Universal Grammar as a Theory of Notation

Universal Grammar as a theory of notation, page 1-17

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Universal Grammar as a theory of notation1

Humphrey P. van Polanen Petel

2006, Axiomathes 16: 460-485

DOI 10.1007/s10516-005-3407-7.

The original publication is available at http://www.springerlink.com/

Abstract

What is common to all languages is notation, so Universal Grammar

can be understood as a system of notational types. Given that infants

acquire language, it can be assumed to arise from some a priori

mental structure. Viewing language as having the two layers of

calculus and protocol, we can set aside the communicative habits of

speakers. Accordingly, an analysis of notation results in the three

types of Identifier, Modifier and Connective. Modifiers are further

interpreted as Quantifiers and Qualifiers. The resulting four

notational types constitute the categories of Universal Grammar. Its

ontology is argued to consist in the underlying cognitive schema of

Essence, Quantity, Quality and Relation. The four categories of

Universal Grammar are structured as polysemous fields and are each

constituted as a radial network centred on some root concept which,

however, need not be lexicalized. The branches spread out along

troponymic vectors and together map out all possible lexemes.

The notational typology of Universal Grammar is applied in a

linguistic analysis of the parts of speech using the English language.

The analysis constitutes a proof of concept in (1) showing how the

schema of Universal Grammar is capable of classifying the so-called

parts of speech, (2) presenting a coherent analysis of the verb, and

(3) showing how the underlying cognitive schema allows for a sub-

classification of the auxiliaries.

Keywords

categories, cognition, language, notation, parts of speech, semantics,

syntax, universal grammar, verbs

1 Introduction Already as far back as the 13

th century, Roger Bacon observed that there are two aspects to

any language. There are those elements that are peculiar to the particular language and there

are others that apply to all languages equally and, on account of their generality, could

conceivably be formalised into a science of language, i.e. a Universal Grammar. De Saussure

(1916) then extended this by noting that Universal Grammar underlies all semiotic systems.

The immediate conclusion that this affords is that one component of Universal Grammar is

simply notation. After all, any system can be formalised and a notation can in principle be

devised for it. However, for a system of notation to be considered a language it needs to be

interpreted. This means that the other component of Universal Grammar is cognitive, albeit

not in the sense of reflecting our experience of the world. Rather, and given that infants are

able to acquire language, I suggest that it is best conceived of as arising from some a priori


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mental structure. I submit that these two components are sufficient and I aim to show in this

article that Universal Grammar can be defined as a system of types of notational elements.

The article is in two parts: theory and application. The first describes Universal

Grammar, the second classifies the parts of speech briefly and the verb in some detail. For

convenience, the language used will be English.

2 Theory A good deal of argument can be avoided if we say that language is at least in part concerned

with the transfer of information. That way, we can in principle recognise two so-called

transport layers: (1) a calculus that controls the coding of information and (2) a protocol that

controls the transfer of information. While the primary purpose of a protocol is to reduce

error (or cope with noise, in the sense of Shannon and Weaver 1949), what it also affords is

a distinction between information being in the world versus being in the head. For

example, consider walking at night along an unlit country road. Normally this is most safely

done on the side of the oncoming traffic (information in the world). Accordingly, when there

is no actual traffic in sight we had better remember the local convention (information in the

head). Alternatively, these layers can be understood as levels of abstraction in the sense that a

calculus abstracts away from the observed relations between referents and a protocol abstracts

away from the communicative habits shared by the parties involved. What this means for us

here is that we can ignore these communicative habits and concentrate on the calculus aspect

and in particular on the phenomenon of notation.

2.1 Notation

Notation is essentially perceived linearly so that an instance of notation is effectively a line of

symbols. Thus, when there is no relation between the individual symbols we have in effect an

unordered set and when there is we have an ordered set. Therefore, the relations between the

sentences in a series of one-word sentences are sentence external and the relations in a

multiple word-sentence are sentence internal. Accordingly, in the case of a single symbol,

the only meaning that can be conveyed is referential, simply because there are no other

symbols to be in a relation with. In the case of a determinate complex of symbols, each

individual symbol, as well as the totality of the complex, can be assumed to convey referential

meaning, but there will also be those that convey structural meaning in addition.

Accordingly, we assume there to be relations of dependence between the individual symbols

so that it must be legitimate to assume, for instance, that the meaning of is different

from and that the meaning of is different from . From this, we can

abstract that symbols are contrasted in two ways: by their identity and by their directional

dependence.

The number of classes in which dependent symbols can be placed is a straightforward

function of the number of dependencies possible. In a linear medium, of course, there are

only two directions, so that there is a maximum of three possible relations, these being

forward, backward and the combination thereof. However, the distinction between forward

and backward is ultimately semantic so that the classes possible are those based on the

number of dependencies a symbol has. Thus, when we interpret an independent symbol as a

symbol with zero dependencies, we get the following: symbols having (1) no relation, (2) one

relation (either direction) and (3) two relations (both directions) and these can be thought of

as, respectively, zero-place, one-place and two-place functions. (Obviously, n-place functions

where n>2 have no place in a one-dimensional medium.) These functions can be called,

respectively, Identifier, Modifier and Connective. The contribution to meaning that notation


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has is that Identifiers are used to refer to (grammatical) objects, Modifiers are used to express

something about referents and Connectives are used to express the structural relation that

obtains between referents.

