8) CATEGORIZATION

When discussing low level syntactic structures we did not take into account the problem of categorization. We said, for instance, that w + w´  = W can be read in phonosyntax as "vowel + consonant = syllable" because syllables always consist of vowels as nucleus, and consonants as margins. However, this statement mixes two types of notions: nucleus and margin are "functions" that sounds can hold in the syllable, while vowel and consonant are "categories", i.e. classes of sounds that fill the above functional slots, respectively. Although functions and categories usually agree, this is not always the case, and for this reason there are phonetic consonantal sounds that behave as syllabic nucleus in some languages (in Czech for example), and phonetic vocalic sounds that are placed in the syllabic margin (in Russian, where the palatal softener adds to some consonants without removing the vocalic nucleus). Notice that as a procedure what we did was to start with functions (i.e with w, w´ , W...) and predict the kind of forms that perform them.

8.1) THE CATEGORIES OF HIGH LEVEL SYNTAX

When approaching high level syntactic structures we are again faced with the "function/category" duality: should we take the universal character of functions for granted and try to predict the categories that correspond to them in each language, or shall we do just the opposite?
As for grammatical tradition, both methods have been practiced: when traditional grammar defined the noun as the class of words that can be a subject, it obviously began with functions which derived into categories; when, on the contrary, it realized that adjectives are words that refer to qualities and that for this reason they syntactically behave as attributes, then it took the opposite direction starting from categories and finishing with functions.
Current approaches to syntax also share both standpoints. From a structuralist point of view priority should be given to functions: for instance, Jakobson's treatment of Russian verbal categories establishes a set of relationships held by the utterance, the sentence, and their respective agents, and goes on to explain the categories (i.e formal classes) of Russian verb as supported by those very functional relationships (R. Jakobson, 1957, Shifters, verbal categories and the Russian verb , Harvard University Press). Generative grammarians, on the contrary, have paid closer attention to categories than to functions, and have tried to derive the latter from the former: in Chomsky's Aspects of the theory of syntax  (pp.70-71) the functional notions "subject of", "direct object of", etc, are considered redundant in phrase markers and are simply stated in an additional  list of definitions as [NP, S], [NP, VP], etc; recent developments share these earlier viewpoints, but have improved them in a more sophisticated way called X-bar-theory (for example R.S. Jackendoff, 1977, X-bar-Syntax.: A Study of Phrase Structure , Ling.Inq.Mon. 2).
Nevertheless, the methodological decision we will finally adopt is not an indifferent one. As a matter of fact science can either predict particular items from universal notions (the hypothetical deductive method) or, on the contrary, it can first collect a sample of items and then try to sum up their common properties by means of a rule (the inductive method). But neither one of those methods can help us in deciding what these properties look like. Are they categories or functions? A comprehensive and rather straightforward answer to this question would be: they are categories that perform functions or, if you wish, they are functions that are performed by categories.
Regrettably this equation does not always work because functions and categories sometimes disagree. When Chomsky -Aspects, 70- criticized the error of regarding functional notions as categorial ones, he pointed out that often a single category, and even a single word, can perform several different functions: for this reason Chomsky said it would be better to establish the different functional slots that each category can fulfill according to its categorial environment (for example, NP can be subject in [NP, S], object in [NP, VP], etc). However, the reverse also proves to be true: the subject can be either a noun -John came-, or a sentence -that you were there annoyed him-, or a verbal phrase -their leaving early surprised me -; in fact the recursive power of the base component of a generative grammar is intended to account for these possibilities in the Chomskian proposal.
The problem does not lie in which notions are constants and which are variables, because both functions and categories vary in every language. It would be better to approach this problem from an interlinguistic point of view: do either of the notions remain unchanged when passing from one language to another? If so, we will choose it as a methodological guide.
However, the decision to embrace several languages does not solve the problem either. It is a well known fact that many languages lack adjectives or articles -i.e categories-, but on the other hand, we will also run into difficulties when we try to apply the notion of subject to ergative languages, and even the notion of indirect object to English as some students have recently pointed out (B. Comrie, 1981, Language Universals and Linguistic Typology,  The University of Chicago Press, 60-61).
In any case I think that the difficulties that could eventually arise are of a fundamentally different kind: in the case of categories it is obvious that they will never prove to be universal because categories are classes of forms and all languages possess some forms that are lacking in others, but are lacking some forms that other languages do possess. On the contrary, nothing prevents functions from being universal because functions are specific ways of behavior: the issue at hand is that the functions that are usually employed in grammatical descriptions -i.e subject, direct object, etc- have proven not to be universal (perhaps owing to the influence of Latin grammatical tradition on modern scholarship), and therefore the problem would be to find the functions that are truly universal. 
