Kenny Anthony. An Illustrated Brief History of Western Philosophy

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logic and the foundations of mathematics

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admit, was due in large part to the ideas of one of his former pupils, Ludwig

Wittgenstein. It was he who was to present, in his Tractatus Logico-Philosophicus,

the most authoritative formulation of the system. It was he too who later, having

repudiated logical atomism, gradually developed the most rewarding philosophy

of the twentieth century.

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XXII

THE PHILOSOPHY OF

WITTGENSTEIN

Tractatus Logico-Philosophicus

Ludwig Wittgenstein was the grandson of a Jewish land-agent and the son of a

steel millionaire who had nine children by a Catholic wife, and baptized all of

them into the Catholic faith. Born in Vienna in 1889, he attended the Realschule

in Linz, where he was a contemporary of Adolf Hitler. At school he lost his faith,

and soon after came under the inﬂuence of Schopenhauer’s idealism. After studying

engineering in Berlin and Manchester he went to Cambridge, where his philo-

sophical gifts were recognized by Russell, who devoted himself with great gener-

osity to fostering his genius. After ﬁve terms at Cambridge he lived in isolation in

Norway, and when war broke out in 1914 he enlisted as a volunteer in the

Austrian artillery, and served with conspicuous courage on the Eastern and Italian

fronts. During this period he wrote his masterpiece, Tractatus Logico-Philosophicus,

which in 1918, as a prisoner of war at Monte Cassino, he sent in manuscript to

Russell. The book was published in German in 1921 and shortly afterwards in

German and English with an introduction by Russell.

The Tractatus is brief, beautiful, and very difﬁcult. It consists of a series of

numbered paragraphs, often containing no more than a single sentence. The two

most famous paragraphs are the ﬁrst ‘The world is all that is the case’ and the last

‘Whereof one cannot speak, thereof one must be silent’. The book’s main concern

is the nature of language and its relation to the world. Its central doctrine is the

picture theory of meaning. According to this theory, language consists of pro-

positions which picture the world. Propositions are the perceptible expressions

of thoughts, and thoughts are logical pictures of facts; the world is the totality

of facts.

Thoughts and propositions, according to the Tractatus, are pictures in a literal,

not just a metaphorical sense. An English sentence such as ‘the rain will spread

across Scotland’ or ‘blood is thicker than water’ does not look like a picture. But

that, according to Wittgenstein, is because language disguises thought beyond all

recognition.

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Figure 45 Wittgenstein’s identity card as an artilleryman in the Austrian

army in 1918.

However, even in ordinary language there is a perceptibly pictorial element.

Take the sentence ‘Bristol is west of London’. This sentence says something quite

different from another sentence made up of the same words, namely, ‘London is

west of Bristol’. What makes the ﬁrst sentence, but not the second, mean that

Bristol is west of London? It is the fact that the word ‘Bristol’ occurs to the left

of the word ‘London’ in the context of the ﬁrst sentence but not the second.

So in that sentence, as in a map, we have a spatial relationship between words

symbolizing a spatial relationship between cities. Such spatial representation of

spatial relationships is pictorial in a quite straightforward way.

Few cases, however, are as simple as this. If the sentence were spoken instead

of written, it would be a temporal relationship between sounds rather than a

spatial relationship on the page which would represent the relationship between

the cities. But this in turn is possible only because the spoken sequence and the

spatial array have a certain abstract structure in common. According to the

Tractatus, there must be something which any picture must have in common

with what it depicts. This shared minimum Wittgenstein calls its logical form.

Most propositions, unlike the untypical example above, do not have spatial form

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in common with the situation they depict; but any proposition must have logical

form in common with what it depicts.

In ordinary language the logical form of thoughts is concealed. One reason

for this is that many of our words, like ‘Bristol’ and ‘London’, signify complex

objects. The relationship between propositions and facts will only become clear if

complex objects are logically analysed into simple ones. In order to carry out this

analysis, Wittgenstein made use of an extension of Russell’s theory of descrip-

tions. For instance, ‘Austria-Hungary’ can be regarded as a deﬁnite description of

the complex object formed by the union of Austria and Hungary, and the sen-

tence ‘Austria-Hungary is ﬁghting Russia’ can be analysed, in accordance with the

theory of descriptions, as follows.

