The Search for Non-Being
From The Philosopher, Volume LXXXX No. 1

Lewis Carroll
and the Search for
Non-Being
Pinhas Ben-Zvi

In which Humpty Dumpty, a true Heraclitean, asserts that there must exist an opposite to a birthday which is an un-birthday.



Humpty Dumpty informs Alice that 'there are three hundred and sixty four
days when you might get un-birthday presents'. It is obvious to him that
un-birthdays are real Beings and not mere utterances. His statement is
another augmentation to one of the oldest and rudimentary philosophical
controversies: whether Non-Being, like Being, exists.
Footprints of this controversy, which was initially conceived by Greek
philosophy, can be tracked all over the two books of Alice. Carroll
conveys, through Alice's discourses with the various figures she meets on
her way, his belief that Non-Being does indeed exist. This stand can be
inferred not just from Humpty Dumpty's statement but from other passages
in Alice as well.
The beginning of the 6th Century B.C. was a defining moment in the history
of mankind intellectual thought. From this time on, for a period that
lasted around 150 years, some Greeks, in later years called the
'pre-Socratics', began to ask new questions and propound new answers about
the nature of the universe. (Most of the pre-Socratics flourished not in
Athens, nor even on mainland Greece, but in Asia Minor, Lower Italy and
Sicily. 'Greek', in this context, is a cultural expression rather than a
geographical one.)
The pre-Socratics were the first to formulate tenets that were based on
reasonable arguments rather than on theological doctrines, and they set
the foundation on which the future intellectual revolution in philosophy
would be created by Socrates, Plato and Aristotle
But before we follow Alice into Wonderland, we should recall the roots of
the controversy, in Elea in Lower Italy, in the early 5th Century BC.
There, Parmenides, asserted in a poem that he had composed, that only the
'Is' is, whilst to speak of the 'Is not' is to take a '. . . wholly
incredible course, since you cannot recognise Not Being (for this is
impossible), nor could you speak of it, for thought and Being are the same
thing.'
The grammar used by Parmenides in his poetic assertion gave rise to
different interpretations. Did he mean 'is' as a predicate, as for
instance in a sentence like: 'Parmenides is Greek', or is it the 'is' of
Existence ?
It seems most likely that the 'IS' means Existence since, later on in the
poem, he characterise the 'IS' as a well-rounded ball, namely having
material properties. Accordingly, to Parmenides, Non-Being was analogous
to Non-existence.
Parmenides' concept, embraced by his disciples (the Eleatics) is
considered to be a refutation of the teachings of his predecessor,
Pythagoras, who claimed that a kind of Non-Being does indeed exist. Other
pre-Socratics, such as Democritus of Abdera, the most prominent of the
atomist scholars, and one who wrote and taught some decades after
Parmenides, also insisted, like Pythagoras, that Non-Being must in fact
exist, in spite of Parmenides' rigorous logic.
Certainly, the pre-Socratic philosophers conceived Being as (being) made
of matter. Democritus for instance, and other Atomists, viewed Being as
comprised of an infinite number of small particles- the word 'atoms'
literally meaning 'indivisible'. Atoms combine to form all the objects in
the universe. They are solid, microscopic, move in space and join one
another to form more complex objects. Movement of atoms is possible since
imbetween each one of them there is a void.
The void is not nothing at all - it is Non-Being. A Non-being that,
however, exists. But Greek philosophy had to pass through another thinking
revolution in order to postulate the existence of non material Beings; The
leading figure in this revolution was Plato who conceived the tenet of the
Forms (Ideai). The Forms are the ultimate real Beings, having no spatial
nor material properties.
In the Sophist dialogue, Plato argues that what 'is not' in some sense
also 'is', refuting Parmenides' concept of the impossibility of the
Non-Being to exist. Non-Being is just a being characterised only by its
difference from 'another' being. He asserted that the antinomy between
Being and Non-Being is false. The only real antinomy is that of a single
object of consciousness and all other things from which it is
distinguished.