Although not every human language has subjects like English subjects, or objects that behave like Spanish objects, we certainly cannot avoid speaking about a speaker and a hearer, nor can we avoid speaking about agents and their actions by means of utterances. These functions -i.e agent of the utterance, agent of the sentence, act of uttering, act referred to by the sentence, etc-, which constitute the background of Jakobson's explanation of the Russian verb as said above, are no doubt universal and could be taken as a starting point to predict categories in any language.
The difficulties of such an approach are of an entirely different nature. They have nothing to do with a lack of universality, but with a lack of limitations to the use of universal notions. This difficulty does not appear in Jakobson's paper, but it is almost inevitable when we minimally extend the domain of the facts we are trying to explain. Consider, for example, not the agent of the sentence but the instrument referred to by it; many acts of daily life are certainly performed by means of instruments, but the question we should ask is rather the following:  do instruments have grammatically specialized behaviors? If so, they would legitimately be considered as functions capable of bearing categorial values. Unfortunately, the answers to this question vary from language to language, and even depend on the theoretical position each scholar holds: in Russian there is a suffix of the noun declension called "Instrumental" that certainly could be related to instruments of normal life, although sometimes one wonders why a noun in a specific construction has been put in the Instrumental case (for example, attributive permanent clauses put the attributed NP in the Nominative case, but temporary ones use the Instrumental: Anton bijl kucher/Anton bijl kucherom); in English the Instrumentals, as pointed out by G. Lakoff's classical paper -1968, "Instrumental Adverbs and the Concept of Deep Structure", Fo. Lang., 4,1, 4-29- are grammatically heterogeneous: they usually are related to "with  + noun" phrases, but also to "use + noun + to + verb" clauses, but not always. Consequently, instruments of reality do not provide an explanatory basis for either Russian declension, nor for English Instrumental adverbials which cannot help but be described in a purely ad hoc manner.
Putting all these facts together it should be apparent that the problem is always one of boundary, whether we take into account categories, or functions, as starting points of the explanation. When choosing categories, as generative grammar does, they prove to be too narrow to provide an adequate basis for interlinguistic explanations, perhaps because of their intralinguistic preferences; when choosing functions, as structuralists do, they not only apply to one specific construction but also to many others, i.e. they are too wide to account for an intralinguistic explanation, perhaps because they prefer the interlinguistic domain.
It seems easier to narrow functions than to widen categories, because of the interlinguistic nature of the former as opposed to the intralinguistic nature of the latter: a category formed as a class of objects in a given language cannot be applied to something else without problems because the classes of other languages are never  homomorphic with it. However, a function that arises within any language can be related to human languages if we are able to consider its explanatory power in relation to linguistic behavior. 
In other words: we will start with functions, but we will not choose such and such functions because they reflect reality in the linguistic mirror -that is, instruments because languages contain Instrumentals, elapsed time because they contain Past tenses, etc-, but precisely because the functions we have chosen are able to explain linguistic utterances and their categories, that is, because they reflect in the metalinguistic mirror.
This formulation seems certainly a bit tautological: functions being metalinguistic, we will choose them according to their metalinguistic power. Nevertheless, it should be noticed that the functions we are aiming to introduce here are not only metalinguistic, but metaperceptual: they constitute adequate explanations for general perceptual processes , and therefore they prove to be adequate to explain linguistic perceptions, i.e utterances, of any language too.
Languages differ in shape, but they are strictly alike as a perceptual strategy. What allows any human to become a native speaker of any language depending on the linguistic community where he/she is born is the fact that his/her awareness of the linguistic utterances that surround him/her can be supported by perceptual strategies that are not language specific. It remains a matter of discussion if these strategies should be innate -as for instance generative grammarians would probably suggest-, or if they are simply acquired in the first months of human life when sensory perceptions (that precede linguistic ones) are tried out.
We are thus faced with our four high level syntactic structures again: due to the fact that the closure, equality, proximity, and good shape Gestalt laws are universal -i.e metaperceptual-, we can legitimately try to predict intralinguistic categories starting from the interlinguistic functions -i.e metalinguistic- that are supported by them; the rective, agreement, textual, and enunciative structures respectively, as all of them have a formal topological nature as we said above.
Therefore the method we will follow in determining linguistic categories will be to predict the class of forms that a specific function is able to perform in every language. Returning to our four structures we will ask, for example, what kind of forms usually fulfill slot v  in  v € w´ , that is, which forms perform the topic function -or better, which forms are sensitive to the topic function- of the textual level in that language.
We could compare this procedure to the mathematical calculation of the values of variables in equation systems. Be:

