Chapter 1 What Is Recursion?
Chapter 2 Language and Recursion
Chapter 3 Do Animals Have Language?
Chapter 4 How Language Evolved from Hand to Mouth
Chapter 5 Reliving the Past
Chapter 6 About Time
Chapter 7 The Grammar of Time
Chapter 8 Mind Reading
Chapter 9 Language and Mind
Chapter 10 The Recurring Question
Chapter 11 Becoming Human
Chapter 12 Becoming Modern
Chapter 13 Final Thoughts


1. What Is Recursion?



In 1637, the French philosopher René Descartes wrote the immortal line "Je pense, donc je suis." Curiously,
this is usually rendered in Latin, as Cogito, ergo sum, and is translated in English as "I think, therefore
I am." In making this statement, Descartes was not merely thinking, he was thinking about thinking, which
led him to the conclusion that he existed. The recursive nature of Descartes's insight is perhaps better
rendered in the version offered by Ambrose Bierce in The Devil's Dictionary: Cogito cogito ergo cogito sum--
"I think I think, therefore I think I am." Descartes himself, though, was more prone to doubt, and expanded
his dictum as "Je doute, donc je pense, donc je suis"--"I doubt, therefore I think, therefore I am." He
thus concluded that even if he doubted, someone or something must be doing the doubting, so the very fact
that he doubted proved his existence. This probably came as a relief to his friends.

In this book, I examine the more general role of recursion in our mental lives, and argue that it is the pri-
mary characteristic that distinguishes the human mind from that of other animals. It underlies our ability
not only to reflect upon our own minds, but also to simulate the minds of others. It
allows us to travel mentally in time, inserting consciousness of the past or future
into present consciousness. Recursion is also the main ingredient distinguishing human language
from all other forms of animal communication.

Recursion, though, is a fairly elusive concept, often used in slightly different ways.1 Before I delve into
some of the complexities, let's consider some further examples to give the general idea. First, then, a not-
too-serious dictionary definition:

　　　　　　　　Recursion noun. See recursion.



One problem here, of course, is that this implies an infinite loop, from which you may never escape in
order to read the other stuff in this book. The following variant suggests a way out: Recursion noun.
If you still don't get it, see recursion. This banks on the possibility that if you do get it after a round
or two, you can escape and move on. If you don't, well I'm sorry.

The postmodern novelist John Barth concocted what is probably both the shortest and the longest story ever
written, called FrameTale. It can be reproduced as follows: Write the sentence ONCE UPON A TIME THERE on one
side of a strip of paper, and WAS A STORY THAT BEGAN on the other side. Then twist one end once and attach it
to the other end, to form a Mobius strip. As you work your way round the strip, the story goes on forever.

A similar example comes from an anonymous parody of the first line of Bulwer-Lytton's infamous novel, Paul
Clifford:

　　　　　It was a dark and stormy night, and we said to the captain, "Tell us a story!" And this is the
　　　　　story the captain told: "It was a dark and stormy night, and we said to the captain, ‘Tell us a
　　　　　story!' And this is the story the captain told: ‘It was a dark . . .'"

Another amusing example is provided by a competition, run by The Spectator magazine, which asked readers to
state what they Figure 1. The thinker thinks of thinking of thinking (author's drawing). What Is Recursion?
would most like to read on opening the morning paper. The winning entry read as follows:

　　　　　Our Second Competition

　　　　　The First Prize in the second of this year's competitions goes to Mr Arthur Robinson, whose
　　　　　witty entry was easily the best of those we received. His choice of what he would like to read
　　　　　when opening the paper was headed, "Our Second Competition," and was as follows: "The First
　　　　　prize in the second of this year's competitions goes to Mr Arthur Robinson, whose witty entry
　　　　　was easily the best of those we received. His choice of what he would like to read when opening
　　　　　the paper was headed ‘Our Second Competition,' but owing to paper restrictions we cannot print
　　　　　all of it."2

Taking a different tack, John Barth's story Autobiography: A Self-recorded Fiction is a recursive tale in
which the narrator is ostensibly the story itself, writing about itself.3 It ends, recursively, in its own end:

　　　　　Nonsense, I'll mutter to the end, one word after another, string the rascals out, mad or not,
　　　　　heard or not, my last words will be my last words.

To my knowledge, no story has yet attempted to write a story of a story that writes about itself.

And then there is the recurring problem of fleas, as penned by the Victorian mathematician Augustus de Morgan:

　　　　　Great fleas have little fleas upon their backs to bite 'em, And little fleas have smaller fleas,
　　　　　and so ad infinitum. And the great fleas themselves, in turn, have greater fleas to go on, While
　　　　　these again have greater still, and greater still, and so on.4

This notion of inserting progressively smaller entities into larger ones ad infinitum can also give rise to
interesting visual effects, as in the examples shown in figure 2. chapter 1



The use of recursion to create infinite sequences is also exploited by mathematics. One such sequence is the
set of natural (i.e. whole) numbers, which I'll write as N. Thus we can generate all of the positive natural
numbers by the definitions

1 is in N
If n is in N then (n + 1) is in N.

This second definition is recursive, because N appears in the condition that needs to be satisfied for N.

You may remember, possibly from schooldays, what factorials are. As a schoolboy I found them amusing in a
childish kind of way, because they were signaled with exclamation marks; thus factorial 3, usually written
3!, is 3 * 2 * 1, and equals 6.5 Similarly, we can compute the following:

5! = 5 * 4 * 3 * 2 * 1 = 120
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320 A

Clearly, this can go on forever, but we can capture the entire set by using just two defining equations:

0! = 1
n! = n * (n − 1)! [where n > 0].

This second equation is recursive in that a factorial is defined in terms of a factorial. We need the first
equation to kick the thing off. The next example is for rabbits, and is called the Fibonacci series, defined
by the following three equations:

fibonacci(0) = 1 f
ibonacci(1) = 1
fibonacci(n) = fibonacci(n − 1) + fibonacci (n − 2)
[where n > 1].