Inasmuch as notation is a proper subset of language, we would now seem to have

identified the basic elements of linguistic structure. To be sure, interpreting the Identifier-

Modifier-Connective typology as a grammar, it would be context-free and strongly generative

(in the sense of Chomsky 1964, p. 53n), because it is logically possible to parse any and all

possible sentences into these types. As it is obvious that all semiotic systems have this in

common, it might perhaps be thought that this is what de Saussure had in mind, but I find this

doubtful. The typology is neither particularly insightful, because it is just a logical

consequence of the nature of notation in a one-dimensional medium, nor is it particularly

useful, because it provides no means to deal with the complexities of syntax, whether of

formal, artificial or natural languages. What is needed is a stronger interpretation of the

elements of notation and to this end the Predicate Calculus offers some useful insights.

2.2 The Predicate Calculus

From the perspective taken here, the Predicate Calculus can be understood as one protocol out

of several that operate in what could be called the discourse of entailment. Commonly, the

vocabulary consists of names, predicates, quantifiers and logical constants. Sentences

describe states of affairs that obtain in the Universe of Discourse in terms of actual and

potential members, what can be said about them, and the logical relations that obtain between

them. These logical relations each represent one aspect of entailment which is why they are

referred to as constants all other relations having been assimilated to the predicate.

From a notational perspective, names are Identifiers and logical constants are

Connectives. What can be said about members falls into the two categories of predicates and

quantifiers and it is this which suggests that, likewise, there be two types of Modifier. What

immediately springs to mind here is the classical distinction between Quality and Quantity

(due to Aristotle, Categories 1995a). Stepping back from the Predicate Calculus, we can

recognise this distinction as a cognitive interpretation. What this gives, then, is a set of four

types of notational elements, viz Identifier, Quantifier, Qualifier and Connective and it is this

interpretation which constitutes Universal Grammar.

Having Universal Grammar as a system of types of notational elements means that

Universal Grammar is eminently simple and that the complexity of any language is a

reflection of use, i.e. of the communicative habits of its speakers. Thus, it is in the protocol

part of language that we find such intricacies as valency, word order and style. The effect of

the notational types of Universal Grammar is to function as a constraint on language use.

2.3 Ontology

Consensus has it that infants have some ability that enables them to acquire language.

However, regardless of how we think it is implemented in the brain, be it as a genetically pre-

determined organ (Chomsky 1980a), as an instinct (Pinker 1994), as a sensori-motor construct

(Piaget 1980) or as a whatever, it is still the case that what counts is how it functions. Thus,

given the distinction between calculus and protocol, we can recognise two separate processes,

although I suggest there are actually three processes operating when a child acquires its first

language. Firstly, the child is learning, secondly, the child is learning to communicate and,

thirdly, the child is learning a way to communicate. The ontology of the first process I

assume to be Chomskys science forming faculty (1980b p. 250). The ontology of the

second process I propose to be the cognitive schema underlying Universal Grammar and it is

this which I submit is constitutive of the calculus-part of language. The ontology of the third


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process I assume to be the behaviourist process of conditioning the individual to his usual

communicative environment. This process would be responsible for moulding speakers to a

social norm, the protocol-part of language.

The cognitive schema underlying Universal Grammar is probably best understood

from the perspective of perception. Translating the types of notational elements into the

perceptual properties they refer to, we get Essence, Quantity, Quality and Relation. Thus, an

Identifier indicates what kind of thing we think our object of perception is, i.e. its essence. A

Connective indicates how we perceive the elements in our perceptual field to be connected,

i.e. the relation that obtains. And, rather obviously, Quantifiers and Qualifiers indicate the

quantity and quality we attribute to the object of our perception. However, the Quantity and

Quality distinction is crucial and, accordingly, I observe that quantities are necessary, but that

qualities are not and that qualities belong, but quantities do not. This suggests a two-fold

dichotomy: one on the intrinsic-extrinsic distinction and the other on the necessary-contingent

distinction. The result is presented in Table 1 and can be thought of as the semantics of

perception. (An inspection will reveal the close affinity with Aristotles major categories.

However, the matter is deep and my understanding of it shallow so that I must refrain from

entering into argument.)

Table 1 Aspects of percepts

Intrinsic Extrinsic

Necessary Essence Quantity

Contingent Quality Relation

Note that an Identifier indicates that element of which we would say that it is both necessary

and intrinsic to the object of our perception, i.e. the essence of what we are talking about.

When we perceive something as a brick it follows that we should also call it a brick.

Connectives indicate those elements which are opposite of that. After all, it is a contingent

fact about the brick that is has the relation of, for instance, being next to some other brick

and relations are certainly extrinsic. Quality and quantity are traditional concepts. Thus, for a

typical Quantifier, when we speak about this brick then the deictic expressed by the

demonstrative does not belong to the brick and so is extrinsic and also it does not really

make sense to say that our pointing is a contingent fact about the brick. For a typical

Qualifier, the colour of a brick belongs to it and is thus intrinsic and surely it is a contingent

fact that a brick has this colour rather than some other colour.

