Kenny Anthony. An Illustrated Brief History of Western Philosophy
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He continued in practice in Vienna until the 1930s, and published a series of
highly readable books constantly modifying and refining his psychoanalytic the-
ories. Fear of Nazi persecution forced him to migrate to England in 1938, and he
died there at the beginning of the Second World War.
In his Introductory Lectures on Psychoanalysis Freud sums up psychoanalytic
theory in two fundamental premises: the first is that the greater part of our
mental life, whether of feeling, thought or volition, is unconscious; the second is
that sexual impulses, broadly defined, are supremely important not only as poten-
tial causes of mental illness but as the motor of artistic and cultural creation. If
the sexual element in the work of art and culture remains largely unconscious,
this is because socialization demands the sacrifice of basic instincts, which become
sublimated, that is to say, diverted from their original goals and channelled
towards socially desirable activities. But sublimation is an unstable state, and
untamed and unsatisfied sexual instincts may take their revenge through mental
illness and disorder.
The existence of the unconscious is revealed, Freud believes, in three ways:
through everyday trivial mistakes, through reports of dreams, and through the
symptoms of neurosis.
What Freud called ‘parapraxes’, but are nowadays known as Freudian slips, are
common episodes such as failure to recall names, slips of the tongue, and mislay-
ing of objects. Freud gives many examples. A professor at Vienna, in his inaugural
lecture, instead of saying, according to his script, ‘I have no intention of under-
rating the achievements of my illustrious predecessor’ said ‘I have every intention
of underrating the achievements of my illustrious predecessor.’ Some years after
the sinking of the liner Lusitania, a husband, asking his estranged wife to rejoin
him across the Atlantic, wrote ‘Come across on the Lusitania’, when he meant to
write ‘Come across on the Mauretania’. In each case Freud regards the slip as a
better guide to the man’s state of mind than the words consciously chosen.
Freud’s explanations of parapraxes are most convincing where – as in the cases
above – they reveal a state of mind of which the person was aware but merely
did not wish to express. This reveals no very deep level of unconscious inten-
tion. Matters are different when we come to the second method of tapping into
the unconscious: the analysis of dream reports. ‘The interpretation of dreams’,
Freud says, ‘is the royal road to a knowledge of the unconscious activities of the
mind.’ Dreams, he maintained, were almost always the fulfilment, in fantasy, of
a repressed wish. He admitted that comparatively few dreams are obvious repre-
sentations of the satisfaction of a wish, and many dreams, such as nightmares or
anxiety dreams, seem to be just the opposite. Freud dealt with this by insisting
that dreams were symbolic in nature, encoded by the dreamer in order to make
them appear innocuous. He distinguished between the manifest content of the
dream, which is what the dreamer reports, and the latent content of the dream,
which was the true meaning once the symbols had been decoded.
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How is the decoding to be done? It is not difficult to give every dream a sexual
significance if one takes every pointed object like an umbrella to represent a penis,
and every capacious object like a handbag to represent the female genitals. But
Freud did not believe that it was possible to set up a dictionary which would
relate each symbol to what it symbolized. It was necessary to discover the signific-
ance of a symbolic dream item for the individual dreamer, and that could only be
done by exploring the associations which he attached to it in his own mind. Only
when that had been done could the dream be interpreted in a way which would
reveal the nature of the unconscious wish whose fulfilment the dream fantasized.
The third (though chronologically the first) method by which Freud purported
to explore the unconscious was by examining the symptoms of neurotic patients.
An Austrian undergraduate patient became obsessed with the (erroneous) thought
that he was too fat (ich bin zu dick). He became anorexic, and wore himself out
with mountain hiking. The explanation of the obsessional behaviour only became
clear when the patient mentioned that at the time his fiancée’s attention had been
distracted from him by the company of her English cousin Dick. The unconscious
purpose in slimming, Freud decided, had been to get rid of this Dick.
The unconscious motivations which surface in the psychopathology of everyday
life are commonly easily recognized and acknowledged by the person in question.