If you are following me, you should be able to compute the series, which goes 1, 1, 2, 3, 5, 8, 13, . . .
What the definition says, then, is that each number in the series is the sum of the two previous ones. Why
rabbits? Fibonacci (c. 1170–1250) was an Italian mathematician who used the series to predict the growth of
a hypothetical population of rabbits.6

For a final informal example, I take you to Kyoto, Japan, where I once happened upon a sign on a gate that
was written in Kanji script. I asked what it meant, and my guide told me, I hope correctly, that it meant
Post no bills. There is a paradox here in that the sign was itself a bill, thereby contravening its own
presence. Perhaps there needed to be another sign that said Post no "Post no bills" bills. But of course
this is itself in violation of its own message, so we might envisage another sign that reads Post no ‘Post
"Post no bills" bills' bills. There is no end to this process, so it might have been more sensible to
have allowed bills on the gate in the first place. In practice, though, limitations of time, space, or mem-
ory will prevent a recursive sequence of structure continuing forever.



Toward a Working Definition



One of the characteristics of recursion, then, is that it can take its own output as the next input, a loop
that can be extended indefinitely to create sequences or structures of unbounded length or complexity.
In practice, of course, we do not get caught up in infinite loops--life is simply too short for that.
For the purposes of this book, then, we shall not be interested so much in the generation of infinite se-
quences as in a definition that might apply usefully to human thought. A definition that meets this require-
ment is suggested by Steven Pinker and Ray Jackendoff, who define recursion as "a procedure that calls it-
self, or . . . a constituent that contains a constituent of the same kind."7 The second part of this defin-
ition is important, especially in language, because it allows that recursive constructions need not involve
the embedding of the same constituents, as in the example of the gate in Kyoto, but may contain
constituents of the same kind--a process sometimes known as "self-similar
embedding." For example, noun phrases can be built from noun phrases in recur-
sive fashion. Tecumseh Fitch gives the example of simple noun phrases such as the dog, the cat,
the tree, the lake, and one can then create new noun phrases by placing the word beside between any
pair: the dog beside the tree, the cat beside the lake.8 Or one might have two sentences: Jane
loves John and Jane flies airplanes, and embed one in the other (with appropriate
modification) as Jane, who flies airplanes, loves John. These can be extended re-
cursively to whatever level of complexity is desired. For example we could extend the noun
phrase to the dog beside the tree beside the lake, or the sentence about Jane and John to Jane who flies
airplanes that exceed the sound barrier loves John, who is prone to selfdoubt. Most languages make use
of recursive operations of this sort--although we shall see in the next chapter that there may be a few
languages that don't operate in this way.

Although it is common to provide illustrations from language, the main theme of this book is that it is in
thought rather than in language that recursion originates. As Pinker and Jackendoff put it, "The only reason
language needs to be recursive is because its function is to express recursive thoughts. If there were not any
recursive thoughts, the means of expression would not need recursion either."9 In remembering episodes
from the past, for instance, we essentially insert sequences of past consciousness
into present consciousness, or in our interactions with other people we may insert
what they are thinking into our own thinking. These themes are explored in later chapters.



Process and Structure



As suggested by Pinker and Jackendoff's dual definition, recursion can be understood either as a process or
as a structure. The distinction can be important. A recursive process may lead to a structure that need not be
seen as itself recursive. For example, suppose we construct a sequence of musical notes with an embedding rou-
tine by pairing pairs of notes, each consisting of a randomly chosen note played on a piano with a randomly
chosen note played on a violin. The first pair is embedded in another pair, and the four-note output then em-
bedded in another pair. This process can be continued indefinitely to create a sequence of notes. As illustrat-
ed in figure 3, though, the sequence can be interpreted, not as a recursively embedded structure, but as a se-
quence of piano notes followed by an equally long sequence of violin notes. This failure to distinguish recur-
sive embedding from recursive structure has led to some confusion, especially in claims about recursion in non-
human species.10

Again, in his most recent theory on the nature of language, known as the Minimalist Program,11 Noam Chomsky
has argued that human thought is generated by a Merge operation, applied recursively.
That is, units are merged to form larger entities, and the merged entities can be
themselves merged to form still larger entities, and so on. This operation underlies the embed-
ded structure of human language, although in Chomsky's theory it applies strictly to what he calls I-language,
which is the thought process preceding E-language, the external language that is actually spoken or signed.
Merge can produce strings of elements, be they words or elements of thought, and although it may be applied
recursively to produce hierarchical structure, that structure may not be evident in the final output. For instance,
even sentences might be regarded simply as words all merged in unstructured sequence, as in ritualized songs
or prayers. Everyday language, too, may include mentally undifferentiated clichés and slogans, or sequences
that are chapter 1 highly automated. Politicians may be especially prone to this kind of talk.



As noted above, recursive processes and structures can in principle extend without limit, but are limited in
practice. Nevertheless recursion does give rise to the concept of infinity, itself perhaps limited to the hu-
man imagination. After all, only humans have acquired the ability to count indefinitely, and to understand
the nature of infinite series, whereas other species can at best merely estimate quantity, and are accurate
only up to some small finite number.12 Even in language, we understand that a sentence can in principle be
extended indefinitely, even though in practice it cannot be--although the novelist Henry James had a damn good
try. Such understandings are indeed part of human mental achievement, and depend on a human capacity for re-
cursive thought. Nevertheless they are not the primary concerns of this book.

The appealing aspect of recursion is precisely that it can in principle extend indefinitely to create thoughts
(and sentences) of whatever complexity is required. The idea has an elegant simplicity, giving rise to what
Chomsky called "discrete infinity,"13 or Wilhelm Humboldt (1767–1835) famously called "the infinite use of
finite means." And although recursion is limited in practice, we can nevertheless achieve considerable depths
of recursive thought, arguably unsurpassed in any other species. In chess, for example, a player may be able
to think recursively three or four steps ahead, P P P P V V V V P P P P V V V V Figure 3. The sequence of Ps
and Vs can be created either by recursively nesting PV pairs in PV pairs (left), or by arranging a sequence
of Ps followed by a sequence of an equal number of Vs (right). The sequence might be generated as in the left
panel, but interpreted as in the right panel. What Is Recursion? examining possible moves and countermoves,
but the number of possibilities soon multiplies beyond the capacity of the mind to hold them.

Deeper levels of recursion may be possible with the aid of writing, or simply with extended time for rehearsal
and contemplation, or extended memory capacity through artificial means. The slow development of a complex
mathematical proof, for example, may require subtheorems within subtheorems. Plays or novels may involve recur-
sive loops that build slowly--in Shakespeare's Twelfth Night, for example, Maria foresees that Sir Toby will
eagerly anticipate that Olivia will judge Malvolio absurdly impertinent to suppose that
she wishes him to re-gard himself as her preferred suitor.14 As in fiction, so in life; we all
live in a web of complex recursive relationships, and planning a dinner party may need careful attention to
who thinks what of whom.

