Three-Dimensional Syntax
John Klosek
Since 1957 syntactic structures have been represented in terms of twodimensional trees. This paper proposes that by representing syntactic structures
three-dimensionally it will be possible to eliminate all movement, reduce
complexity, and make universal syntactic representation possible for propositions
expressed in any human language.
Modern study of language has focused on syntactic phenomena since the structuralists
first segmented the words in a sentence into immediate constituents, where the proximity
of words to one another was used to define syntactic relationships (Wells, 1947).
Generative grammar in its earlier incarnations also accepted precedence as a fundamental
property of language (Chomsky, 1957, 1964, 1981). It is perfectly reasonable that
constituent order has long been viewed as an essential component of syntax, especially
when analyzing a language such as English, which relies heavily on word order to convey
grammatical information. However, in many languages the order of words is often
grammatically irrelevant and the constituents can be arranged in many different
permissible sequences. Typological studies of natural languages reveal that surface
orders vary widely (Comrie, 1989). In different languages the argument structure can be
SVO, SOV, VSO, VOS, OSV, and/or OVS. Which of these structures should be taken as
the “basic” one for all languages? Kayne (1994) maintains that SVO is the basic order of
constituents for all languages. Other linguists argue that word order is a property of the
phonological component (Marantz (1984), Chomsky (1995), and Cinque (1990).
Although these authors maintain that word order is not a crucial feature of the syntactic
component, they still find it necessary to move constituents within a sentence in the
course of a derivation.
Precedence at first blush would appear to be a self-evident property of human language.
After all when we speak, the words have to be articulated one at a time and they line up
neatly one after the other when we write them down. From ancient times language
analysis had assumed that the order of words in a sentence is sequenced and onedimensional until Chomsky (1957) introduced two-dimensional representation through
the use of hierarchical tree structures. Chomsky also argued that a grammar is not just a
set of rules found in a grammar book; rather, it is a hypothesis about the knowledge that
speakers and hearers have of their language. Although we produce sequenced strings of
words when we speak or write, there is no empirical evidence that the representation of
sentence constituents in the minds of speakers and hearers should be one-dimensional as
it had been traditionally assumed, or two-dimensional as Chomsky hypothesized. We live
in a three-dimensional world and our brains have evolved to perceive and interact with
the three-dimensional phenomena of the environment. It is certainly possible that the
underlying architecture of natural language is also three-dimensional.1 Chomsky
Three-dimensional models have prevailed over two-dimensional models in other
sciences, most recently in cosmology. The dominant theory proposed by Steven Hawking
was that as an object enters a black hole, all information about it is destroyed. The
1
1
demonstrated that two-dimensional hierarchical structures revealed generalizations about
syntax that were beyond the reach of one-dimensional grammar. This paper will argue
that by representing syntactic structure three-dimensionally, it will be possible to
eliminate much of the complexity inherent in two-dimensional grammar, and open the
door to the potential for universal syntactic representation of synonymous propositions
expressed in any language.
Three-dimensional representation of syntactic structure is the natural next step in the
evolution of the study of grammar. The technical challenge is to find a way to represent
the syntactic structure of a sentence in a non-linear fashion from which sequenced surface
forms can flow in various languages. One way this can be accomplished is to replace
traditional two-dimensional trees with three-dimensional trees.2 The model has to
possess many of the properties inherent in a traditional phrase-structure tree, while
providing a three dimensional representation of the tree, which will allow for random
access to all the constituents in the tree. The best way to visualize a tree with these
characteristics is to think of an infant’s crib mobile.3 A three-dimensional tree is just like
a two-dimensional tree with branching nodes, dominating binary subconstituents;
however, because the constituents are not ordered in a linear sequence, at each of the
branching nodes, the order of the subconstituents can be “reversed.” That is, viewing a
node from the front, it appears that the subconstituents are in one sequence, but viewing
same node from the rear, it appears that they are in the opposite sequence. If we think of a
tree structure as a three-dimensional object which can be viewed from different angles-front, back, left, right, and points in between--each of the angles can yield a distinct
sequence of constituents, while preserving the dominance relationships. The traditional
two-dimensional tree (1a) can be represented as a three-dimensional tree (1b)4
problem with this view is that it violates a fundamental law of physics--that matter is
never destroyed-- it can only be transformed from one state to another state. Leonard
Susskind (2008) realized that because Hawking was relying on a two-dimensional model
of black holes, his theory could only account for the facts if it violated the laws of
physics. A three-dimensional model, Susskind argued, would account for the same
phenomena without demolishing the first law of thermodynamics--a vastly simpler
solution.
