Philosophy and Philosophers - an Introduction to Western Philosophy - Chapter 8

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CHAPTER EIGHT

Analytical philosophy: Russell, Wittgenstein

Analytical philosophy refers as much to a method as to a body of

philosophical doctrine. It is extremely difficult to give a unifying

characterization of analytical philosophy that picks out what is

common to all its instances. It was regarded as revolutionary; but it is

questionable whether the new philosophy really marks such a

discontinuity from what came before.

Analysis is a process which aims to elucidate complexes by reducing

them to their simpler elements and the relations between those

elements. This can apply to complex concepts, entities, or

philosophical problems. In analytical philosophy, the analysis is

characteristically linguistic. It is done through analyzing the language

in which a complex philosophical problem, say, is expressed;

perplexing complex philosophical concepts are dealt with by resolving

the complexes into what are logically equivalent related simple

constituents, which can be better understood.

The origins of analytical philosophy lie in work done in the latter

half of the nineteenth century and the beginning of the twentieth

century on logic and the foundations of mathematics. This work

involved the construction of a new and powerfully expressive formal

logical symbolism. Much of this work was carried out independently

by the German logician Gottlob Frege (1848–1925). The culmination of

the work in England was Principia mathematica (1910–13), written

jointly by Bertrand Russell and Alfred North Whitehead (1861–1947).

The motivation for this work was the rejection of psychologism, and

indeed all forms of naturalism, as providing a foundation of

mathematical truth; the new view embraced objective logicism

concerning mathematical truths. What this amounted to was the

attempt to show that mathematics was reducible in principle to the

propositions of logic. The philosophical significance of this is that

203

mathematical truths were shown to be independent of human thought,

such as structural features of our way of thinking, and were absolutely

necessary objective truths. This meant that mathematical truths were,

contrary to Kant’s view, independent of whether they expressed even

essential features of human thought. Nor did such mathematical truths

express extremely general empirical facts as John Stuart Mill (1806–73)

suggested. Mathematical truths were shown to be necessary and

objective because they depend only on certain basic rules of logic

which hold independently of mind or the empirical world. The new

logical language is formal in that the rules governing its terms are

known exactly; it is powerful in that, unlike traditional Aristotelian

logic, it is able to express an enormously richer range of meanings.

Aristotelian logic, which dealt with the relations between classes, is

shown to be only a tiny fragment of the new logic, which could deal

with whole propositions and the internal structure of propositions.

Analytical philosophers saw in the new symbolism a way of

tackling old philosophical problems. The new logic delivered an ideal

or perfect language which was at the same time powerful enough for

the formulation of propositions and arguments previously only

expressible in ordinary everyday language. Ordinary language

developed for purposes which mean it is ill-suited for the expression

of philosophical concepts and problems. The precision, clarity and

unambiguity that were possible in the new logic promised to give a

way of reformulating philosophical problems so that their solution

would become apparent, or the original problem would simply

disappear as a pseudo-problem—this perhaps describes the essence

and promise of analytical philosophy. Even those philosophers who

did not actually reformulate the propositions of philosophy, and the

propositions of science and common sense, into formal symbolism saw

that the ordinary language in which the propositions were expressed

could be systematically misleading, and that we must logically analyze

the propositions into their underlying logically related constituent

parts to understand what they really mean, if they are meaningful at

all, so better to assess how their truth or falsity might be discovered.

This process of analysis chiefly involves revealing the underlying

structure, or logical form, of propositions in everyday language so as

not to be philosophically misled by the apparent grammatical

structure. The apparent linguistic structure can be misleading because

it can be taken as mirroring structures in the world; but there is no

reason why this is necessarily the case. The logical form expresses only

what are the essential or common features of apparently different

linguistic expressions, thus characterizing all expressions of the same

given sort. A simple example is “The flower is red” or “The book is

red”, which can be expressed as “a is F” and “b is F”; the common

logical form is “x is F”, or more concisely “Fx”.

For example, if we take the proposition “I see nobody coming down

204 Analytical philosophy

the road”, we might be tempted to think “nobody” functions

grammatically as a proper name and names someone, in the same way

that in “I see Alan coming down the road”, “Alan” functions as a

proper name and names someone. If we take the example of the

proposition “Numbers can be both odd and even”, we might think that

“numbers” functions in the proposition in just the same way as

“tables” does in “Tables can be both large and small”, and so assume

that there must exist things called “numbers” in the same way that

there exist things called “tables”. Philosophical problems might then

arise in deciding in what peculiar sense numbers exist.

Often it is the case that the surface grammatical form is not the same

as the underlying logical form. In everyday use this rarely matters; but

if we are asking philosophical questions, we can be misled not only by

ambiguities of sense but also by what the grammatical form apparently

implies; we thus misunderstand the philosophical implications or

philosophical meaning of the proposition. This misunderstanding can

be brought out by revealing the logical form of the propositions, which

is to say that all that is ambiguous and grammatically misleading is

removed. We then understand what kind of philosophical problem, if

any, we are still really confronted with.

Analytical philosophy is characterized by an awareness of the

need for self-consciousness in the use of language as the vehicle of

human thought about the world. In its less ambitious moods,

analytical philosophy has sought to clarify through pre-emptory

analysis philosophical problems, and to show that some were only

problems at all because we were misled by language, but some

philosophical problems remain genuine. In its more ambitious

moods, analytical philosophy has sought to show that all

philosophical problems are illusory pseudo-problems which originate

in our being misled by the language in which they are expressed,

resulting in misunderstanding. The former position is more

characteristic of Russell and the latter of Wittgenstein. Russell saw

the new logic as an ideal language which in philosophy could

sometimes replace the vagaries of ordinary language. Wittgenstein

saw the new logic as revealing the essential structure of ordinary

language itself; ordinary language was in logical order, but this

needed to be shown through logical analysis.

The account so far presents mostly the negative or destructive side

of analytical philosophy. For philosophers who think that logical

analysis reveals all philosophical problems as pseudo-problems, the

negative side is all there is. For others there is also a positive or

constructive side. If ordinary language is misleading in philosophy,

then it has led, among other things, to bad metaphysics. For example,

the subject-predicate structure of ordinary sentences has led to our

positing the existence of all kinds of puzzling entities apparently

denoted by the subject-terms of propositions. In this way we

Russell, Wittgenstein 205

misconstrue the true nature of reality by supposing certain things must

exist which need not. The positive side of analytical philosophy is that

if we display the true logical form of propositions through a full

analysis, rather than disposing of metaphysics, we also produce a true

metaphysics: in our new language we do reveal the true essential

nature of reality, that to which we are ontologically committed

whatever else we might suppose is real. The displaying of logical form

involves making explicit, behind the apparent structure, what is the

implicit but true structure.

Ordinary language contains, chiefly inherent in its structure,

implicit metaphysical assumptions. We can either clear these

assumptions away and conclude that there are no metaphysical

problems left, or we can clear the assumptions away to reveal a true

metaphysics: a description of the essential structural features of reality.

In Russell and Wittgenstein, in rather different forms, this metaphysics

is that of logical atomism. It can be supposed that analysis must come

to an end somewhere: if complexes depend, in a general sense, upon

related simpler elements, we must, if we are not to embark on an

infinite regress, reach ultimate elements which cannot and need not be

further analyzed.

Generally speaking, Russell’s interest in analysis is epistemological:

complexes are better understood and our knowledge of them secured

by their analysis into better understood elements with which we are

most directly acquainted. Sentences with complex meanings, if they

are to be understood, must be composed wholly of constituent atomic

meanings which are understood through their reference to atomic

entities with which we are directly acquainted. The tendency of

Wittgenstein’s thinking is metaphysical: he thinks that there simply

must be such atomic elements in order to make the understanding of

everyday language possible, but not that we need to be directly

acquainted with such elements.