The structures resulting from recursive processes need not reveal the nature of those processes, just as a
loaf of bread may not reveal the processes of kneading that went into the making of the bread, or the taste
of wine the picking and trampling of the grapes. Often, though, the structure of a sentence or stream of
thought may reveal recursive embedding--interpretation of a sentence may require the understanding of phrases
embedded in phrases, regardless of how the embedding was actually accomplished, and an internal understanding
of a stream of thought may require the segmentation of episodes within episodes.



What Recursion Is Not



Recursion is not the only device for creating sequences or structures of potentially infinite length or size.
I now consider some examples that do not meet the criteria for recursion. Repetition Simple repetition can
lead to sequences of potentially infinite length, but does not classify as true recursion. For example, the
sentence that opens chapter 9 of A. A. Milne's Winnie the Pooh 10 chapter 1 goes It rained and it rained
and it rained. This could go on forever--or at least until Piglet is drowned--but the repetition simply con-
veys the information that it rained rather a lot, causing Piglet some ennui. It is not recursive because each
addition of and it rained is not driven by the previous one; it is simply added at the discretion of the writer.

In any event, repetition does not distinguish human activity from that of nonhuman animals. Birdsong, for ex-
ample, is relentlessly repetitive, but each repeated theme does not embellish or qualify the previous one.
At most, the repetition might signal urgency, or simply signal continuing presence, as one might repeatedly
knock on a door in the hope of arousing someone inside. Repetition is ubiquitous in human and animal life,
in activities ranging from the repeated jaw movements in eating, to the curiously repetitive nature of sexual
activity. The spider, no less, is capable of repetition, as in Walt Whitman's Leaves of Grass: 15

　　　　　A NOISELESS, patient spider
　　　　　I mark'd, where, on a little promontory, it stood, isolated;
　　　　　Mark'd how, to explore the vacant, vast surrounding,
　　　　　It launch'd forth filament, filament, filament, out of itself;
　　　　　Ever unreeling them--ever tirelessly speeding them

Information can also be aggregated in nonrecursive fashion, as when the short-story writer Saki (H. H. Munro)
wrote, "Hunger, fatigue, and despairing hopelessness had numbed his brain."16 Aggregation of different
phrases similarly compounds meaning additively, as when the historian Peter Hennessy wrote:

The model of a modern Prime Minister would be a kind of grotesque composite freak--someone with the dedication
to duty of a Peel, the physical energy of a Gladstone, the detachment of a Salisbury, the balls of a Lloyd
George, the word-power of a Churchill, the administrative gifts of an Attlee, the style of a Macmillan, the
managerialism of a Heath, and the sleep requirements of a Thatcher.17

The sentence itself has recursive elements, but the aggregation of phrases to describe the freakish composite
is not recursive in that each does not call the next. Instead, they are effectively elements in a list, inser-
ted to add information. Nonhuman species may well have a similar ability to accumulate information, as when
understanding a predator as large, fierce, and with sharp teeth and claws.



Iteration



A slightly more subtle variant on repetition and aggregation is iteration, where a process is repeated, but
in this case there is input from the previous application of the process. In this respect it is like recursion,
and indeed considered by mathematicians to belong to the class of "general recursive functions." For the
main purposes of this book, though, it does not qualify as true recursion because each output is discarded
once it has been entered into the next application. The dictionary definition of recursion that I gave earlier
in this chapter was also really an example of iteration rather than recursion, because you just keep going
round and round the loop, without any added structure. The iterations therefore do not lead to added complexity.

Iterative procedures are used in computational mathematics to arrive at increasingly accurate solutions to a
problem. The basic idea is to start with a preliminary solution--perhaps a guess--and then use a procedure to
compute a new solution. This solution is then used as the starting point for the next computation, and the
new solution is then the starting point for the next round. The cycle is repeated until the solutions stabi-
lize to some acceptable criterion.19 Feedback systems operate in much the same way, typically as a means of
maintaining homeostasis. For example, a thermostat may involve a system for raising or lowering temperature,
and the goal is to achieve some given temperature. The actual temperature is fed into the system, which op-
erates to raise or lower the temperature until the desired is reached. The body is awash with feedback sys-
tems to maintain homeostasis of temperature, iron, energy, blood composition, and so on. The main regulator
is the hypothalamus, in the limbic system of the brain. Such systems again do not differentiate humans from
other animals.

Sometimes the distinction between recursion and iteration may be a matter of interpretation. In the in-
finite loop created by the 12 chapter 1 parody of Paul Clifford, one might say that each beginning
of the story is initiated by the previous one, which is then forgotten. The parody is best appreciated,
though, if the story is seen as an endless, ever deepening whirlpool, with each segment remaining as part
of it. I'm told the story works best if each segment is spoken with a different accent.

Consider too this line from a well-known children's verse:

　　　　　This is the dog that worried the cat that killed the rat that ate
　　　　　the malt that lay in the house that Jack built.

To understand this sentence as truly recursive, one must appreciate that it describes a state of affairs
as a complex whole, and refers to particular cases of a dog, cat, rat, malt, house, and fellow called Jack.
It is not simply the stringing together of a dog that worried a cat, a cat that killed a rat, and so forth. A
young child, though, might process it in this piecemeal way, as a succession of unrelated events.