2
deVries (2003) proposed a much more restricted three-dimensional model to resolve
conflicts of precedence in coordinate structures.
Kempen and Harbusch (2001) use mobiles in their psycholinguistic model of sentence
production to represent the initial hierarchical level of grammatical functions in a
sentence.
3
4
In (1b) we happen to be looking at the three-dimensional tree from a perspective that
yields an SVO sequence. However, as this is a model of a three-dimensional mental
structure, the constituents are not arranged in any particular linear order.
2
(1a)
TP
DP1
VP
V
TP
DP2
V
(1b)
VP
DP1
DP2
In this model the dominance relationships among the constituents remain constant no
matter what the order of the terminal nodes in the phonetic form may turn out to be. With
three-dimensional trees, it is theoretically possible to arrange the constituents of a
sentence in any sequence without having to move them from fixed initial positions.
In (1b) there are two branching nodes that can be viewed5 from different angles: the
constituents dominated by the TP and the constituents dominated by the VP. The threedimensional representation in (1b) can be realized as six possible temporal/linear
sequences (2 a-f).
Viewing the three-dimensional tree from the left/front, the sequence of terminal nodes
will be DP1-V-DP2, which will be referred to as S-V-O, in line with linguistic typology
(Comrie, 1989):
(2a)
TP
V
VP
DP1
DP2
The word “view” should not be interpreted literally, as there is no autonomous entity in
the brain to perform such an act. “View” refers to the way the brain computes threedimensional syntactic structures. It is used here to help us envision how it is that
unordered constituents in a three-dimensional tree of the mental grammar can appear as
an ordered string in phonetic form.
5
3
Viewing the tree from the right/front yields DP1-DP2-V (S-O-V):
(2b)
TP
VP
DP2
DP1
V
Viewing the tree from the left/rear yields V-DP2-DP1 (V-O-S):
(2c)
TP
VP
DP1
DP2
V
Viewing the tree from the right/rear yields DP2-V-DP1 (O-V-S):
(2d)
TP
VP
DP1
V
DP2
Viewing the tree from the top/right yields DP2-DP1-V (O-S-V):
4
(2e)
DP1
TP
VP
DP2
V
Viewing the tree from the top/left yields V-DP1-DP2 (V-S-O):
(2f)
V
DP2
VP
TP
DP1
The figures in (2a-f) are given to illustrate the versatility of three-dimensional syntactic
representation, which can yield six distinct constituent orders. Remember that this is just
one three-dimensional tree that we are “viewing” from different perspectives, which
correspond to apparently different sequences of constituents in phonetic form, but
nothing really changes. There is no movement of any kind in the mental threedimensional tree!
Three-dimensional trees are quite difficult to draw and can be replaced with more
conventional-looking three-dimensional trees to represent the potential sequences as long
as we understand that the flat-looking trees maintain all the same dominance relationships
among the constituents. For example, (2f) can be drawn as (2g):
5
(2g)
TP
DP1
V
VP
DP2
We have to remember that “trees” are only models of the mental syntactic structures that
help us visualize the underlying dominance relationships within sentences. The stretched
lines may be somewhat unorthodox in appearance, but three-dimensional trees reveal that
in spite of the apparently different orders (2a-f), the hierarchical relationships among the
constituents are identical.
(2a-f) represent all the possible linearizations for (1a). Some languages may allow just
one possible surface order for two argument verbs, while others may allow all six. In
English the preferred order of constituents, or the default sequence, is (2a) S V O in
active sentences and (2c) O V S in passive sentences, as an alternate sequence. 6 Natural
languages differ from one another in how they set the parameters that determine word
order. No matter how many of the surface tokens of (2a-f) a language allows as
expressions of one proposition, the reality is that all the potential sequences in phonetic
form are realizations of just one mental three-dimensional tree that represents the
predicate and arguments in an unordered hierarchical array. Regardless of the constituent
order in phonetic form, the argument structure of the proposition in the mental grammar
is not altered.
