The Oxford Companion to Philosophy Part 45 ppt

belief-forming processes might also possess various epi-
stemic virtues, such as reliability. It is an open question
whether a given belief, produced by such a process, is true,
or reflects available evidence. Would mere failure of a
belief to withstand self-awareness about its origins or
open social discussion of its content constitute a genuinely
epistemic defect?
What is the structure of ideological explanations of
beliefs and values? Is there a credible theory of the social
psychological mechanisms by which social interests or
symbolic needs shape individuals’ beliefs and values in the
unacknowledged ways that are presupposed when ideolo-
gies are claimed to have a functional role?
Finally, what does normative use of the concept of
ideology presuppose about the existence of contrasting,
epi-stemically respectable ways of knowing? In particular,
does the normative notion of ideology presuppose the
availability of notions of objective inquiry or objective
interests of the very sort that attention to the social char-
acter of knowledge and valuation renders suspect? p.r.
*historical materialism; noble lie.
T. Eagleton, Ideology: An Introduction (London, 1991).
R. Geuss, The Idea of a Critical Theory (Cambridge, 1981).
J. Habermas, Knowledge and Human Interests (Boston, 1971).
K. Mannheim, Ideology and Utopia (London, 1946).
K. Marx and F. Engels, The German Ideology (1846; first pub. 1932).
idiolect. The term ‘idiolect’ is intended to mark the notion
of a *language which is not the language of a community
(sociolect) but rather of an individual. Idiolects more than
sociolects have been the focus of much philosophical inter-
est in recent years because of the close connection between

the language or meanings of an individual and his inten-
tional states. Idiolects are the place where philosophy of
language and philosophy of mind meet.
It is possible that one should have a highly social con-
ception of idiolects, but that would still not spoil the idea
that when one studies idiolects one’s object of study is the
individual’s linguistic competence and performance
rather than the language of a community. There is, in
other words, no contradiction in the idea that one should
think of idiolects as being socially constituted. In fact Tyler
Burge holds precisely such a view of idiolects. This is an
important point because it puts us on guard against the
widespread and careless use of the term ‘idiolect’ to talk of
a non-social or individualistic conception of the language
of an individual. So care must be taken to distinguish
between objects of study such as sociolects and idiolects
on the one hand (such as Oxford English and Peter Straw-
son’s English respectively) and on the other hand an indi-
vidualist or social conception of these objects of study
(such as those of Chomsky and of Tyler Burge respect-
ively). The term ‘idiolect’ strictly applies only to a certain
object of study (i.e. to an individual’s language), not to an
individualist conception of an individual’s language. a.b.
Akeel Bilgrami, Belief and Meaning (Oxford, 1993), 66–73.
Tyler Burge, ‘Wherein is Language Social?’, in Reflections on
Chomsky, ed. A. George (Oxford, 1989).
idols. The danger of allegiance to false gods is a premiss of
all orthodoxies which acknowledge nevertheless their
powerful appeal to the common people and seek to per-
suade them that idol-worship is not only futile but also

dangerous. For the Christian philosophers Boyle, Male-
branche, and Berkeley, idolatry is implied by such com-
mon-sense beliefs as the self-sustaining power of nature,
the causal efficacy of created things, and the mind-
independent existence of the sun, moon, stars, and other
objects. The theory of idols is transformed into a general
theory of *ideology in the first book of Bacon’s Novum
Organum, which describes the epistemologically perni-
cious effects of human attachment to the fictions created
by language, tradition, custom, and imagination. The
accusation of idolatry continues to have philosophical
importance in Nietzsche’s attacks on Socrates and Kant in
his Twilight of the Idols, and in the attempts of Marx, Freud,
and other social critics to demystify social and economic
structures and to assist people in relinquishing their devo-
tion to things which don’t actually exist but which have
power over them anyway. cath.w.
F. Bacon, Novum Organum, in Works, ed. J. Spedding, R. L. Ellis,
and P. D. Heath, 14 vols. (Cambridge, 1857–61; repr. Stuttgart,
1961–3), viii.
if: see conditionals.
iff. Abbreviation for the *biconditional connective ‘if and
only if’. ‘P if and only if Q’ abbreviates ‘P if Q, and P only if
Q’. On the *truth-functional treatment of ‘iff’, ‘P iff Q’ is
true just when P and Q are both true or both false; so ‘P iff
Q’ and ‘Q iff P’ are equivalent. In ordinary contexts, how-
ever, reversing the order in a biconditional can make a dif-
ference. ‘Alicia comes down for lunch if and only if we
serve alligator stew’, for example, differs in meaning from
‘We serve alligator stew if and only if Alicia comes down

for lunch’. d.h.s.
James D. McCawley, Everything that Linguists have always Wanted
to Know about Logic (but were Ashamed to Ask), 2nd edn.
(Chicago, 1993).
David H. Sanford, If P, Then Q: Conditionals and the Foundations of
Reasoning, 2nd edn. (London, 2003).
ignoratio elenchi.
Literally, ignorance of refutation. A
*fallacy of traditional logic, where it was usually taken to
mean ‘ignorance of what is to be refuted’ or, more inclu-
sively, ‘of what is to be proved’. Ignoratio elenchi is arguing
for one thing as if it proved another thing. For example, it
is ignoratio elenchito use an argument against euthanasia as
if it proved that you shouldn’t eat the dead. The ‘ignor-
ance’ is in the mind of the would-be refuter or prover, and
often arises from confusion of similar-seeming conclu-
sions. The rhetorical trick of deliberately infecting an audi-
ence with such confusion is not really this fallacy. c.a.k.
C. L. Hamblin, Fallacies (London, 1970).
illocutions: see linguistic acts.
420 ideology
illusion, arguments from. The classic example of such an
argument appears in the epistemology of *perception;
modern versions focus on cases of total hallucination,
where one seems to see something when there is nothing
there at all, rather than on illusions such as the famous
bent-stick case in which there is something there (the stick)
which looks one way and is another. The argument,
which is still called the argument from illusion, starts from
the seemingly undeniable fact that it is impossible to dis-