Recursion and Evolutionary Psychology

In emphasizing recursion as a unifying concept, the approach taken in this book contrasts with that a-
dopted by so-called evolutionary psychologists, who have argued that the mind has multiple facets. The
basic tenets of evolutionary psychology were laid out in the 1992 volume The Adapted Mind, edited by
Jerome Barkow, Leda Cosmides, and John Tooby, and popularized by Steven Pinker in his influential
1997 book How the Mind Works. 20 Thus Pinker writes that the human mind "is not a single organ but
a system of organs, which we can think of as psychological faculties or mental modules."21 In examin-
ing present-day human behavior, the evolutionary psychologist's agenda is to discover independent pro-
cesses as the basic modules, and relate them to conditions that prevailed in the Pleistocene, when hu-
mans existed primarily as huntergatherers. As Pinker puts it, the aim is to carve the mind at its joints,
so to speak, and "reverse-engineer" its components, or modules, back to the epoch during which the
human mind was formed. What Is Recursion? 13 In this view, the mind is really a collection of miniminds,
each beavering away on its own specific problem, among which are language and theory of mind. This
has been called the Swiss-armyknife model of the mind, with a blade for every purpose.22

The danger with this approach is that it becomes too easy to postulate modules and to tell "just so"
stories about how they evolved, so that there is a risk of returning to the now-abandoned instinct
psychology of the early twentieth century.23 Instinct psychology perished under the sheer weight of
numbers--the author of one text counted 1,594 instincts that had been attributed to animals and humans
24--and evolutionary psychology may also drown in a sea of modules, if not of mixed metaphors. Pinker
suggests that we like potato chips because fatty foods were nutritionally valuable during the Pleistocene,
but scarce enough that there was no danger of obesity; we like landscapes with trees because trees pro-
vides shade and escape from dangerous carnivores on the Africa savanna; flowers please us because they
are markers for edible fruits, nuts, or tubers amid the greenery of the savanna; and so on. "There are
modules," he writes, "for objects and forces, for animate beings, for minds, and for natural kinds like
animals, plants, and minerals."25

This is not to say that the Swiss-army-knife model is without merit. Some of the postulated modules
do provide insight into the human condition, and are reasonably well founded. For example, foundational
work in evolutionary psychology by Leda Cosmides provided good evidence for a "cheater-detection
module"--an instinctive ability to detect those who flout social conventions for their own gain.26 A
recent study suggests that humans possess a "category-specific attention system" that is especially
adapted for attending to animals;27 one of the authors, John Tooby, is quoted as saying, "Even dull
animals like pigeons . . . recruit a surprising amount of attention--as do turtles resembling rocks."28
This book is not intended to deny that there are many specific dispositions that shape our mental
and social lives; rather, my aim is to suggest that there are deeper aspects of human thought that
are governed by similar principles, and that recursion is one of those principles--and perhaps the most
important one.

To be fair, too, not all evolutionary psychologists have insisted that modules are completely en-
capsulated, shut off from any communication with one another. Even Steven Pinker, for example,
writes, "[Modules] accomplish specialized functions, thanks to their specialized structures, but don't
necessarily come in encapsulated packages."29 Steven Mithen, although scarcely a cardcarrying evolution-
ary psychologist, argued that the human mind evolved its distinctive character precisely because
reviously encapsulated modules began to "leak," creating what he calls "
cognitive fluidity."30 It is as though the modules stopped minding their own businesses, and
began to gossip. My approach in this book is not entirely at odds with this view, in that I argue a
common principle might underlie a number of our dis-
tinctive abilities.

Others are also beginning to question the Swiss-army-knife model of the human mind more starkly.
David Premack, for example, adopts an approach similar to that offered in this book. Reviewing the
evidence for discontinuity between humans and other animals, he writes: "Animal competencies are
mainly adaptations restricted to a single goal. Human competencies are domain-general and serve num-
erous goals."31 This in effect reverses the evolutionary psychology argument--the mind has become
less rather than more modular. The tide may well be turning.

In any event it is unlikely that recursion can be considered a module. As we shall see, recursion
seems to be an organizing principle in very different spheres of human mental activity, from language
to memory to mind reading. Recursive thinking probably depends on other mental attributes. One of
these is what has been termed working memory, which holds information in consciousness. In o-
rder to embed processes within processes it is necessary to remember
where one had got to in the earlier process when an embedded process
has been completed. For instance, in a sentence like My dog, who eats bananas, often gets
sick, one must hold the early part of the sentence (My dog) and link it to the next part (often gets
sick). Dwight W. Read has argued that nonhuman primates, even our closest relatives the chimpan-
zees, have a working memory that is too limited to allow this kind of embedding.32 Recursion probably
also depends on an executive process that or14 chapter 1 What Is Recursion. 15 ganizes what is to
be embedded in what, and this may depend on the frontal lobes of the brain. The ability to organize
and carry out recursive operations may therefore depend on several processes.

Although I do not embrace the modular view assumed by evolutionary psychologists, I am at one with them
in proposing that a distinctively human mind evolved during the Pleistocene, the epoch that stretched from
around 2.6 million years ago to some 12,000 years ago. How that happened will be told in the later chap-
ters of this book.



Plan of the Book



The book is divided into four parts.

Part 1 deals with language. Although recursion is not limited to language, it is most commonly invoked
to explain why human language differs from other forms of animal communication, an insight largely
attributable to Noam Chomsky. Chapter 2 discusses the nature of language, with particular emphasis
on the role of recursion. Chapter 3 then raises the age-old question of whether other animals have
anything resembling human language. Chapter 4 develops the idea that language evolved from manual
gestures--an idea that suggests greater evolutionary continuity between humans and other primates
than the more common assumption that language emerged from vocal calls.

Part 2 deals with mental time travel, the ability to bring to mind events removed from the present in
both time and place. Chapter 5 starts with memory, and develops the idea that memory for specific
episodes is unique to humans. Chapter 6 extends the notion of episodic memory to the imagining of
possible future events, leading to the concept of the self as existing through time.
This leads to the notion, discussed in chapter 7, that language itself evolved to enable people to share
their memories and plans, and so to communicate about events that are not present
in the immediate environment. This leads also to fiction--the telling of stories
that need not be based on fact, but that nonetheless hone the capacity to deal with the
episodic exigencies of human social life. 16 chapter 1

Part 3 deals another recursive aspect of human thought, namely, theory of mind--or the ability
to understand what others are thinking or feeling. Chapter 8 introduces mind-reading,
not as a psychic phenomenon, but as a natural ability to infer the mental perspectives of
other people. This ability is again critical to social cohesion and cooperation. Chapter 9
explains how theory of mind was also critical to the emergence of language.

Part 4 delves more specifically into the question of how the recursive mind evolved. Chapter 10 sets
this question in the context of the classic debate between Cartesian discontinuity and Darwinian con-
tinuity. Chapter 11 examines some of the steps by which the hominins,33 after splitting from the line
leading to modern chimpanzees and bonobos, began to assume human-like attributes. Chapter 12 then consid-
ers the final step to "modern" Homo sapiens, the sole surviving hominin species--dominant, manipulative,
Machiavellian, and capable of pondering our own nature and status on the planet. That, perhaps, is the
ultimate triumph of the recursive mind.