                        ax + by + cz = 0
                        dx + ey + fz = 0                  
                       ..............................
                        lx + my + nz = 0

Mathematicians have developed subtle procedures that permit to predict numerical values for x, y, and z -for example x = o, y = p, z = q- depending on the numerical values held by the constants a, b, c, d, e, f,.....l, m, n.
Human languages do not substantially differ from equation systems. In fact every language consists of a set of utterances (i.e of equations) where some constant values -call them words- are attached to relational abstract notions -call them functions-. For instance if the variables (the x, y, z) were subject -S-, verb -V-, and direct object -O-, and the constants were the items of the English dictionary, then we could have a sample of the English language as follows:

the boy  (S) saw  (V) the cat  (O) = sentence
my mother  (S) is cooking  (V) a pie  (O) = sentence
.........................................................................................................
we  (S) run out of  (V) gas  (O) = sentence

If, on the contrary, the same variables -i.e subject, verb, and direct object- were attached to the entries of the Spanish dictionary, we would obtain a sample of this language. Notice, however, that when substituting one language for another, the "function-item" couples do not always agree: for example, Spanish yo  (S) tengo  (V) hambre  (O) does not match English  I am hungry  which is not a S+V+O sentence; on the other hand, the English we  (S) run out of  (V) gas  (O) corresponds to Spanish el gas  (S) se nos  (O) acabó  (V) with exactly the opposite distribution of roles.
These facts are responsible for linguistic categorial disagreements: the class of words that the English object function can represent does not entirely agree with the class of words that the Spanish object allows as a filler of its functional slot (functions are a bit more abstract than the traditional "subject", "object", etc are, as I said above: I argue with them only for the sake of argument).
Categorize, therefore, means to take advantage of the universal nature of perceptual linguistic functions in order to allow them to be filled in by partially different classes of words in several languages. In a sense categorization, as we have just established it, makes use of strict distributional procedures, although the starting point is in this case hypothetical deductive and not inductive as any distributionalist would have taken for granted: the classical method collects samples of data that fill the same generalized pattern, and later it proposes a functional label capable of explaining all of them; on the contrary, the deductive categorization method I aim to introduce at this point begins with the functional slots provided by the axioms of topology and goes through to the classes of linguistic items that supposedly accommodate to them.
However, the size of functional patterns to be looked into varies from the unit to the structure, both poles being relevant to high level syntax as said above:
If we make a certain unit symbol stand out against the other unit symbols of a shared structure, we will obtain a type of category that we will call absolute category as, for instance, in:
TOPOLOGICAL REPRESENTATION              
"v" vs. v´
("v" being highlightened)
GESTALT REPRESENTATION

 If, on the contrary, we make an entire structure stand out against any other structure, we would obtain a type of category that will be called relative category as, for instance, in:

TOPOLOGICAL REPRESENTATION
                                                                           [w  vs. v´] vs.[v  vs. w´ ] vs.["v vs.v´"] vs.[wvs.f wvs.w´]
("v vs.v´" being highlightened)
                                                              
GESTALT REPRESENTATION

(These relative categories are further contrasted in order to alternatively emphasize each of their units as obvious)

The absolute and relative categories appear to correspond to semosyntactic and morphosyntactic high level categories respectively. For example, a semosyntactic category such as "adjective" is commonly attributed to only one word in the sentence, or perhaps to several words where each of them may be "adjective" on its own, but this is never said of any word of the sentence. In John is getting angry  we can say that angry  is an adjective, but neither John  nor is getting  are adjectives. An analysis of this sentence made out of absolute categories would be as follows:

Sentence=John (Noun) + is getting  (Verb) + angry  (adjective)
      0     =  a         x    +           b       y    +    c          z 

From a perceptual point of view this analysis means that when we highlighten -i.e when we are interested in- the function(s) that in English is/are typically played by adjectives (the attributive function, for example), we see adjectives -in this case angry- instead of other classes of words. But if we had highlightened -if we had been interested in- some other function such as the predicative, for instance, we would have seen the verb first, as exemplified by the string of words is getting, and so on.
The second type of emphasizing process that gives rise to relative categories, occurs when one function characterizes every word in a sentence. For example, in the above mentioned sentence John is getting angry  we would say that the verb is in a present continuous tense: nevertheless, properly speaking  all three words, John, is getting, and angry,  refer to a non habitual present situation. For this reason we would not normally say   *dinner is looking good  (as the durative aspect of the verb to look would be incompatible with the present continuous tense), nor would we normally say ?mankind is getting angry  (as the generic nature of the noun excludes a non habitual state of the adjective), nor.even *John is getting dead  (as the permanent adjective also rejects the present continuous).
There are typically morphosyntactic categories like tense, mood, diathesis, etc, which can be said to be relative. Notice that relative means that they characterize all of the words of the sentence, but that they are in a (coordinate or oppositive) relationship with other sentences in the same text: we put the above sentence in present continuous tense because the preceding one was, perhaps, in the past perfect -for example Peter has just blamed him /and hence/John is getting angry  (but Peter had blamed him/and hence/John got angry)-; similarly the Spanish sentence que Juan llegara a tiempo  is in a subjunctive mood because the verb of the preceding sentence was dudo, or maybe, me gustaría, etc ({dudo, me gustaría} / que /Juan llegara a tiempo : notice once more that not only llegara, but also Juan and a tiempo  undergo the possible-world-like influence of the subjunctive).
We have just said that an absolute category bracketing of a sentence resembles an equation of several variables like ax+by+cz+..= 0. On the other hand, relative category specifications look like polynomic equations in which a single variable takes several exponential values. This is due to the fact that while the adjective cannot be said to represent a degree of "verbness" or of "nounness", for example, the adjective only corresponding to x, and never to y or z (even if some scholars have merged adjectives with verbs or nouns in a single class), the indicative is a less modalized mood in comparison with the subjunctive (it corresponds to the real world, that is, it only represents one of the possible worlds that characterize the latter), and therefore it shows a degree of "moodness".
 For this reason we can compare the string of sentences that constitute a text : 

sentence1     +    sentence2       +  sentence3    =   text
(...mood/tensei)   (...mood/tensej)    (...mood/tensek)

to a polynomic expression like ax1+bx2+cx3+ +...gxn=0, where i,j,k.., as 1,2,3,...n, are divisions in a scale.
How will the predictive process work in the case of these relative categories? Now we will not predict the category that corresponds to a given function as above, but we will predict the related set of degrees that defines a relative category by assigning one of those degrees to each symbol of a structure. For example, given the "illocutionary force (Speaker, Hearer)" substructure (i.e the dialogic enunciative substructure), we can formulate the hypothesis that in a given language this substructure will cover the mood system, and that it will distinguish three degrees:
-the "subjective" which is related to a "subjunctive" mood and hence highlightens the "subject" of enunciation (i.e the Speaker)
-the "addressee" which is related to an "imperative" mood and hence highlightens the "addressee object" of enunciation (i.e the Hearer)
-and finally the "neutral" which has no marked modal value at all and fits the requirements of the "illocutionary force" without any particular shade, i.e the "indicative";
 this seems to be the situation of the Spanish verbal mood system:
  "illocutionary force (Speaker, Hearer)".
.                    ≠                            ≠              ≠
                        indicative                       subjunctive     imperative