tinguish (from the inside, as it were) a hallucination of
being faced with an elephant from the state of actually
being faced with an elephant. What conclusion can we
draw from this?
Suppose we hold that there are two states at issue here,
a veridical one which is a relation between perceiver and
(external) object, and a hallucinatory one which is a non-
relational state of the perceiver. The argument from illu-
sion then maintains that since there is no distinguishable
difference between the two states, we must give a broadly
similar account of them both. This suggests that the
veridical state consists of two elements, one (the common
element) which obtains even in hallucination, and the
other (the presence of the outer object) which obtains
only if we are lucky.
The argument is sometimes supposed to take us
beyond this, and to support a particular account of the
common element, the ‘act-object’ theory. The idea here is
that since the deluded are not aware of outer things but
are still aware of something, they must be aware of an
inner thing (an appearance). We then appeal to the indis-
tinguishability of hallucination and genuine perception to
argue that in success too we are (primarily) aware of an
appearance, sometimes called a *‘percept’, ‘sensum’, or
*‘sense-datum’, and only secondarily aware of the outer
object. But this move amounts more to an assertion of the
act-object theory than an independent argument for it.
For it assumes without argument that the content or
nature of the hallucination is an inner object, when this
was exactly what was in question. The adverbial theory,

which denies that assumption, is equally compatible with
the argument from illusion.
There is a different, sceptical form of argument from
illusion. This is just a special case of Cartesian *scepticism.
Descartes argued that we do not know that we are fully
clothed, because we cannot distinguish the state of being
clothed from that of being naked while dreaming that
we are clothed. This is an argument from the general pos-
sibility of error; it argues from perceptual error to the
conclusion that we never know that things are the way
they look.
If that conclusion is intended to be entirely general, the
premiss must be that there is no case at all in which we can
distinguish our being right from our being wrong; all
seemingly veridical states may for all we know be hallucin-
atory ones. This is a strong claim, and it is one which the
first argument from illusion had no need to make. In
attempting to support the ‘common element’ theory, one
need only suppose that in a reasonable range of cases we
are unable to distinguish hallucination from genuine per-
ception.
Both of the arguments from illusion that we have con-
sidered so far concern perception. But their starting-point
is one about indistinguishability. Considered in very gen-
eral form, the argument from illusion argues from the
indistinguishability of two states, one of which is a success
and the other a failure, to what we might call the ‘con-
junctive thesis’ that what one gets in success is a conjunc-
tion of two independent elements: (1) something which
success and failure have in common and (2) something

only present in successful cases.
If this is the general nature of arguments from illusion,
there will be other examples to be found wherever there is
indistinguishability. One such tries to persuade us that
knowledge is some form of belief. You cannot tell (from
the inside) whether your cognitive state is one of knowing
or merely one of believing (truly or falsely, it doesn’t
matter which). Therefore, knowledge must be defined as
belief plus something—e.g. as belief plus truth and justifi-
cation, as in the tripartite definition. (*Gettier.) This is a
‘conjunctive’ theory of knowledge.
In these ways arguments from illusion have been a
potent weapon in establishing a broadly Cartesian view of
the mind. j.d.
*oar in water.
A. J. Ayer, The Foundations of Empirical Knowledge (London, 1969).
F. Jackson, Perception (Cambridge, 1977), 107–11.
J. McDowell, ‘Criteria, Defeasibility and Knowledge’, in J. Dancy
(ed.), Perceptual Knowledge (Oxford, 1988).
H. H. Price, Perception (Oxford, 1932).
image. The nature of mental imagery and its relation to
thought and imagination (as creative thought) are long-
standing issues. Aristotle called attention to the mind’s
ability to present objects for itself (phantasia). ‘Imagists’
take picture-like entities to form the elements of all repre-
sentational states, and some include here perception.
Others claim that no such entities occur even in memory
and imagining. The role of imagery in memory and
problem-solving is contested in *cognitive science, where
Frege’s contrast between image as psychological incident

and thought is echoed in the view that images are simply
arrays on the brain’s ‘visual buffer’, their content fully
accountable in general or syntactical terms. ‘Pictorialists’
argue plausibly that the content has an irreducibly spatial
aspect. Some claim that the whole issue, as much in phil-
osophy besides, rests on unexamined imagery in another
sense, that is on analogy and figure of speech. a.h.
*imagination; eidetic imagery.
Alastair Hannay, Mental Images: A Defence (London, 1971).
Michael Tye, The Imagery Debate (Cambridge, Mass., 1991).
Alan R. White, The Language of Imagination (Oxford, 1990).
imagery, eidetic: see eidetic imagery.
imagination. Imagination is the power of the mind to
consider things which are not present to the senses, and to
imagination 421
consider that which is not taken to be real. Just as the imagin-
ary contrasts with the real, so imagination contrasts
with both *perception and *cognition. Certain philoso-
phers have nevertheless assigned it to a central role in
explaining the mind’s ability to represent any reality: thus
Hume, despairing of the powers of both the senses and
reason, explained the genesis of our idea of body by refer-
ence to the imagination; and Kant appealed to the imagin-
ation in his explanation of how thought or experience of
an objective order was possible. The resources of the
imagination have often been thought to be bound by the
deliverances of the senses—the power of imagination
being the recombination of simple elements presented to
the mind through the senses. On accounts of thinking in
the tradition of *empiricism, imagination has been impli-

cated through the role of imagery in all thought, the limits
of imagination becoming the limits of thought. Berkeley
notoriously argued for *idealism by claiming that it was
impossible to imagine a tree unperceived, and hence that
it was impossible to conceive of objects existing independ-
ently of us.
Most heat has been expended debating the nature of
mental *images, those exercises of the imagination which
correspond to our perceptual modalities. Certain acts of
imagination have a distinctive phenomenology which
others do not. In complying with the request to imagine
that Scotland should be an independent country, one need
not perform an act of the former sort, while one would do
so in visualizing the destruction of the Houses of Parlia-
ment. Correlative to visualizing are other acts of imagin-
ation corresponding to the other sense modalities: for
example, people are capable of auditory, gustatory, and
olfactory imagining. Questions arise concerning both the
relation of mental imagery to the corresponding percep-
tions and the differences between them, for Hume the
problem of distinguishing impressions from ideas.
According to the picture theory of imagery, having a
mental image consists of being aware of some mental
entity before the mind which represents the external
scene imagined. Inasmuch as this provides an inner surro-
gate for the outer object of a mental state, this account par-
allels the *sense-datum theory of perception. There is now
almost universal hostility to both views, not least because
of the model of the mind they present: that of the subject
surveying the mind’s contents as the sole audience within