For some x and some y, x = Austria

and y = Hungary

and x is united to y

and x is ﬁghting Russia

and y is ﬁghting Russia.

In the sentence thus analysed, no mention is made of Austria-Hungary, and so

we have got rid of one complex object. However, this is obviously only a ﬁrst

step; Austria and Hungary are each of them, in their turn, highly complex objects,

consisting of many different kinds of object in spatial and other relationships.

If we proceed with the analysis of a proposition, Wittgenstein believed, we

will in the end come to symbols which denote entirely non-complex objects. So

a fully analysed proposition will consist of an enormously long combination of

atomic propositions, each of which will contain names of simple objects, names

related to each other in ways which will picture, truly or falsely, the relations

between the objects they represent. Such full analysis of a proposition is no doubt

humanly impossible; but the thought expressed by the proposition already has the

complexity of the fully analysed proposition. The thought is related to its expres-

sion in ordinary language by extremely complicated rules which we operate un-

consciously from moment to moment.

The connection between language and the world is made by the correlation

between the ultimate elements of these concealed thoughts and the simple objects

or atoms which constitute the substance of the world. How these correlations are

made Wittgenstein does not explain; it is a deeply mysterious process which, it

seems, each one of us must make for himself, creating as it were a private language.

Much of the Tractatus is devoted to showing how, with the aid of various

logical techniques, propositions of different kinds can be analysed into combina-

tions of atomic pictures. The truth-value of propositions of science would depend

upon the truth-value of the atomic propositions from which they were built up.

The propositions of logic were tautologies, that is to say, complex propositions

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which are true no matter what truth values their atomic propositions take; an

obvious example is the proposition ‘p or not p’, which is true whether p is true or

false. Would-be propositions which are incapable of analysis into atomic proposi-

tions reveal themselves as pseudo-propositions which yield no pictures of the

world. Among these, it turns out, are the propositions of philosophy, including

the propositions of the Tractatus itself. At the end of the book he compared it to

a ladder which must be climbed and then kicked away if one is to see the world

aright.

Metaphysicians attempt to describe the logical form of the world; but this is

impossible. A picture must be independent of what it pictures; it must be capable

of being a false picture. But since any proposition must contain the logical form

of the world, it cannot picture it. What the metaphysician attempts to say cannot

be said, but can only be shown. Philosophy is not a theory, but an activity: the

activity of clarifying non-philosophical propositions. Once clariﬁed, the propositions

will mirror the logical form of the world, and will show what the philosopher

wishes to, but cannot, say.

Neither science nor philosophy can show us the meaning of life.

6.52 We feel that even when all possible scientiﬁc questions have been answered,

the problems of life remain completely untouched. Of course, there are then no

questions left, and this itself is the answer.

Even if one could believe in immortality, it would not confer meaning on life;

nothing is solved by surviving for ever. An eternal life would be as much a riddle

as this one. ‘God does not reveal himself in the world,’ Wittgenstein wrote; ‘it is

not how things are in the world that is mystical, but that it exists’. Philosophy

could in one sense do very little for us; but what it could do, Wittgenstein

believed, had been done once for all by the Tractatus. The book contained all

that was essential for the solutions of the problems of philosophy; and so, having

written it, Wittgenstein gave up the subject.

Logical Positivism

The Tractatus quickly became famous. Oddly enough, though it was itself highly

metaphysical, as well as austerely logical, its most enthusiastic admirers were the

anti-metaphysical positivists of the Vienna Circle. This group, which grew up round

Moritz Schlick after his appointment as Professor of the Philosophy of Science in

Vienna in 1922, consisted of philosophers, mathematicians, and scientists; among

its members were Friedrich Waismann, Rudolf Carnap, and Otto Neurath. In

1929, after a congress in Prague, the circle issued a manifesto, the Wissenschaftliche

Weltauffassung der Wiener Kreis, which proclaimed the launch of a campaign

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against metaphysics as an outdated precursor of science. The ideas of the circle were

publicized in the journal Erkenntnis, founded in 1930 and edited by Carnap in

conjunction with Hans Reichenbach of Berlin. The circle was broken up in 1939

as a result of political pressure, after Schlick had been killed by an insane student.