Nevertheless, sometimes it is not possible to contrast one structure with other structures. This is the typical situation of structures that are manifested as phrases and not as sentences: in this case they fail to manifest the morphosyntactic values of mood, tense, etc, because they simply exhibit relative categories borrowed from the sentence in which they are included (for example, in John praised Mary's politeness  it is obvious that the noun phrase Mary's politeness  must also be understood in the past, although it does not show any past morpheme at all, because it takes advantage of the past morpheme of praised ).
From a Gestalt point of view these reductive situations, that yield a new type of categories which will be called absolute-relative categories, could be represented as follows:

Their topological counterpart would be a scheme where the four high level syntactic structures were simultaneously comprised, something like:

               w1 € v2 / w´3 € v´4

with a complex set v/w´ that can be understood either as a closed set (v), or as an open one (w´), or as both; starting from this scheme we would read :
-[1+3] as rective structure:"w"€v / "w´"€v´(= w€jw€w´)
-[2+4] as agreement structure: w € "v" / w´ € "v´" (=v € v´)
-[2+3] as textual structure: w € "v "/" w´" € v´ (= v € w´)
-[1+4] as enunciative structure: "w" € v / w´ € "v´" (= w € v´)

This complex reductive situation could be compared to equations that simultaneously exhibit more than one variable and exponential variation, that is:
 a xi yj zk  + b xi+1 yj+1 zk+1  + ..+ g xi+n yj+n zk+n = 0

The absolute-relative categories that such a scheme is able to predict would be the units that exhibit complementary distribution -as absolute units do-, and free variation at the same time -as in the case of relative units-, and moreover those units that are restricted to domains smaller than a sentence .
 As the phrase is the high level unit that embraces strings smaller than a sentence, we will call this scheme the phraseological structure: 

relative : sentence (whether past,present,or future)¨free variation
     +
absolute: sentence predicate (verb,not noun,not adjective,etc) ¨compl.dist

Phonosyntactic frames typically behave in this way: in languages where diphthongs are not single phonemes (such as English whose diphthongs will be studied later by means of induced topology), free variation is shown in the syllabic nucleus, but their components -i.e. glides that behave as margins, and full vowels that behave as a head- are not mutually substitutable and therefore display a complementary distribution (Spanish diphthongs [ai], [ei], [ja], and [je] alternate as syllabic nucleus in [bái-le], [al-béi-tar], [bjá-xe], [bjé-xa], but *[aj], *[ej], *[ia], *[ie] are not possible). Phonosyntactic categories will be predicted with reference to the complex scheme above w € v/w´ € v´ by providing adequate fillers for every functional slot.
It is worth noticing that although phonosyntactic patterns can also be contrastive when applied to sentences -for example, a suprasegmental sentence with an interrogative intonation followed by a declarative intonation-, this is only true if they convey some specific semantic or morphologic information (the latter when an emphatic accent substitutes morphemes like precisely, etc). When phonosyntactic patterns apply to the phonological domain alone and do not carry any meaning at all they are restricted to the strings inside the sentence, precisely because of the plural articulation of human languages that requires sound-meaning units to be analyzed into smaller sound units. For this reason we will use the above complex scheme -that formally represents a minimal pattern as we said- to predict absolute-relative categories in phonosyntax, but we will be able to predict not only absolute semosyntactic categories or relative morphosyntactic categories, but also absolute-relative categories in semosyntax (i.e. phrase structures) and in morphosyntax (morphemes that tie phrase components together, such as gender in the Romance language, for example).
The entire high level syntactic categorization that a topological grammar should perform would read as follows:

high level semosyntax                                                    
Provide absolute categorial values for each functional symbol of the type "w",      "v", "w´", "v´" , and "€" of the extended space of integration  ESI below, in every human language. Provide absolute-relative categorial values for the string of functional symbols of the reduced space of integration RSI below, in every human language.

high level morphosyntax
 Provide relative categorial values for each functional structure of the ESI below, and alternative functional values for each symbol within it in every human language. Provide absolute-relative categorial values for the string of functional symbols of the RSI below in every human language,

high level phonosyntax
Provide absolute-relative categorial values for the string of functional symbols of RSI below in every human language.
 
Reduced space of integration  Extended space of integration

                                      ¨semosyntaxÆ           
 phraseological :                                             enunciative:   w € v´
 w € v/w´€ v´                     ¨phonosyntax       textual :          v € w´
                                                                             agreement :      v € v´ 
                               ¨morphosyntaxÆ   rective :       w € jw € w´