a private theatre.
Those with leanings towards *behaviourism often
show the most hostility to the idea of mental imagery. The
denial that there is any imagery is likely to be taken as evi-
dence of the sceptic’s own lack of imaginative powers
while attempts to explain imagination purely in terms of
outer performance lack plausibility: for example, Ryle’s
attempt to explain imagination in terms of pretence.
Mental imagery has become the focus of a debate
within psychology since research has suggested that
imagery is involved in certain kinds of reasoning. Subjects
often report employing imagery in solving certain tasks,
such as answering the query ‘Do frogs have lips?’ Imagery
also seems to be exploited in certain forms of spatial rea-
soning. This has led to a debate in both psychology and
philosophy over the nature of the imagery involved in
these cases, in particular whether there are distinct forms of
representation within the brain, although it is not clear
whether this new debate is continuous with the more trad-
itional debates about imagery and imagination. m.g.f.m.
G. Currie and I. Ravenscroft, Recreative Minds: Imagination in Phil-
osophy and Psychology (Oxford, 2003).
P. F. Strawson, ‘Imagination and Perception’, in Freedom and
Resentment (London, 1974).
M. Tye, The Imagery Debate (Cambridge, Mass., 1992).
B. Williams, ‘Imagination and the Self’, in Problems of the Self
(Cambridge, 1973).
imagination, aesthetic. The *imagination has often been
put forward as the mental capacity most essential to the
production and appreciation of *art. Fictional representa-

tion is an obvious case in point. Instead of believing that
we are seeing or reading about real persons and actions,
we imagine them. Even if we see a real actor, it is the
imagination that converts what we see into the character
we are interested in. This form of imagination, which is
continuous with a form of childhood play, may also be
termed ‘make-believe’.
The value of such activity no doubt lies in its broaden-
ing of our understanding beyond what we encounter in
our own lives. It is a familar fact—which some philoso-
phers, including Plato, have found disconcerting—that
emotional identification is to some extent indifferent to
the barrier between reality and make-believe: while insu-
lated from the imaginary scene, we can nevertheless ‘feel
for’ the characters. Imaginative involvement with fiction
seems to be of value because it allows us to experience vul-
nerability to a wide range of feelings, whilst not threaten-
ing us with the real-life predicament of actually having to
do something.
It is arguable that all aesthetic experience brings the
imagination into play. To hear a piece of music as expres-
sive of a mood or feeling is not merely to hear sounds of a
certain pitch and duration: the mind appears to be active
in grouping together what it literally perceives into a form
with added significance. Wittgenstein’s *duck-rabbit
drawing provides a kind of analogy, where what is literally
present is neither duck nor rabbit, but where the imagin-
ation has freedom to see the drawing as one or the other.
Kant’s idea that aesthetic experience involves a ‘free play
of the imagination and the understanding’ has been

prominent among the influences on this line of thinking.
c.j.
*aesthetic attitude.
R. Scruton, Art and Imagination (London, 1974).
K. Walton, Mimesis as Make-Believe (Cambridge, Mass., 1990).
immediate inference: see inference, immediate.
immortality. According to Christian and other Western
theology, God is immortal in the strictest sense that he can
422 imagination
never die, either because he is essentially everlasting (i.e.
his nature is such that if he exists at one time, he exists at all
times) or because he is eternal or timeless (i.e. he exists out-
side time). Other things—e.g. angels and human souls—
have also often been supposed to be immortal in the less
strict sense that their nature is such that they will exist ever-
lastingly unless God were to choose to eliminate them.
Plato (Phaedo 78b–80c) argued that the *soul, being
immaterial and not occupying space, has no parts; that the
destruction of a thing consists in separating from each
other its parts; and so that the soul can not be destroyed.
Many subsequent philosophers—e.g. Berkeley—have
repeated Plato’s argument. However, it does seem that
things can be destroyed (e.g. atoms reduced to energy)
without their parts being separated.
Kant argued that the immortality of the soul was a ‘pos-
tulate of pure practical reason’—that acting morally only
made sense if thereby the agent made progress towards
being totally holy, something he could attain only in
unending life. Others have argued that acting morally
only makes sense if there is a life after *death in which the

good are rewarded. An obvious response is that acting
morally makes no sense unless there is some point in so
acting at the time in question. The traditional Christian
and Islamic doctrine of an unending life—in heaven or
hell—does not, however, require that living for ever is
natural for humans. It requires only that they live for ever,
and that may happen because God intervenes in the nat-
ural order to resurrect the dead—either souls alone or
embodied humans. Many modern Christian theologians
have held that resurrection rather than natural immortal-
ity is what the New Testament and the early Christian
Fathers taught; and that revelation, not a priori reasoning,
is what provides the grounds for belief in life after death.
(A few very radical theologians have interpreted talk of
‘immortality’ or ‘resurrection’ in terms of the eternal sig-
nificance of our present-life choices and attitudes.)
Indian religions teach that the dead are often reincar-
nated in new bodies, human or animal, on earth, in accord-
ance with the law of karma—i.e. those who have led good
lives are reincarnated as superior beings, those who have
led bad lives as inferior beings. Those who continue to live
good lives eventually reach ‘liberation’ and escape the
round of rebirth. For Hindus *reincarnation is reincarna-
tion of a soul; for Buddhists, some sort of continuity
of experience. ‘Liberation’ is variously interpreted as
merging into the one infinite consciousness, or as mere
nothingness.
Those who hold that *personal identity is constituted
by sameness of body (or brain) can believe it coherent to
suppose that humans survive death only if human bodies