We can bring to the surface what is implicit under the grammatical

structure of ordinary language: by complete analysis we can reach the

ultimate logical form or true structure. Complete logical analysis

reveals the logical form, not of any particular proposition expressed in

ordinary language, but of the essential structure, or the minimal

conditions, for any language capable of representing or describing the

world at all. Full logical analysis reveals what must be common to any

possible language capable of representing reality; in that way the

logical analysis also reveals what must be common to any possible

world; it displays the essential nature of reality. Logical analysis is

required because we cannot assume that the structure of everyday

language reveals the essential nature and ultimate constituents of

reality as a whole; for that we must look to the essence of language and

leave out what is accidental and inessential. The absolutely minimal

structure for any language capable of describing the world or reality at

206 Analytical philosophy

all must also reveal the essential structure of the world or reality itself.

It does not reveal contingent features of the world—those are to be

discovered by science—but it reveals the logically necessary minimal

features of any reality or any world by revealing the necessary

minimal features of any language capable of representing any reality

or world. Philosophy cannot reveal, for example, what are the facts,

but it might reveal that the world is ultimately constituted of

independent facts. Language has a structure; the world has a structure;

the essential structure of language which is the condition for its being

capable of mirroring reality at all must be the same as the essential

structure of reality, because without this similarity of structure

language could not mirror the world at all. What kind of minimal

entities a fully analyzed language requires to function meaningfully

are the ultimate entities of the universe. What can be represented or

described in language pared down to the logical minimum of

descriptive power, beyond which it is logically impossible to go, is

what must be part of reality; much else may be a reality, but need not

be. If language derives its meaning from its relation to the world, then

what must be the case about reality, if language descriptive of reality is

possible at all, is what is essential or common to all possible real

worlds, however else they may differ. But this conclusion can be

interpreted variously: it is unclear whether we have revealed the

structure of any possible reality or only any reality that is describable.

Russell

Bertrand Russell (1872–1970) was born into an aristocratic family; his

father was the son of the first Earl Russell. His life was eventful and

often controversial, and he is notable among philosophers, mainly

because of his public activities and his social and ethical views, in

being extremely well known even outside philosophical circles. He

was noted for the analytic sharpness of his intellect and wit. He was

a passionate advocate of reason and debunker of superstition; we

should seek out evidence for beliefs no matter how much this might

mean abandoning beliefs we may wish to be true. He came to

recognize the limits of human certainty and the limits on attaining

timeless impartial objective knowledge of the world. After his early

years Russell was an atheist, and regarded the existence of God and

personal immortality as at best mere logical possibility, and belief in

God as generally harmful as well as false. The evidence for a belief in

the existence of God was totally insufficient and must therefore be

regarded as false. As a boy he was educated privately at home. He

took an early interest in mathematics, and in 1890 he went up to

Trinity College, Cambridge, to study mathematics. He soon became

interested in philosophical matters through dissatisfaction with the

Russell 207

foundations of mathematics. He became a Fellow of Trinity College

in 1895.

In 1912 Wittgenstein came to Cambridge from the University of

Manchester to study with Russell the foundations of mathematics.

Russell was impressed by Wittgenstein, and was greatly influenced by

his early work. Russell was briefly imprisoned for his pacifist activities

during the First World War. In 1931 Russell became Lord Russell when

he succeeded to the peerage. In 1938 he moved to America, teaching at

the University of Chicago and the University of California in Los

Angeles. In 1944 he returned to be re-elected Fellow of Trinity College,

Cambridge. In 1950 he was awarded the Nobel Prize for Literature. His

last substantial philosophical work, Human knowledge: its scope and

limits, appeared in 1948; but he was disappointed by the poor attention

it received; this he put down to the rise of ordinary language

philosophy and to Wittgenstein’s later approach to philosophy, which

differed sharply from Russell’s; he regarded both as largely

misconceived. In the last part of his life Russell had an increasingly

high public profile by becoming embroiled in social and political

issues. His outspoken opinions on private and public morality caused

considerable opprobrium to be heaped on him. Russell died at the

great age of ninety-eight.

In his early thought Russell swiftly moved through two

diametrically opposed philosophical positions: Hegelian absolute or

monistic idealism and extravagant pluralistic realism. He then moved

to a third view that was supported by a belief in analysis and the

process of logical construction: parsimonious pluralistic realism—this

he held in various forms from then on.

Russell started with Hegelian monistic idealism, which holds that

the world is essentially mental and apparently independent facts are

really imposed abstractions which cannot really be characterized or

understood in isolation, but can be properly understood only in

relation to the whole of reality. Initially Russell was a convinced

advocate of Hegelianism. But the Hegelian denial of external relations

made mathematics impossible, since the terms of mathematics could

not then be characterized in isolation. The denial of external relations,

and the consequent doctrine of internal relations, amount to a

rejection of ultimately independent facts and entities in the universe;

any relation between facts is reducible to properties of each fact

concerned and ultimately the whole which they form; in this way no

fact can be fully conceptually characterized in isolation and the

characterization must eventually expand to the only independent and

therefore fully real entity: the universe as a whole. It followed from

this doctrine that no proposition concerning less than the whole

universe could ever be wholly true. Russell rejected monistic idealism,

not only because it undermined mathematics, but also because he

thought it was plain that propositions were true because they

208 Analytical philosophy

corresponded to individual facts alone by expressing the structure of

the relation of the constituent elements of the facts. Monistic idealism

also makes any philosophical analysis into intelligible simple or

atomic entities impossible, because one cannot understand the

constituent elements in isolation but only after one sees how they fit

into the whole.

The rejection of monistic idealism moved Russell to a form of

extravagant realism where all the apparent references of propositions

have being in some extralinguistic way. It involved adopting a form of

Platonic realism. This applied to mathematical truths and concepts: the

necessary truth of mathematical propositions derived from their

describing the timeless relations between immutable entities which do

not exist in physical space. But that such things as numbers existed in

some Platonic heaven eventually offended Russell’s intuitive sense of

reality.

This leads to the final position which in various forms Russell held

for the rest of his life: parsimonious pluralistic realism. It amounts to

the view that the world consists of a plurality of independent

elements, but that many apparent entities are “logical fictions” that

are really constructs of other simpler elements. Through the notion of

logical construction, entities whose existence is doubtful or

problematic can be replaced by entities whose existence is more

certainly known and better understood. The view applies a version of

Ockham’s razor: “Whenever possible, substitute constructions out of

known entities for inferences to unknown entities.” The three

important areas to which Russell applies this principle are

mathematics, physical objects, and mind. The purpose of this is in

part metaphysical and in part epistemological, and it is sometimes

difficult to disentangle the two; the former concerns what there is,

the latter our knowledge of what there is—and these matters are,

however, distinct.

As far as knowledge of entities, as opposed to knowledge of truths,

is concerned, Russell holds that we can know with greatest certainty

the nature and existence of those entities with which we are most

directly acquainted; knowledge of the nature and existence of all other

entities, where a reduction to entities with which we are directly

acquainted is not possible, will involve some kind of inference from

those entities with which we are directly acquainted. This inference

will involve various degrees of certainty, and our aim should be to see

how certain this inference is in various cases. The way of making the

belief in certain entities most secure is logically to reduce everything

we wish to say about the doubtful entities to propositions concerning

entities about which we have less or no doubt. On the one hand this

has the epistemological purpose of revealing what justification, if any,

we have for asserting the existence of entities with which we are not

directly acquainted; on the other hand it might have the metaphysical

Russell 209

purpose of suggesting that if statements about entities with which we

are not directly acquainted can be reduced without loss of meaning to

propositions about entities with which we are directly acquainted, it is

the entities with which we are directly acquainted which are the basic

elements of the universe. Thus among knowledge of things we must

distinguish between “knowledge by acquaintance”, where we have

knowledge of things by direct awareness of the things concerned,

without any intermediary inference or knowledge of truths being

involved, and “knowledge by description”, where we have no direct

awareness of the things concerned, but have knowledge only by

inference from direct awareness of intermediary things and knowledge

of truths. There is no state of mind in which we are directly aware of

the things known by description; all knowledge of such things is really

knowledge of truths concerning those things; we never know the

actual things themselves. Russell’s considered position is that what we

can justifiably claim to know about posited entities irreducible to

objects of immediate acquaintance is inferred from entities with which

we are immediately, non-inferentially, acquainted. Thus we have

knowledge by description of such physical objects as tables, which it is

possible to doubt exist, through our direct acquaintance with senseperceptions,

which it is not possible to doubt exist. The logical

reduction to objects of direct acquaintance does not show necessarily

that such reduced entities do not exist; it shows merely that we are not

committed to their existence; we can say everything we want to say

without mentioning them. If we honestly examine our experience, the

objects with which we are directly acquainted are not continuous

invariable physical objects but the discontinuous variable immediate

data of sense-perceptions and introspection. At one time Russell

included ourselves and universals as objects of direct acquaintance.