The variability among languages in the use of word order and inflection presents
considerable obstacles for a comprehensive theory of grammar that relies on a twodimensional model to represent syntactic structures. The three-dimensional model reflects
the intuition that in many languages constituents, which appear to be “displaced” in a
two-dimensional tree, retain all the grammatical relations as if they were in “canonical”
form. The three-dimensional model hypothesizes that no structural changes take place in
the three-dimensional representation of a proposition in the mind of the speaker, even if
the words happen to be articulated in more than one order. The same three-dimensional
structure is just viewed from different angles to produce the distinct constituent
sequences. Similarly, when we process a sentence, the words of necessity have to be
received in a linear/temporal sequence, but in the mind we project an unordered threedimensional hierarchical structure which enables us to interpret the proposition
expressed.
In a two-dimensional model, the representation of the VP in a language such as Russian
is problematical because in some word sequences (O-S-V and V-S-O) the subject DP
6
Please note that no transformation is required to account for the two structures if in the
lexicon transitive verbs are subcategorized for the active voice (Subject—Verb—Object)
and the passive voice (Subject of the Passive—be –en—Verb —by-Phrase) .
6
appears to intervene between the V and the direct object DP. The subject DP seems to
become part of the VP, which is clearly counterintuitive because each sentence retains the
original propositional content and speakers of Russian interpret the sentences as if they
were in S-V-O form. In Russian which is highly inflected, where subjects and direct
objects are marked morphologically for case, gender and number, it is possible, for
example, to arrange the constituents in the three word sentence (3) into six different sets
of terminal nodes (4a-f):
(3) Sobaka ukusila koshku
(The dog bit the cat)
sobak +a
dog +NOM,+FEM,+SING
(4)
ukusi +l
+a
bite +PAST, +FEM,+SING
a. sobaka ukusila koshku
b. sobaka koshku ukusila
c. ukusila koshku sobaka
d. koshku ukusila sobaka
e. koshku sobaka ukusila
f. ukusila sobaka koshku
koshk +u
cat +ACC,+FEM,+SING
S-V-O
S-O-V
V-O-S
O-V-S
O-S-V
V-S-O
The +NOM, +FEM,+SING suffix “-a” indicates that “sobaka” is the subject of the
sentence, and the +ACC,+FEM,+SING suffix “-u” indicates that “koshku” is the direct
object, so the position of the words in relationship to one another in phonetic form is
irrelevant. The three-dimensional trees below illustrate how in Russian the constituent
sequence (precedence) can vary while the hierarchical relationships (dominance) remain
unchanged.
(5a)
TP
VP
V
DP1
sobaka
7
ukusila
DP2
koshku
(5b)
TP
VP
DP2
DP1
V
koshku
sobaka
ukusila
TP
(5c)
V
VP
DP1
ukusila
DP2
sobaka
koshku
(5d)
TP
DP2
VP
DP1
koshku
V
sobaka
ukusila
8
(5e)
TP
VP
DP1
sobaka
V
DP2
ukusila
koshku
(5f)
TP
VP
DP1
sobaka
DP2
V
koshku
ukusila
In (5a-f) one three-dimensional mental tree structure is expressed as six distinct phonetic
strings, and each of them retains the propositional content of a sentence in canonical SVO
form. The six phonetic tokens all have the same exact argument structure because each
one is just a snapshot of the same three-dimensional syntactic tree in the mind of the
speaker/hearer—like one statue that is photographed from six different angles. There is
one structure, of which six distinct pictures have been snapped. There is no need to
hypothesize that these six different constituent orders have been derived through
transformations or movement of some sort because nothing moves in the structure of the
mental grammar as we articulate a three-dimensional mental tree as a one-dimensional
phonetic string. The proposition in the mind remains unchanged. Articulation of a onedimensional phonetic string only makes it appear that the words are in a different
sequence when we produce different tokens of the three-dimensional tree. That is, the
snapshot from a particular angle determines the order of constituents as they are produced
in real time; however, in the mental grammar nothing moves.
9
Modern English differs from Russian in that word order conveys crucial information
about the thematic roles of the words in the sentence. When we perceive a simple active
declarative sentence in English, we know that the first DP is usually the AGENT (or
subject of the sentence), and the DP following the verb is the PATIENT (or the direct
object). If no pronouns are used, there are no other markers to tell us what the subject is
and what the direct object is in the English sentence. In Old English, which had a much
richer morphology, word order was much less rigid (Jespersen, 1955). Modern English,
like many other languages, due to the lack of elaborate inflectional morphology, relies
heavily on word order to signal thematic roles and grammatical relations. All languages
are capable of expressing the same propositions whether they use word order, inflection,
or function words to signal thematic roles and grammatical relations. Three-dimensional
syntactic representation accounts for the fact that a single proposition conceived by the
human mind can have distinct realizations in different languages; that is, synonymous
sentences in different languages can be shown to have the same propositional structure in
the mental grammar. The three-dimensional model makes it possible to provide universal
syntactic representations for synonymous propositions expressed in any language.