2.4 Universal Grammar

The four types of notational elements, Identifier, Quantifier, Qualifier and Connective, map

onto Table 1 as shown in Table 2.

Table 2 Types of notational elements

Intrinsic Extrinsic

Necessary Identifier Quantifier

Contingent Qualifier Connective

Table 2 gives all the possible types of notational elements and thus constitutes an ontological

catalogue of the words and word-forms of any language. Certainly, the languages of the

world are many, yet they all represent so many standards of communication. Consequently,


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each and every one of them can be expressed through an appropriately defined notation and

can therefore be schematised. (Obviously, whether a notation exists for a given language or

not does not detract from the fact that such abstraction can in principle be made.) Table 2

presents Universal Grammar in schematic format. As a system it is generative in the sense

that we can generate all language samples from it. However, in order to show how that works

we need the notion of troponymy.

2.5 Troponymy

Lexemes and types are not the same kind of things. Rather, types constitute the categories by

which lexemes are sorted. Accordingly, the meaning of a lexeme is ultimately an

instantiation of some type. For example, consider the following.

1. A girl and a pony cross the stream.

2. A girl with a pony crosses the stream.

3. A girl leading a pony crosses the stream.

In (1) the connection is that they both cross the stream. In (2) this connection is elaborated by

indicating that there is a relation of dependence in the sense that the presence of the pony is

somehow implied by the presence of the girl. In (3) this dependence is further elaborated by

indicating the action that causes the dependence. The two elaborations constitute a strand in a

semantic network. Another strand would be as follows.

4. A girl on a pony crosses the stream.

5. A girl riding a pony crosses the stream.

Here the connection of (1) is elaborated in (4) as a physical relationship which is further

elaborated in (4) to indicate the character of that relationship. The idea is that a category can

be envisaged as a polysemous field centred on the notion that characterises the category.

Charles Fillmore and Beryl Atkins (2000 p. 100) definition of polysemy stipulates

three elements:

A. the various senses of a polysemous word have a central origin,

B. the links between these senses form a network, and

C. understanding the inner one contributes to understanding of the outer one.

The one qualification we must make is that the root of the category need not be lexicalised.

Other than that, the concept is obvious. Without it there would be no such concepts as core

and periphery, no such concept as normality. People are quite capable of dealing with

reality regardless of linguistic niceties otherwise they would simply not be there. Indeed, as

David Gil (1991) reports, the Maricopa have no equivalent for the English word and in their

language, but are managing quite well. The various relevant relations are solved using

different linguistic structures. What this shows is basically the distinction between a

conceptual field and a lexical field. However, whether the absence of a lexeme constitutes a

lexical gap depends not on some theory but on the shared verbal habits of the people

employing the relevant conceptualisation. Accordingly, it is not valid to say that speakers of

Maricopa are lacking the lexeme and. Rather, it is we (e.g., speakers of English) who would

experience the lack.

The way the various senses in a polysemous field are related can be characterised as

troponymy. The notion, originally proposed by Christiane Fellbaum and George Miller

(1990 p. 566), can be understood as the presence of a manner relation between two lexemes.

Some examples they gave are to nibble is to eat in a certain manner, and to gorge is to eat in

a different manner. Similarly, to traipse or to mince is to walk in some manner. Likewise,


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the various members of the lexical field centred on and exhibit a manner relation between

each other. Thus, leading is a manner of being with which is a manner of being together and

riding is a manner of being on.

What we have here then is a Connective category where the root meaning is expressed

by the lexeme and which is vague, because its meaning derives in part from its co-text.

Centred on and is a radial network (Lakoff 1987 Ch. 6) that can be understood as spreading

out along semantic vectors. Thus, and is linked to with which is linked to leading as shown in

the examples above. Arguably, the number of branches at each node reflect the number of

conceptual distinctions made. However, the network consists of two layers. Analogous to the

noun-verb distinction we have static Connectives and dynamic Connectives. Thus, on a level

parallel to and we have, for example, the verb join expressing the concept of coming

together with its own branches radiating out. Whether strands merge or not is unclear, but

the fact that there are no true synonyms would seem to suggest that each strand in the network

represents a unique way of looking at reality. This concludes the theory.

3 Application A new theory requires a proof of concept. Accordingly, I first demonstrate how Universal

Grammar classifies the so-called traditional terms, then I give a brief analysis of the verb.

First, however, a word of caution is in order.

There are still many controversial issues in linguistics and some of the following

might not seem to do justice to the understanding accumulated since antiquity. However, it is

important to keep in mind that controversies only arise where there is unclarity about

fundamental issues. Here the two most important factors would seem to be (1) the lack of

distinction between calculus and protocol and (2) the incorrect assumption that linguistic

structure is ultimately of a subject-predicate nature (due to Plato, Crat 399; and Soph 262a-

263d). Thus, given the foundational nature of the theory presented in the foregoing section

and also given the novelty of the theory, it seems appropriate to remain at a descriptive level

that might otherwise be thought superficial. Indeed, there is no logical reason why analyses

cannot be simple and yet sufficient and this should be kept in mind throughout the following

sections.

