions in which terms like
prixid
and
proceid
appear: it is one thing to know that it is logically incorrect to say that a prixid is not a proceid; it is quite another to say what a proceid is, and, if it means anything to say that terms have a meaning, the classification does not supply that meaning.

Gil (1981: 1027) suggests that genera and species may be used as extensional parameters (classes), whereas only the differences decide the intensional regime. This is tantamount to saying that the meaning of a term depends on the differences and not on the genera or the species. Now, what makes it difficult to regiment the differences under a Porphyrian tree is that the differences are accidents, and accidents are infinite or at least indefinite in number.

The differences are qualities (and it is no accident that, while genera and species, which represent substances, are expressed by common nouns, the differences are expressed by adjectives). The differences come from a tree that is not the same as the substances, and their number is not known a priori (
Metaphysics
VIII, 1042a–1042b). Granted, Aristotle makes these remarks about nonessential differences, but at this point who can say which differences are essential and which not? Aristotle plays on a few examples (like
rational
and
mortal
), but when he speaks about species other than human, such as animals or artificial objects, he becomes much more vague and the differences multiply.

In theory we are entitled to put forward the hypothesis that Aristotle would not have been capable of constructing a finite Porphyrian tree, but in practice as well (on the basis, that is, of the philological evidence), when we read
On the Parts of Animals,
we see that he gives up
in practice
on constructing a single tree and readjusts complementary trees according to the properties whose cause and essential nature he wishes to explain (cf. Balme 1961 and Eco 1983a).

The notion of specific difference is, rhetorically speaking, an oxymoron. Saying
specific difference
is tantamount to saying
essential accident.
But this oxymoron conceals (or reveals) a far more serious ontological contradiction.

The thinker who understood the problem without prevarication (though he pointed it out with his customary prudence) was Thomas Aquinas. In his
De ente et essentia
he says that specific difference corresponds to substantial form (another ontological oxymoron, if we may put it that way, since the most substantial thing we can think of is identified with an accident). But Thomas’s thought does not leave room for misunderstanding: what defines substantial form is difference as an accident.

In order to justify such a scandalous conclusion, Thomas excogitates—with one of his habitual strokes of genius—an extremely brilliant solution. There exist essential differences; but which and what they are we do not know; what we know as specific differences are not the essential differences themselves, but are, so to speak, signs of them, symptoms, clues, superficial manifestations of the being of something else that we cannot know. We infer the presence of essential differences through a semiotic process, with knowable accidents as our point of departure.
¹¹

That the effect is a sign of the cause is Thomas’s customary idea (much of his theory of analogy depends on this assumption, which is, if we were to trace it back, Stoic in origin: effects are
indicative
signs). The idea reappears, for instance, in
Summa Theologiae
I, 29, 2 ad 3 and I, 77, 1 ad 7: a difference such as
rational
is not the real specific difference that constitutes the substantial form.
Ratio
(reason) as
potentia animae
(a power of the soul) appears outwardly
verbo et facto
(in word and deed), through exterior actions, psychological and physical behaviors (and those actions are accidents, not substances!). We say humans are rational because they demonstrate their rational powers by means of acts of cognition, or by an internal discourse (the activity of thought) or an external discourse, that is, by means of language (
Summa Theologiae
I, 78, 8 co.). In a decisive text in the
Contra Gentiles
(3, 46, n. 11)
,
Thomas says that human beings do not know what they are
(quid est),
but they know what they are like
(quod est)
insofar as they perceive themselves as actors in rational thought. We know what are our spiritual powers only “ex ipsorum actuum qualitate” (“from the nature of these same acts”). Thus
rational
is an accident, and so are all the differences into which the Porphyrian tree can be dissolved.

From this discovery, Thomas does not draw all the conclusions he should have regarding the possible nature of the tree of substances: he cannot bring himself (psychologically perhaps) to call the tree into question as a logical tool for obtaining definitions (something he could have done without going out on a limb), because the entire Middle Ages is dominated by the conviction (however unconscious) that the tree mimics the structure of reality, and this Neo-Platonic conviction also affects the most rigorous of Aristotelians.

It is clear, however, if we follow its inner logic, that the tree of genera and species, however constructed, explodes into a swirl of accidents, into a nonhierarchizable network of
qualia.
The dictionary dissolves of necessity, as a result of internal tensions, into a potentially orderless and limitless galaxy of elements of knowledge of the world. It becomes, in other words, an encyclopedia, and it does so because it was already in fact an encyclopedia without knowing it, an artifice invented to camouflage the inevitability of the encyclopedia.

We see a return to the dictionary model in the linguistics of the second half of twentieth century, when the first attempts appear to postulate or recognize—in order to define the contents expressed by the terms of a natural language—a finite system of
figures
possessing the same characteristics as a phonological system (based on a limited number of phonemes and their systematic oppositions). Thus, a
feature semantics
(features being primitive semantic atoms) was postulated, designed to establish the
conditions necessary and sufficient
for a definition of meaning, excluding knowledge of the world. In this way, in order to be recognized as a cat, something must have an ANIMAL feature, but it is not requested that it meows. These necessary and sufficient features are dictionary markers. Something along these lines was anticipated by Hjelmslev (1943[1961]) when he proposed to analyze the concepts corresponding to the twelve terms
ram, ewe, boy, girl, stallion, mare
through a combination of the
male/female
opposition and the assumed primitives SHEEP, HUMAN BEING, CHILD, HORSE.