With universals included as objects of acquaintance it is easy to see

how propositions could be made up of elements with which we are

acquainted. The key general point is that understanding and

knowledge of propositions describing entities or states of affairs with

which we are not directly acquainted must be composed wholly of

elements with which we are directly acquainted.

The following general characterization can be given of Russell’s

mature philosophy. There are two kinds of truths: logical and

mathematical truths, and factual truths. Logical truths are necessary

and can be known to be true a priori, since the truth of such

propositions is independent of any facts about the world; such truths

are tautologies; tautologies are true because of their intrinsic logical

form and regardless of content. A proposition is a tautology if it always

comes out true regardless of the truth or falsity of its constituent parts;

because of this it can tell us nothing about the world; it is devoid of

factual content, since it remains true regardless of the truth or falsity of

any propositions stating facts about the world; such a proposition is “p

210 Analytical philosophy

or not-p”. There is no a priori way of proving the existence of anything.

The world consists of a plurality of logically independent facts. Factual

truths are contingent and can be known to be true only a posteriori,

through experience, since the truth of such propositions depends on

their corresponding to non-necessary facts about the world; such a

proposition is “p or q”. If facts are complex, then sentences are true if

they express the relation of the constituent parts of the complex facts.

All non-logical truths are true in virtue of their accurate

correspondence with some independent extralinguistic fact about the

world, and are false otherwise; and such facts can logically stand in

complete isolation from any other facts and the universe as a whole.

Some facts about the world we know directly, without inference, and

some only by inference from facts we do directly know. Our

knowledge of facts that we do not know directly, if they cannot be

logically reduced without loss of meaning to facts that we do know

directly, depends on inferences from facts that we do know directly by

principles of inference that are non-demonstrative. No deductive or

demonstrative relation exists between ultimate matters of fact, since it

is logically possible—it implies no contradiction—that an isolated fact

could be the case although the rest of the universe has been

extinguished. If deductive relations existed between matters of fact

they would be necessarily connected; but, properly analyzed, facts are

never necessarily connected. That facts can appear to be logically

dependent arises from our putting together two facts as if they were

one fact. From “A and B are men” it logically follows that B is a man;

but from the truth “A is a man” alone we cannot deduce anything

whatever about B. Russell sharply differentiates between truth and

knowledge: between a truth and verification or proof of that truth.

Primarily, beliefs, and derivatively propositions, are true in virtue of

objectively and correctly corresponding to the facts. A belief or

proposition just is true if it corresponds to the facts, regardless of

whether anyone knows or could know it to be true by its actual

verification, and regardless of any other beliefs or propositions

thought to be true. The fact in virtue of which a belief or sentence is

true is called its verifier. Russell is adamant that there are many true

beliefs that no one will ever know to be true; what is true is not limited

by our capacity for knowledge of truths and powers of verification.

Increasingly he was forced to admit the perspectival nature of our

knowledge, and our inability to attain complete certainty, impartiality,

and objectivity divorced from our point of view; nevertheless, such an

objective point of view should be our aim so we can mirror the world

with as little distortion as possible.

Russell clearly rejects both the pragmatist theory of truth, where a

proposition is held to be true in virtue of the satisfactory practical

consequences in relation to our experiences of its being accepted, and

the coherence theory of truth, where the truth of a proposition is

Russell 211

dependent on its consistency with other propositions which form a

complex system. Truth, apart from in logic and mathematics, consists

of a relation to non-linguistic facts that are in general non-human.

In the philosophy of logical atomism Russell argues for a

metaphysics in which the world consists ultimately of logically atomic

objects or particulars qualified by properties or standing in relation;

these are atomic facts; logical relations between atomic facts form

complex facts. Particulars are logically independent; there is no logical

impossibility involved in saying the universe might consist in one

particular. Thus the truth of any complex proposition concerning a

complex fact depends on whether it correctly describes the relation of

the elements of the complex fact. Complex propositions are

compounds which depend for their truth or falsity on the truth or

falsity of their constituent parts: they are truth-functional compounds

of atomic propositions. So there must be ultimately simple objects

whereby analysis comes to an end. The ideal logical language would

clearly show what was simple and what complex. The simplest objects

are those that can only be denoted by logically proper names; that is,

names that have no hidden descriptive content which would imply the

objects named have parts. The meaning of a proper name is fully given

by an acquaintance with the particular named. Either a logically

proper name names a particular or it has no meaning. The simplest of

atomic facts would be stated as “Fa”, where “a” is a logically proper

name qualified by a predicate “F”, or “aRb”, which expresses the

relation between atomic objects a and b which have the logically

proper names “a” and “b”. This gives a logical definition of what

particulars would be; whether there are any is another matter.

The only logically proper names which are guaranteed meaning,

because they cannot fail to have a reference, seem to be the

demonstratives “this” and “that”, which refer to the smallest

perceptibly distinguishable part of a sense-datum (a minimum

sensible); that is, they must refer to an absolutely simple part of the

immediate present content of our sense-experience; thus we might

have the atomic fact “This is white” if this means the minimal sensible

sense-datum of my immediate sense-experience. But a consequence of

this would be a vocabulary private to the speaker and shifting in

meaning, for “this” and “that” would mean different things for

different speakers, and different things for the same speaker at

different times, since “this” and “that” refer only to the minimal

content of experience at a moment. A molecular proposition is a truthfunctional

compound of atomic propositions, such as “Fa and Gb”.

Such qualified proper names as “a” and “b” either name an object or

are not meaningful at all. Logically proper names do not name

physical objects, since they are complex. The names of physical objects

might cease to be meaningful if the complex physical object named

ceased to exist through its disintegrating; such names can be replaced

212 Analytical philosophy

ultimately by descriptions of atomic facts that describe senseexperience.

Later Russell came to see problems with logical atomism and to

think that whether there are atomic facts and objects which are

unanalyzable was a question which did not need answering, and the

lack of an answer did not detract from the value of analyzing

complexes into constituent parts.

Russell maintained a deep respect for the findings of science;

whatever doubt we may have about the details of the discoveries of

science, he thought that the scientific view of the universe,

particularly as derived from the most basic science of physics, was

essentially true. The existence and nature of the world or reality are

almost entirely non-human, and are quite independent of mind,

modes of cognition, or capacity for knowledge. Fundamental features

of the world are not in any way dependent on concepts contributed

by mind. Most of the universe is governed by laws in which the mind

plays no part, and in which mind—in particular the human mind—

occupies only a tiny fragment of space and time. How we know is

itself only a small part of what we know; otherwise, Russell says, we

would be inclined to think that the mind in some way determined the

nature of the world. Russell accepts that there might be things we

cannot know. These views fit with Russell’s rejection of idealism,

including the philosophy of Kant, and also of some tendencies of

empiricism.

This connects with Russell’s attitude to extreme scepticism, as

practised by Descartes. Russell, although initially sympathetic to

scepticism because he saw it as a way of discovering certainty, came to

think no progress can be made from the starting point of extreme

scepticism. He is not an insincere sceptic who would reject beliefs that

no one acquainted with the current state of knowledge could seriously

doubt; we should accept the best current knowledge of the time unless

we have specific reasons for rejecting it. Scepticism can, however, be

useful as a methodological device to see how many assumptions can

be eliminated as unnecessary, so making our knowledge more secure

by eliminating the number of assumptions required to be accepted.