Carroll was no stranger to Greek philosophy, which was one of the subjects
he studied as part of the Classics curriculum at Christ Church. It seems
that he embraced Platonic Ideational thought by asseverating the existence
of un-birthdays - un-birthdays are non-material beings.
Nor are they the only ones to be found in Carroll's realm of non-material
beings. There also is the dog's temper. The Red Queen urges Alice :
'Try another Subtraction sum.
Take a bone from a dog: what remains?
Alice considered. 'The bone wouldn't remain, of course, if I took it
-and the dog wouldn't remain; it would come to bite me -- and I'm sure I
shouldn't remain!'
'Then you think nothing would remain?' said the Red Queen.
'I think that's the answer.'
'Wrong, as usual,' said the Red Queen: 'the dog's temper would remain.'

'But I don't see how -'
'Why, look here!' the Red Queen cried. 'The dog would lose its temper,
wouldn't it?'
'Perhaps it would,' Alice replied cautiously.
'Then if the dog went away, its temper would remain!' the Queen
exclaimed triumphantly.'
Carroll is over and over again seen to be fascinated by the idea that
Nothingness is more than what meets the eye:
Take some more tea,' the March Hare said to Alice, very earnestly.
'I've had nothing yet,' Alice replied in an offended tone, 'so I can't
take more.'
'You mean you can't take LESS,' said the Hatter: 'it's very easy to take
MORE than nothing.'
The Cheshire cat's grin too is a non-material being. The cat appears from
the void and slowly vanishes back into it leaving behind him just a grin.
Can a cat's grin exist without its master? Carroll does not hesitate, he
is certain that it does. For it is clear that to Carroll a grin is just a
Platonic Form - a nonmaterial being which has real existence. He is not at
a loss to see the phenomena of the cat's head without its body, the
possibility of which brings about a heated disputation between the king
and the executioner.
The executioner's argues that: 'You couldn't cut off a head unless there
was a body to cut off from', but the king is not at all convinced. To him,
like to Carroll: ''anything that had a head could be beheaded.' and the
executioner's philosophical observations are just 'talking nonsense'.
However, there is a philosophical hurdle for un-birthdays. Birthdays and
Un- birthdays are of course also expressions of time. Plato did not
consider time as a form. He held that: 'The moving images of eternity we
call time, days and nights, are the parts of time' (Timaeus). One must
therefore question whether Birthdays or Un-birthdays are indeed Platonic
Forms.
Humpty Dumpty is not in the least troubled by this philosophical hurdle.
He remembers well that the Hatter told Alice that he 'knew Time' and that
one cannot 'talk about wasting it' because Time is 'him'. Time, says the
Hatter, is someone that if you only 'knew how to keep on good terms with
him, he'd do almost anything you liked with the clock', for instance 'you
could keep it to half-past one as long as you liked'.
To Humpty Dumpty, as well as to the Hatter, Time is a real entity. Once we
become aware of this reality, Plato's concept presents no hindrance to the
existence of either birthdays or un-birthdays. As with Time, Numbers too
are portrayed by Carroll as real entities. Upon entering the garden Alice
comes up to three card gardeners presented by Carroll as Two, Five and
Seven. To Carroll, the Christ Church mathematician, Numbers, like Time,
are more than just abstract figures - they are real Beings. Carroll
venerates here Pythagoras' concept about Numbers. Aristotle records that
the Pythagoreans held that Numbers were: the first things in the whole of
nature' and that 'the elements of numbers are the elements of all things'
Numbers also play an important role in Plato's philosophy. It is commonly
construed that he inclined to interpret his theory of the Forms in terms
of mathematics as in the Timaeus dialogue; Mathematical entities have real
existence; they are nonmaterial entities that exist in the realm of the
Forms.