What the Positivists claimed to take from the Tractatus was the idea that neces-

sary truths are necessary only because they are tautologies. In the past, logical and

mathematical propositions had presented serious difﬁculties for empiricism. Few

empiricists were willing to follow Mill in denying that such propositions were

necessary. It was much more attractive to accept that they were necessary but that

they told us nothing about the world. Empiricists could now reafﬁrm their claim

that knowledge about the world is acquired only by experience, and devote

themselves with a clear conscience to the attack on metaphysics.

The great weapon in this attack was the Veriﬁcation Principle. This, in its ori-

ginal form, ruled that the meaning of a proposition was the mode of its veriﬁca-

tion. Such a view of meaning enabled one to rule out of court as meaningless all

statements which could neither be veriﬁed nor falsiﬁed by experience. Faced with

a dispute about the nature of the Absolute, or the purpose of the Universe, or

Kantian things-in-themselves, the Positivist could expose the emptiness of the

quarrel by saying to the warring metaphysicians: ‘What possible experience could

settle the issue between you?’

Almost as soon as the Veriﬁcation Principle was stated disputes broke out

about its status and its formulation. The principle did not seem to be itself a

tautology, a mere matter of deﬁnition. Was it, then, veriﬁable by experience? If

not, it seemed to stand self-condemned as meaningless. Moreover, not only meta-

physical propositions, but scientiﬁc generalizations, were incapable of conclusive

veriﬁcation. Should we say then that the criterion of signiﬁcance was not veri-

ﬁability but falsiﬁability? Thus general propositions would be signiﬁcant because

they were conclusively falsiﬁable. But how, on this view, were assertions of existence

signiﬁcant? Short of an exhaustive tour of the universe, no experience could con-

clusively falsify them. So the principle was reformulated in a ‘weak’ form which

laid down that a proposition was signiﬁcant if there were some observations

which would be relevant to its truth or falsity. And it was allowed that there were

many signiﬁcant propositions which, while ‘veriﬁable in principle’, could not be

veriﬁed in practice. Even thus qualiﬁed, it was not easy to apply the Veriﬁcation

Principle to matters of history; and any further modiﬁcations of the principle ran

the risk of making it so wide as to admit metaphysical statements.

The Positivists accepted the Tractatus view that the true task of philosophy

was to clarify non-philosophical statements. In clarifying the language of science,

the philosopher must show how all empirical statements were built up truth-

functionally from elementary or ‘protocol’ statements, which were direct records

of experience. In knowing which experiences would make one accept or reject any

particular protocol one would, in virtue of the Veriﬁcation Principle, understand

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what it meant. The words occurring in non-protocol statements derived their

meaning from the possibility of the translation of such statements into protocol

statements; and the words occurring in protocol statements derived their mean-

ing from the possibility of an ostensive deﬁnition – of a gesture which would point

(literally or metaphorically) to the feature of experience to which the word referred.

A difﬁculty here presents itself. What protocol statements record seems to be

something which is private to each individual. If meaning depends on veriﬁabil-

ity, and veriﬁcation is by mental states which I alone experience, how can I ever

understand anyone else’s meaning? Schlick tried to answer this by making a

distinction between form and content. The content of my experience – what

I enjoy or live through when I look at something green – is private and incom-

municable. But the form, the structural relationship, between my private experience

and other people’s private experience is something public and communicable. I

cannot know whether, when I see a tree or a sunset, other people enjoy the same

experiences as I do; for all I know, when they look at a tree they see the colour

which I see when I look at a sunset. But as long as we both agree to call a tree

green and a sunset red – as long, that is, as the form or structure of our experience

patterns is similar – we are able to communicate with each other and construct

the language of science. Few people found this answer wholly satisfactory, and

the threat of solipsism was not adequately dealt with until Wittgenstein returned

to philosophy.

Philosophical Investigations

After the war, having inherited a share of his father’s fortune, Wittgenstein found

himself one of the wealthiest men in Europe. Within a month of returning he

gave away all his money. For some years he supported himself as a gardener or as

a schoolmaster in rural schools. When his career as a schoolmaster came to an

unhappy end after allegations of cruelty to his pupils, he returned to the study of

philosophy and for a while he took part in the discussions of the Vienna Circle.