3.1 Universal Grammar and the parts of speech

Grammars typically give a list of the so-called parts of speech as the elements out of which

sentences are built. The traditional terms for these, noun, verb, adjective, adverb, preposition,

conjunction, pronoun, article and interjection, are essentially the same as those in the Techne

grammatike by Dionysius Thrax (c100 BC). Interestingly, Richard Hudson (1981 p. 335) ran

an inquiry on the opinions of linguists and found that many of the traditional terms were used

with approximately their established meanings. The suggestion is of some consensus that

there is something systematic underlying these traditional terms, although there is no

consensus about what this something systematic might be which would go some way

towards explaining why there are still so many controversies concerning the traditional terms.

However, because there is here no space to enter into argument, one simple test is to see

whether the traditional terms do indeed fit the categories of Universal Grammar.

Accordingly, it should be rather straightforward to classify the various terms on notational

grounds and if not then an intelligent solution should be easily available. And this is indeed

the case. Table 3 lists all the various terms bar one under the notational categories from Table

2. The verb is the one term that does not fit and the solution is given in the next section.


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Table 3 The parts of speech

Intrinsic Extrinsic

Necessary Identifier noun pronoun interjection

Quantifier article

Contingent Qualifier adjective adverb

Connective conjunction preposition

The primary criterion for Table 3 is the number of dependencies the various traditional terms

have, the secondary criterion is the type distinction between Quantifier and Qualifier. Thus,

nouns, pronouns and interjections all qualify as Identifiers for the simple reason that they can

stand alone. Conjunctions and prepositions qualify as Connectives simply because they

depend on two other elements. The case for conjunctions needs no elaboration. Prepositions

can be thought of as connecting a noun phrase to that constituent which, traditionally, they are

a post-modifier of. For instance, in A girl on a pony crossed the stream the preposition on can

be thought of as connecting the NP a girl with the NP a pony. Adjectives, adverbs and

articles depend on one element and are therefore Modifiers. Classifying adjectives and

adverbs as Qualifiers while classifying articles as Quantifiers should be obvious. However, as

already mentioned before, verbs do not fit this schema.

The schematic representation of Universal Grammar shows the possible lexical types.

However, whether some concept is expressed as one or the other type (Identifier, Quantifier,

Qualifier, Connective) depends entirely on the perspective chosen by speaker. Using the

same lexeme in different categories would be called conversion, but really that notion is

nothing more than an artefact of starting out with a particular list of kinds. Thus, it would be

better to think in terms of concepts that are represented by lexemes and which are further

presented in such a form as required by the rules of grammar, part Universal Grammar, part

protocol. Typically, suffixes would be used to cast a lexeme into some type other than its

customary typological sense. Using this notion of casting allows us to get a better grip on

the traditional notion of verb.

3.2 Universal Grammar and the verb in English

Verbs are typically discussed in contradistinction with nouns. This would be due to Plato

(Soph 262a) where he differentiates between the action and the performer of the action.

Platos distinction would seem to be informed by his insistence that A sentence must and

cannot help having a subject (Soph 262e) with the noun representing the doer of the action

as the typical subject. However, the difficulty with his interpretation is the lack of distinction

between words and phrases, resulting in the conflation of noun-phrases as doers with nouns

as things. Even so, the distinction between nouns and verbs is real and, in fact, all known

natural languages express a grammatical distinction between them (Sapir 1921 p. 119).

Popularly, nouns are often called thing words, while verbs are called doing words

and, indeed, there is only a minority of verbs which cannot be so interpreted. Consider.


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6. It rains.

7. It is raining.

8. She knows.

9. *She is knowing.

Typically, (9) is seen as not grammatical. The progressive aspect can be said to emphasise

the transient nature of something, but while it is natural to think that it will stop raining

sometime, we do not (normally) think that of knowing. What is needed here is a fresh start

and to that end I propose to employ the notion of a thing-event continuum. (Although it is

not properly a continuum, but rather a case of opposite perspectives.) Considering that all

lexemes have some referential component, it is appropriate to start with Identifiers.

3.2.1 Verbs as Identifiers

Assuming with Aristotle that a verb is what additionally signifies time (Int 16b6) we can

conceive of things as enduring events. For instance, when we say this stone is black we

know that it will not be so anymore after we have ground it into powder or bleached it with

some chemical, because in the first situation there is no longer a stone and in the second

situation there is, but it is no longer black. When we say this triangle is equilateral we know

that it will not be so anymore after we have wiped it off the board, because it will then have

ceased to exist. However, it is different when we say pi is the ratio of the circumference of a

circle to its diameter. After all, we cannot very well alter the predicate and still expect to be

dealing with pi. The difference lies in the fact that we can refer to a stone and a triangle, but

not to a pi. More specifically, the former are universals while the latter is a particular. The

reason why we cannot say a pi is that the definiendum denotes a phenomenon that is properly

unique. Thus, we can say there is an Amsterdam in the USA, because there does indeed exist

a township of that name in that part of the world. Proper names are unique within some

domain, but only properly unique if they are unique in all domains. Now, we can say that

piing is the activity of calculating the ratio of the circumference of a circle to its diameter and

we have then named an activity that is properly unique. The problem is that there is no real

difference between the definiens of pi and of piing, because both contain the notion of ratio

so that both are effectively descriptions of the process that should issue into the state

nominated as pi. The point is that we should recognise that verbs signify time only

derivatively and that it would be better to say that nouns emphasise the sensible aspect and

verbs the durative aspect of phenomena. Now, consider the following.