8.2) CATEGORIES THROUGH COMPONENTS

One of the main benefits grammar will get by starting from functions in order to yield categories, and not the reverse, is that a single function can undergo several categorial readings, one for each component or subcomponent of the grammar; on the contrary, although categories logically fulfill more than one functional pattern, they always remain related to the basic functional frame. This asymmetric relationship between functions and categories:
                      component1,..  component2, .......componentn
functioni Æ categoryi.1,categoryi.2 ....categoryi.n
functionj Æ categoryj.1,categoryj.2 ...categoryj.n
..................  Æ ......................   ,  .......................................................
lays the foundation for transformational methods in grammatical description. For example, we can say that John's shooting the deer, John shot the deer, and the deer was shot by John  are transformationally related because, no matter how much the categorial appearances of some items may vary -shooting (noun),shot (past),(was) shot (participle)-, the functional relationships held by the three elements do not change at all (transformational relationships only work within a grammatical component, never among heterogeneous components like semosyntax and phonosyntax f.ex., of course). But when the same category shows several functional shades, we could hardly speak of transformations: although Mary  in Mary loves John  is the very Mary  of John loves Mary,  i.e a proper noun, we could not say that either of the sentences has been transformationally derived from the other.
The set of categorial readings related to each perceptual function in each topological component together with the linguistic behavior of each category is what properly constitutes the grammar of a given language. In the past ten years suitable overall categorial readings have been proposed for two Romance languages, Spanish and Catalan, and also for Basque, an entirely different non indoeuropean language. There have also been attempted partial readings in other linguistic areas like French and English. Nonetheless, topological linguistics is still in its beginnings, and further and deeper research is still required. In order to get an idea of what such a grammar would look like in a very tentative manner, let's follow the categorial readings of the "w" function of rective level "w € jw € w´" in English.

8.2.1) FIRST STEP SEMOSYNTAX

As said above the rective structure consists of two substructures:
-The predicative substructure that reflects the internal linguistic relationship shades of w € jw € w´ in the form:
             Governor  +  Governed
                    w          jw        w´
-The argumental substructure that reflects the external linguistic relationship shades of the very w € jw € w´ in the form:
           Government(Governor, Governed)
                     jw       (       w        ,        w´       )

In English (and in many other languages, but not necessarily in all) the predicative substructure usually occurs as "logical subject + logical predicate", and the argumental substructure as "Verbal functor (Subject, Set of objects [objecti, objectj...objectn])".
Coming back to function w in w € jw € w´ we discover that the Governor unit represents a class of words whose main structural role would be to fill the subject slot: it seems reasonable to predict that in English w of the rective structure supports the category of nouns because nouns are, primarily, the typical subjects in this language.
Nevertheless, due to the dual point of view from which we can grasp the rective structure, this Governor function appears as:
i) either as requiring the Governed function without any attention paid to the referent in the predicative substructure.
ii) or as being dominated by the Government verb in the same position as the set of objects, although maintaining some outstanding character over it, as happens to be the case in the argumental substructure. 
Formally:         
                             "w "€ jw € w´
                       jw  ("w" , w´ )
The interpretation I would like to propose to account for this duality is that the class of nouns can be primarily subcategorized into two subclasses of nouns: i) nouns that have nothing to do with external reality and that are defined as such not because of their referential properties but only according to the linguistic system, and ii) nouns that hold referential ties and whose noun condition is, properly speaking, determined by external reality. It is easy to see that proper nouns accommodate to i), and common nouns to ii). Nouns like Mary, or William, or Washington  do not describe the being they are referring to (as logicians say, they are denotative, not connotative): Mary is not a particular type of woman, but just a woman whose name is Mary; Washington  is a place people know as Washington, but also a woman or a man whose surname is Washington; William  and Mary  can be said of two people whose names are respectively William and Mary, or of a university college in the state of Virginia, etc; a given referent will then be Alison  if her name is Alison , Jill  if her name is Jill, and even George (Sand ) if she decides to be known as such, and none of these names tells us anything about her, not even that her  is the appropriate pronoun to use.
On the contrary, common nouns like house, or bread, or tiger  are obviously arbitrary, but once we have chosen the word tiger for a certain type of animal in English, we will have a representation of the kind of being that is being referred to each time we hear the word tiger: this is due to the fact that common nouns are dependent on their referents; they are subjects, but subjects that take part in the referential-like scene of the sentence, together with objects and verbs.
In conclusion: "w of the predicative substructure vs. w of the argumental substructure" are able to predict a major subcategorization of the class of nouns -of the ws of the rective structure- : noun Æ -/+ common.

Looking further into the situation of w in the argumental substructure notice that w is a subject that shares with a class of objects the fact that it is governed by the verb, and for this reason both belong to the same structural level. From this point of view, they are interchangeable in some circumstances, for example in the passive -John saw the picture  Æ the picture was seen by John-, or in some attributives -John is Mr. Brown / Mr. Brown is John-. But the class of objects that the subject is to substitute can be considered from two perspectives, either as a set of specific countable items such as "direct object, indirect object, place object, time object, etc", or simply as a set of non-specific non-countable items: the first point of view lays the foundations of the English pronoun system substitutions, i.e. John gave Mary1 a book2 yesterday3 Æ{John gave her1 a book yesterday, John gave it2 to Mary yesterday, John gave a book to Mary then3}; the second point of view, on the contrary, explains the language-specific behavior of English objects when they become the subjects of the passive construction, and any kind of object is able to do so -direct object: a book was given to Mary by John; indirect object: Mary was given a book by John; circumstantial object: this house was lived in by many students.
So, the second subcategorization we are dealing with has to do with the objects that any argumental subject can be related to, and since only common nouns are predicted by the argumental substructure, proper nouns are not affected (notice that proper nouns as grammatical objects behave in exactly the same way as common nouns, that is, as if they were common ones; this is due to the fact that the verb always subcategorizes its subject, but often leaves the nature of its object free: although Washington  can be either a place or the first president of the USA, and we will select either one reading or the other according to the verb that takes it as a subject -i.e Washington has one million people, Washington talked to Jefferson, etc-, when this word fills an object functional slot its value could not depend on grammar, but on the world -I like Washington-, just as if it were a common noun). Like their corresponding objects the common nouns that fulfill the argumental subject function will be divided into countables and non-countables: common noun Æ +/- countable.