It is different with the significance of dreams and obsessional behaviour. This can
only be detected, Freud believed, by long sessions in which the analyst invites the
patient freely to associate ideas with the symbolic item or activity in question. The
analyst’s decoding of the symbolism is often initially rejected by the patient. For
a cure to be effective, the patient has to acknowledge the desire which, according
to the analyst, the decoded symbol reveals.
There is a certain circularity in Freud’s procedure for discovering the uncon-
scious. The existence of the unconscious is held to be proved by the evidence
of dreams and neurotic symptoms. But dreams and neurotic symptoms do not,
either on their face or as interpreted by the unaided patient, reveal the beliefs,
desires, and sentiments of which the unconscious is supposed to consist. The
criterion of success in decipherment is that the decoded message should accord
with the analyst’s notion of what the unconscious is like. But that notion was
supposed to derive from, and not to precede, the exploration of dreams and
symptoms.
The pattern to which the unconscious was to conform was laid out by Freud
in his theory of sexual development. Infantile sexuality begins with an oral stage,
in which physical pleasure is focused on the mouth. This is followed by an anal
stage, between one and three, and a ‘phallic’ stage, in which the child focuses on
its own penis or clitoris. Only at puberty does an individual’s sexuality perman-
ently focus on other persons. Freud, from an early stage in his career, regarded
neurotic symptoms as the result of the repression of sexual impulses during child-
hood, and saw neurotic characters as fixated at an early stage of their development.
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Figure 42 Freud’s own sketch of the Ego and the Id.
(Standard Edition, vol. XXII; by permission of Sigmund Freud Copyrights/
Paterson Marsh Ltd, London)
Freud attached great importance to the onset of the phallic stage. At that time,
he believed, a boy was sexually attracted to his mother, and began to resent his
father’s possession of her. But his hostility to his father leads to fear that his father
will retaliate by castrating him. So the boy abandons his sexual designs on his
mother, and gradually identifies with his father. This was the Oedipus complex, a
central stage in the emotional development in every boy, and also, in a modified
and never fully worked out version, of every girl. The recovery of Oedipal wishes,
and the history of their repression, became an important part of every analysis.
Towards the end of his life, Freud replaced the earlier dichotomy of conscious
and unconscious with a threefold scheme of the mind. ‘The mental apparatus,’ he
wrote, ‘is composed of an id which is the repository of the instinctual impulses, of
an ego which is the most superficial portion of the id and one which has been
modified by the influence of the external world, and of a superego which develops
out of the id, dominates the ego, and represents the inhibitions of instinct that
are characteristic of man.’
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Freud claimed that the modification of his earlier theory had been forced on
him by the observation of his patients on the couch. Yet the mind, in this later
theory, closely resembles the tripartite soul of Plato’s Republic. The id corres-
ponds to the appetite, the source of the desires for food and sex. Freud’s id is
ruled by the pleasure principle and knows no moral code; similarly, Plato tells us
that if appetite is in control, pleasure and pain reign in one’s soul instead of law.
Both the id and the appetite contain contrary impulses perpetually at war. Some
of the desires of the appetite, and all those of the id, are unconscious and surface
only in dreams. Plato goes so far as to tell us that some of appetite’s dreams are
Oedipal: ‘In phantasy it will not shrink from intercourse with a mother or anyone
else, man, god, or brute, or from forbidden food or any deed of blood.’
Freud’s ego has much in common with Plato’s reasoning power. Reason is
the part of the soul most in touch with what is real, just as the ego is devoted to
the reality principle. Like reason, the ego has the task of controlling instinctual
desires, providing for their harmless release. Using one of Plato’s metaphors,
Freud compares the ego to a rider and the id to a horse. ‘The horse supplies the
locomotive energy, while the rider has the privilege of deciding on the goal and
guiding the powerful animal’s movement.’ Both Plato and Freud use hydraulic
metaphors to describe the mechanism of control, seeing id and appetite as a flow
of energy which can find normal discharge or be channelled into alternative
outlets. But Freud departs from Plato in regarding the damming up of such
energy as something which is likely to lead to disastrous results.