10. Swimming is fun.

The term (or rather phrase) swimming here constitutes the subject and can be substituted with

anything conceivable as long as it will successfully identify the subject. Thus, the difference

between the following is not that they are about different subjects, but about different aspects

of the one subject.

11. Pi is fun.

12. Piing is fun.

In fact, we can say that (11) is ambiguous between (12)(14).

13. Using pi is fun.

14. Using the result of piing is fun.

What this means is that there is no effective distinction between a verbal noun and a gerund.

They each perform the same function, namely, they are Identifiers. Accordingly, the benefit

of using these notions outside a historical context must be regarded as illusory.


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The characterisation of the noun-verb distinction as a thing-event continuum is facile

in the sense that there is a certain intuitiveness about thinking of things as opposed to

events. Research in psychology has isolated the notion of object permanence as a critical

stage in the cognitive development of children (Reber 1985 p. 485). The awareness that

objects persist even when they are no longer interacted with is seen as a crucial step towards

the ability of adapting to the environment. However, it is not at all clear what constitutes an

object. Considering that basic level terms are the ones first learned by children (Brown

1958) and that these tend to be natural kind terms (Gelman and Coley 1991 p. 190) it is

significant to realise that they are sortal terms, i.e. referring to sorts of things in the sense of

sorting things together. Xu (1997) suggests that the first sortal that children learn (and

which adults still use) is the notion of physical object. Arguably, the term thing is the

obvious term to refer to physical objects. However, the distinction can be made more

precise.

The thing-event distinction is effectively the difference of a quantitative versus a

qualitative emphasis, in other words, the difference between analysis and synthesis. We see

something as a thing when we see it as the part of some whole, when it is the result of our

analysis of the situation. The traditional term to use here is noun. We see something as an

event when we see it as a whole of some parts, when it is the result of our synthesis of the

elements of the situation. The traditional term to use here is gerund.

Simon (1962 p. 479) refers to the thing-event distinction as one between state and

process, between the world as sensed and the world as acted upon. Using this distinction, we

should now be able to identify those verbs or verb-forms that can be classified as Qualifier,

Quantifier or Connective.

3.2.2 Verbs as Qualifiers

For a verb to be recognised as a Qualifier it must express an instance of synthesis where some

dynamic element contributes to the identification of the denotatum. This dynamic element

must be seen as both intrinsic and contingent. The colour of a cake is a static element that is

both intrinsic and contingent, in other words, the colour is perceived as an attribute. But we

can also shift our position on the thing-event continuum and thereby take up a different

perspective. From there we see the cake not as a thing, but as an event, so that its colour

becomes a symptom of its developmental phase. When we place the dough in the oven we

know when approximately the cake will be ready, but we will be checking the colour to see if

it is so indeed. Thus, we treat the changing colour as an index into the baking process which

effectively makes the colour into a dynamic element and we might perhaps make comments

as follows.

15. The cake is getting a nice colour.

16. ?The cake is colouring nicely.

17. *The colouring cake gave us an appetite.

The intended meaning of (17) is blocked by a pre-existing construction which suggests a

reading of used for colouring as in, for example, colouring crayons. Perhaps (16) is

uncomfortable in English, but in Dutch it is perfectly alright to say:

18. De cake kleurt al aardig.

Taking this further, we can include time and get the following.


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19. The baking cake

20. The baked cake

21. The falling stone

22. The fallen stone

The first of the pairs in (19)(22) indicate that the process is still ongoing, the second that it is

complete, but in all four the perspective is dynamic. Certainly, the ensuing state is static, but

that is not at issue as can be seen from the following.

23. The baked cheesecake

Here the crucial information is that the cheesecake has undergone a baking process resulting

in a very different texture. Thus, it is not simply a matter of taking the distinction between an

adjective and a participle as one of a static versus a dynamic perspective. In fact, from a

purely syntactic point of view it is totally irrelevant whether we take one or the other

perspective. Accordingly, the simple conclusion must be that both adjectives and participles

are Qualifiers. However, there is, of course, also a more complex conclusion, although

perhaps only complex insofar as we hold on to traditional methods of analysis.

The thing-event continuum allows us to describe something as seen from either end of

the spectrum. Where this concerns a mixture of static and dynamic elements, there is in

principle a choice of focus. Thus, while the following describe exactly the same situation, the

choice of focus emphasises one aspect over the other.

24. That swimming girl is fast.

25. That girl is swimming fast.

26. That girl swims fast.

Concerning sentences like (25) and (26), Aristotle commented (Met 1017a23-30) that there are

as many senses of being as there are figures of predication. Accordingly, says Aristotle,

there is no difference in truth-value for these. His examples were:

27. The man is recovering.

28. The man recovers.

29. The man is walking or cutting.

30. The man walks or cuts.

While his examples are simple, they readily extend to the more complex ones of (25) and (26)

and it should be obvious that the notion extends to sentences like (24) as well. However,

Aristotle opens the section by saying Things are said to be (1) in an accidental sense, (2) by

their own nature (Met 1017a7) and although he does not elaborate this (at least not in this

section) it should alert us to the fact that sentences can be ambiguous when taken out of

context. For example, assume a situation where the members of a female swimming team are

playing about in the pool during a break in a swimming contest. Sentences (24)(26) will

then have different truth-values depending on whether we focus on the situation now (as they

are playing in the pool), currently (as they have been performing in the contest) or normally

(as they can be expected to perform). However, within the same context the three sentences

will all have the same truth-value. From this follows that the referent is the same in all three.