With three-dimensional syntactic representation, grammatical relations in a sentence are
specified on the basis of the hierarchical positions of the arguments in the threedimensional tree, as they have been analyzed traditionally in the two-dimensional trees of
generative grammar: the DP immediately dominated by the TP is the subject, and the DP
immediately dominated by the VP is the direct object, etc. As there is no movement of
constituents in three-dimensional grammar, syntactic structure and functional structure
are isomorphic. Dominance plays a preeminent role, while precedence, the position of a
constituent in a linear string, plays no role in three-dimensional mental representation.
Precedence is a feature of the temporal phonetic form only. The dominance relationships
of the various constituents in the sentence remain the same regardless of in which
sequence they are realized in the phonetic form. What are traditionally thought of as
syntactic structures in various languages are just the idiosyncratic phonetic realizations of
the universal three-dimensional hierarchical configurations of predicates and arguments
in the mind of the speaker/hearer. The three-dimensional structure encodes all the
hierarchical dominance relationships of the predicate and arguments in a sentence;
therefore, the sequential position of the constituents in a three-dimensional tree is simply
not an issue.
More generally, the directionality of the constituents within all phrases--not just
predicates and arguments--is not an issue either. As in mainstream generative grammar,
phrase structure consists of a Specifier, Head, and Complement, but without any specific
order. The six distinct sequences illustrated below (6) are realized as snapshots of the
same set of constituents from different perspectives. Just as in the case of arguments, it is
analogous to photographing one three-dimensional object from six different angles. The
three-dimensional object/tree remains unchanged but six distinct tokens are produced.
The six apparently different tokens are just phonetic realizations of one universal
syntactic type, which exists only in the mind of the speaker/hearer:
10
(6)
XP
XP
S
X’
H
S
X’
C
H
H
X’
C
H
XP
S
C
S
C
XP
X’
XP
X’
C
XP
S
H
S
H
X’
C
The three-dimensional trees above represent identical hierarchical relationships among
Specifier, Head, and Complement. However, by viewing them from different angles, six
distinct forms emerge. In reality, the apparent sequence of constituents in the phonetic
form is an artifact that results from representing a three-dimensional mental structure in
one-dimensional or two-dimensional space. Temporal/spatial sequence is a practical
necessity for human speech. In a natural language two or more words cannot be uttered
or written simultaneously; however, it does not mean that when we think, we line them
up one after the other. In our minds the constituents are arranged hierarchically, but they
are unordered. Of course, individual languages differ in the word sequences they allow
due to the parameters they set in the core and the surface constraints they may impose in
the periphery.
Movement transformations in English present a formidable challenge for twodimensional syntax. Take, for example, the classical case of WH-questions. The
traditional generative treatment begins with a D-structure (7) where the WH-word
appears under an object DP, then the WH-word is moved to an empty C node in initial
position dominated by CP, leaving behind an empty node (or a trace or a copy of whom).
Finally, the formerly empty C node is changed to a DP. A similar movement happens
with the auxiliary verb will, where it moves from the T node dominated by T’ to an
empty C node dominated by C’, leaving behind an empty node (or a trace or a copy of
will). Finally, the formerly empty C node is changed to T (8).
11
CP
(7)
C’
C
C
TP
T’
DP
the dog
T
will
VP
V
bite
DP
whom
CP
(8)
C’
DP
whom
T
will
the
TP
T’
DP
dog
T
__
VP
V
bite
DP
__
The traditional analysis posits the existence of empty nodes, the duplication of nodes, and
the stranding of empty nodes. All these potent devices are necessary to account for the
apparent “movement” of constituents. As a result, the hierarchical relationships among
the predicate and arguments which are clearly evident in the D-structure become
obscured in the S-structure. Compare (8) with how the same sentence would be
represented under the three-dimensional analysis where there is no movement and the
grammatical functions of all the constituents are unaffected by the sequence of terminal
nodes7:
7
Unlike in traditional generative analysis where word order is established by reading the
constituents from left to right beginning at the top of the tree, in a three-dimensional tree
word order is determined by reading the words from left to right without regard to how
high up in the tree they appear.