There remain Freud’s superego and the part of the Platonic soul called ‘tem-
per’. These are alike in being non-rational, punitive forces in the service of
morality, the source of shame and self-directed anger. For Freud, the superego is
an agency which observes, judges, and punishes the behaviour of the ego, partly
identical with the conscience, and concerned for the maintenance of ideals. It
upbraids and abuses the ego, just as Plato’s temper does. Superego and temper
are alike the source of ambition. However, the superego’s aggression is directed
exclusively at the ego, whereas the temper in a Platonic soul is directed at others
no less than oneself.
Both Freud and Plato regard mental health as harmony between the parts of
the soul, and mental illness as unresolved conflict between them. But only Freud
has a worked out theory of the relation between psychic conflict and mental
disorder. The ego’s whole endeavour, Freud says, is ‘a reconciliation between its
various dependent relationships’. In the absence of such reconciliation, particular
disorders develop: the psychoses are the result of conflicts between the ego and
the world, depressive neuroses are the result of conflicts between the id and the
superego, and other neuroses are the result of conflicts between the ego and
the id.
While Freud’s general tripartite anatomy of the soul bears a close resemblance
to Plato’s, his particular treatment of the superego reminds the historian rather
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more of Newman’s description of the conscience. Freud believed that the supergo
had its origin in the injunctions and prohibitions of the child’s parents, of which
it was the internalized residue.
The long period of childhood, during which the growing human being lives in
dependence on his parents, leaves behind it as a precipitate the formation in his ego
of a special agency in which this parental influence is prolonged. It has received the
name of superego.
Newman’s portrayal of conscience as echoing the reproaches of a mother and the
approval of a father seems more like a description of the formation of the super-
ego than a proof of the existence of a supernatural judge.
Freud would be indignant at figuring in a history of philosophy, since he
regarded himself above all as a scientist, dedicated to discovering the rigid deter-
minisms which underlay human illusions of freedom. In fact, most of his detailed
theories, when they have been made precise enough to admit of experimental test-
ing, have been proved to lack foundation. Among medical professionals, opinions
differ whether the techniques which took their rise from his practice of psycho-
analysis are, in any strict sense, effective forms of therapy. When they achieve
success, it is not by uncovering unalterable deterministic mechanisms, but by
expanding the freedom of choice of the individual. Despite the non-scientific
nature of his work, Freud’s influence on modern society has been pervasive: in
relation to sexual mores, to mental illness, to art and literature, and to interpersonal
relationships of many kinds.
The permissive attitude to sex of many societies in the late twentieth century
is undoubtedly due not only to the increased availability of efficient contracep-
tion, but also to the ideas of Freud. He was not the first thinker to assign the
sexual impulse a place of fundamental importance in the human psyche: so did
all those theologians who regarded the sin of Adam, which shaped our actual
human condition, as being sexual in origin, transmission, and effect. If, as
some people believe, nineteenth-century prudery succeeded in concealing the
importance of sex, the veil of concealment was even then easily torn away. As
Schopenhauer wrote, in a passage Freud loved to quote, it is the joke of life
that sex, the chief concern of man, should be pursued in secret. ‘In fact’, he said,
‘we see it every moment seat itself, as the true hereditary lord of the world, out
of the fullness of its own strength, upon the ancestral throne, and looking down
from there with scornful glances, laugh at the preparations which have been made
to bind it.’
Freud’s emphasis on infantile sexuality was one of the elements of his teaching
which contemporaries found most shocking. But the sentimental attitude to early
childhood which he attacked was one of comparatively recent origin. It was not,
for instance, shared by Augustine, who wrote in his Confessions:
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What is innocent is not the infant’s mind, but the feebleness of his limbs. I have
myself watched and studied a jealous baby. He could not yet speak and, pale with
jealousy and bitterness, glared at his brother sharing his mother’s milk. Who is
unaware of this fact of experience?
What links Freud’s work with modern sexual permissiveness is not medical
research, but the persuasive character of his literary style. He did not assemble a
statistical demonstration of a connection between sexual abstinence and mental
illness; nor, in his published writings, did he recommend sexual licence. What he
did do was to give widespread currency to the metaphors which he shared with
Plato: the vision of sexual desire as a psychic fluid which seeks an outlet through
one channel or another. Seen in the light of that metaphor, sexual abstinence
appears as a dangerous damming up of forces which will eventually break through
restraining barriers with devasting effect on mental health.