Chapter 13 presents the final summary and conclusions.




2. Language and Recursion




In 1871, Charles Darwin published The Descent of Man in Relation to Sex, in which he found the courage
to declare that humans were descended from African apes. Just two years later, Friedrich Max Müller,
who held the chair of philology at the University of Oxford, took exception:

　　　There is one difficulty which Mr. Darwin has not sufficiently appreciated. . . . There is
　　　between the whole animal kingdom on the one side, and man, even in his lowest state, on the
　　　other, a barrier which no animal has ever crossed, and that barrier is--Language. . . . If
　　　we removed the name of specific differences from our philosophical dictionaries, I should
　　　still hold that nothing deserves the name of man except what is able to speak . . . a speak-
　　　ing elephant or an elephantine speaker could never be called an elephant. Professor Schlei-
　　　cher, though an enthusiastic admirer of Darwin, observed once jokingly, but not without a
　　　deep meaning, "If a pig were to say to me, ‘I am a pig’ it would ipso facto cease to be a
　　　pig."




Language as Recursion



As anticipated in chapter 1, a common answer is recursion, which provides for what Chomsky once referred
to as the generativity of language. Mark Hauser, Noam Chomsky and Tecumseh Fitch, in an influen-
tial article, have described recursion as the “minimum characteristic” distinguishing human language from animal
comunication. The capacity to embed structures within structures in recursive fashion
has endowed our species with a limitless capacity to create sentences to express
an equally unbounded set of possible meanings. At least within the limits of one’s memory and
processing capacity, we can combine phrases to make sentences as long and complex as we like. The well-
known children’s story, The House That Jack Built, again provides a useful example:

This is the house that Jack built.
This is the malt that lay in the house that Jack built.
This is the rat that ate the malt that lay in the house that Jack
　　built.
This is the cat that killed the rat that ate the malt that lay in the
　　house that Jack built.

And so on . . . and on. Young children quickly understand that the sentence can be extended ad infinitum,
or at least until you run out of breath. The recursive rules of grammar also allow phrases to be moved
around instead of simply being tacked on to the beginning or end. The most demanding kind of recursion
is what is called center-embedded recursion, in which phrases are embedded within
phrases, instead of being tacked on. For example, if one wanted to highlight the malt in the
story, one could embed phrases as follows:

The malt that the rat that the cat killed ate lay in the house that Jack built.

This may require a moment or two to unpack. Too much concatenization like this can boggle the mind, pro-
bably because centerembedded recursion requires one to keep place markers where each phrase is interrupted
by an embedded one. This places a strain on memory. In fact, sentences with more than one level of center
embedding (the above sentence has three) are extremely rare, and considered by some to be incomprehensible.

The recursive nature of grammar can be expressed more formally in the so-called rewrite rules that specify
how grammatical sentences are formed. As the examples from The House That Jack Built illustrate, sentences
(S) can be constructed from phrases (P), which are then combined in recursive fashion. Three kinds of phrases
are noun phrases (NP), verb phrases (VP), and prepositional phrases (PP). On a visit to a publishing house
in Hove, England, I was once greeted by the publisher with the unlikely sentence Ribena is trickling down
the chandeliers. (It was.) Here, the sentence can be broken down into a NP (Ribena) and a VP (is trickling
down the chandeliers). But the VP is itself composed of a verb (is trickling) plus a PP (down the chandel-
iers), which in turn is composed of a preposition (down) plus a NP (the chandeliers).



Once linguistic structures are established, we can then use language to refer to language, at another level
of recursion. Consider the following sentence:

This sentence is a sentence.

As we may remember from school days, a sentence needs a verb, and this one has the verb is so the sentence
is indeed a sentence, and is therefore true. But we can take that sentence and embed it in another sentence,
as follows:

“This sentence is a sentence” is a sentence.

As it turns out, this is also true. And of course we could continue to embed each sentence so formed into the
format X is a sentence, ad infinitum. Sentences are the basic units of language that allow us to express pro-
positions about the world, and propositions are in turn descriptions about states or actions that have so-
called truth-value, which is to say that they are either true or false. Correspondingly, the sentences that
express propositions are generally also either true or false, which gives humans the possibly unique privilege
of being able to lie.

There are a few tricky sentences, though, that cannot be declared either true or false, such as the enigmatic

This sentence is false.

It cannot be true, for if it were it would be false, and if it were false it would be true, if you catch my
drift. Sentences like this have greatly exercised philosophers and logicians



Noam Chomsky has sought deeper rules that would apply to all languages. These rules are known as universal
grammar. In the previous chapter I briefly referred to the most recent theory, known as the Minimalist Program,
according to which language, at its most fundamental level, can be reduced to a single operation, which Chomsky
calls unbounded Merge. It is “unbounded” in the sense that it can be applied recursively, so that merged en-
tities can themselves be merged to build up any desired level of complexity



The Merge operation, though, strictly holds for what Chomsky calls I-language, which is the internal language
of thought, and need not apply directly to E-language, which is external language as actually spoken or signed.
In mapping I-language to E-language, various supplementary principles are needed.



Because I-language is assumed to be the basis of all language, Chomsky argues that it must have no external
reference, and therefore cannot have evolved through natural selection. Instead, it must have emerged in a
single step, perhaps a mutation, probably within the past 100,000 years. He writes as follows:

Within some small group from which we are descended, a rewiring of the brain took place in some individual,
call him Prometheus, yielding the operation of unbounded Merge, applying to concepts with intricate (and lit-
tle understood) properties. . . . Prometheus’s language provides him with an infinite array of structured
expressions.



The Piraha



As young missionaries, Daniel L. Everett and his wife went to Brazil in 1977 with the aim of converting a re-
mote Brazilian tribe known as the Piraha (pronounced roughly as peed’a-han) to Christianity. Their aim was
to learn the language to the point that they could translate the Bible, and so expose the Piraha to the teach-
ings of Christ. The language was so impenetrable to foreigners that earlier missionaries had been unable to
learn it, but the Everetts lived among the Piraha for six years, and Daniel Everett did succeed in acquiring
their language.14



In the course of his stay there, he began to have doubts about religion, and eventually became an atheist.
Everett’s religious doubt appears to have stemmed from his discovery that the Piraha have little
sense of time, and live essentially in the present. They have no fiction or crea-
tion myths, or any sense of history, which were no doubt formidable barriers to the understand-
ing of Christianity, or indeed any religion.