are reformed with largely the same matter (e.g. around
the original bones in the cemetery). That cannot always
happen, for bodies may be destroyed beyond the possibil-
ity of reassembly. Those who believe in life after death for
all (on earth or elsewhere) must hold a non-bodily criter-
ion of personal identity—as consisting in the continued
existence of an immaterial soul, or perhaps in mere con-
tinuity of psychological states; even if resurrected persons
have bodies (old or new), sameness of body cannot be
what constitutes sameness of persons. r.g.s.
*atheism and agnosticism.
J. Hick, Death and Eternal Life (London, 1976).
imperialism. The concept of imperialism is very general,
involving the oppression or *exploitation of weak and
impoverished countries by powerful ones, though for
most of its intellectual career ‘imperialism’ was a term of
approbation. The word goes back to the Roman Empire,
recent examples being the British Empire, which saw its
heyday at the end of the nineteenth century, the recently
deceased Russian Empire, and the contemporary Ameri-
can Empire, known as the New World Order. This latter
involves a net transfer of resources from the under-
developed countries to the developed ones, a process
orchestrated by such American-dominated institutions as
the International Monetary Fund.
Modern ideas of imperialism owe much to Lenin, who
characterized the phenomenon as comprising emphasis
on the export of capital, increasingly centralized produc-
tion and distribution, merging of banking and industrial
capital, and division of the world into spheres of influence

between capitalist powers who then fight each other over
their share of the spoils as, for example, in the First World
War. In more recent decades, Lenin’s ideas tend to have
been replaced by views, going back to Kautsky, which
look at imperialism as the relation between developed and
underdeveloped countries and argue that conflict
between developed countries is disappearing. These
views are best exemplified in the trend known as depend-
ency theory, which maintains that exploitation occurs
through trade between the centre and the periphery of the
world economy which embodies an unequal exchange
with a long-run tendency for the terms of trade for Third
World countries to worsen.
Explanations of imperialism are as varied as theories of
human nature; and several versions of imperialism,
including Lenin’s and dependency theory, found it diffi-
cult to incorporate recent phenomena such as the newly
industrializing countries. But it remained the concept
around which thinking about international relations in the
twentieth century revolved. d.m
cl.
*international relations, philosophy of.
Anthony Brewer, Marxist Theories of Imperialism: A Critical Survey
(London, 1980).
George Lichtheim, Imperialism (London, 1971).
implication. Ordinary uses of ‘implication’ are varied and
often equivocal. Two important uses for logic are:
1. Implication understood as a relation between a set of
premisses and a conclusion deducible from or a
logical consequence of those premisses.

2. Implication understood as the relation between
antecedent and consequent of a true *conditional
proposition.
implication 423
On use (2) the truth of ‘(P ⊃ Q)’ of the propo-sitional cal-
culus is read as ‘P materially implies Q’ or ‘P implies Q’.
Given the weak conditions for the truth of (P
⊃ Q) and the
attendant ‘paradoxes of material implication’, alternative
systems have been devised with stronger conditionals.
C. I. Lewis’s systems of *strict implication introduce the
symbol ‘
—
3
’, where the truth of ‘(P —
3
Q)’ is read as ‘P
strictly implies Q’. (P
—
3
Q) is equivalent to ٗ (P ⊃ Q),
where ‘
ٗ’ is a necessity operator. Other systems with
stronger conditionals are those of Carnap’s system of
L-implication, and more recent formal systems of entail-
ment. A motivation for such efforts is to bring the condi-
tional more into line either with (1) or with those uses in
(2) which suppose further connections in meaning
between antecedent and consequent. r.b.m.
*truth-function.

A. Anderson and N. Belnap, Entailment, i (Princeton, NJ, 1975).
C. Lewis and C. Langford, Symbolic Logic (New York, 1959).
implicature. Meaning that is supplementary or contrary
to that logically entailed by a sentence. For example, in
‘What did you think of his argument?’, ‘Impeccable schol-
arship’. The discovery of conversational and conventional
implicature by Paul Grice in the 1960s cast doubt on the
solution or dissolution of philosophical problems by *lin-
guistic philosophy, because it suggests meaning cannot be
wholly and appropriately displayed by *conceptual analy-
sis. If you ask someone, ‘Could you direct me to the
library?’, and they smugly answer only ‘Yes’, it is appropri-
ate to ask them if they have heard of conversational
implicature. s.p.
Paul Grice, Studies in the Ways of Words (Cambridge, Mass., 1989).
impredicative definition. A definition is impredicative if
it refers to a collection which contains the object to be
defined. For example, the ‘least upper bound’ of a set is
defined to be ‘the smallest among the upper bounds’ of the
set; and the ‘Russell set’ is the set of all sets that don’t con-
tain themselves. The former is a common definition, usu-
ally uncontested. The latter leads to Russell’s paradox. If
one thinks of definitions as somehow creating or
constructing the defined objects, then impredicative
definitions are circular. s.s.
*vicious circle; types, theory of; reducibility, axiom of;
mathematics, history of the philosophy of.
Allen Hazen, ‘Predicative Logics’, in D. Gabbay and F. Guenth-
ner (eds.), Handbook of Philosophical Logic, i, (Dordrecht, 1983).
incommensurability. Within philosophy of science, the-

ories which, in a radical sense, cannot be compared are
often said to be incommensurable, a term first given wide
currency by Kuhn. Scientific revolutions, which involve
wholesale discarding of one set of theories in favour of
another, are thought typically to produce such radical
shifts of meaning that the concepts employed in the the-
ories propounded after revolution simply cannot be
expressed in terms of the concepts of pre-revolutionary
theory. Commitment to such an incommensurability
thesis is liable to lead on to a strong *relativism or anti-
rationalism. But the very intelligibility of this thesis is
questionable. Genuinely incommensurable theories can-
not be judged incompatible; but then why, and how, do
scientific revolutions result in discarding theories—why
not just preserve both the earlier theories and the later the-
ories incommensurable with them? j.l.
T. S. Kuhn, The Structure of Scientific Revolutions, 2nd edn.
(Chicago, 1970).
incommensurability, moral. The idea of the incommen-
surability of scientific paradigms has been borrowed by
moral philosophers to express the idea that, because there
is a plurality of values, moral dilemmas may sometimes be
irresolvable. The idea is best illuminated by its converse;
*utilitarianism is the classic example of a moral theory
which supposes all values to be ultimately reducible to the
one value of ‘happiness’, so that in any situation the vari-
ous possible courses of action can all be weighed against
one another by considering how much happiness each
will produce. If, however, there is not just one ultimate
value, then in some cases it may be impossible to weigh