This attitude to scepticism amounts to an admission that extreme

scepticism cannot ultimately be refuted; but Russell also denies there

are any grounds for thinking it true. It is logically possible that the

whole universe came into existence five minutes ago with our having

false memories apparently of a time before that; everything now is as it

would be if the universe had existed before that time—there is no way

of showing such a hypothesis to be impossible. There would be no way

of proving that it did not exist earlier; indeed all the evidence would

point the other way. That scepticism cannot be ultimately refuted does

not mean that its grounds cannot be minimized; it is just that it is

logically possible that it is true. The only way of giving an absolute

Russell 213

refutation of any position, including extreme scepticism, is by showing

that it involves a logical contradiction and is hence logically

impossible; this often cannot be done. But that does not mean any

view that cannot be shown to be logically contradictory must be

equally believed to be true. Intellectual honesty demands that reasons

or evidence for and against should be the overriding consideration in

deciding what we do and do not believe. Russell reduces, in his later

work, his expectations as to how much certainty is possible. Essentially

his view is that absolute certainty of the sort that would satisfy

exaggerated scepticism exists only with respect to logical truths (and

only then because they are contentless tautologies) and with respect to

our awareness of the immediate content of our minds; elsewhere

absolute certainty is impossible and doubt logically possible.

Russell was convinced that much bad philosophy was a product of a

naive acceptance of the structure or syntax of ordinary language as

reflecting the structure of the world. The ambiguity of the vocabulary

of ordinary language produces additional but less profound

difficulties. Language could display the metaphysical structure of

reality—the logically basic, or essential, features of the world—but

only if the language in question were purified of the accidental

accretions which lead to unwarranted metaphysical commitments. The

purification of ordinary language is carried out by displaying the

logical form buried in the grammatical form of ordinary language.

Otherwise we find ourselves ontologically committed to some entities

having some kind of being which both is problematic and which leads

to paradox. The purpose of constructing such an ideal language is to

eliminate unnecessary assumptions as to the existence of certain

entities by paraphrasing expressions which denote those kinds of

entities and seem to presuppose their existence in expressions which

do not contain such a presupposition. The question of whether such

entities actually exist is not a matter that can be settled by logic alone;

but we are not committed by our language to supposing that such

entities must exist.

An application of this idea, and of logical analysis, can be seen in

Russell’s theory of descriptions. Russell assumes that the meaning of a

name is to be identified with the object that it denotes; he also assumes

that if we have a meaningful declarative sentence, it must be either

true or false. Take the proposition “The present King of France is bald”,

when there is no King of France. This obviously seems to be a

meaningful declarative sentence. By a denoting phrase Russell means

an expression of the form of “the so-and-so”. If a denoting phrase such

as “The King of France” functions as a name, and expressions in which

the phrase occurs are to be meaningful, we seem to be committed to

the existence, in some sense, of an object named by the denoting

phrase. Moreover, any proposition in which a predicate is ascribed to a

subject would seem to involve the implication that there is an object

214 Analytical philosophy

which the subject term denotes. Indeed decidedly paradoxical results

arise where we wish to deny the existence of objects; if “X does not

exist” is to be meaningful, “X” must denote an object, so we seem to

have to suppose that X after all has being in some way. The way

Russell deals with this problem is with his theory of descriptions. He

denies that definite descriptions function as names; so for them to

contribute to the meanings of propositions in which they occur there

need not be objects that they denote. The temptation to assume that

there must be an object which a definite description denotes is

removed by making explicit the implicit assumption and paraphrasing

the propositions so that the definite description does not occur.

Thus the full and correct analysis of “The present King of France is

bald” is a conjunction of three propositions:

(a) There is a King of France

&

(b) There is not more than one King of France

&

(c) There is nothing which is both King of France and is not bald.

More formally this can be stated as follows:

There is an x such that

(a’) x is now King of France

&

(b’) For all y, if y is now King of France, y is identical with x

&

(c’) x is bald.

This shows that although the whole original proposition, “The

present King of France is bald”, is meaningful, there is thereby no

need to find oneself committed to assuming the existence of any

object denoted by the subject term of the proposition. The analysis

enables us to affirm or deny what was merely assumed, that there

exists an object denoted by the subject term of the original

proposition. It also maintains the principle that all meaningful

declarative sentences must be determinately true or false, because the

whole original proposition is false. The whole original proposition is

false because (a) is false, that is, (a’) is false for every value of x, and

if one of a set of conjuncts is false, then the whole set is false. If the

King of France did exist but was not bald, then the whole original

proposition would be false because (c) is false, that is, the conjunction

(a’) & (b’) & (c’) would be false for every value of x, while (a’) & (b’)

was true for some x.

Russell’s logical constructionism involves the construction wherever

possible of the world from those items with which we are directly

acquainted, unless we are forced to do otherwise. This means that

entities X can be constructed out of entities Y. The principle of this

logical construction proceeds through showing that all sentences about

Russell 215

Xs can be translated without loss of meaning to sentences about Ys; the

direction of the construction always involves the construction of those

entities of whose existence and nature we are most doubtful out of

those entities about which our knowledge is least doubtful and most

secure. This attempts to give greater security against doubt to beliefs

concerning the nature and existence of entities.

Russell applies this idea to mathematical truths; here the aim is to

minimize the number of truths that have to be accepted without

proof, and the number of entities that need to be postulated. The aim

is to show that all mathematical truths can, in principle, be stated in

terms derived from logic alone. Mathematics seems to refer to

various problematic entities—for example, numbers; but numbers are

not empirical entities and do not seem to be in space or time at all. It

is extremely unclear, in that case, what sort of being such entities can

have. The strategy here is to define numbers in terms of classes: the

number one is the class of all classes in which any member is

identical with any other member; the number two is the class of all

classes of couples, and so on. We must note that the number of

members a class has is defined in a non-circular manner using the

notion of “similarity” of classes where there is a one-to-one relation

which correlates the members of the one class each with one member

of the other class. Thus the need to posit problematic entities outside

space and time is avoided, and we can think of numbers as classes of

classes of unproblematic entities. In the end Russell came to accept

reluctantly Wittgenstein’s view that mathematics consisted of

tautologies; he was reluctant to do this because it destroyed the idea

that mathematics was a system of certain discoverable eternal truths

about a non-human world beyond the uncertainty concerning the

world revealed by the senses. The conclusion is that the interest of

mathematics for us derives entirely from our limited intellectual

power, and its truths would to a mind of sufficient power be as trivial

as 2+2=4.

The same logical constructionism is applied to our knowledge of

physical objects and mind. Russell’s convictions with respect to our

knowledge of the world are basically empiricist, but he accepts certain

limitations to empiricism; experience alone is not sufficient to justify

many of our non-logical knowledge claims. He accepts that our

knowledge of the world must be through experience, while at the same

time he holds that certain of the suppositions required for such

knowledge, given the range of what we wish to claim to know, cannot

be justified by experience. If strict empiricism were followed, we

would seriously have to limit our claims to know by being unable

justifiably to go beyond the information we strictly immediately

experience. Either what we normally claim to know we do not really

know, or we must accept certain principles not justifiable by

experience in order to claim such knowledge.

216 Analytical philosophy

Russell accepts the traditional view that we do not directly

experience physical objects; rather, we directly and indubitably

experience private objects, actual sense-data and possible sense-data—

sensibilia—which are not thereby necessarily something mental, and it

is from these that physical objects are to be either constructed or

inferred. This is because when we say we are perceiving a table, we

and other people perceive different things depending on things about

us (our position, for example); since there is no reason to show

favouritism and say that any one of the perceptions is the “real” table

(its real shape or colour, for example), what we actually perceive

cannot be the real table itself, but must be something else.