Aristotle however held (in the Metaphysics) that Plato thought of the
Number as an intermediate substance between the Forms and the world of
appearances. The Neo-Platonics, who flourished after Aristotle, believed,
contrariwise, that numbers were identified by Plato with Forms. Whatever
is the right meaning that Plato intended for the numbers, it is widely
agreed that the Pythagorean number theory is the direct ancestor of the
Platonic theory of Forms.
Numbers afford Carroll creative freedom. The gardeners' numbers are
equivalent to their identities, so it is only natural for the Queen,
coming upon the gardeners, to ask: 'And who are these?' Since the
gardeners 'were lying on their faces', 'she could not tell whether they
were gardeners or soldiers, or courtiers, or three of her own children'.
Plato, as part of the cave allegory, asserts that the identity of a human
being is not derived from their body but from the character of the their
soul. Carroll, in pure Platonic reasoning, professed that a Number like
the soul, is a nonmaterial entity that harbours the true identity of its
subject. The gardeners' bodies are visible but, alas, their numbers are
out of sight, hence their identity vanished and their very existence is in
doubt.
Another issue that Carroll coped with was the question raised by Greek
philosophy about the true nature of the Being. Ever since the
pre-Socratics, Greek philosophers have disagreed with each other about the
very nature of Being. Is it one or is it many? Can it move or is it
immovable?
This controversy is interwoven in the two Alice books. In order to follow
Carroll's adaptations in this respect, one must go back to the
pre-Socratics' tenets and 'Begin at the beginning'.
At the beginning, Parmenides taught that the IS, namely Being, or sole
existence, is characterised as being one and not many, as neither
generated nor capable of being extinguished, and as complete, not
divisible into parts and immovable. Being is immovable- due to its being
one and as such filling the whole universe with nowhere further to extend.

Alice, it seems, is aware of this concept. After drinking from the 'DRINK
ME' bottle and growing in size to such an extent that her whole Being
fills the room completely leaving no space for anything else, she observes
: 'Oh, you foolish Alice!' she answered herself. 'How can you learn
lessons in here? Why, there's hardly room for YOU, and no room at all for
any lesson-books!'
Parmenides' disciple, Zeno of Elea, formulated a few paradoxes to
demonstrate his masters' teachings that Being is one and motionless. The
most famous of his paradoxes is Achilles and the tortoise. If, in the
race, the tortoise has a start on Achilles, then Achilles can never reach
the tortoise for, while Achilles traverses the distance from his starting
point to that of the tortoise, the tortoise will have gone a certain
distance and, while Achilles traverses this distance, the tortoise goes
still further, ad infinitum. Consequently, Achilles may run indefinitely
without overtaking the tortoise.
The Achilles paradox purported to force upon the listener the truism that
motion is impossible and what we see as motion is an illusion. Pursuant to
Zeno's paradox Carroll wrote a lovely short piece which he called What the
tortoise said to Achilles. Achilles, trying to follow the tortoise's
reasoning, is left by the end mentally near despair failing to understand
Carroll's adaptation of Zeno's paradox which leads to infinity.
Parmenides further portrayed the IS as: 'perfect from every direction,
like the mass of a well-rounded ball, in equipoise every way from the
middle'. This portrayal raised a question - if that is so then the IS
extends only as far as the periphery of the ball. What exists beyond?
Parmenides' pupil, Melissus, was aware of this seeming inconsistency and
added his own refinement. He negated every form of void: to him, Being is
infinite in space as well as in time. Any other possibility will be
inherently contradictory since it will imply a presence of some Non-Being
beyond the edge.
Another pre-Socratic who conceived a tenet about the nature of Being was
Heraclitus of Ephesus, in Asia Minor, a predecessor of Parmenides, who
lived about 500 B.C. Unlike Parmenides' 'oneness' concept, Heraclitus
taught that existence is dualistic - both 'oneness' and plurality. He
further asserted that the nature of all things is governed by one
universal principle- that of the logos, the ultimate reality, which is
manifested by the interdependence of the opposites and by the process of
flux (Panta Rhei) and change. His teaching is defined as the unity of the
opposites.