the competing claims of, say, *‘justice’ against those of
*‘friendship’, or the claims of ‘honesty’ against those of
*‘utility’. If these values are incommensurable, it may
then be an illusion to suppose that there is always such a
thing as ‘the right thing to do’. Indeed, there may be situ-
ations of ‘moral tragedy’ where there is no action open to
us which would not be morally wrong. r.j.n.
R. Chang (ed.), Incommensurability, Incomparability, and Practical
Reason (Cambridge, Mass., 1997).
Christopher W. Gowans (ed.), Moral Dilemmas (Oxford, 1987).
incompatibilism: see compatibilism.
incompleteness. A logical system is complete just in case
there is no truth of the system that it is incapable of prov-
ing. By a theorem of Kurt Gödel in 1931, no formalization
of ordinary arithmetic is complete. Either arithmetic is
inconsistent or there is at least one of its truths which
arithmetic cannot prove. More technically, Gödel demon-
strated that any consistent first-order theory of arithmetic,
if equipped with an effective procedure for recognizing its
own proofs, is incomplete. Alternatively, let T be a first-
order formalization of arithmetic and P be the predicate ‘is
a proof of T’. If the class of objects satisfying P is a decid-
able class, then T is incomplete.
The incompleteness theorem came as a nasty shock to
mathematicians influenced by Hilbert’s programme, for
whom mathematical truth consisted in demonstrability.
j.w.
*completeness; Gödel’s theorem.
Ernest Nagel and James R. Newman, Gödel’s Proof (New York,
1958).

incomplete symbol. A symbol that is a constituent
of meaningful sentences but that has no meaning in
424 implication
isolation. An incomplete symbol is amenable only to a
contextual definition, not an explicit one. The idea of
incomplete symbol gained prominence primarily through
Russell, who used it to express distinctive views in logic
and metaphysics. Thus Russell held that the theoretical
terms of physics (e.g. ‘particle’) are incomplete symbols,
meaning thereby that these terms do not mean or refer to
anything in isolation, but sentences containing theoretical
terms can be analysed using only non-theoretical vocabu-
lary. Observe that the notion of incomplete symbol is
quite different from Frege’s notion of *unsaturated
expression. An extended discussion of incomplete
symbols and their applications in logic is contained in
chapter 3 of A. N. Whitehead and B. Russell, Principia
Mathematica, i (Cambridge, 1927). a.gup.
*descriptions.
incongruent counterparts. Two hands may be identical
except that one is left, the other right. An object capable of
having an incongruent counterpart (whether or not one
actually exists) is called an enantiomorph. This phenom-
enon was thought by Kant to show that space exists inde-
pendently and is not merely a matter of relations between
things. In terms of the spatial relations—distances and
angles—between their parts, the two hands are indistin-
guishable. Since God might have created nothing but a
single hand, which would still have been left or right, the
spatial relations of the hands to each other or to other

things is irrelevant. The difference between the hands
must then consist, Kant argued, in a relation to *space
itself, though it is not clear how space is supposed to turn
the explanatory trick. m.c.
G. Nerlich, The Shape of Space (Cambridge, 1976).
inconsistent triad. A set of three propositions that cannot
all be true together. For example, ‘She was an orphan; Tim
outlived her; Tim was her father’. Often it will be implied
that all the subsets of the triad—the units and pairs within
it—are consistent. Inconsistent sets can be of any size, and
the triads do not deserve special attention. c.a.k.
incontinence: see weakness of will.
incorrigibility. The property of not being open to correc-
tion. One philosophical response to epistemological
*scepticism is to argue for the existence of a class of propos-
itions which have the property. They would be propos-
itions about which we could not be mistaken. Such
incorrigible statements are taken by some philosophers to
be a sure basis for our entire knowledge of the world.
They are said to include assertions of present sensations
and appearances, such as ‘I am in pain’ and ‘It looks green
to me’. It can be argued, however, that such statements
may be false even if the speaker is sincere, through an
error of misidentification or expression. w.e.a.
*certainty; given, the.
William Alston, Epistemic Justification (Ithaca, NY, 1989).
independence, logical. Let s be a sentence and let T be a
set of sentences in a formal language. Informally, s is
independent ofT if Tdoes not determine the truth-value of s.
In other words, s is independent of Tifs is not a logical con-

sequence of T and the negation of s is not a logical conse-
quence of T (some authors omit the last clause). In
particular, s is deductively independent of T if neither s nor
the negation of s can be deduced from T, and s is semanti-
cally independent of T if there is an interpretation of the
language in which every member of T is true and s is true,
and also there is an interpretation of the language in which
every member of T is true and s is false. In a logical system
consisting of axioms and rules of inference, an axiom is
‘independent’ if neither it nor its negation can be deduced
from the other axioms by the rules. s.s.
Elliot Mendelson, Introduction to Mathematical Logic, 3rd edn.
(Princeton, NJ, 1987).
indeterminacy in law. It is a view widely held among
legal philosophers that, when competent lawyers dispute
about the answer to some difficult question of *law, there
is generally no single right answer—the law does not in
fact resolve the issue either way, but leaves it open until it
is resolved either by new legislation or by the decision of a
judge exercising a discretion to make new law.
Such was the view of the advocates of *legal positivism,
including John Austin and H. L. A. Hart, who said that
there is no right answer in controversial cases because law
is only what past authoritative statements or conventions
have declared it to be, and in such cases convention or past
decisions have not settled the issue either way. It is also the
view of more radical legal philosophers, such as the Ameri-
can legal realists and critical legal scholars, who argue that
there is never a right answer to a legal question because
past legal doctrine is not sufficiently consistent to yield a