Initially Russell adopted a dualism of mind and matter and a triadic

structure for our sense-perception. In any act of sense-perception there

are said to be three elements: act, content, object. By “act” is meant the

subject’s act of awareness; by “content” is meant the private sense-data

of which the subject is aware; by “object” is meant whatever is the

cause of the sense-data. The problem that immediately arises is how

one is to justify the belief in the existence of public physical objects if

one is never directly aware of them. This problem, along with the fact

that the supposed act of awareness, as distinct from what one is aware

of, is also never a datum of experience, led Russell to adopt a form of

neutral monism. This view accorded, Russell believed, more exactly

with modern science. According to this view, neither matter nor mind

constitutes the ultimate stuff of the universe (neither are substances);

both are logical constructs out of something more fundamental: events.

Events are analyzable into qualities in some space-time region, space

and time being constructs out of relations between qualities. These

events, in so far as knowledge rather than truth is concerned, are

identified by Russell with “percepts”, which are the immediate data of

our experience, but which as possible objects of experience can exist

unperceived. In this way both matter (physical objects) and mind can

be logically constructed out of percepts, and the only difference

between matter and mind consists in the way in which they are

collected into related bundles. Objects are constructed out of the class

of all actual and possible appearances or aspects; subjects are the class

of percepts which constitute a perspective bound together by memory.

Roughly we can think of this as “act” and “object” being collapsed into

“content”.

What I am immediately aware of is a percept in my private

perceptual space, which is an event in my brain; but my brain, for me,

does not form part of my private perceptual space, although my brain

is an object in public neutral space. In saying “I see X” I am directly

aware of percepts in private perceptual space, the necessary and

sufficient conditions for which are brain events in public neutral space,

and such events are causally linked in some way to events constituting

X in public space. Particular percepts which I experience are associated

Russell 217

with two places: the place associated with the group of particulars,

which is my biography, and the place associated with the group of

particulars, which is the “thing” X; these are two ways of grouping the

same percepts.

With respect to knowledge of the world we are acquainted

indubitably without inference only with present private experiences;

the problem then arises as to the principles by which we are justified in

claiming knowledge beyond the evidence of our immediate

experience. We claim to know truths about the past, and the future,

and universally valid laws of science. Russell holds that whatever the

required principles might be, they cannot be deductive, because no

deductive connections hold between matters of fact. The inference

from matters of fact with which we are immediately acquainted, if

they cannot be reduced without loss of meaning to propositions about

immediate experience, must depend on a non-demonstrative principle

of inference. Russell is asking what logical justification there can be for

beliefs beyond what we immediately experience; he is not asking in

what circumstances we are in fact caused to make such inferences and

have such beliefs.

We can ask, for example, what is the justification for the belief in

material objects that continue to exist unperceived? There is also the

problem that inference from “Some As are Bs” to “All As are Bs” is

never deductively valid, for there is no logical contradiction in

supposing that the next observed A will not be a B. The principle we

are seeking to justify such an inference is one that somehow validates

the move from things that we have observed to things that we have

not observed. Russell ultimately rejects the view that this principle is

one of simple enumerative inductive inference: that the more observed

As have been Bs, the more probable it is that the next A will be a B. He

rejects it because it is more likely, if unlimited by common sense, to

lead to false beliefs than to true beliefs. Given any finite set of facts,

there is, logically speaking, an infinite number of possible theories

which will fit the facts, all of which are equally probable. If, however,

we start with certain assumptions about the world antecedent to our

empirical investigation, then some outcomes, following the empirical

gathering of facts, will be more probable than others. These Russell

outlines as five “postulates” in Human knowledge. These postulates are

indemonstrable; if they were logical a priori principles, then they

would, through being tautologies devoid of content, be unable to fulfil

their function of factually describing the world by ruling out certain

factual possibilities, going beyond mere logical non-contradiction. On

the other hand, such postulates cannot be verified by experience, for

they are being presupposed in all empirical reasoning. Although the

postulates cannot be proved, Russell’s valuing of them is justified by

his claim that they distil from obvious cases of scientific practice the

details of what is actually assumed in such empirical inquiry. This fits

218 Analytical philosophy

with Russell’s general notion of philosophical analysis: the aim is not

to speak obscurely about science, and empirical inferences, being a

valid practice; the aim is to make clear by analysis exactly what that

practice logically assumes. Although the ensuing postulates cannot be

proved, we at least know where we stand, and what exactly is being

assumed. These postulates in turn mark the limits of empiricism, but

limits which Russell in one sense does not overstep because he does

not think that the postulates could have other than an empirical

justification; the limitation arises from the fact that no empirical

justification is possible. He does not suggest that they can be known to

be objectively valid by being Kantian a priori principles because he

does not think the mind can legislate for facts about the world; mind

cannot dictate facts to the world.

The problem with empiricism as a theory of knowledge is its

inability to justify our knowledge of things which we clearly wish to

claim to know; it is unable to do this because it would require, but

cannot justify empirically, principles of inference which take us beyond

what is justified by private present immediate experiences. Empiricism

as a theory of knowledge must have limits, since it will involve some

general proposition about the dependence of knowledge on

experience, such as “All knowledge is based on experience”, which is

not itself knowable by experience; so, if true, empiricism cannot be

known to be so.

Wittgenstein

Ludwig Wittgenstein (1889–1951) was born in Vienna into a wealthy

merchant family; he was the youngest of eight children.

Wittgenstein’s paternal grandfather had been a wealthy Jewish

merchant who had converted to Protestantism. Wittgenstein’s mother

was a Roman Catholic, and he was brought up in that faith. The

house was one of great cultural sophistication, particularly with

regard to music, Brahms and Mahler being regular visitors. The

attempt was made to tutor the children at home; but this proved a

failure academically. At an early age, Wittgenstein showed great

aptitude for practical engineering, and constructed a small sewing

machine. His poor academic performance meant that he failed to

enter Vienna University, and instead went to a technical college in

Berlin. He left the college in 1908 and went to the University of

Manchester as a student of aeronautical engineering. Naturally his

work involved the application of mathematics; this led him to be

interested in the foundations of mathematics itself. He asked who

had done work in this area and was directed to Bertrand Russell’s

Principles of mathematics. This proved a revelation to Wittgenstein,

and he was advised by Frege to study with Russell in Cambridge,

Wittgenstein 219

which he did in 1912. Although the personalities of Russell and

Wittgenstein were frequently at odds, Russell soon developed a deep

respect for Wittgenstein’s early philosophical and mathematical

ideas.

Wittgenstein went to Norway in 1913 and built himself a hut in a

remote location in which to continue his work on logic. When the First

World War broke out, Wittgenstein enlisted in the Austrian army. He

survived the war and was taken prisoner by the Italians. One result of

the war was that a new austerity or asceticism characterized his life.

Throughout his time in the army he had been completing his first great

book, the Tractatus logico-philosophicus; this was eventually published in

1921. Since he thought that the Tractatus disposed of all the problems

of philosophy, he quite consistently gave up the subject. From 1920 to

1926 he was a primary school teacher in rural Austria. Under the

influence of discussions with other philosophers, and through

dissatisfaction with the Tractatus, Wittgenstein resumed his

philosophical activity. In 1929 he returned to Cambridge and received

a PhD for his Tractatus. Around this time Wittgenstein began the

transition from his early philosophy to his later ideas.

After returning to Cambridge Wittgenstein was, with Russell’s

recommendation, awarded a Fellowship at Trinity College. During

this time the second, and in many ways quite different, phase of his

philosophy in the Philosophical investigations developed, although

there are connections with his earlier thought. After another year in

the hut in Norway Wittgenstein was in 1939 made Professor of

Philosophy at Cambridge. As he had always done, he continued to

travel restlessly. In 1949 he discovered he had cancer, and he lived

with friends in Oxford and Cambridge until his death at the age of

sixty-two.

Wittgenstein was in many ways an extraordinary person. He was a

man of lacerating self-criticism, troubled about his own life. He could

be extremely difficult, but he elicited great loyalty from his friends.