12
(9)
TP
T’
DP
the dog
T
VP
will
DP
V
whom
bite
As there is no movement, there is no need for a CP at the top of the tree with an empty C
node. There is no need for the C’ and C nodes. Finally, no empty T and DP nodes are left
behind. In the unordered three-dimensional tree no movement of any kind takes place
because the dominance relationships among the constituents do not have to be altered in
order to arrive at the word order in phonetic form, which is the consequence of
expressing a three-dimensional mental syntactic structure as a one-dimensional phonetic
string. In three-dimensional syntax, precedence is not a fundamental property of sentence
structure; consequently, there is no need for any movement, copies, traces, or empty
modes.
Now consider how the same proposition would be expressed in Japanese, a language
which differs from English in terms of the WH-phrase parameter. While English fronts
the WH-phrase to form questions, in Japanese there is no apparent movement in
questions, so the question word remains in situ. In the Japanese sentence (10) below
affixed to the arguments, there is a subject marker “ga” following the subject (signifying
the AGENT thematic role) and a question word “ka” and an object marker “o” following
the object (signifying the PATIENT thematic role):
(10) inu ga
dog SUB
dare ka o
kamu
darou?
who Q OBJ
bite
will
The three-dimensional tree for this sentence is (11):
13
(11)
TP
T’
DP
inu ga
VP
T
DP
V
dare ka o
kamu
darou
Syntactically, English and Japanese differ in terms of how they set some key parameters,
which results in distinct sequences of constituents. English is a head first language, while
Japanese is a head final language, so in Japanese the direct object precedes the verb.
Also, in English the wh-phrase appears at the beginning of the sentence, while in
Japanese the question word appears in situ. Note that the three-dimensional tree for the
English sentence (9) and the three-dimensional tree for the Japanese sentence (11)
contain the same exact nodes with the same hierarchical constituent structure. The
apparent constituent orders in the two languages stem from differences in how the head
parameter is set in each language and how thematic roles are assigned.
Although the constituents in (11) are shown ordered in accord with Japanese rules for
thematic role assignment (AGENT, PATIENT, VERB), this is done for expository
purposes only. At the psychological level in the three-dimensional tree, they are assumed
to be unordered, just as they are unordered in the three-dimensional tree representing the
English sentence (9), which follows the rules for thematic role assignment in English
(AGENT, VERB, PATIENT). Nonetheless, a proposition that can be expressed in
English can be represented in terms of the same three-dimensional tree structure as a
synonymous proposition expressed in Japanese. This situation obtains because all
languages are patterned on universal grammar, where the constituents are arranged
hierarchically. The order of terminal nodes in the phonetic form is just a superficial
language-specific phenomenon.
A more serious challenge to two-dimensional syntax comes from languages that appear to
allow the “scrambling” of sentence constituents. Working under the strictures of twodimensional syntax, Van Valin and LaPolla (1997) go so far as to argue that there are
languages whose sentences cannot be analyzed into immediate constituents because
elements which typically comprise an XP occur away from sister elements. They present
evidence from Dyirbal, a prototypical so-called non-configurational language spoken in
Australia, in which the sentence “The man saw the woman” can have the following
sequence of constituents (15):
14
(15) ba-ŋgu-l
DEIC-ERG-I
ba-la-n
yaɽa-ŋgu
buɽan
DEIC-ABS–II
man-ERG
saw
dugumbil-ø
woman-ABS
(Van Valin and LaPolla, 1997, p. 23)
“ba-ŋgu-l” is a modifier of “yaɽa-ŋgu” and “ba-la-n” is a modifier of “dugumbil-ø,” but
the modifiers are not adjacent to the respective nouns; thus, they do not fit the
conventional conception of an NP. These apparently discontinuous constituents,
however, are an artifact of the two-dimensional system of syntactic analysis. Using the
three-dimensional model even so-called non-configurational languages like Dyirbal with
seemingly “scrambled” constituents can be analyzed as having a uniform hierarchical
constituent structure once the surface fog is blown away. Below the same sentence is
illustrated as a three-dimensional tree (16):
(16)
S
NP
ba-ŋgu-l
VP
yaɽa-ŋgu
NP
ba-la-n
V
buɽan
dugumbil-ø
In (16) the relations among the sentence constituents are crystal clear. The apparent lack
of constituent structure in so-called non-configurational languages stems from attempting
to represent a three-dimensional structure of the mind as a two-dimensional tree on paper.