Later, he distanced himself from the Circle and returned to Cambridge, where

he submitted the Tractatus as a Ph.D. dissertation and was awarded a fellowship

at Trinity, where, in the 1930s, he became the most inﬂuential teacher of phi-

losophy in Britain. The philosophy which he taught in this period differed from

that published in the Tractatus; it was not presented in print during his lifetime.

During the Second World War Wittgenstein served as a medical orderly; he

returned to Cambridge only brieﬂy as Professor of Philosophy. From 1947 until

his death in 1951 he lived privately, alone in Ireland, or with friends in Oxford,

Cambridge, and Ithaca, New York. The book which he had long worked on was

published posthumously as Philosophical Investigations in 1953.

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After his return to philosophy in the early thirties, Wittgenstein quickly aban-

doned a number of the characteristic doctrines of the Tractatus; he ceased to

believe in logical atoms, or to look for a logically articulated language cloaked in

ordinary language. One of the crucial elements of logical atomism was the thesis

that every atomic proposition was independent of every other one. This was

clearly not true of the protocol statements which were the positivists’ candidates

for atomic propositions: the truth-value of ‘this is a red patch’ is not independent

of the truth-value of ‘this is a blue patch’. At one time Wittgenstein had thought

that this showed that these propositions were not elementary, but needed further

analysis. Now, instead, he gave up the idea that elementary propositions were

independent of each other, and this led to a questioning of the distinction be-

tween elementary and non-elementary propositions. The rest of the system of

logical atomism soon began to unravel. Wittgenstein gave up the idea that the

ultimate elements of language were names designating simple objects, and came

to believe that the words ‘simple’ and ‘complex’ have no absolute meaning, but

vary in meaning according to context.

Wittgenstein retained, however, and never abandoned, the Tractatus view that

philosophy is an activity, not a theory. Philosophy does not discover any new

truths. Philosophical problems are solved not by giving new information, but by

arranging what we have always known in a way which prevents us overlooking

what is in itself most obvious. Philosophy allows us to have a clear view of what

we are doing when we are using language non-philosophically in our ordinary

life. In a striking phrase, Wittgenstein said that the function of philosophy was

to untie the knots in our thinking. If this is right, the philosopher will have to

make very complicated movements; but the results of philosophy will not be an

elaborate structure, but something as plain as a piece of string.

Taking his cue from Freud, Wittgenstein sometimes depicts philosophy as a

therapy, a therapy to cure the bruises we get by banging our understanding

against the limits of language. The philosopher, like a psychoanalyst, encourages

us to express doubts and puzzlement which we have been taught to repress; he

cures us of the confusions we nurture in our minds by encouraging us to bring

them out to the light of day, turning latent nonsense into patent nonsense.

Philosophy, Wittgenstein sometimes said, is nothing more than the dissolution

of philosophical problems. But if that is what philosophy is, why do philosophy at

all? If you never get as far as the problems, you will never need the solutions!

Wittgenstein’s answer is that while it is true that philosophy is only useful against

philosophers, there is, whether we know it or not, a philosopher within each of

us. In the very language we use there is a philosophy which bewitches us. This

philosophy is not a set of theories or propositions: it is embodied in the mislead-

ing nature of the grammar of natural languages, which disguises the actual way in

which words are used.

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Philosophical misunderstanding will not harm us if we restrict ourselves to

everyday tasks, using words within the contexts which are their primitive homes.

But if we start upon abstract studies – of mathematics, say, or of psychology, or

of theology – then our thinking will be hampered and distorted unless we can

free ourselves of philosophical confusion. Intellectual inquiry will be corrupted by

mythical notions of the nature of numbers or of the mind or of the soul.

Both early and late, Wittgenstein believed that the surface grammar of lan-

guage concealed its true nature. But whereas in the Tractatus what was concealed

was the complex nature of a thought buried deep in our minds, in the later phi-

losophy what was concealed, and had to be set out in plain view, was the diversity

of ways in which language functioned as a social, interpersonal, activity. Wittgenstein

thought that in his earlier work he had, like other philosophers, grossly over-

simpliﬁed the relation of language to the world. The connection between the

two was to consist of two features only: the linking of names to objects, and the

match or mismatch of propositions to facts. This, he now came to believe, was a

great mistake. Words look like each other, in the same way as a clutch looks very

like a foot-brake; but words differ from each other in function as much as the

mechanisms which are operated by the two pedals. Wittgenstein now emphasized

that language was interwoven with the world in many very different ways: and to

refer to these tie-ups he coined the expression ‘language-game’. ‘We remain un-

conscious of the prodigious diversity of all the everyday language-games because

the clothing of our language makes everything alike.’