Although cultured, he was relatively unread in the philosophical

classics. It is difficult to identify philosophical influences on

Wittgenstein; some known influences are Spinoza, Schopenhauer,

Kierkegaard (1813–55), William James (1842–1910) and also Frege and

Russell. He also admired writers such as Dostoyevsky and Tolstoy. He

was driven by his character to think about philosophical problems;

good philosophy was not seen by him as something that could be

compartmentalized as a professional job distinct from the rest of one’s

life and the deepest considerations as to how we ought to live;

philosophy and wisdom were, or ought to be, interlinked. His thought

was profound, and yet he had doubts about the nature, function and

value of philosophical thought. He had a deep desire to solve

philosophical problems, and not use them as a field for mental

exercise.

220 Analytical philosophy

In order to understand the Tractatus it is necessary to give an

account of its overall aim, motivation and method. The aim of the book

is to draw the limits of the thinkable; and this is the same as drawing

the limits of language; beyond those limits the attempt to say things

can only produce nonsense. This brings us to the motivation for the

book; this can be seen as ethical, or perhaps aesthetic. In the face of

that which is “higher”, matters concerning ethics, religion, aesthetics

and profound questions about the meaning of life, we should stand in

silence; the attempt to say things about such subjects offends not only

against the logic of what language is capable of saying, but also against

a cultured sensibility which refuses to babble futilely in the presence of

what is awesome and mystical. The attempt to say things about what

cannot be said is worse than silence, not only because it is a waste of

time, but also because it leads us to corrupt and destroy the true nature

of that of which we speak. This idea accords with the intuition of many

that words are somehow inadequate in the face of the things that really

matter most—the most profound aspects of the human condition—and

that silence is the only proper response; the attempt to speak only

sounds gauche, shallow and tactless.

Much of philosophy has been concerned to tackle philosophical

problems head-on by trying to develop answers to the problems as

stated. The notion that there are limits to thought and language can be

applied to the problems and questions of philosophy itself.

Wittgenstein rigorously develops the critical tradition in philosophy.

There is some similarity with Kant’s assault on transcendent

metaphysics. To give a philosophical critique is to describe the logical

limits of something, such as knowledge, thought or language. In the

Tractatus the aim of the critique is to show that the problems of

philosophy do not need to be addressed because they are pseudoproblems

which arise from illegitimately going beyond logical limits.

Thus we should try not to tackle philosophical problems head-on but

rather to show that they are not genuine problems; they are necessarily

nonsense, and no more require to be answered than “How many goals

have been scored in this cricket match?” requires an answer in terms of

the number of goals. Philosophical problems are not solved but

dissolved.

In Wittgenstein the method used to carry through this critique is

deceptively simple: how every and any language acquires its meaning

determines the limits of what is meaningful in language. These limits

are determined by discovering the essence of language: what all

meaningful language must have in common, that without which it

would not be meaningful language. Wittgenstein regards the limits of

language as the limits of thought; beyond those limits we not only lack

any possibility of knowledge, we also reach what is unthinkable. It is

vital to realize that Wittgenstein assumes that language at bottom has

an essence, a single or unified logic; there is a single universal form of

Wittgenstein 221

language. There are features common to all and only languages that

make them language. Anything that has these features is a language,

and anything that is a language has these features. In short, it is

possible to define language by a set of features that are together

necessary and sufficient for anything to count as language.

Language is considered as the totality of propositions. Propositions

are linguistic expressions that can be determinately true or false. What

we have to show is the way that words and propositions, the basic

units of our language, acquire their meaning. We analyze the essential

way that propositions—such as “The cat is black”—acquire their

meaning or sense; all that can be meaningfully said can be expressed in

propositions; it follows that we cannot speak, or can speak only

nonsense, if we try to use propositions to talk about subjects in which

they cannot have a meaning. In short, we must study the way

language essentially acquires its meaning in order to show that there

are limits to what can be meaningfully expressed in language. That is,

the discovery of the necessary and sufficient conditions—the essential

features—in virtue of which any linguistic expression is meaningful

entails that anything that fails to satisfy those conditions must be

meaningless. The limits of the meaningful mark the limits of genuine

propositions, and thus of language.

It must be pointed out that, generally speaking, the propositions

in which philosophical problems are stated appear meaningful. But

this appearance is an illusion; once we understand the logic of our

language, that is, how ultimately and necessarily language becomes

meaningful, we will see that such propositions do not accord with

what can be meaningful. Russell in the theory of descriptions had

shown that certain philosophical problems disappear once we see

the underlying logical form beneath the apparent surface grammar.

Such insight into the nonsense of the apparent propositions of

philosophy reveals itself not immediately, but only after analysis.

According to Wittgenstein, it is unnecessary to do this analysis

piecemeal; one can show the limits of meaningful language, and that

philosophy lies outside those limits, all at once. The aim is to

indicate what cannot be said by clearly presenting what can be said;

we thus indicate what cannot be said from inside the boundary of

what can be said.

Wittgenstein’s inquiry is not an empirical one; it is a matter of pure

logic; it is a matter of showing how any propositions of any language

acquire their meaning by showing in what that meaning essentially

consists or must consist when all superficial differences are removed.

There is just one way all language is meaningful. This involves

showing what must be the case in the deep structure of language and

the nature of the world if meaningful language is to be possible—as it

obviously is—at all. The key to this is to understand that ultimately

language gets its meaning from its having a certain relation to the

222 Analytical philosophy

world; apparently meaningful expressions which cannot have that

relation are not really meaningful.

If we are able to determine the essential conditions required for

meaningful descriptive language, and these derive from something

about the world, we have also displayed the essential nature of

reality; that is, how any possible world logically must be if any world

exists at all. There will of course be all sorts of contingent features

about the world which we cannot determine by logic alone; but there

must be some essential features that are common to all possible

worlds regardless of their contingent differences. The minimal

conditions for having a meaningful descriptive language at all reveal

the minimal nature of any possible world—the substance of the

world. Basically this will come down to what is common between the

essential structure of meaningful language and the essential structure

of the world.

In giving an account of how language gets its meaning, it must be

understood that we are looking below the surface structure of

language to the hidden deep structure on which its meaningfulness

depends. Wittgenstein is saying: if language has meaning, then, as a

matter of logical necessity, this, at its deepest level, is how language

must be.

Language gets its meaning in virtue of a relation between it and the

world. So language that cannot have this relation is meaningless. The

starting-point of Wittgenstein’s view of language is roughly outlined

as follows. The meaning of a word is the object for which it stands; the

meaning of a word is the object to which the word refers. Words are

basically names. The world is made up of objects, and the relations

between objects form facts. Propositions describe the facts by

describing how the objects stand in relation to each other. If the

relation of the objects expressed in the proposition is the same as the

relation of the objects themselves, then the proposition is true,

otherwise it is false. What the facts are is quite independent of

language or thought; we do not make the facts.

As an account of ordinary language the above seems obviously

inadequate. If the meaning of names is their objects, then names

referring to objects that cease to exist, or never did exist (such as

“Excalibur”), become, or are, meaningless. This means that any

proposition containing such names will also be meaningless. Also

there are various components of ordinary language that do not seem to

be names at all—such as “is”, “or”, “must”—so their meaningfulness is

unexplained. The answer to this is that ordinary language hides a

complexity that can be revealed by analysis.

Suppose we have a proposition “p” asserting “x is F”, but x does

not exist. If “x is F” is false just because x does not exist, then “x is

not-F” is also false; but it is a principle of logic that propositions “p”

and “not-p” cannot both be false or both true. So what the

Wittgenstein 223

proposition “p” really asserts is that some related complex

combination of objects constituting x in fact obtains. But although the

elements of the complex exist, the described relation between them

concealed in the name “x” does not hold; “x” covertly describes a fact

rather than names an object. So “x is F” is false because part of what

it describes, under the guise of the term “x”, is false; the complex

combination of objects constituting x does not obtain, although the

constituent objects exist.