The opposites may appear different but at the same time they are held
together in unity as, for instance, health and disease, or hot and cold.
They in fact define each other. As Heraclitus put it: 'Justice, which is a
good, would be unknown were it not for injustice, which is an evil'.
The existence of the opposites depends only on the difference of the
motion on 'the way upwards' from that on 'the way downwards'; all things,
therefore, are at once identical and not identical.
Humpty Dumpty, a true Heraclitean, asserts that there must exist an
opposite to a birthday which is an un-birthday. Alice enters the world
where Humpty Dumpty lives through the looking glass, and, as is common in
mirror worlds, every image has its opposite. The mirror images are
different, right appears as left and vice versa, but at same time they are
identical, since after all they are images of the same object.
Lewis Carroll rejects Parmenides' concept of oneness and the impossibility
of movement; Equally Heraclitean he embraces the view that everything is
in an everlasting process of flux, change and transformation, while its
essence remains the same. This is evidenced by Alice's encounter with the
Caterpillar: Who are you', asks the Caterpillar and Alice answers:
'I - I hardly know, Sir, just at present I know - at least I know who I
was when I got up in this morning, but I think I must have been changed
several times since then'. Alice is uncertain: 'I can't understand my
self, to begin with; and being so many different sizes in a day is very
confusing.'
The caterpillar, unlike Alice, is 'not at bit' confused and does not 'feel
queer' at his transformation 'into a chrysalis, some day, and then after
that into a butterfly'. And why should he? As an Heraclitean thinker he
knows that the process of his transformation does not change his essence
and identity.
Carroll submits more evidence that sameness is not lost due to change. In
one instance Alice refers to her previous height changes when she briefly
suffers an identity crisis:
'I wonder if I've changed in the night? Let me think; was I the same
when I got up this morning?'
And the unavoidable question: 'But if I am not the same, who in the world
am I ?' She ponders whether she 'could have been changed for any one' of
the children she knew - Ada or Mabel. For a moment she believes that 'I
must be Mabel and shall have to go and live in that poky little house and
ever so many lessons to learn!' To avoid such a grim prospect, Alice,
still deeply doubtful about her identity, expresses her preference to stay
down in words that immediately call to mind Heraclitus' 'up and down'
language:
'I'll stay down here! It'll be no use their putting their heads down and
saying 'come up again, dear!' I shall only look up and say 'who am I,
then? Tell me that first, and then, if I like being that person, I'll
come up; if not, I'll stay down here till I'm somebody else.'
After another short cycle of height transformations Alice gains self-
confidence and, with indisputable Heraclitean conviction she is 'very glad
to find herself still in existence'. Alice still experienced another
alarming transformation. After tasting the mushroom she found that 'all
she could see, when she looked down, was an immense length of neck'.
Luckily she was delighted to find that her 'neck would bend about easily
in any direction, like a serpent'.And indeed a Pigeon, protecting his
hatched eggs, insists that Alice is a serpent, not just by her snakelike
shape but also in accordance with Aristotelian Categorical syllogism,
which the pigeon applies in an upside down manner:
All Serpents eat eggs
Alice eats eggs
Alice is 'a kind of serpent'
Carroll, the author of several books on logic, is paying here tribute to
Aristotle, the founder of logic as a branch of philosophy, and to
Aristotelian syllogistic propositions of two premises and a conclusion
like :
All Greeks are mortal
Socrates is Greek
Socrates is mortal.
The right Aristotelian syllogism, the Pigeon should have used, is of
course:
Serpents eat eggs
A is a serpent
A eats eggs
One must excuse a Pigeon in distress for such a fallacy when many people,
in more relaxed circumstances, reach similar false conclusions. Carroll
suggests that in spite of all the changes that have transpired, Alice's
existence has not been affected.
After the great Greeks, nearly all eminent philosophers, through the ages,
have taken part in the disputation about the existence and nature of the
Non-Being.
This issue is still debatable and open on the philosophical scene.