single result. But judges, at least in Anglo-American law,
never refuse to decide a legal dispute on the ground that
the law is indeterminate, and rarely claim to be exercising
a discretion to create new law and apply it retroactively.
Even in very controversial cases they give answers to the
questions of law in dispute which they claim to be, at least
in their opinion, the right ones. Either the judges are lying
to the public, or they are themselves under an illusion, or
the no-right-answer thesis, in spite of its popularity, is
wrong.
Arguments for the no-right-answer thesis are often cor-
rupted by a failure to distinguish it from other, more plau-
sible, claims. Suppose it is controversial among lawyers,
for example, whether someone injured in a particular kind
of accident has a legal right to be compensated for his emo-
tional as well as his physical injuries. We must take care to
distinguish among the following propositions: (1) The
legal case for such a right is, in these circumstances, and
all things considered, stronger than the case against it.
(2) The case against it is, all things considered, stronger.
(3) Competent lawyers disagree about which case is
stronger. (4) There are strong arguments on both sides
of the issue, and neither view is unreasonable. (5) It is
indeterminacy in law 425
uncertain which is stronger. (6) It is indeterminate which
is stronger: the only ‘right’ answer is that there is no right
answer.
Proposition 6—the no-right-answer claim—must of
course be distinguished from proposition 3: it does not fol-
low from the fact that lawyers disagree about a controver-

sial case that neither side has the stronger arguments. Nor,
obviously, is 6 the same as either 4 or 5: it does not follow
from anyone’s uncertainty about which case is stronger
that neither is. Once these distinctions are made, it is
unclear what kind of legal argument could show that
proposition 6, rather than one or some combination of the
other five choices, is the most accurate description of the
law governing recovery for emotional damage. If we
define law as the legal positivists did, of course, then
proposition 6 might be true in virtue of that definition. But
that would be circular reasoning: we should define law to
match the practices of lawyers and judges, not redescribe
those practices to suit some invented definition of law.
Legal philosophers sometimes make the mistake of
thinking that in such a case proposition 6 is true by default:
that is, when neither the case for the plaintiff nor for the
case for the defendant is obviously much stronger than the
other, and reasonable arguments can be made on both
sides, it just follows that there is no right answer in the
case. But that assumption neglects the difference between
6 on the one hand and 3, 4, and 5 on the other. Proposition
6 makes a very strong legal claim. It claims not just that we
have no decisive reason to take one side or the other, and
may never have one, but that, no matter how hard we
look and think, we will not find any consideration or argu-
ment that would make the case on one side even margin-
ally stronger than the case on the other. That is obviously
a very ambitious claim, and, given the very wide range of
considerations that lawyers regard as pertinent to legal
argument, it would seem foolhardy to make it, at least in

advance of the most painstaking research and reflection,
about any particular legal controversy, let alone about all
controversial cases taken together.
In fact, any lawyer or judge or law teacher or law stu-
dent is likely to form an opinion about which side has the
stronger legal argument in any particular case he or she
studies, even though in difficult cases that opinion may be
hesitant or unstable, and is very likely to be controversial.
In practice, that is, almost no one accepts the no-right-
answer thesis, even legal philosophers who are most vig-
orous in its theoretical support. The theoretical popularity
of the thesis can be traced, I suggest, to two widespread
assumptions. The first is the sound assumption that moral
considerations are among the considerations that prop-
erly figure in controversies about what the law is. The sec-
ond is the dubious view that there are often no right
answers to moral disputes. r.d.
*law and morals; moral scepticism.
John Austin, The Province of Jurisprudence Determined, ed. and intro.
H. L. A. Hart (London, 1954).
Ronald Dworkin, A Matter of Principle (Cambridge, Mass., 1985),
ch. 10.
H. L. A. Hart, The Concept of Law (Oxford, 1961).
John Mackie, ‘The Third Theory of Law’, Philosophy and Public
Affairs (1977).
indeterminacy of meaning. A thesis advanced by W. V.
Quine on the basis of his famous argument for the inde-
terminacy of translation. Meaning is what we aim to pre-
serve in translating between languages, and if there is no
fact of the matter as to which of two or more incompatible

translations of a speaker’s words is correct, there is no fact
of the matter as to what precisely the words mean. The
indeterminacy of meaning is taken to be a consequence of
the indeterminacy of translation. Quine’s argument for
the latter assumes that the only facts that could settle
which of two rival translations is correct are facts about
the speaker’s behaviour and circumstances: facts on show
to other speakers. When a speaker of an unknown lan-
guage utters the word ‘gavagai’ in the presence of a rabbit,
there is nothing to indicate whether his utterance is to be
translated as ‘rabbit’, or perhaps as ‘undetached rabbit
part’. Since there is no other evidence to decide the issue,
there is nothing to chose between the two translations.
Quine concludes that translation is indeterminate, and
therefore meaning is indeterminate.
Chomsky has criticized Quine’s argument for assuming
that only behaviourist evidence can settle questions about
the nature of linguistic reality. Others have pointed out
that while we can deploy Quine’s argument from the
third-person perspective to a group of speakers we
observe, the conclusion makes no sense from the first-
person perspective. For how can we understand the two
rival hypothesis about the meaning of the word ‘rabbit’
unless we can mean one thing by ‘rabbit’ when considering
one hypothesis and another thing by ‘rabbit’ when consider-
ing the other hypothesis. And if we can understand each of
these hypotheses, how can we accept a conclusion that is
supposed to show that we cannot succeed in determinately
meaning one thing or another by ‘rabbit’? b.c.s.
W. V. Quine, Word and Object (Cambridge, Mass., 1960), ch. 2.