It has no words for colors, and no words for numbers except for words that might be roughly translated as
one, two, and many. There are no tenses other than a simple distinction between present and not-present,
reflecting the fact that the Piraha seem to live in the present, with little understanding of past or fu-
ture. Of special interest, though, is Everett’s claim that the Piraha language has no embedding
of phrases, and indeed no recursion. The Piraha have remained monolingual despite more than
200 years of trading with Portuguese-speaking Brazilians



the Piraha use sentences without embedded phrases to say things that in other languages would be expressed
in sentences with embedding. That is, they have thoughts involving recursion, but use
nonrecursive language to express them. For example, the Piraha have no verbs like say, want,
or think, which in English are normally used with embedded clauses, as in I said that John intends to leave.
In Piraha this would be expressed as the equivalent of My saying John intend-leaves. 16 In describing the
grammatical paucity of Piraha language, Everett is adamant that he is not casting any aspersions on their
intelligence. “I am not,” he writes, “making a claim about Piraha conceptual abilities but about their ex-
pression of certain concepts linguistically, and this is a crucial difference.”



Even the parts of speech, the building blocks of theories of grammar, may not be universal. Nicholas Evans
points out that there are languages without prepositions, adjectives, articles, or adverbs, and that there
is no consensus among linguists on whether all languages even distinguish between nouns and verbs. Even if
they do, it is not clear which words belong in which category. Evans gives the examples of paternal aunt,
which is expressed by a verb in the Australian aboriginal language Ilgar; know, which is an adjective in
Australian Kayardild; and love, which is simply a suffix in the South American language Tiriyo.2



Michael Tomasello concurs that “there are very few if any specific grammatical constructions or markers
that are universally present in all languages.”26 He suggests that theories of language have been unduly
influenced by the characteristics of written language, and are therefore confined to only a tiny fraction
of the world’s languages. Literacy emerged long after language itself, and is still far from universal.
We should therefore not be contemptuous of the Piraha, or indeed of other cultures relying on oral or
signed communication and having no tradition of literacy. As mentioned above, even speakers of Western
languages rarely use centerembedding in speech; an analysis of one corpus showed that 96 percent of that
clauses, as illustrated in The House That Jack Built, were end-embedded and only 3 percent were center-
embedded. The remaining 1 percent were initially embedded (as in That Jack built the house is not disput-
ed).27 Written language is more tolerant of multiple center-embedding, perhaps because the sentences re-
main in front of us while we try to process them. The ancient Greeks and Romans may have been partly to
blame. Aristotle laid down the rules for the construction of sentences according to the doctrine of per-
iods; a periodic sentence was defined as one with at least one center-embedding. The Latin scholars Cicero
(106–43 BC) and language and Recursion 29 Livy (64 BC–AD 13) developed the periodic form, and their writ-
ing served as stylistic icons for centuries; their influence persists in the present-day languages of
Europe.28

It should be noted that, in principle at least, Chomsky’s approach does accommodate at least some degree
of diversity in E-languages—the languages we actually speak or sign. The mapping from a universal I-lan-
guage to E-language, he writes, “might turn out to be intricate, varied, and subject to accidental hist-
orical and cultural events: the Norman conquest, teen-age jargon, and so on.” Diversity can also arise
in the way in which different cultures fit E-language to the constraints of speech. This is called line-
arization, since spoken language, at least, is constrained by the fact that words
are spoken strictly in sequence, whereas I-language is unconstrained by lin-
earization. The critical question, then, is not whether the Chomskyan view can accommodate linguistic
diversity, but whether the degree of diversity recorded by authors such as Evans and Levinson could have
arisen in so short a time. What seems more likely is that grammar itself evolved gradually rather than as
a singular event within the past 100,000 years. Some views on how this might have happened are captured
in the concept of grammaticalization.



Grammaticalization



If grammar does not depend on some inborn, universal set of principles, what does it depend on? Grammati-
calization is the view that it emerged through a gradual process, driven more by practical concerns than
by any biological predisposition.30 One of the processes involved in grammaticalization has to do with
the changing role of words, leading to more efficient and economical expression.31 For example, many of
the words we use do not refer to actual content, but serve functions that are purely grammatical. These
are called function words, and include articles, such as a and the, prepositions such as at, on, or about,
and auxiliaries such as will in They will come. Function words nevertheless almost certainly have their
origins in content words. A classic example 29 30 chapter 2 is the word have, which progressed from a
verb meaning to seize or grasp (Latin capere), to one expressing possession (as in I have a pet porcu-
pine; Latin habere), to a marker of the perfect tense (I have gone) and a marker of obligation (I have
to go). Similarly, the word will probably progressed from a verb (as in Do what you will) to a marker
of the future tense (They will laugh).



In the Beginning Was the Word



According to the linguist Mark Aronoff, even words may have gained combinatorial structure over time.
Words are generally considered to be made up of parts. At one level, they are composed of phonemes, the
smallest units of speech or signed language that make a difference to meaning. In English, the words cat
and bat differ only in the first phoneme, with corresponding differences in meaning, but those same pho-
nemes /c/ and /b/ are used in combinations with each other and with other phonemes to create countless
other words. The “phonemes” (earlier called cheremes) of American Sign Language are defined in terms
of location, hand configuration, and movement, and similarly combine to form different signed words.34
At the next level of structure, phonemes are themselves combined to form morphemes, which are the small-
est units of meaning. Words like jump and cat are morphemes, but so are the endings of words that alter
their grammatical status, such as the addition of -ed to signal the past tense, or the addition of -s
to indicate the plural.



ABSL seems to defy what has been called duality of patterning, the fact that language
involves combinations of elements at two levels, the phonological and the
grammatical. The linguist Charles F. Hockett listed duality of patterning as one of the “design
features” of language,36 so its absence in ABSL may be taken to mean that ABSL is not a true
language. Y



Morphology may well arise with the compression of what were separate words into compounds. For
example, the addition of –ed　to a verb to signal the past tense probably derives from the verb to do.
Hence, roughly speaking, sentences like He laughed may have derived from something like He
laugh did. This follows a　dictum stated by the functional linguist Talmy (“Tom”) Givón that　
“Today’s morphology is yesterday’s syntax.”