Hjelmslev’s was not the only modern proposal for a dictionary representation, though the many others proposed in the area of linguistics or of analytic philosophy, almost always in ignorance of Hjelmslev’s proposal, did no more than repropose his model.
¹²

Reconsidering Hjelmslev’s model, we see that a dictionary representation would allow us to solve the following problems (as Katz 1972 will suggest later):
synonymy
and
paraphrase
(a ewe is a female ovine);
similarity
and
difference
(the pairs ewe and mare and mare and stallion have some features in common, while we can establish on the basis of what other features they can be distinguished);
antonymy, complementarity,
and
contrariety
(
stallion
is the antonym of
mare
);
hyponymia
and
hyperonymia
(
equine
is the hyperonym of which
stallion
is the hyponym);
sensibleness
and
semantic anomaly
(
stallions are male
makes sense while
a female stallion
is semantically anomalous;
redundancy (male stallion); ambiguity
(the terms
bear
and
bull
, for example
,
have more than one meaning); analytical truth (
stallions are male
is analytically true, because the definition of the subject contains the predicate);
contradictoriness
(there are no male mares);
syntheticity
(that ewes produce wool does not depend on the dictionary but on our knowledge of the world);
inconsistency
(
this is a ewe
and
this is a ram
cannot be equally true if referred to the same individual);
semantic entailment
(if ram, then ovine).

Unfortunately this model does not permit us to represent what we must know about sheep and horses if we are to understand many discourses about them. It does not allow us, for instance, to reject expressions like
the stallion was bleating desperately like a ram
(justifiable only in a metaphorical context, and a very daring one at that), given that the mechanism of definition does not explain what sound horses naturally emit.

And this is not all. Even if a system of this kind could be implemented based on assumed
primitives,
and if SHEEP and HORSE were primitives, they would serve to define only a very limited share of the terms concerning part of the animal kingdom. How many primitive features would be needed to define all the terms in any given lexicon? And how do we define a “primitive” feature?

It has been said that primitives are innate ideas of a Platonic nature, but not even Plato succeeded in satisfactorily deciding how many or of what kind were the universally innate ideas (either there is an idea for every natural genus, like
equinity,
in which case the list is an open one, or there are a few far more abstract ideas, like the One, the Many, the Good, or mathematical concepts, which are insufficient to distinguish the meaning of lexical terms).

It has been said that primitives are elements of a whole that, by virtue of the systematic relationship between its terms, cannot be anything but finite: but this would be a simplified Porphyrian tree or a tree of genera and species good only for the purposes of classification.

It is hard to define primitiveness by distinguishing between analytical and synthetic properties, a distinction severely criticized by Quine (1953a), in part because the notion of analyticalness is completely circular (if a property contained in the definition of a term is analytic it cannot be a criterion for establishing the appropriateness of a dictionary definition).

The possibility of positing a difference between
necessary
and
contingent
properties must also be excluded, because if it were necessary for a cat to be mammiferous and contingent for it to meow, then all “necessary” would mean is “analytic.”

It has been proposed that
finiteness
is a requirement for a packet of primitives (primitives ought to be limited in number, considering that it would be anti-economical to have as many primitives as there are lemmata to define), but it is precisely the cataloguing of this finite number of semantic atoms that has turned out so far to be problematic.

It has been suggested that primitives are simple concepts, but it is difficult to define a simple concept (the concept of
mouse
seems more simple and immediate than that of
mammifer,
and it is easier to define concepts like
emphyteusis
than verbs like
to do
).

It has been suggested that they depend on our experience of the world, or that there are (as Russell 1905 suggested) “object-words” whose meaning we learn directly by ostension, and “dictionary-words” that can be defined by other dictionary-words—but Russell was the first to recognize that
pentagram
is a dictionary-word for most speakers, but would be an object-word for a child who grew up in a room in which the wallpaper was decorated with pentagrams.

The requirement of
adequacy
has been proposed (primitives should serve to define all words), but, if we consider as primitives sufficient to define the concept of “bachelor” features like HUMAN MALE ADULT UNMARRIED, why does it seem inadequate to call a Benedictine monk a bachelor? We would have to add other constrictions (for example, a bachelor is an adult human unmarried male
who has not taken a vow of chastity
), and with that we have introduced encyclopedic elements into our dictionary.

The requirements of
independence
(primitives should not depend for their definition on other primitives) and
absence of further interpretability
have been proposed, but not even HUMAN seems without further interpretability if we consider the whole debate over abortion and cloning that is taking place today precisely on the subject of what it means to be human. In reality, in any lexicon any term is potentially interpretable by means of other terms in the same lexicon, or other semantic devices, according to the criteria of
interpretance
and
unlimited semiosis
established by Peirce.

Lastly, if primitives are rooted in our way of thinking, the principle of
universality
suggests itself. It is assuredly possible that certain experiences related to our bodies are universal, such as
above/below, eat/sleep, be born/die,
but in the first instance it is unthinkable that we can define all the objects and events in the universe in terms of these ideas, and, secondly, universal does not mean primitive, given that a universally understood concept such as
dying
needs to be further defined, as is demonstrated by the debates on end-of-life decisions and the harvesting of organs.