VanValin and LaPolla provide an even more opaque surface realization of the same
proposition (17), which to them, in terms of two-dimensional syntax, appears to lack any
constituent structure at all:
15
(17)
S
NP?
NP?
N
DET
V
Dugumbil-ø baŋgul
buɽan
NP?
NP?
DET
N
balan yaɽaŋgu
(VanValin and LaPolla, 1997, p. 24)
They contrast the scrambled Dyirbal sentence (17) with a synonymous sentence in
English (18):
(18)
S
NP
VP
DET
N
V
The
man
saw
NP
DET
the
N
woman
(VanValin and LaPolla, 1997, p. 24)
In the two-dimensional tree (17), it appears that there is no constituent structure, but in
the three-dimensional tree (19), the constituent structure is obvious:
(19)
S
VP
NP2
dugumbil-ø
ba-la-n
ba-ŋgu-l
16
V
buɽan
NP1
yaɽa-ŋgu
The two-dimensional analysis utterly fails to provide any insight into the structure of
sentence constituents in Dyirbal because when a sentence is uttered in real time, the
words appear to be scrambled. The sequence of terminal nodes does not correspond to
how the sentence constituents are hypothesized to be represented in the mind. This
radical sort of “scrambling” of constituents is found only in languages that explicitly
mark the grammatical relations and thematic roles of sentence constituents, which makes
it possible for the hearer to reconstruct the hierarchical structure of a proposition that
appears to be scrambled. In three-dimensional grammar, however, the hierarchical
dominance relationships among the constituents remain unchanged in the mind of the
speaker after the sentence is transmitted to the hearer as a one-dimensional phonetic
string which is reconstructed three-dimensionally in the mind of the hearer. Therefore,
under the three-dimensional hypothesis, no distinction needs to be made between
configurational and non-configurational languages because languages whose surface
constituents seem to have no structure can be shown to have the same constituent
structure as languages that have rigid word order.
The three-dimensional model holds that word order emerges as the unordered threedimensional mental structure is articulated. When the sentence constituents are arranged
in accord with how the parameters have been set in a given language, the result is a
grammatical sentence, which can be articulated as a one-dimensional phonetic string.
However, the hierarchical structure of the sentence remains unchanged in the mind of the
speaker, even after the words have been uttered. The linear, one-dimensional phonetic
string has no hierarchical structure. Hierarchical structure exists only in the mental
grammar. Once the words leave the speaker’s lips, all that exists in phonetic form is a
string of words with no hierarchical structure.
Three-dimensional syntax sheds light on a major unresolved question in Minimalism: If
language is “perfect,” why does the phonetic form diverge from the “inner nature” of
language?
This property of language might turn out to be one source of striking departure
from minimalist assumptions in language design: that objects appear in sensory
output in positions ‘displaced’ from those in which they are interpreted, under the
most principled assumptions about interpretation. This is an irreducible fact
about human language, expressed somehow in every contemporary theory of
human language (Chomsky, 1995, p. 222).
For Chomsky’s two-dimensional model the displacement of constituents is a significant
challenge, but for three-dimensional syntax this is a non-issue. Language in its purest
form—in the mind—is indeed perfect as Chomsky hypothesizes. However, when
perfectly formed mental three-dimensional propositions are expressed in specific
languages one-dimensionally in phonetic form, the words have to appear in a linear
sequence. In Chomsky’s model this is achieved through movement, while in threedimensional syntax, the same “perfect” structure can be expressed as different sequences
of terminal nodes with no movement. Individual languages choose to order the sentence
17
constituents in idiosyncratic ways, so that in phonetic form the internal logic of human
language sometimes may seem to be obscured. However, that is only an illusion created
by the sequence of terminal nodes. At its core the inner nature of language is unaffected
by the phonetic form.