We might say “x is F” is not false but meaningless if x does not exist.

On Wittgenstein’s view of language, if we find a complex expression

that contains a name referring to an object that does not exist, then it

would seem that the whole expression must be meaningless. If the

expression is to be meaningful, then the terms referring to the object

that does not exist must really be a description using terms referring to

more fundamental objects that do exist and to the relation between

them. Then the original whole expression is not meaningless, but

simply false, because one of its constituent parts describes a relation

between fundamental objects that does not hold, although those

objects themselves exist. Because those objects exist, the whole

expression referring to them is meaningful, although the relation it

describes as holding between them is incorrect.

The implication of this is that proper or real names (“simple signs”)

should refer to simples—atomic objects that are logically without parts

and so cannot break up—if expressions which include names are not to

run the risk of being meaningless or nonsense when the object named

does not, or ceases to, exist. “Excalibur has a sharp blade” is

meaningful whether Excalibur exists or not; so the word “Excalibur” is

really a description which must by analysis be eliminated and replaced

by names of simple parts, which, if they are not combined in a certain

way, means that Excalibur does not exist, but to which the names

cannot fail to refer and so have meaning.

If we are not to embark on a regress in which we are unable to

guarantee that propositions have a determinate sense, we must reach

real names that cannot fail to refer to objects; that is, absolutely simple

objects that cannot be described. If the terms of propositions did not

ultimately name objects that are not complexes, then any proposition

could always fail to have meaning, since it might be constituted of

terms that had no reference, and hence no meaning. The only way to

guarantee that terms have meaning is that they are ultimately

constituted of terms that cannot fail to refer to objects that exist if the

world exists at all. This means the objects cannot be complexes, but

must be without parts. If they are without parts, they cannot be

described but can only be named, for a description is an analysis into

constituent parts. This is the only way of guaranteeing that

propositions have meaning; otherwise any proposition could fail to

have a meaning by containing terms that are ultimately words

224 Analytical philosophy

referring to non-existent entities. Wittgenstein calls these ultimate

terms simple or atomic names and their references simple or atomic

objects. Thus Wittgenstein gives an account of what must be the case if

language is to be guaranteed as meaningful.

This emphasizes the requirement that sense be determinate;

propositions must have a definite sense, for a proposition without

definite sense could not be said to have a sense at all, and could not be

determinately true or false.

Wittgenstein’s aim is to produce a theory of language whereby

propositions have meaning even when they appear to refer to nonexistent

objects. If the meaning of words consists in the objects for

which they stand, and propositions are made up of words, then, for it

to be the case that propositions are guaranteed a sense even when

they apparently name non-existent objects, at a deep level it must be

the case that language as the totality of propositions consists of

names that cannot fail to have meaning by having objects for which

the names cannot fail to stand. At the deepest level language, as the

totality of propositions, must consist of names of logically simple

indestructible objects.

When completely analyzed, the structure of language mirrors the

structure of the world. The most basic constituents of language are

atomic names which mean their atomic objects; the meaning

(Bedeutung) of a name is the object to which it refers. Atomic names

and objects are, respectively, the simplest constituents of language and

of the world. Atomic objects are the substance or form of the world in

that they are common to any possible world. These objects are logically

atomic: they can only be named and not described, for if they could be

described they would consist of a complex combination of elements

which would mean they were not simple; but atomic objects are

indestructible, permanent and unchanging. Atomic objects are the

constant elements of all change and enter into combination with other

atomic objects to form a state of affairs or atomic fact (Sachverhalt). The

possible ways in which atomic objects can enter into combination with

other objects fix the form of such objects, the sum of which ways is the

possible states of affairs in which such an object can be an element.

This form is the timeless order determining all the possible states of

affairs into which it can enter. When we know (kennen) an atomic

object, it is “given”; we then know all the possible states of affairs into

which it can enter; in that sense we then know all other objects and all

possibilities. Possible and actual states of affairs, which are

arrangements of atomic objects, are depicted by elementary

propositions, which are concatenations of atomic names. In elementary

propositions atomic names substitute for, or stand proxy for, objects.

The totality of existent and non-existent states of affairs is the totality

of possible arrangements of atomic objects. Understanding the essence

of a proposition means understanding its constituent atomic names

Wittgenstein 225

which means knowing their atomic objects, and that is to know all

possible combinations of those objects: all possible states of affairs or

the whole of logical space. An elementary proposition is meaningful or

has sense (Sinn) in virtue of its describing a possible state of affairs in

logical space; it is true if it describes an actual state of affairs and false

otherwise. Thus an elementary proposition will be meaningful even

when it is false in virtue of its being wholly a concatenation of names

which cannot fail to have meaning because they cannot fail to stand

for their atomic objects.

The meaning of a name is its reference; but a name does not have a

sense; a name does not say anything about the world; it does not

describe the world, but stands for objects in it; names cannot be true or

false. Propositions are true or false; they describe how things stand in

the world. Propositions have a sense in that they each describe

possible facts in the world; the sense of a proposition is what would be

the case if it were true.

The world is the totality of facts. When complex facts (Tatsachen) are

broken down this ultimately means the totality of states of affairs as

described by elementary propositions. The facts are always constituted

by rearrangements of the same constant atomic objects. Every

proposition which is not an elementary proposition can be analyzed

into one, and only one, compound of elementary propositions.

Such elementary propositions consist entirely of concatenations of

names. An atomic fact might be that object a is to the left of b; we

might write this as “aRb” where “R” stands for the relation between a

and b. But ultimately “R”, if it is not a name standing for an object,

must be eliminated so we have only atomic names. Indeed, “ab” does

show the relation of the named objects a and b. The arrangement of

names within the proposition, if it is true, directly shows how things

are in the world. This is the picture theory of language, whereby the

way that language depicts facts in the world ultimately derives from a

common logical form: a structural isomorphism between language

and the world. Language models or maps the world. How this

picturing takes place in propositions is unclear. Even allowing for the

spatial ab relation, there are more kinds of relations than spatial

relation to be depicted. Nevertheless, it can be pointed out that a

variety of relations is depicted in other areas, such as that which

occurs between a musical score and the music itself. This picturing

relation is not apparent for the sentences of ordinary language but

holds at a deep level. The idea is that to represent something there

must be a one-to-one correlation between elements in the picture and

elements in the state of affairs represented; some kind of arrangement

or ordering of the elements in the picture shows how the

corresponding elements in the world stand to each other. The nature

of the ordering of the elements depicted and the nature of the ordering

in that which depicts may be different, but the ordering itself is in

226 Analytical philosophy

both as their common logical form: the minimum required for picturing

to occur at all. It is in virtue of their logical form that propositions are

able to depict facts. This minimum universal logical form cannot itself

be depicted, since it is what is common to all pictures; to picture

logical form alone one would need to stand outside all ways of

picturing; but then one could not picture at all.

This picturing theory applies to thoughts; a thought is a

proposition; for a thought to be of a possible fact in the world it must,

like the proposition, be constituted from an arrangement of psychical

elements that correspond to the elements making up the fact in the

world. What cannot be stated in a proposition cannot be thought. That

which does the representing of a fact is itself a fact, not something

other than a fact.

Wittgenstein makes an important distinction between showing and

saying. The thinking here is that ultimately we must reach propositions

that simply show their sense; their sense is manifest. Proposition “p”

says that things are so-and-so. We might attempt to explain the sense of

proposition “p” by proposition “q”; but if “p” is to have a sense, we

must ultimately reach elementary propositions whose sense simply

shows itself. In a sense one cannot say what the meaning of a

proposition is. If “q” does its job of explaining the sense of “p”

properly, then we have got no further, but have merely re-expressed

the same sense. The sense must show itself, and what can be shown

cannot be said. Wittgenstein is convinced that the cardinal problem of

philosophy has been the attempt to say what can only be shown; that is,

the attempt to explain by saying things which can only be shown; and

that can only produce nonsense.