This does not mean that language has no genetic component—it is, after all, restricted to our own
species, as I shall argue in the next chapter. It remains something of an open question just how
much of language depends on innate components specific to language itself, and how much on more
general aspects of the human mind. It may depend not so much on what Steven Pinker, echoing
Chomsky’s notion of universal grammar, called “the language instinct”41 as on what has been term-
ed an “instinct for inventiveness,” 42 coupled with a drive toward increased efficiency,
that covers many other aspects of our lives, including art, music, and machines—not to mention
filing systems.



What of Recursion, Then?



Languages, then, appear to have evolved gradually, adapting themselves to particular cultures, and
undergoing progressive modifications. In the case of the Piraha, for example, their lack of
concern for time seems to have been critical. Everett writes:

[The] apparently disjointed facts about the Piraha language--gaps that are very surprising from just
about any grammarian’s perspective--ultimately derive from a single cultural constraint in Piraha,
namely, the restriction of communication to the immediate experience of
the interlocutors.

Morten Christiansen and Nick Chater, in an influential article, suggest that the sheer diversity of
languages, and the rapidity with which they change, mean that language adapted to the brain,
rather than the brain adapting to language. That adaptation, moreover, must have depended on
mental functions that were not themselves primarily linguistic, and that
were heavily influenced by environmental factors such as culture and geography.

The nature of those thought processes is explored in later chapters of this book. In particular,
I will focus on mental time travel and theory of mind as nonlinguistic pro-
cesses involving recursive processes that shaped how language evolved. Whereas Chomsky
viewed thought through the lens of language, I (and others) suggest that language should be
viewed through the lens of thought. This can have a liberating effect on our understanding of
language and its evolution.



Second, any universal principles underlying language can be regarded as principles of human
thought, and not specific to language. Even recursion appears not to be universal, and may be
absent in many indigenous languages. There is therefore some doubt about whether it is truly
the “minimum characteristic” that distinguishes human language from animal communication,
as recently claimed.45 The fact that many, perhaps most, human languages use recursion is of
course good evidence that the human mind is capable of it, even if language can generate any
number of different meanings without it. In oral societies such as the Piraha, word combinations
and repetition of phrases may be sufficient to generate all of the meanings required without
recourse to the embedding of phrases or other recursive devices. And as Everett pointed out,
there is no question that the Piraha are capable of recursive thought.

It is perhaps ironic that a human capacity often said to depend on recursion can function without
it, at least in the sense of phrases being embedded in phrases—languages like Piraha may well be
recursive in that the I-language underlying them may depend on a recursive operation, such as
Chomsky’s Merge. Moreover, language might still depend on the recursive nature of theory of mind,
as I argue in chapter 9. It might be suggested that recursion is merely part of a toolkit for con-
structing language, and that not all languages use all of the tools.4 A universal toolkit, though, is
not quite the same as universal grammar. What the use of recursion in language does illustrate,
though, is that recursion is a property of the human mind, employed when needed. As we shall
see in later chapters, it is not specific to language.

That said, it remains highly likely that language itself is specific to humans. We have a compulsion
to talk, or develop signing systems if speech is prevented, and children do seem to go through
preprogrammed steps in learning language. The emergence of language in our species probably
depended on the evolution of intentional systems of thought, and the
adaptiveness of sharing our thoughts. The communicative imperative
also drove anatomical changes, such as the redesign of the vocal tract to permit greater
variety of sounds, and perhaps changes in breathing and intentional control.



3. Do Animals Have Language?


The least thing upset him on the links. He missed short putts
because of the uproar of the butterflies in the adjoining meadows.
—from The Clicking of Cuthbert, by P. G. Wodehouse


Having grown up on a farm, I suspect that the above quotation is
an unwarranted slur on the gentle butterfly, but vocalization is
ubiquitous among animals, including insects--and of course ourselves.
It has therefore seemed natural to suppose that human language
must have evolved from animal calls. Only in fiction, though, do
animals actually speak and hold meaningful conversations. Most
examples, from Winnie the Pooh to the Beatrix Potter books, are
written for children, but my favorite example comes from a short
story entitled Tobermory, by Saki, who made a brief appearance
in the previous chapter. Tobermory is a cat who has been taught
to speak, to the consternation of guests at a house party. Here is
what Tobermory says to a woman who is foolish enough to ask his
opinion of her intelligence:

"You put me in an embarrassing position," said Tobermory, whose
tone and attitude certainly did not suggest a shred of embarrassment.
"When your inclusion in the house party was suggested Sir Wilfred
protested that you were the most brainless woman of his acquaintance,
and that there was a wide distinction between hospitality and
the care of the feeble-minded. Lady Blemley replied that your lack of
brain-power was the precise quality which had earned you your invitation,
as you were the only person she could think of who might be
idiotic enough to buy their old car."

To everyone’s relief, Tobermory was killed shortly afterwards by a
tomcat from the Rectory.

In most respects, though, animal vocalizations have little in common
with human speech. For the most part, they are genetically
fixed, and under emotional rather than voluntary control. They are
organized in the midbrain, with little or no input from the cortex,
the seat of higher mental functions. For example, electrical stimulation
of a region of the midbrain called the periaqueductal grey
induces hissing, growling, screaming, howling, and meowing in the
cat, shrieking, yelling, yapping, cackling, and trilling in the squirrel
monkey, echolocation sounds in the bat, and laughing in humans.
These vocalizations seem to be organized downstream from
the periaqueductal grey, in the ancient depths of the brain.2 Thus,
destruction of the periaqueductal grey causes rats, cats, squirrel
monkeys, and humans to become mute.

Human laughter, then, belongs in the category of innate vocalizations
unrelated to speech, and is correspondingly difficult to
produce voluntarily or to suppress. Robert Provine, in his book
Laughter: A Scientific Investigation, records that a girls’ boarding
school in Tanzania had to be closed because of an uncontrollable
epidemic of hysterical laughter.3 And conversely, it takes a trained
actor to laugh convincingly in the absence of the emotional state,



Even the calls of chimpanzees, our closest living relatives, appear
to be largely involuntary. Jane Goodall, who lived among
the chimpanzees in the wild at Gombe National Park in Tanzania,
once recorded the instance of a young chimp that had discovered a
cache of bananas, and evidently wanted to keep them for himself.
But when chimpanzees discover food, they characteristically emit
a pant hoot call, drawing the attention of other members in the
troop. The young chimpanzee was unable to suppress the emotionally
driven call, but did the best he could to muffle it by placing a
hand over his mouth. Conversely, chimpanzees find it difficult to
produce a call voluntarily. Goodall remarks, “The production of
sound in the absence of the appropriate emotional state seems to
be almost an impossible task for a chimpanzee.”

