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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