Wittgenstein gives as examples of language-games obeying and giving orders,

describing the appearance of objects, expressing sensations, giving measurements,

constructing an object from a description, reporting an event, speculating about

an event, making up stories, acting plays, guessing riddles, telling jokes, asking,

cursing, greeting, and praying. He also speaks of language-games with particular

words. Wittgenstein was not putting forward a general theory of language-games:

the use of the expression is simply meant to stress that words cannot be under-

stood outside the context in which they are used. We need, in giving an account

of the meaning of a word, to look for the part it plays in our life. The use of

‘game’ is not intended to suggest that language is something trivial; the word was

chosen because games exhibit the same kind of variety as linguistic activities do.

Some games are competitive, others not so; some have rules, others are spontan-

eous; some are played with balls, others on boards; some demand skill, others do

not. There is no common feature which marks all games as games: rather, different

games share different features with each other as different members of the same

family will resemble each other not in one single way but in a variety of ways.

Similarly, there is no one feature which is essential to language; there are only

family-likenesses between the countless language-games.

Philosophy does, in a sense, show us the essence of language, but not by

revealing the existence of some ghostly mechanism lurking within us, but by

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bringing into clear view what we already confusedly know, namely, the way in

which we use words. Philosophy can give us a clear view of this, and thus of the

world which we grasp by means of the concepts of our language.

Like the positivists, Wittgenstein is hostile to metaphysics. But he attacks meta-

physics not by the blunt instrument of some positivistic veriﬁcation principle, but

by the careful drawing of distinctions which enable him to disentangle the mix-

ture of truism and nonsense in the metaphysician’s concept of mind. Moreover,

the kind of metaphysics which he criticizes is one of which many positivists were

themselves guilty. For Wittgenstein, metaphysics consists above all of grammar

masquerading as science.

Philosophers are constantly tempted to mimic the claims and methods of sci-

ence. The eighteenth-century philosophers who sought to construct a Newtonian

physics of the mind are conspicuous illustrations of this temptation. Wittgenstein

repeatedly attacks metaphysical representations of the mind as a mysterious medium,

different from a physical medium, in which special laws operate which it is the

philosopher’s task to discover and enuntiate. ‘When philosophers use a word –

“knowledge” “being” “object” “I” “proposition” “name” – and try to grasp the

essence of the thing, one must always ask oneself: is the word ever actually used in

this way in the language which is its original home? – What we do is to bring

words back from their metaphysical to their everyday use.’

An example of Wittgenstein’s criticism of the bad metaphysical conception of

the mental is his attack on the notion that meaning is a mental process. Wittgenstein

was no behaviourist; he did not deny that there were things which could be called

‘mental processes’ – a psychological process, for instance, such as the recitation of

a poem in one’s head. Where philosophers have gone wrong is in believing that

meaning a sentence, and understanding a sentence, was a mental process under-

lying the utterance, or accompanying the hearing, of the sentence. Reﬂection

shows that this cannot be right.

If meaning was a mental process accompanying the utterance of a sentence, it

should be possible for the process of meaning to take place without the sentence

being uttered at all. Can one, in fact, perform the act of meaning without uttering

the sentence? If you try to do so, you are likely to ﬁnd yourself reciting the sentence

itself under your breath. But of course it would be absurd to suggest that simultane-

ously with every public utterance of a sentence there is a private one too: it would

surely take great skill to ensure that the two processes were exactly synchronized

with each other! And how terrible if the two came slightly out of synchrony, so

that the meaning of one word got mistakenly attached to the next one!

Moreover, the question whether somebody understands a sentence, and whether

she really means it, can be raised about sentences uttered in the privacy of the

imagination no less than about sentences uttered before a public audience. In-

furiated by a curmudgeonly relation, I may mutter to myself ‘I wish he would

drop dead!’ Luckily, I don’t mean it. I hum in my mind a Russian folk-song,

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