“In order to design characters that directly denote notions (if not the things themselves that these notions reflect), two conditions must be fulfilled: (1) the identification of primitive notions; (2) the organization of these primitives into a system which represents the model of the organization of content.
It is for this reason that these languages qualify as philosophical and a priori. Their formulation required individuating and organizing a sort of philosophical “grammar of ideas” that was independent from any natural language, and would therefore need to be postulated a priori.
Only when the content-plane had been organized would it be possible to design the characters that would express the semantic primitives. As Dalgarno was later to put it, the work of the philosopher had to precede that of the linguist.
For the polygraphers, invention was simply the job of assigning numbers to a collection of words from a given natural language. The inventors of philosophic a priori languages needed to invent characters that referred to things or notions: this meant that their first step was to draw up a list of notions and things.
This was not an easy task. Since the lexicon of any natural language is always finite in number, while the number of things, including physically existing objects, rational entities, accidents of all types, is potentially infinite, in order to outline a list of real characters it is necessary to design an inventory which is not only universal: it must also be in some way limited.
It is mandatory to establish which notions are the most universally common, and then to go on by analyzing the derivative notions according to a principle of compositionality by primitive features.
In this way, the entire set of possible contents that the language is able to express has to be articulated as a set of “molecular aggregates” that can be reduced to atomic features.
Suppose we had three semantic atoms such as ANIMAL, CANINE and FELINE. Using them, we might analyze the following four expressions:
Yet the features that analyze the content of the above expressions ought to be entities totally extraneous to the object language.
The semantic feature CANINE, for example, must not be identifiable with the word canine. The semantic features ought to be extra-linguistic and possibly innate entities. At least they should be postulated as such, as when one provides a computer with a dictionary in which every term of a given language can be split into minor features posited by the program.
In any case, the initial problem is how to identify these primitive and atomic features and set a limit on their number.
If one means by “primitive” a simple concept, it is very difficult to decide whether and when one concept is simpler than another. For the normal speaker, the concept of “man” is simpler–that is, easier to understand–than the one of “mammal.”
By contrast, according to every sort of semantic analysis, “mammal” is a component of (therefore simpler than) “man.” It has been remarked that for a common dictionary it is easier to define terms like infarct than terms like to do (Rey-Debone 1971: 194ff).
We might decide that the primitives depend on our world experience; they would correspond to those that Russell (1940) called “object-words,” whose meanings we learn by ostension, in the same way as a child learns the meaning of the word red by finding it associated with different occurrences of the same chromatic experience.
By contrast, according to Russell, there are “dictionary-words” that can be defined through other words, such as pentagram. Yet Russell remarks, for a child who had grown up in a room decorated with motifs in the form of a pentagram, this word would be an object one.
Another alternative would be to regard primitives as innate Platonic ideas. This solution would be philosophically impeccable; yet not even Plato himself was able to establish what and how many these innate ideas were.
Either there is an idea for every natural kind (for horses, platypuses, fleas, elms and so on–which means an atomic feature for every element of the furnishing of the world), or there are a few abstract ideas (the One, the Many, the Good and mathematical concepts), but through them it would be difficult to define compositionally a horse or a platypus.
Suppose instead we decided to order the system of primitives by dichotomic disjunctions so that, by virtue of the systematic relations obtaining between the terms, they must remain finite in number.
With such a structure we would be able to define by a finite number of atomic primitives a great number of molecular entities. A good example of this alternative is the reciprocally embedded system of hyponyms and hyperonyms used by lexicographers.
It is organized hierarchically in the form of a tree of binary disjunctions: to each opposed pair of hyponyms there corresponds a single hyperonym, which, in its turn, is opposed to another hyperonym to form the next level of hyponyms, to which a further hyperonym will correspond, and so on.
In the end, regardless of how many terms are embedded in the system, the whole structure must finish at its apex in a single patriarch-hyperonym.
Thus the example of the table on p. 222 above would take the following format:
According to many contemporary authors, this kind of semantic structure would analyze the content in the format of a dictionary (as opposed to an encyclopedia).
In an encyclopedia-like representation one introduces elements of world knowledge (for example that a tiger is a yellow cat with stripes on its fur), and these elements are potentially infinite in number.
In a dictionary-like representation the features are, on the contrary, analytic, in the sense that they are the only and necessary conditions for the definition of a given content: a cat is necessarily a feline and an animal and it would be contradictory to assert that a cat is not an animal, since the feature “animal” is analytically a part of the definition of cat.
In this sense it would be easy to distinguish analytical from synthetical judgments. “A tiger is a feline animal” would be analytical, so uniquely depending on our rigorously organized dictionary competence (which is exclusively linguistic), while “tigers are man-eaters” would depend on our extra-linguistical world knowledge.”
Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 221-5.