But when opposed to a non-specific, non-countable set of objects the argumental subject can in fact behave by either keeping in mind that they are a non-specified set of extensional objects -i.e S vs. "Oi+1, Oi+2 ..."-, or simply that the subject is opposed to the intensional quality of the object as such -i.e S vs. "O"-. The concrete extensional not countable objects allow some subjects that the abstract intensional objects do not allow, without any change in the nature of the verb (for example, we can say bread likes butter  and John likes butter, but only John likes sincerity, and never *bread likes sincerity ). 
This possibility gives rise to the third subcategorization we are able to predict from the w function of the rective structure, i.e not countable Æ +/- abstract.

This minimal system of noun subcategorization (noun Æ +/- common, common Æ +/- countable, not countable Æ +/- abstract) agrees with the first steps of similar subcategorization processes that can be found in current literature on the English noun; the following steps, that usually distinguish +/- animate  and  +/- human, have little to do with grammar but with semematics, and they will not be considered here (notice, for example, that proper nouns do not take determiners, or when they do the article cannot be removed; on the other hand, countable nouns accept some determiners while non-countable nouns accept others; abstract nouns, as opposed to concrete nouns, normally reject plural morphemes, etc: however, in English no specific morphemic behavior characterizes animate nouns, nor human ones either).
To sum up: the function w of the rective structure not only allows us to predict the class of forms that will fill its functional slot in English (i.e the noun), but also to outline the main directions of its subcategorization, and hence of its grammatical behavior.

8.2.2) SECOND STEP SEMOSYNTAX

We have said that w of the rective structure w € jw € w´ is a much more general concept than the notion of subject. It is for this reason that w can receive not only the noun categorial interpretation we have just examined, but also morphosyntactic and even phonosyntactic interpretations that we will try to develop later. 
For the moment it is worth noting, however, that our attempt to predict the categorial behavior of the English noun has been undertaken by directly starting from the concept of subject, and not from the more abstract w unit. Consequently it stands to reason that somewhere in the prediction system this notion of "subject" must also have been attained.
The role of the further specification of the semosyntactic component is to yield three new subcomponents -Formal semosyntax, Actantial semosyntax, and Constructional semosyntax, cfr. chapter 5- which provide a kind of categorial meanings attached to the lexical items that do not help to classify these items into word classes, but that, even so, remain categorial. 
Are notions like "object", "Instrument", or "transitive" of a functional or of a categorial nature? Notice that if, as we concluded above, functions must be universal notions whereas categories must be intralinguistic ones, then it results that they must be categories, as not every language deals with direct/indirect objects like in English, or as not every language shows Instrumental-like behavior of its noun phrases -although Instruments always belong to the referent, of course-, or since not every language has the same transitive patterns. 
What kind of categories will they look like? It is interesting to point out that, curiously enough, they appear to be morphological concepts in the sense that they are unthinkable without a scale where they represent a degree: for example, direct objects are those functions (?) that, with respect to government relationships, behave stronger than indirect objects but weaker than subjects; Instrumentals can be put between Agents and Objectives on a semantic scale; transitives are placed halfway between intransitives and ditransitives, etc.
In short: once all of the sememes have got a semosyntactic categorial value, such as noun, or verb, or adjective, etc, they combine together in order to yield strings of sememes that receive a second step categorial reading which establishes the degree each categorized sememe occupies within the sentence. These degrees are related to the first step categorial value of the sememe: for example, although nouns can become either subjects, or direct/indirect objects, or circumstantial objects, a noun is properly thought of as a subject, and for this reason we find grammatical categories other than nouns acting as circumstantial objects -John was driving with care/carefully - much more easily than as subjects; in a similar way the verb is the predicate proper, though verbal phrases (or sentences) could likewise appear as subjects -Being turned down in the job annoyed me-.
As we established in chapter 5) there are three kinds of categorial scales a string of semosyntactic categories can be attached to: formal,  actantial, and constructional categories. Coming back to the roles a noun typically plays in relation to them we can predict:
-That w in English formal semosyntax defines the subject, i.e the most dominant "formal category" in w € v/w´ € v´ (formal semosyntax does not start from the rective but from the phraseological structure, because it is a purely formal subcomponent in the same sense as phonosyntax: nevertheless, this fact leaves the symbol w unchanged, and thus we will skip it).
-That w in English actantial semosyntax predicts the type of behavior that characterizes the Agent, i.e the most salient actantial category (as a matter of fact when we highlighten w we are putting across the agentivity rather than the Agent, but let's simplify it for the sake of argument). Notice that subjects and Agents, both coming from the Governor w function, are clearly related: if an Agent is present in a sentence, then it must become the subject.
-That w in English constructional semosyntax predicts the intransitive construction in the sense that it always pivots on one nominal argument (that is, intransitive sentences are built around a nominal argument, but biargumental ones can show adverbial arguments -it fits well -, or adjectival ones -Mary is tall - as well).