Therefore, the Identifier is modified in an equivalent way in all three. This means that the

type of Modifier must be the same in all three so that given the fact that swimming is a

Qualifier, both is swimming fast and swims fast must be Qualifiers as well. Now, the

difference in the case of Aristotles examples (27)(30) is the same as in (25) and (26). But

even though there are subtle distinctions to be made on the basis of the meaning of the

lexemes involved, it would roughly be true to say that the progressive lends an air of

transience to the object of description. (While the notion of aspect is more complex, this is


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the only facet that is relevant here.) Thus, the contrast is really between (24) and (26) which

is effectively the same contrast as in the following.

31. The broken glass is there.

32. The glass broke there.

Here, while the truth-values are not necessarily the same, the distinction still is. In (31) the

focus is at the thing-end of the scale, while in (32) it is at the event-end. The more complex

solution is then as follows.

If we take up a thing-perspective we thereby interpret everything as static. When the

qualifying element is static we call it an adjective, but when it is dynamic we need to cast it

as static which result we call a participle. If we take up an event-perspective we thereby

interpret everything as dynamic. When the qualifying element is dynamic we call it a verb,

but when it is static we need to cast it as dynamic, but here there is no term available. The

only suffix en is not very productive and typically changes the meaning from x to

becoming x. However, the fact that English says It is red instead of It reds does not at all

detract from the reality of casting. Indeed, there are many languages where it is possible

(Sapir 1921 p. 117). Thus we have the following.

33. The girl laughed.

34. The laughing girl.

35. His dark face.

36. His face darkened.

The dynamic element laughed in (33) is cast as a static element in (34) and the static element

dark in (35) is cast as a dynamic element in (36). This demonstrates that while the traditional

notion of verb is descriptively adequate, it is too narrow to be explanatorily adequate.

As should be obvious from the foregoing discussion, the notion of Qualifier covers

what is generally known as the intransitive verbs. The next two sections discuss the others.

3.2.3 Verbs as Connectives

Traditionally, the category of conjunction includes neither the copula nor the transitive

verbs. However, a copular verb can be said to connect a subject with the subject complement

and a transitive verb can be said to connect a subject with the direct object (the indirect object

is perhaps better envisaged as a Modifier). Likewise, rather than treating the preposition as

the head of the prepositional phrase, we can say that it connects the prepositional complement

to whatever the phrase is a post-modifier of. Consider the following.

37. A girl and a pony cross the stream.

38. A girl with a pony crosses the stream.

39. A girl leading a pony crosses the stream.

In (37) there is no ellipsis, but a simple connection of two noun phrases. This connection is

elaborated in (38) by the preposition with which expresses a relation and which is further

elaborated in (39) by the participle leading which expresses the character of the relation.

Obviously, the presence of the pony is both extrinsic and contingent to the girl so that any

elaboration of their conjunction cannot but remain so as well. The lexeme expressing this

conjunction is properly called a Connective.

The question arises as to which element is the head of the complex noun phrase that

constitutes the subject. In (37) the subject is plural and must be substituted with they, while in

(38) and (39) it is singular and must be substituted with she. Traditionally, this has been

reflected in the categorisation of with a pony and leading a pony as, respectively, a


12

prepositional complement and a non-finite clause. This, of course, implies that a girl should

be the head in all three which, however, cannot be substantiated in (37). From a formal point

of view the truth of each sentence depends in part on the element expressing the relation

between a girl and a pony. Therefore, it must be the case that the Connective is in each case

the head of the noun phrase constituting the subject. Thus, it is respectively and, with and

leading which express the synthesis of the two situational elements that make up the subject

and are therefore the heads. But this is easier to see in sentences that are simpler.

40. The girl has a pony.

41. The girl leads a pony.

Here the relation between the girl and a pony is elaborated as, respectively, having and

leading. Consensus would have it that the verb is the head of the sentence and (40)(41)

show that this must indeed be the case, because the truth-value of each sentence depends on

whether a relation of having and leading does in fact obtain between the girl and a pony.

Typically, complex situations allow an alternative focus. Compare (39) with the

following.

42. A girl leads a pony across the stream.

The situation in (39) is identical to the situation in (42), but in the former the focus is on the

act of crossing, while in the latter the focus is on the act of leading. This has an interesting

consequence for when we convert the sentences into the passive.

43. The stream is crossed by a girl and a pony.

44. The stream is crossed by a girl with a pony.

45. The stream is crossed by a girl leading a pony.

46. A pony is led across the stream by a girl.

47. A pony being led by a girl crosses the stream.

48. The stream is crossed by a pony being led by a girl.

There are two actions, namely leading and crossing, so we can convert by pivoting on either.

Pivoting on crossing we convert (37)(39) into (43)(45). Pivoting on leading we convert

(42) into (46). Also pivoting on leading we convert (39) into (47) and then on crossing into

(48) which thereby effectively becomes doubly converted. Accordingly, we can focus on

whichever dynamic element we wish by expressing that as the main verb and we can profile

whichever party involved by expressing that as the subject.