The very concept of mental health, in its modern form, dates from the time
when Freud and his colleagues began to treat hysterical patients as genuine
invalids instead of malingerers. This, it has often been said, was as much a moral
decision as a medical discovery. But it was surely the right moral decision; and
hysteria was close enough to the paradigm of physical illness for the concept of
mental illness to have clear sense when applied to it. In ordinary illness the causes,
symptoms, and remedies of disease are all physical. In mental illness, whether or
not physical causes and remedies have been identified, the symptoms concern the
cognitive and affective life of the patient: disorders of perception, belief, and
emotion. In the diagnosis of whether perception is normal, of whether belief is
rational, of whether emotion is out of proportion, there is a gentle slope which
leads from clinical description to moral evaluation. This is strikingly seen in the
case of homosexual attraction, which was for long regarded as a psychopathologi-
cal disorder but has come to be regarded by many as a basis for the rational
choice of an alternative life-style. Forms of behaviour which before Freud would
have been regarded as transgressions worthy of punishment are now often judged,
in the courthouse no less than in the consulting room, as symptoms of maladies
fit for therapy. It is often said that Freud was not so much a medical man as a
moralist; that is true, but it is truer to say that he redrew the boundaries between
morals and medicine.
Perhaps Freud’s greatest influence has been on art and literature. This has a
certain irony, in the light of his unflattering view of artistic creation as something
very similar to neurosis: a sublimation of unsatisfied libido, translating into phantasy
form the unresolved conflicts of infantile sexuality. Since Freud’s theories became
well known, critics have delighted to interpret works of art in Oedipal terms, and
historians have turned with gusto to the writing of psychobiography, analysing
the actions of mature public figures on the basis of real or imagined features of
their childhood. Novelists have made use of associative techniques similar to
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those of the analyst’s couch, and painters and sculptors have taken Freudian
symbols out of a dream world and given them concrete form. All of us, directly or
indirectly, have imbibed so much of Freud’s philosophy of mind that in discus-
sion of our relations with our family and friends we make unselfconscious use of
Freudian concepts. No other philosopher since Aristotle has made such a contri-
bution to the everyday vocabulary of morality.
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logic and the foundations of mathematics
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XXI
LOGIC AND THE
FOUNDATIONS OF
MATHEMATICS
Frege’s Logic
The most important event in the history of philosophy in the nineteenth century
was the invention of mathematical logic. This was not only a refoundation of the
science of logic itself, but had important consequences for the philosophy of
mathematics, the philosophy of language, and ultimately for philosophers’ under-
standing of the nature of philosophy itself.
The principal founder of mathematical logic was Gottlob Frege. Born on the
Baltic coast of Germany in 1848, Frege (1848–1925) took his doctorate in
philosophy at Göttingen, and taught at the University of Jena from 1874 until
his retirement in 1918. Apart from his intellectual activity his life was uneventful
and secluded; his work was little read in his lifetime, and even after his death
his influence was exercised originally through the writings of other philosophers.
But gradually he came to be recognized as the greatest of all philosophers of
mathematics, and as a philosopher of logic fit to be compared to Aristotle. His
invention of mathematical logic was one of the major contributions to the devel-
opments in many disciplines which resulted in the invention of computers. Thus
Frege affected the lives of all of us.
Frege’s productive career began in 1879 with the publication of a pamphlet
with the title Begriffschrift, or Concept Script. The concept script which gave the
book its title was a new symbolism designed to bring out with clarity logical rela-
tionships which were concealed in ordinary language. Frege’s own script, which
was logically elegant but typographically cumbersome, is no longer used in symbolic
logic; but the calculus which it formulated has ever since formed the basis of
modern logic.