Propositions compounded of elementary propositions are called

molecular propositions. Molecular propositions are truth-functions of

their elementary propositions: that is, the truth or falsity of whole

molecular propositions depends entirely on the truth or falsity of their

constituent elementary propositions. Molecular propositions have

logical structures which are compounded from elementary

propositions by truth-functional logical constants. These truthfunctional

constants are defined by the way in which they determine

the truth or falsity of complex propositions in which they occur. These

truth-functional constants, “or” (v), “and” (&), “not” (–), “if…then… ”

(®), “…if and only if…” (=), are now a standard part of prepositional

logic. In addition there is the apparatus of predicate logic, which

includes within it prepositional logic, and which takes us “inside”

propositions, which involves as logical constants the universal

quantifier “all” (") and the existential quantifier “some” ($). A

particular proposition “p”, “The chair is red”, might be expanded and

symbolized as “a is F” or “Fa”, where “a” names an individual thing

(the chair), and “F” is a predicate term (is red). The common structure

or general logical form of all propositions like “p” can be symbolized

Wittgenstein 227

as “Fx”, where “x” is an individual variable (for which constant terms

denoting individual things can be substituted) and “F” a predicate

term. The logical form of the conclusion we can draw, given any one

proposition such as “p”, that is “Fa”, is expressed in the propositional

function “There is some (at least one) x such that x is F” which is

symbolized as “($x)(Fx)”.

Take “and” (&) as an example of a truth-functional constant: it is

clear that a molecular proposition “p & q” is true just in that case

where both “p” is true and “q” is true, and is false otherwise. With

“not” (–) or negation, for example, we can see that if “p” is true, then

“–p” must be false, and vice versa. The way that truth-functional

connectives operate is displayed in truth-tables. For example:

The most important point is that all molecular propositions can be

analyzed into elementary propositions by truth-functional analysis

and that the truth or falsity of the whole original molecular

proposition is a function of the truth or falsity of its constituent atomic

propositions related by truth-functional connectives.

The essential structure of language, at its various levels of simplicity

and complexity derived from analysis and synthesis, mirrors the

world. This can be displayed in the diagram opposite, in which the

arrows show the direction of analysis. That a proposition describes a

possible fact gives the proposition its sense; it describes an

arrangement of objects in the world; that the fact is actual or not actual

determines the truth or falsity of the proposition. Propositions have a

sense even when they are false because they are ultimately a

concatenation of atomic names that cannot fail to have meaning

because they cannot fail to stand for atomic objects.

The truth of all elementary propositions is logically independent: it

is impossible from one elementary proposition to deduce the truth or

falsity of any other and impossible for any elementary proposition to

contradict another. From the existence of one state of affairs it is

impossible to deduce any other state of affairs. If one proposition can

be deduced from another, then the proposition from which it is

deduced cannot be elementary, but must be a truth-functional

compound. One proposition can be deduced from another only if the

deduced proposition is contained in the original proposition. For

example, “p” is deducible from “p and q”, because “p” is already

228 Analytical philosophy

contained in the complex proposition “p and q”. A deducible

proposition is contained in the proposition from which it is deduced

by being a truth-functional component of the complex proposition

from which it is deduced. If the individual propositions “p” and “q”

are really elementary propositions, and are not compounds of simpler

propositions, then there is no complex for any other proposition to be

contained in. This logical independence should show itself clearly in

the ideal notation; we can see that if “p” and “q” are elementary

propositions, “q” cannot be deduced from “p”, and vice versa; “p and

not-q” is never a contradiction and “not-(p and not-q)” is never a

tautology.

This brings us to logically necessary truths, and contradictions. No

elementary proposition can be necessarily true or necessarily false;

such propositions are essentially bipolar: true-false, that is, contingent.

The only necessarily true propositions are logically necessary truths or

tautologies; the only necessary false propositions are contradictions.

Necessary truths are necessary because they are truth-functional

compounds formed of simpler propositions in such a way that,

whatever the truth or falsity of their component parts, the whole

proposition is always true. Necessary falsehoods or contradictions are

truth-functional compounds formed of simpler propositions in such a

way that whatever the truth or falsity of their component parts, the

whole proposition is always false. Tautologies say nothing about the

Wittgenstein 229

world precisely because they are true independently of whatever the

facts are about the world which give a truth-value (true or false) to the

components of the tautology. Contradictions are false regardless of any

facts about the world. Wittgenstein suggests that both tautologies and

contradictions are in fact called true or false “propositions” only by

courtesy of genuine propositions which are contingently true or false.

Tautologies and contradictions are thus senseless (sinnlos), but not

nonsense (Unsinn). Although tautologies and contradictions say

nothing factual about the world, they show the logical structure of the

world and language, and show the boundaries within which all

propositions which can say anything about the world must fall. They

mark the boundaries of factual discourse, and only factual discourse

has sense; language gets its meaning from the world, the totality of

facts, it cannot therefore say anything about matters outside the world;

ethics, values, religion, the meaning of life lie outside the world of

facts; they make themselves manifest to us; they show themselves, but

we cannot say anything about them. Genuine propositions state

possible facts, and can have sense only by doing so, or are tautologies

or contradictions. Beyond those boundaries there is only nonsense

which does not say anything, but merely shows itself to be nonsense. In

short, language gets its entire meaning from the world—ultimately from

names of objects—and so language is meaningful only when it states

facts about the world. The following diagram summarizes this view.

Many problems arise from the Tractatus, some of which led to

Wittgenstein’s later thought. One is the absence of any examples of

atomic objects and atomic names. An atomic object must be such that it

cannot be described, but only named, and the name is guaranteed to

have a reference, and hence a meaning. Russell suggested such real or

proper names might refer to the present content of our senseexperience

(sense-data): that is, demonstratives such as “this” and

“that” are the only logically proper names, which cannot fail to point

to the present content of our sense-experience and hence to their

reference. But the fleeting nature of such objects of experience means

they are not what Wittgenstein wants. A real name should not only

have a guaranteed reference, but must also refer to the same enduring

and unchanging object if its meaning is to be fixed and determinate.

But “this” and “that” will mean different things depending on the

present content of experience which will vary within the same person

230 Analytical philosophy

and between different people. So Wittgenstein could not share

Russell’s view. Indeed it seems inevitable that atomic objects are

ineffable in that we cannot say anything about them because to say

anything about them would be to describe them, and in that case they

could not be simple. Wittgenstein’s view seems to be that as a logician

it is not his job to decide what are atomic objects, atomic names, and

the ultimate psychical constituents of thoughts; but it is a matter of

logic that there must be such things if the propositions of language are

to have a sense. We cannot even say of a simple object a, that “a exists”,

for the assertion is either meaningless in the case where a does not

exist, or trivially redundant.

An important problem is the status of the propositions of the

Tractatus itself. It is not uncommon in philosophy for a philosophical

theory or system to cut off the branch on which it is sitting. The

attempt to assert and show that some ways are the only ways of being

intelligible or knowing things turns out to go beyond those ways and

involve just those ways which are said to be unintelligible or

unknowable. The point of the Tractatus is to put an end to philosophy,

or at least all metaphysics, by revealing its propositions to be

nonsensical (unsinnig). More generally it reveals what can and what

cannot be said; what can be said are the propositions of natural science

which are factual: they state facts about the world. This means that

about important matters, such as ethics, religion and the meaning of

life, nothing can be said, since they are not concerned with facts about

the world. It is not that ethics, religion, and the meaning of life are

nonsense; what produces nonsense is the attempt to say things about

them. But in attempting to make its point it would seem that by its

own criteria the propositions of the Tractatus itself are just such

nonsense. They do not state facts about the world, but say things about

the necessary structure of all fact-stating and the necessary structure of

the world, which are not themselves further facts about the world.

Wittgenstein is aware of this, and declares that one must transcend the

propositions of the Tractatus: one uses it like a ladder up which one

climbs, and which, once used to make clear that metaphysics and the

propositions of the Tractatus are nonsense, can be thrown away.

Wittgenstein 231

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