What all this shows is that transitive verbs behave like conjunctions and prepositions.

The effective difference in meaning between a girl and a pony and a pony and a girl is that

the first-mentioned has a higher profile than the second-mentioned. With prepositions there is

usually a sense of direction which is especially clear with locative prepositions. Thus, while

we do not normally speak of passivising constructions such as the vase on the table, we could

(in principle) convert this into the table under the vase. Likewise, with verbs the difference

between active and passive constructions is effectively one of focus. The conclusion we can

draw is that transitive verbs are Connectives.

3.2.4 Verbs as Quantifiers

Auxiliaries are verbs that modify verbs and thus emphasize some aspect of an event. This

means that the categories by which auxiliaries can be sorted are essentially the same as the

categories of Table 1, but here seen from an event-perspective. Whereas things are in space,

events are in time so that we are here concerned with those properties in respect of which an

event can be said to be in time. Auxiliaries, then, quantify events in respect of those

properties as per the schema in Table 4 (retaining the labelling of Table 1 for reference).


13

Table 4 The aspects of events

Intrinsic Extrinsic

Necessary Essence process

Quantity state

Contingent Quality possibility

Relation effect

The labelling of Table 4 is tentative, because much more work needs to be done. Still, the

schema shows the possible ways in which we can quantify an event. The degree to which

these categories are grammaticalised will depend on the culture in which the language is

current, but the distinctions themselves are semantic and therefore available in principle. The

following elaborates the schema by presenting an analysis of auxiliaries on the basis of it.

Process can be understood as quantifying the essence of an event in the sense of the

manner in which it is in time. It is partly grammaticalised in English and commonly

referred to as aspect. The Progressive distinguishes events on the basis of whether it is

known to terminate or not. If we know that a process will terminate we say it is transient, in

all other cases we assume it to be permanent. This distinction between permanence and

transience can be exemplified with the notions of ability and action as follows.

49. John sings.

50. John is singing.

In (49) it could be either ability or action, but because the former is a precondition for the

latter, we assume it says that John has the ability to sing. However, in (50) we do know that

he will stop singing sooner or later, based on our common understanding of reality. The

default is permanence and we use the Progressive to mark transience. However, transient

processes also have beginnings and ends. Consider the event of John singing a ballad.

51. John has sung a ballad [and now Mary is about to perform her juggling act].

52. John is to sing a ballad [after Mary has finished her juggling act].

In (51) the Perfective, using the auxiliary have, indicates that the event has completed and in

(52) the to infinitive, with the auxiliary be indicates that the start of the event is immanent.

To be sure, traditional grammars typically treat the Perfective as part of a system of tense,

but the status of some process is not obtained by asking when. The decision to treat the to

infinitive in (52) as an expression of aspect is perhaps unusual, but should not be

unexpected given the cognitive basis of these categories.

Possibility can be understood as the quality of the event, the sense in which we

should understand it. Things are the way they are, but they can be quantified according to

perspective. Given that qualities are intrinsic, but contingent, we have room for individual

judgement, including doubts about the veracity of what was said. Consider the following

examples (ignoring tense).

53. John is happy.

54. John may be happy [but I dont see it].

55. John can be happy [but he isnt now].

56. John must be happy [but I cant see whether he is].

Thus, (54)(56) indicate various ways in which the possibility of (53) can be quantified, but

there are also these.


14

57. John used to be happy [but isnt anymore].

58. John ought to be happy [but isnt].

Here (57) calls into question whether Johns state of mind is enduring, while (58) claims that

there is some necessity as to why John should be happy. Regarding the future, we have the

following.

59. John shall be happy [because I will make sure he will be].

60. John will be happy [because he really wants that present].

Both (59) and (60) quantify in some respect the necessity of John being happy at some future

moment. Typically, shall and will are classed as modals on the argument that English has no

obvious future tense. Perhaps this expresses an awareness that future events involving

humans are contingent. Possibility is not grammaticalised in English, but the category is

commonly referred to as mood. Centred on this category of possibility would be a

polysemous field mapping out all the ways in which something is imagined to be possible.

The modals then constitute the nodes of the field and together express the category.

State can be understood metaphorically as describing the event as an object in

conceptual space, meaning that we differentiate events on the basis of their location in time.

Thus, state is a necessary, but extrinsic property. The location in time is quantified by

indicating whether it is in the past, present or future and whether it is irrealis or not.

Basically, we conceive of two timelines, the one where reality is played out and the other

where we entertain possibilities and which in a sense describes an alternate reality.

Traditionally, the future is held to be uncertain other than for those events that are understood

to be fixed in some way. Thus, we know that the sun will rise tomorrow because we know

that the relevant laws of nature are true today and we know that we will go to Paris tomorrow

because we decided to do so. Accordingly, we can express futurity with tomorrow and use

the present tense as follows.

61. Tomorrow the sun rises at 6:45.

62. Tomorrow we leave at 8.

Theoretically, a comet could strike before tomorrow and none of this would actually occur,

but at the time of utterance (61) and (62) are true in virtue of what we know at that time.