indeterminacy of translation: see translation, indetermin-
acy of.
indeterminism. A view incompatible with *determinism.
Since there are several versions of determinism and many
kinds of incompatibility, there are many varieties of inde-
terminism. This article uses a definition of determinism
cast in terms of causal sufficiency. (*Causality; *necessary
and sufficient conditions.)
When one state or event is causally sufficient for the
occurrence or obtaining of another, it determines it. It is
causally impossible, when one state of affairs determines
another, for the first but not the second to obtain. The
thesis of determinism includes the view that everything
that happens or obtains is determined by something earlier.
By itself, this does not ensure that any particular event is
determined by a state of affairs that obtained a week (or
day, or hour) earlier. As Łukasiewicz points out, an
426 indeterminacy in law
infinite series of intervals, ordered by temporal priority,
may have a finite total temporal extent. Consider, for
example, an infinite series of intervals in which the final
interval is twenty minutes long, and each interval is twice
as long as its predecessor. The thesis of determinism
requires some further specification such as that everything
is determined by something not merely earlier, but earlier
by a certain time increment, such as one second. This does
support what determinists generally assume, namely that
for any event e at time t and any earlier time t–1, some
conditions obtaining earlier than time t–1 determine the
event e. Support for the simpler principle that the con-

ditions determining e are not just earlier than but exactly
at time t–1 requires principles beyond the scope of this
article. According to determinism, the state of the world
long before you were born, a world you never made,
determines everything that happens.
In one very weak version of indeterminism, its incom-
patibility with determinism is simple *contradiction.
Determinism is false; its negation is true. This view is true
so long as somewhere in the universe some occurrence
violates the thesis of determinism.
By way of maximum contrast, an extremely strong ver-
sion of indeterminism is strongly *contrary rather than
merely contradictory to determinism. The world at any
time and in all its aspects is totally independent of its state
at any earlier time. Successive events are never causally
related in any way. This form of indeterminism appears to
be incompatible with the existence of successive events.
Between these extremely strong and weak versions of
indeterminism, views of intermediate strength hold that
there are many events, widely scattered in space and time,
that violate determinism. These events need not be totally
independent of earlier states of the world. Determination
and indetermination admit of degrees. The state of the
world ten minutes ago may, for example, be causally suffi-
cient for your now being somewhere in the general vicin-
ity without exactly determining your current location. If
something determines that a person acts in a certain gen-
eral way (which thereby precludes acting in many other
ways), such as either to walk home on Divinity Avenue or
to walk home on Oxford Street, it need not thereby deter-

mine which route the person chooses. Intermediate var-
ieties of indeterminism do not imply that our behaviour is
‘of an erratic and jerking phantom, without any rhyme or
reason at all’. A person with good reason for walking
home may have neither good reason nor prior determin-
ation for choosing one route over another.
Current science has no deterministic explanations for
the emission of alpha particles by radio-active isotopes and
some other very small-scale phenomena. One of the
philosophical problems of *physics is to examine the claim
that deterministic explanations of these phenomena are
impossible without a radical revision of physics.
It is hard to know, if the world does manifest a degree of
indeterminism, how much actions and occurrences that
matter to us are affected by undetermined micro-events
that seem insignificant in themselves. It is possible that
they are affected a great deal. When sensors, switches, and
amplifiers are hooked up in the right way, for example,
indeterministic emissions of a few alpha particles can
decide the location of the 2008 Olympic Games. Within
our brains, perhaps there is often a similar amplification of
indeterminacy. d.h.s.
*chaos theory.
G. E. M. Anscombe, ‘Causality and Determination’, in E. Sosa
(ed.), Causation and Conditionals (Oxford, 1975).
C. D. Broad, ‘Determinism, Indeterminism, and Libertarianism’,
in Ethics and the History of Philosophy (London, 1952).
John Earman, A Primer on Determinism (Dordrecht, 1986).
Ted Honderich, A Theory of Determinism (Oxford, 1988).
R. Kane (ed.), The Oxford Handbook of Free Will (New York, 2001).

Jan Łukasiewicz, ‘On Determinism’, in Storrs McCall (ed.), Polish
Logic 1920–1939 (Oxford, 1967).
indexicals. The pronouns ‘I’, ‘here’, ‘now’, ‘this’, and
related expressions like ‘today’, ‘my grandmother’, ‘your
house’, etc. are known by philosophers of language as
‘indexicals’. The term derives from C. S. Peirce; indexicals
are sometimes called ‘demonstratives’ or ‘token-reflexives’.
(*Logically proper names.) These expressions seem to fall
into the semantic category of singular terms or referring
expressions—i.e. terms whose function in a language is to
pick out a particular thing. But where indexicals seem to
differ from other apparent singular terms, like names and
descriptions, is that they pick out different objects or
places or times in different contexts of utterance. So your
utterance of ‘I’m hungry’ picks out you, while my utter-
ance of the same sentence picks out me.
One way of appreciating the philosophical interest of
indexicals is to look at them in the light of Frege’s influen-
tial theory of *sense and reference. For Frege, the sense of
a word determines its reference. If two words have the
same sense, they have the same reference; if ‘oculist’ and
‘eye-doctor’ have the same sense, they have the same ref-
erence—they refer to the same entity. Similarly, if two
words have different references, they have different
senses; if ‘the Pope in Rome’ and ‘the Pope in Avignon’
refer to different things, they must have different senses.
How can this theory apply to indexicals? The trouble is
that if the sense of ‘I’ determines its reference, then my
utterance of ‘I’ has a different sense from yours. But surely
our uses of these terms have something semantic in com-

mon, something it is natural to call their common mean-
ing? Likewise with ‘here’ and ‘now’; the common
meaning of all tokens of these types is something like ‘the
place of this utterance’ and ‘the time of this utterance’. But
the common meaning cannot be the sense of these terms,
since the meaning determines different references in dif-
ferent contexts.
Non-Fregeans (e.g. David Kaplan and John Perry) have
therefore distinguished two components of the meaning
of a sentence containing an indexical: (i) The first is the
*‘proposition’ expressed by the sentence. This is thought
of in the ‘Russellian’ style as being composed out of
objects and properties. Thus my utterance of ‘I’m hungry’
indexicals 427
expresses a different proposition from yours, but
expresses the same proposition as your utterance of
‘You’re hungry’, addressed to me. (ii) The second compon-
ent is the common meaning of the indexical type-
expression, which Perry calls the ‘role’ of the indexical and
Kaplan calls its ‘character’. The role of an indexical sen-
tence is standardly thought of as a function taking the con-
text of utterance into the proposition expressed by the
utterance. Thus my utterance of ‘I’m hungry’ has the
same role or character as your utterance of that sentence,
but has a different role from that of utterances of ‘You’re
hungry’. Neither proposition expressed nor role or char-
acter corresponds to Frege’s notion of sense, so these
philosophers conclude that Frege’s theory breaks down at
this point.
Fregeans (e.g. Gareth Evans) have responded by claim-