As an illustration of the process that allows us to yield categories from functions, we have begun with the rective function w that predicts the category "noun" and its subclasses -"proper"/"common" ("countable"/ "non-countable" ("concrete"/"abstract")-, and that in a second step characterizes it as a typical "subject", "Agent", and "intransitive pillar". This procedure must be fulfilled in relation to all other symbols of the four main structures (of ESI and RSI) before we can complete the grammar of a given language: the above suggestions are only intended to outline how such a grammar could be deductively reached -and in fact it has already been reached for the Spanish language-.

8.2.3) FIRST STEP MORPHOSYNTAX  

When looking into morphosyntax we discover that the first step categorial type is the one that constitutes a degree of a scale, while the second step type is simply manifested by being linked with a particular sememe.
Instead of:
word-like                  #John #   # walks #   #(calmly) #  
1st step semosyntax concepts       noun         verb          adverb
---------------------------------------------------
sentence-like               #John walks calmly#
2nd step semosyntax concepts  [subj,Ag]+[intr]+[prep.ob,Man]  
                                          Ø        Ø        Ø
           semosyntax :             formal    actantial   constructional

we have, for example, in tenses:
   
sentence-like                  # John walks calmly #
1st step morphosyntax concepts  past >.....> present >.....> future
---------------------------------------------------------------
word-like           # John #    # walks #     #calmly #
2nd step morphosyntax concepts   [allom.-s, 3d per.sing., stem]        
                                                                Ø                       Ø                 Ø
              morphosyntax:     morphophonemics  inflectional     derivative

This complementary disposition of semosyntax and of morphosyntax allows the two sound-meaning components of grammar to group together in order to face the sound component (i.e. phonosyntax) as a coherent cluster.

How does the w function of the rective structure work in this first step morphosyntactic component? Note that the "Governor - Government - Governed" structure (i.e. the rective structure) allows a kind of internal deixis where the arguments are put in some functional position relative to other arguments through the verb: thus, while a past tense implicitly or explicitly locates the verbal process before a present tense, a prepositional construction like the book is on/over/under...the table puts the subject noun phrase the book  in a certain place relative to the object noun phrase the table which constitutes the origin of coordinates (in other words, we emphasize the Governed). We can then say that in English there is a prepositional gradation: according to the kind of object we choose as an origin, we will obtain either normal prepositional phrases, or prepositional adverbs, or prepositional verbs (I have developed this problem extensively in A. López García, 1988, "A characterization of perceptual linguistics with a sketch of the English verbal system in liminar grammar", LynX, I, 9-51).
Nevertheless, when the concentration of perception -i.e. the  highlightening of a specific functional symbol- affects the Governor (the subject), a contradiction will occur: the preposition is an object marker, but the perceptive saturation is applied to the subject. The procedure used by the English language in order to solve this contradiction would be the following: the object, what should have taken the preposition, is turned into the subject, while the subject is added as a mere adjunct preceded by a preposition: hence the passive voice, that is simply a particular case of the more general phenomenon of prepositional verb behavior in English.
It is worth noticing that the explanation just proposed -the morphosyntactic emphatization of function w in rective structure w € jw € w´- is able to account for some characteristics of the English passive, in the same sense as the above definition of the noun category -the semosyntactic emphatization of this very w- yielded a subcategorization of the noun: thus, compared with the passive of other languages, the English passive is not a pattern which depends on the verb to be (there are passives with to get  or with to grow ), nor on the direct object (because other kinds of objects can also become the subject of the passive, as seen above).

8.2.4) SECOND STEP MORPHOSYNTAX

When we compare the English and the Latin passives, for example, it is immediately apparent that they both behave quite differently from the morphophonemic point of view: in Latin there are special passive morphemes -for instance, amo, "I love", but amor , "I am loved"-, in the same sense as there are subjunctive (mood) -amem -, or past (tense) -amabam- morphemes; in English, on the contrary, the passive takes advantage of all the tense and mood morphemes of the active voice: to put a sentence in the passive voice means to choose the corresponding form of the verb to be  or to get  with the former tense/mood morphemes (which exhibited the active construction), and to add the past participle of the stem verb to it -John saw [simple past] the book  Æ  the book was [simple past] seen by John, etc-.
Therefore what we expect of the second step morphophonemic component -which, as a formal component, does not start from the four main functional structures, but from the phraseological one- is that it justifies such a morphophonemic use.
The nuclear nature of the unit w of the phraseological structure is able to do this. Notice that in w € v§w´ € v´ the w symbol means an obligatory one, the v´ symbol an optional one, and the v/w´ symbol a unit that is halfway between the former, being obligatory from one point of view, and optional from the other (for example, when applied to the noun phrase, the phraseological structure could be interpreted as if w were the noun, v´ the adjective, and v/w´ the determiner: there are noun phrases that consist of only a noun -man (is mortal)-, noun phrases that consist of a noun and a determiner -the man (came)-, and noun phrases that consist of a noun, an adjective, and a determiner -the young man (came)- , but no noun phrase can be constructed in English without the head noun -for instance *the young came (but the young one came), nor without the determiner if there is also an adjective -for instance *young man is mortal, but young men are mortal too where the plural morpheme acts as a determiner-.
Similarly a passive verbal construction governed by w is a construction where all verbal morphemes have to appear; on the contrary, there are verbal constructions where only some morphemes, but not all, must appear -e.g. imperative constructions fail to combine with the past, but they can join any grammatical person-, and verbal constructions where any morpheme, except the stem, are optional -this happens to be the case of non-finite clauses: leaving the room I fell down/I will go to the movies.
Anyway, the meaning of the passive string of morphemes must always implicitly include an active argument, that is a "doer", in the background. Notice that the combination "inflected form of to be/to get  + participle" need not be a passive construction: for example, John was bored all the time  is an attributive construction, but John was bored by the movie is a passive one. This requirement is precisely what the second step derivative morphology reading of w is accounting for: while the first step reading of the rective structure w symbol was interpreted as "passive", and the second step morphophonemic reading established that the passive will be compatible with any verbal morpheme, this second step morphological reading demands, furthermore, an Agent (i.e. a highlightened Governor) to support the construction, and for this reason it establishes that the Agent noun has to be preceded by the preposition by, which denotes the doer of the process and constitutes the derivative morphological index of it.
Finally, we reach the question of why English passive consists of the combination "inflected form of to be  + participle": it is the second step inflectional morphological component which is responsible for providing an adequate answer to this question. Notice that the English passive looks like the perfect tenses, as both are composed of an auxiliary verb (to be/to get and to have respectively) plus a form that from the inflectional point of view is a participle. How can such a common pattern be justified?  I think two aspects are worth noting here: first, the perfect tenses are intended to represent "priority relationships" (when they entered the room, I had written the letter ); second, to have is a transitive verb, to be  is an intransitive one. Therefore he has come  shows the process of to come  as something that happened, i.e. as a result of a previous action, while he is punched (by X)  simply means priority without subsequent result, that is, a kind of "internal result". But this is what the passive properly means: by highlighting the Governor symbol w in the second step inflectional morphology subcomponent we are predicting that the meaning of the string of formatives provided by the morphophonemic subcomponent must be "a process that is shown as a result by itself", that is a passive process.