Location in time is partly grammaticalised in English and commonly referred to as tense,

but covering only past and present. Where the future is felt to be immutable, as in (61) and

(62), we are dealing with the future realis for which English uses the simple present. The

irrealis is expressed by the modals shall and will (future irrealis) and by should and would

(past irrealis). (Perhaps shall is the residue from an erstwhile future tense, but current usage

certainly appears to be modal; also, the issue is somewhat clouded by different patterns of

usage in regional and international varieties (cf. Fowler 1965 pp. 549, 713), but there is no

space to discuss this.) Past irrealis has traditionally been interpreted as a form of

subjunctive.

Effect can be understood as being caused by an event and thus as being both

contingent (because it could have been otherwise) and extrinsic (because it is not part of the

action). The connection between cause and effect expresses the relational aspect of events.

The notion of effect interprets an event from a passive perspective, complementary to the

active perspective, and thus allows a thematic emphasis on the undergoer rather than on the

doer. (To be sure, other thematic roles have been recognised, but these would seem to be

variations, merely requiring some subsidiary perspective.) The cause-effect distinction is

grammaticalised in English and commonly referred to as voice. In line with the distinction

between permanence and transience, there is the further option of choosing between the

be-passive and the get-passive.


15

63. The constable shot the robber.

64. The robber was shot by the constable [and not by the detective].

65. The robber got shot by the constable [as he tried to get away].

Accordingly, we have an emphasis on the doer in (63) and on the undergoer in (64)(65)

while in (64) the focus is on the outcome of the event and in (65) on the event itself.

However, events need not have a doer expressed as in (66).

66. The glass broke during the juggling act.

67. The glass was broken during the juggling act.

68. The glass got broken during the juggling act.

Still, the perspective in (67) and (68) is exactly the same as in (64) and (65). The difference

being that (67) and (68) are further towards the thing-end of the thing-event continuum than

(64) and (65). However, we can shift even further.

69. The glass is broken.

Here, in (69) the dynamicity of the event is reduced to merely an aspect of a thing and broken

is commonly assumed to be an adjective functioning as a subject complement. However, that

would be an incorrect analysis, simply because it ignores the fact that breaking is a causal

event.

3.2.5 Summary

This section has shown that the traditional concept verb can be meaningfully differentiated

using the categories of Universal Grammar and the underlying perceptual categories. Table 5

presents a summary.

Table 5 The types of verbs

Intrinsic Extrinsic

Necessary Identifier gerund

Quantifier auxiliary verb

Contingent Qualifier intransitive verb participle

Connective transitive verb

The coherence of Table 5 further demonstrates the explanatory power of Universal Grammar

as presented in Table 2. Still, the analysis must be acknowledged as tentative until further

research has had the opportunity to re-think the various syntactic categories currently in use.

As it is, Table 5 completes the classification of the parts of speech in Table 3.

One last comment should be made regarding the notion of do support. Typically, the

verb do is considered to be an auxiliary, although it is acknowledged that it also has a

normal meaning. However, the idea that it would have no individual meaning as an

auxiliary is problematic. Chomskys notion of Full Interpretation (1986 p. 98) demands that

all lexical elements have meaning. The way out of this conundrum would be to recognise

auxiliary do as belonging to the domain of protocol. Indeed, as an element of protocol it

would be appropriate for it not to have individual meaning otherwise it could not be used for

its formal meaning. However, that issue awaits further research.


16

4 Conclusion De Saussure held that the nature of language-systems can only be discovered after taking into

account what they have in common with all other semiotic systems. In this article I have

argued that this commonality is the patterning inherent in the cognitive interpretation of the

elements of notation. This conclusion is both profound and trivial. It is profound because it

means that wherever information is transferred there is an awareness of meaning somewhere.

It is trivial in comparison with the complexities of cognition as evident in the diversity of

communicative habits.

The cognitive interpretation of notational elements amounts to what has often been

referred to as Universal Grammar, which means nothing more nor less than that the possible

types of lexeme are restricted to the four categories of Identifier, Quantifier, Qualifier and

Connective. Language can then be understood as the combination of Universal Grammar and

some manner of application of this patterning. Universal Grammar represents the calculus

part of language and is what allows us to control the coding of information, the manner of

application represents the protocol part of language and is what allows us to control the

transferring of information. By the calculus we settle issues of truth and validity, by the

protocol we settle issues of identity and propriety. Thus, any language will serve to assert

some proposition, but only English will serve to identify speakers as being English,

whatever that might be taken to mean. All languages allow hearers to determine whether

some proposition is valid, but only English allows hearers to determine whether some sample

of speech is proper English. All languages abstract from observations of reality, but only

English abstracts from the communicative habits of speakers being English. And this of

course will hold mutatis mutandis for any language. Communicative habits are what

differentiates one language from another; the typology of lexical elements is what they all

have in common and what I have argued to be Universal Grammar.

Notes 1 This article is based on my masters thesis at Monash University (2003). I thank Keith

Allan for commenting on an earlier draft any remaining infelicities are mine only.

Bionote

Humphrey van Polanen Petel came to linguistics after a long career in computing. Having

received his masters degree in 2004, he is currently working as an Honorary Research

Associate at Monash University. His interests are mainly in foundational issues of language.

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Documents

Universal Grammar as a Theory of Notation