ing that senses can be, as it were, context-sensitive: index-
icals express ‘ways of thinking’ that are tied to particular
objects, times, and places (e.g. my uses of ‘I’ all express the
particular way I have of thinking about myself ). Essential
to Evans’s claim is the idea that, in order for an indexical to
have sense, this sense does not have to be expressible by a
definite description uniquely true of the reference of the
indexical.
The issue is important because many philosophers
have plausibly argued that indexical thought is essential to
our thinking about time, space, the self, and material
objects. In particular, indexical thought seems essential to
agency: my getting off the bus at Trafalgar Square can
only be fully explained by attributing to me the belief that
Trafalgar Square is here, which is not equivalent in explan-
atory power to any merely descriptive belief. t.c.
Gareth Evans, ‘Understanding Demonstratives’, in Palle Your-
grau (ed.), Demonstratives (Oxford, 1990).
Gottlob Frege, ‘Thoughts’, in Collected Papers (Oxford, 1984).
David Kaplan, ‘Demonstratives’, in J. Almog et al. (eds.), Themes
from Kaplan (Oxford, 1991).
John Perry, The Problem of the Essential Indexical and other Essays,
new edn. (Stanford, Calif., 2000).
Indian philosophy. The beginnings of philosophical
speculation in India can be traced back to the ancient
body of oral literature called Veda. This was compiled
and divided into R
.
g-Veda, Sa¯ma-Veda, Yajur-Veda,
and Atharva-Veda. Apart from hymns to nature-gods and

recipes for rituals each Veda contained cosmological,
moral, and mystical reflections which were later collected
into *Upanishads.
The eternally existent Vedic wisdom was believed to
have been revealed to clear-minded sages who saw the
truth from different points of view. Hence, the Sanskrit
term for philosophy also stands for seeing. ‘Seers’ of the
R
.
g-Vedic hymns, at least as early as 1500 bc, raise the ques-
tion ‘What did the universe come from?’ and record an
intellectual tussle between ‘the existent’ and ‘the non-
existent’ as answers to it, with the agnostic hint that even
gods, being part of the universe, would not know the right
answer. Notice, also, the self-referring reflections on
thought, life, and language in the opening verse of an
ancient Upanishad: ‘Propelled by what does a directed
mind fall upon its objects? By whom was life first set in
motion? Urged by whom are these words being spoken?
Which God harnesses the eyes and the ears?’ The answer
given shows that the enterprise was not theology but a
phenomenological *ontology of ubiquitous conscious-
ness; no object ‘that is worshipped as a this’ could be the
subjective spring of action, thought, and speech, according
to these Vedic proponents of transcendental subjectivity.
Systematic philosophies grew up gradually through
attempts to understand, rationalize, and react against the
Vedic tenets. In spite of mystics and sceptics trying to
prove the futility of metaphysical argumentation and the
question-begging nature of all ‘proofs’, many major

schools of philosophy—each with its own metaphysics,
epistemology, and life-ideal—flourished in India, not in
successive waves but side by side until their growth was
arrested by colonial education which, however, did pro-
mote their preservation as intellectual antiques.
The schools are traditionally classified according to a
dichotomy between those who accept the authority of the
revealed wisdom of the Vedas and those who do not. Into
the class of those who affirm the Vedas fall the following
six systems: (1) Sa¯m
.
khya (distinctionists), (2) Yoga (mind-
stilling theorists), (3) Nya¯ya (logicians), (4) Vais´es
.
ika
(atomists), (5) Mı¯ma¯m
.
sa¯ (ritualists), and (6) Veda¯nta
(hermeneutists). Veda¯nta, in turn, divides into several
schools, including (a) pure monists, (b) qualified monists,
and (c) dualists. Another Vedic school, the ‘panlinguistic
monists’, was developed by the philosophers of grammar,
who identified ultimate reality with the eternal Verbum
manifesting itself as both words and the world.
Into the class of those who deny the Vedas fall (1) the
Ca¯rva¯ka materialists, (2) the *Jaina alternativists, and the
four schools of *Buddhist philosophy, namely (3)
Vaibha¯s
.
ika direct realism, (4) Sautra¯ntika representative

realism, (5) Yoga¯ca¯ra subjective idealism, and (6)
Ma¯dhyamika voidism. Besides these there are the earthy
but subtle broadly monistic power-and-process philoso-
phies of (7) *Tantra¯, and finally (8) Shaivism. The last-
named tradition perhaps had pre-Vedic roots in the
conception of Shiva as the Lord of fettered animals, that is,
us. According to Shaivism, we can only be freed and saved
by worshipping Lord Shiva with the utmost love.
In ontology these schools came up with competing def-
initions of reality. In Sautra¯ntika Buddhism to be real is to
be causally efficacious. In non-dualistic Veda¯nta to be real
is never to be negated, spatially, temporally, or otherwise.
For the Nya¯ya– Vais´es
.
ika, reality consists in having a
determinate nature unique to oneself and hence is being
knowable and nameable. These assumptions result in
diverse metaphysics. Reality must be changeful and
impermanent for the Buddhist, whereas for the non-
dualist Veda¯nta only the changeless and eternal is real. Since
all the anti-Vedic schools, and Sa¯m
.
khya and Mı¯ma¯m
.
sa¯
among the Vedic schools, were openly atheistic, the exist-
ence of God was a standard topic of rational disputation.
428 indexicals
confucius was a contemporary of the early Greek
philosophers, but the school of philosophy he inspired is

still prominent in Chinese thought today.
nishida kitaro
-
, the leading figure in twentieth-century
Japanese philosophy, developed a systematic philosophy
of ‘pure experience’, drawing together Zen Buddhism
and Western thought.
rabindranath tagore: poet and philosopher, champion
of Bengali culture, humanist and internationalist.
sarvepalli radhakrishnan was a rare example of a
philosopher-ruler. President of India and interpreter of
the Indian and European philosophical traditions to each
other.
eastern philosophy