In conclusion: by highlighting the Governor w symbol through each morphosyntactic subcomponent we are able to predict the following:

First step           Second step morphosyntax
morphosyntax     morphophonemics     inflectional        derivative
w Æ passive             wÆany form   wÆ + participle      wÆ+by  
                                of the verb         which yields an           (Agent)
                                                                             "internal result"
                                                      meaning

8.2.5) PHONOSYNTAX

The last aspect of syntactic categorization I will briefly examine here is that of phonosyntax. As said above, phonosyntax aims to predict the patterns where the phonemes which have previously been defined by induced topology occasionally meet, that is, it does not predict the phonemic combinations that one can find by looking in a dictionary (i.e. paradigmatic combinations), but the combinations that appear as a result of the phonic perfomance of utterances (i.e. syntagmatic -syntactic- combinations). When we first introduced this component we said that, as a purely formal one, it only takes advantage of phraseological structure w € v§w´ € v´, and we exemplified it by means of Spanish diphthongs because these vowel combinations occur as a consequence of the speakers' will (in Spanish, we can pronounce the word viaje, "trip", as [bi-á-xe] without diphthong, or as [bjá-xe] with diphthong).
In English, diphthongs do not behave in this way - we cannot say *['ba-it] for bite, but only ['bait], the diphthong [ai] being a single phoneme. Nevertheless, in English there is a situation that closely reminds us of this type of behavior: when some very frequent words meet in the utterance, they can be freely contracted or they can be left unchanged, depending on the speakers' wish as well (I do not go/I don't go, etc); one interesting aspect of English phonosyntax would then be to bring up how the phraseological structure is able to predict these syntagmatic contractions.
Three main types can be predicted:
i) If you consider the w € v/w´€ v´ structure carefully it should be apparent that as the "w" type units (w or w´) are obligatory, i.e. vowels, and the "v" type units (v or v´) are optional, i.e. consonants, the phraseological pattern expresses the fact that a "vowel+consonant" combination (w € v) followed by another "vowel+consonant" combination (w´ € v´) can join by reducing the first consonant and the second vowel to a single unit, that is: 
w1 € v2 + w´3 € v´4   Æ  w1 € [v/w´]2-3 € v´4
as is the case with (d)o1 n2o3t4  Æ (d)o1n2-3't4 , must not Æ mustn't, has not Æ hasn't, etc. Notice that all these contractions result when we take w € v/w´ € v´ in this precise order, that is, when the phonosyntactic pattern highlightens w as the beginning of the perception of the string, and therefore any other vowels must be lost because of their incompatibility with it; the second consonant, as an optional one, can be ruled out freely, and hence the he's, I'm, etc combinations.
ii) If, on the contrary, we had highlighted v´, i.e. if the string had been of the form v´1 € w´2/v3 € w4 , that defines the pattern C-V/C-V, we would have obtained another type of contraction as in w1i2ll3 n4ot   Æ w1o2-3n4't  where it is the second consonant that must be lost (in this case, type ii) is followed by a type i) contraction -and for this reason n stands for the vowel o- because consonants cannot govern vowels, but both of them share the emphatic relationship - notice that the highlighted unit v´ cannot be dropped as above).
iii) Finally, we could simultaneously begin with w and v´: in this case the contracted form loses a vowel and a consonant, that is, the entire v/w´, as in you1 h2a3d4 Æ you1'd4 and similarly in you'll  (you will ), I'd (I would ), etc.
Contractions in English, like diphthongs in Spanish, are syntagmatic processes that consist of losing some phonemes. Nevertheless, the kind of phonemes that are lost cannot be predicted on the basis of pure phonic facts (for example, because of the more frequent pattern CV one could expect do not  to contract as *do no'  but it does not work in this way and even the [du] pronunciation of do  changes in the contracted form): contractions are phonosyntactic processes governed by formal rules, and it is up to the phonosyntactic component to predict them.