This may nevertheless be something of an exaggeration. Different
pant hoot calls have been recorded in different regions of Africa,
suggesting a degree of cultural influence. But even here the variation
may not be so much in the actual sounds as in their timing.5
Pant hoots are often accompanied by drumming, in which the animals
repeatedly hit their hands or feet against a surface—including
their own chests. Groups have a characteristic beat,



captive chimps were more likely to produce two attention-getting
sounds, the “raspberry” and the “extended grunt,” when a human
appeared with a favorite food than when either the human or the
food appeared alone.



Human speech is not only intentional, it also requires the learning
of new sound patterns. Although most animals and many birds
vocalize, very few are capable of vocal learning. Just why this is so
is something of a mystery. Erich D. Jarvis suggests that there has
been selection against vocal learning because it introduces variation,
and makes the calls more noticeable to predators—just as we
humans tend to notice the sound of a new voice. Jarvis suggests
that animals that do learn new patterns are the ones without major
predators, with humans at the top of the list. Apart from humans,
killer whales are the top predators of the ocean, and are vocal learners.
Adult elephants are also vocal learners, and do not have natural
predators, although lions, hyenas, and crocodiles sometimes
prey on young elephants.



If an animal cries “wolf” it is important that a wolf be actually present, otherwise
her mates may not believe her next time and fall victim to that
voracious animal. Human talk, in contrast, is notoriously untrustworthy,
as the poet Robert Graves warns in his poem
BewareMadam!
Beware, madam, of the witty devil
The arch intriguer who walks disguised
In a poet’s cloak, his gay tongue oozing evil.

If animals aren’t conversing with one another, one may well ask
what all the noise is about. Usually, it has to do with essentially
instinctive or emotional situations such as mating, aggression, territorial
claim, or warning of predators



But simple imitation is not the same as speech produced through
the use of grammatical rules. Closer to the mark was Alex, an
African gray parrot, who also died recently. Alex’s voice has been
described as like a recording from an old-style Victrola.27 He did
not merely mimic, but was able to answer simple questions about
the colors or shapes of objects, or about the number of objects up
to about six. He was said to have had the speech capabilities of a
two-year-old human child.28 This is progress indeed, but just as
the two-year-old has not yet developed true grammatical speech,
neither did Alex.

For the birds, I should also mention another African gray parrot
called N’kisi, and featured in a BBC News report of 26 January,
2004. N’kisi belongs to Aimee Morgana (or her to him), and
is said to have a vocabulary of 950 words and to generate novel
utterances.



What, then, of our closest relatives, the chimpanzee and bonobo?
Even at the acoustic level, without any consideration of
meaning, the vocal exchanges between chimpanzees differ mark
edly from the exchanges that occur in human conversation. When
people converse, they generally choose words, and therefore sounds,
that are different from those they have just heard—the answer to a
question, for example, is not the same as the question itself, unless
perhaps it comes from a postmodernist, or a psychoanalyst. The
sounds that chimpanzees emit during vocal exchanges are similar
to what they have just heard.31 Their echoed exchanges probably
have to do simply with maintaining contact, rather than with telling
what Bobo said to Mimi last night over dinner.



Do Animals Understand Us?



Although nonhuman animals have little or no ability to produce
anything resembling human speech, they may have surprising ability
to understand it. One of the more remarkable instances comes,
not from an ape, but from a border collie.36 His name is Rico,
and he is able to respond accurately to spoken requests to fetch
different objects from another room, and then to either place the
designated object in a box or bring it to a particular person. In experimental
trials, he was given 10 objects randomly selected from
200 objects that he knows, and chose correctly in 37 out of 40 trials.
Rico collects the designated object from a room in which there
is no person who might cue him about the correct selection, which
rules out any “Clever Hans” effect. If he is given an unfamiliar
name of an object to fetch, he will choose the one object among
the otherwise familiar selection that is novel. Four weeks later, he
demonstrates that he still knows the name of this object, indicating
what has been termed “learning by exclusion.” This ability to
apply a label on a single trial is known as “fast mapping,” and has
hitherto been thought to be restricted to humans.37 Rico’s exploits
may not come as a surprise to people convinced that their pet dogs
or cats can understand them.

Rico’s performance is somewhat comparable to that of Kanzi, a
bonobo raised by Sue Savage-Rumbaugh. Kanzi is unable to speak,
but as we shall see he has acquired an impressive facility to communicate
by using manual gestures. What is interesting here is that
his ability to understand spoken language far exceeds his ability to
produce it. He can respond correctly to quite long sentences. For
example, when asked, “Would you put some grapes in the swimming
pool?” he immediately got out of the water, fetched some
grapes, and tossed them into the pool. When visiting his friend
Austin, a chimpanzee, he was told, “You can have some cereal if
you give Austin your monster mask to play with.” He responded
by finding his mask and giving it to Austin, and then pointing to
Austin’s cereal. His ability to respond to such commands is not
perfect, though. In one controlled study, he was given a list of 660
unusual spoken commands, some of them eight words long, and
responded correctly on 72 percent of them. Kanzi was nine at the
time, and did a little better than a two-and-a-half-year-old girl
called Alia, who managed to get 66 percent correct.38
These examples suggest that comprehension of speech far outstrips
production, also a common observation in children acquiring
language.39 They also suggest a surprising ability to break sentences
down into words, hitherto considered a uniquely human
capacity. Although this is something that seems natural to most
of us, there is virtually nothing in the acoustic signal that tells us
where one word ends and another begins,40 and it is really only
experience with the language that enables us to break a sentence
down in this way.41 Doyoufollowme? We become aware of this
only when listening to a language that is completely foreign, when
all the words seem to run together in a meaningless babble. When
we teach children to speak, we help them to separate the words
with an exaggerated form of speech known as “motherese.”

The Origins of Human Language, Thought, and Civilization