Unlike Chomsky’s two-dimensional computational system of human language, which
relies on derivations that move, delete, and add constituents, with three-dimensional
syntactic representation there is no need for any derivations; thus all the complications
associated with having to move constituents from fixed initial positions can be avoided:
Viewed derivationally, computation typically involves simple steps expressible in
terms of natural relations and properties, with the context that makes them
natural “wiped out” by later operations, hence not visible in the representations
to which the derivation converges. Thus in syntax, crucial relations are typically
local, but a sequence of operations may yield a representation in which the
locality is obscured. Head movement, for example, is narrowly ‘local,’ but
several such operations may leave a head separated from its trace by an
intervening head. This happens, for example, when N incorporates to V, leaving
the trace tn and the [v V-N] complex then raises to I, leaving the trace tv: the
chain (N, tn) at the output level violates the locality property, and further
operations (say, XP-fronting) may obscure it even more radically, but locality is
observed by each individual step (Chomsky 1995: 223-4).
With three-dimensional syntactic representation, the natural context is not “wiped out”
because no movement of any kind takes place in the constituent structure of the tree.
Speech production involves ordering unordered constituents represented in three
dimensions in the mind into one-dimensional phonetic strings. The assumption that at the
psychological level, syntax is represented two-dimensionally is a fundamental fallacy in
modern linguistic theory, which has led to the creation of ever more complex devices for
moving constituents from fixed positions. The result is a grammar that is so complex that
it appears in theory to be un-learnable. It has to be recognized that at the psychological
level the representation of syntax is three-dimensional and hierarchical, and the threedimensional, hierarchical organization is activated in the minds of people as they produce
and comprehend one-dimensional strings of words. Although the terminal nodes of the
phonetic form have to be articulated in a sequence, the underlying three-dimensional,
hierarchical syntactic structure remains intact in the mind of the speaker and is
reconstructed in the mind of the hearer in order for the sentence to be comprehended.
It is obvious that the words in the sentences printed on this page are arranged in a linear
sequence; however, there is no evidence that in the mental grammar these words are
arranged sequentially. The rigid ordering of constituents in two-dimensional syntactic
trees is just a traditional, common sense assumption without any independent
justification. Three-dimensional syntax posits that in the mind of the speaker the
structure of a sentence is hierarchical and three-dimensional, and the constituents are
unordered. It is only at the point of articulation that the words, of necessity, have to be
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sequenced as an ordered stream. The order of constituents is determined by the
principles of universal grammar, the values of parameters set in each language, and the
idiosyncratic surface constraints that each language imposes on constituent order. There
is no need for any kind of movement of constituents, no need for empty nodes, and no
need for complex projection principles to relate distinct levels of syntax because there is
just one level.
Under the three-dimensional hypothesis, as the words are uttered as a phonetic string,
they are stripped of their hierarchical, three-dimensional structure. That is, the phonetic
form is just a one-dimensional string of words with no hierarchical structure. However,
the phonetic form holds subtle clues to the underlying relationships thanks to word order,
function words, and inflections unique to each language. These devices are part of the
code shared by members of a speech community--what we traditionally call the grammar
of a natural language. By virtue of knowing a language, a listener has the power to take
the one-dimensional phonetic form that he hears and in his mind project it into a threedimensional structure like the one that had originated in the mind of the speaker. In threedimensional syntax there is one level of structure, and it exists only in the mental
grammar. When they are articulated, the terminal nodes form a linear phonetic string
with no hierarchical structure. Compare this view to Chomsky’s position: “The hearer
identifies words, and on the basis of their lexical properties, projects a syntactic structure
as determined by principles of universal grammar and the values of the parameters”
(Chomsky, 2001, 593-4). In Chomsky’s model, however, the structure that the hearer
projects is the S-structure, which then has to be reconciled with the D-structure through a
complex series of computations that move, add, and delete constituents.
In three-dimensional grammar speech perception involves the hearer receiving a onedimensional phonetic string and projecting it into the three-dimensional syntactic
structure that had its origin in the mind of the speaker. Although the terminal nodes
being uttered appear in a linear sequence, the underlying relationships of the hierarchical,
three-dimensional structure remain intact in the mind of the speaker as they are linearized
for output in real time, and they are reconstructed three-dimensionally in the mind of the
hearer. Communication using language can be compared to the way a computer
compresses, or zips, large files in order to send them to another computer, which unzips
and reconstructs the files to their original form. In linguistic communication the threedimensional syntactic structure in the brain of the speaker is compressed into a onedimensional linear string of words through articulation and then reconstructed to the
original three-dimensional structure in the brain of the hearer. Computers have programs
to compress large amounts of data for easy transmission. Humans also have devices for
compressing three-dimensional syntactic mental representations into one-dimensional
phonetic strings of constituents in order to transmit them to other humans. Those devices
are called grammars of natural languages.
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