Instead of the Aristotelian syllogistic, Frege placed at the front of logic the
propositional calculus first explored by the Stoics: that is to say, the branch of
logic that deals with those inferences which depend on the force of negation,
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conjunction, disjunction etc. when applied to sentences as wholes. Its funda-
mental principle – which again goes back to the Stoics – is to treat the truth-value
(i.e. the truth or falsehood) of sentences which contain connectives such as ‘and’,
‘if ’, ‘or’, as being determined solely by the truth-values of the component sen-
tences which are linked by the connectives – in the way in which the truth-value
of ‘John is fat and Mary is slim’ depends on the truth-values of ‘John is fat’ and
‘Mary is slim’. Composite sentences, in the logicians’ technical term, are treated
as truth-functions of the simple sentences of which they are put together. Frege’s
Begriffschrift contains the first systematic formulation of the propositional calculus;
it is presented in an axiomatic manner in which all laws of logic are derived, by
specified rules of inference, from a number of primitive principles.
Frege’s greatest contribution to logic was his invention of quantification theory:
that is to say, a method of symbolizing and rigorously displaying those inferences
that depend for their validity on expressions such as ‘all’ or ‘some’, ‘any’ or ‘every’,
‘no’ or ‘none’. This new method enabled him, among other things, to reformulate
traditional syllogistic.
There is an analogy between the inference
All men are mortal
Socrates is a man
So Socrates is mortal
and the inference
If Socrates is a man, then Socrates is mortal
Socrates is a man
So Socrates is mortal.
The second inference is a valid inference in the propositional calculus (if p then
q; but p, therefore q). But it cannot be regarded as a translation of the first, since
its first premiss seems to state something about Socrates in particular, whereas
if ‘All men are mortal’ is true, then
if x is a man, then x is mortal
will be true no matter whose name is substituted for the variable ‘x’. Indeed, it
will remain true even if we substitute the name of a non-man for x, since in that
case the antecedent will be false, and the whole sentence, in accordance with the
truth-functional rules for ‘if’-sentences, will turn out true. So we can express the
traditional proposition:
All men are mortal
in this way
For all x, if x is a man, x is mortal.
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This reformulation forms the basis of Frege’s quantification theory: to see how,
we have to explain how he conceived each of the items which go together to
make up the complex sentence.
Frege introduced into logic the terminology of algebra. An algebraic expres-
sion such as ‘x/2 + 1’ may be said to represent a function of x: the value of the
number represented by the whole expression will depend on what we substitute
for the variable ‘x’, or, in the technical term, what we take as the argument of the
function. Thus 3 will be the value of the function for the argument 4, and 4 will
be the value of the function for the argument 6. Frege applied the terminology of
argument, function, and value to expressions of ordinary language as well as to
expressions in mathematical notation. He replaced the grammatical notions of
subject and predicate with the mathematical notions of argument and function,
and he introduced truth-values as well as numbers as possible values for expres-
sions. Thus ‘x is a man’ represents a function which for the argument Socrates
takes the value true, and for the argument Venus takes the value false. The expres-
sion ‘for all x’, which introduces the sentence above, says, in Fregean terms, that
what follows (‘if x is a man, x is mortal’) is a function which is true for every
argument. Such an expression is called a quantifier.
Besides ‘for all x’, the universal quantifier, there is also the particular quantifier
‘for some x’ which says that what follows is true for at least one argument. Thus,
‘some swans are black’ can be represented in a Fregean dialect as ‘For some x, x
is a swan and x is black’. This sentence can be taken as equivalent to ‘there are
such things as black swans’; and indeed Frege made general use of the particular
quantifier in order to represent existence. Thus, ‘God exists’ or ‘there is a God’ is
represented in his system as ‘For some x, x is God’.
Using his novel notation for quantification, Frege was able to present a calculus
which formalized the theory of inference in a way more rigorous and more
general than the traditional Aristotelian syllogistic which up to the time of Kant
had been looked on as the be-all and end-all of logic. After Frege, for the first
time, formal logic could handle arguments which involved sentences with mul-
tiple quantification, sentences which are as it were quantified at both ends, such
as ‘Nobody knows everybody’ and ‘any schoolchild can master any language’.
Frege’s Logicism
In the Begriffschrift and its sequels Frege was not interested in logic for its own
sake. His motive in constructing the new concept script was to assist him in the
philosophy of mathematics. The question which above all he wanted to answer
was this: Do proofs in arithmetic rest on pure logic, being based solely upon
general laws operative in every sphere of knowledge, or do they need support
from empirical facts? The answer which he gave was that arithmetic itself could be
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