The Oxford Companion to Philosophy Part 14 pdf

reconciled with the causal theory of knowledge. (b)
*Vagueness. A brief but provocative paper by Gareth Evans
(‘Can There Be Vague Objects?’), which appeared in 1978,
inspired a considerable amount of work on the question
whether vagueness was simply a feature of language or
knowledge or also of the world itself. There has been a
flowering of work on traditional ontological issues, con-
cerning *causality, *identity, *modality, *time, *proper-
ties, and *particulars.
Ethics. Three important developments should be men-
tioned. (a) The work of Bernard Williams, Alasdair Mac-
Intyre (based in the USA since 1972), and Derek Parfit has
highlighted the central place of the self, and ideas of the
self, in ethics. Parfit in particular has questioned our ordin-
ary view of the self as retaining its numerical identity
through time, and shown how his alternative view breaks
down the boundaries between persons and so undermines
*egoism. (b) John Mackie’s influential critique of moral
*objectivism (Ethics: Inventing Right and Wrong, published
in 1977) has provoked two kinds of critical response. One
is a defence of objectivism, or realism, championed by
Jonathan Dancy, John McDowell (based in the USA since
1986), and David McNaughton. Although realism has its
American proponents, the British version rejects *ethical
naturalism (the view that moral properties are reducible
to non-moral properties). The other response, offered by
Simon Blackburn is ‘quasi-realism’ or ‘projectivism’,
which takes ethical values to be real, though mind-
dependent, qualities. (c) British moral philosophers have
also played in influential role in the revival of interest in
two central ideas in ethics: *consequentialism and the

*virtues. Here we should name, on the one hand, R. M.
Hare (arguably the father of contemporary moral theory
(d. 2002)), and on the other, Elizabeth Anscombe
(d. 2001), and Phillipa Foot.
Philosophy of science. Perhaps the most striking develop-
ment in philosophy of science in recent years has been the
detailed engagement with the philosophical and meta-
physical implications of quantum physics, pioneered by
Michael Redhead and Nancy Cartwright (based in the UK
since 1991), and pursued notably in Oxford, London,
Cambridge, and Leeds.
Engagement with continental philosophy. *Continental phil-
osophy is, by definition, not British in its origins, aims,
and methods. Nevertheless, a significant feature of the
national scene in recent years has been the increasing
interest and specialization in continental philosophy
within British departments. Traditionally, analytic philoso-
phy has been hostile to the continental style, culminating
in the publicly voiced objections to the award in 1992 of an
honorary degree to Jacques Derrida by Cambridge Uni-
versity. Recent work, however, has attempted something
of a rapprochement.
Philosophers and public debate. Although much philosoph-
ical work is conducted within academic institutions,
prominent philosophers have from time to time been
appointed to leading roles on Government committees,
especially on ethical matters. Examples of this contribu-
tion of philosophers to the formulation of policy include
Bernard Williams’s chairing of the Committee on Obscen-
ity and Film Censorship, Mary Warnock’s chairing of the

Committee of Inquiry into Human Fertilization, which
produced the much discussed Warnock Report in 1984,
and Anthony O’Hear’s work as a government adviser on
education. A recent high-profile discussion was Onora
O’Neill’s 2002 BBC Reith Lectures, A Question of Trust, on
accountability, deception, and freedom of the press.
Political constraints. The 1980s was a time of crisis for phil-
osophy in Britain, in economic, rather than intellectual,
terms. University cut-backs saw the freezing of posts and
the closure of some departments. The overall situation
improved during the 1990s, and with the increasing popu-
larity of philosophy as a university subject, some depart-
ments have actually expanded. However, one significant
determinant of the fortunes of individual departments has
been the five-yearly national Research Assessment Exer-
cise, instituted in 1991, which rates quality of research out-
put, with corresponding implications for the research
funding allocation to universities. Partly, but not wholly,
as a result of this, there has been a significant increase in
productivity (as measured by publications), and research
activity is now widespread rather than concentrated in a
few dominant departments. r.le p.
*Cambridge philosophy; English philosophy; London
philosophy; Oxford philosophy; Scottish philosophy;
Wittgensteinians.
Julian Baggini and Jeremy Stangroom (eds.), New British Philoso-
phy: The Interviews (London, 2002).
Margaret Little, ‘Recent Work on Moral Realism II: Non-
Naturalism’, Philosophical Books (1995).
Bryan Magee, Talking Philosophy: Dialogues with Fifteen Leading

Philosophers (Oxford, 2001).
Andrew Pyle, Key Philosophers in Conversation: The Cogito Inter-
views (London, 1999).
G. J. Warnock, English Philosophy since 1900 (Oxford, 1969).
Broad, Charles Dunbar (1887–1971). Judicious and witty
Cambridge philosopher, author of many thorough works
on science, mind, ethics, and psychical research. Broad’s
typical method was an elaborately exhaustive classifica-
tion of all possible answers to some carefully clarified
question, a judicious weighing-up of the pros and cons of
each, and a tentative suggestion for the most plausible. He
believed that in *perception we are presented with ‘sensa’,
whose occurrence is the effect of events in the brain in
virtue of a peculiar kind of causation, that these sensa are
not literally spatio-temporal parts of the perceived objects
but provide literally true information about their spatio-
temporal character and relations, and that physical objects
must also have other characteristics which provide their
qualitative filling. He developed a notion of absolute
becoming to explain the greater reality of past than future
and postulated a
ψ component which combined with
the brain to produce consciousness. He judged the
110 British philosophy today
empirical evidence on our survival of *death finely
balanced. t.l.s.s.
C. D. Broad, An Examination of McTaggart’s Philosophy (Cam-
bridge, 1933, 1938).
P. Schilpp, (ed.), The Philosophy of C. D. Broad (La Salle,Ill., 1959).
Brouwer, L. E. J. (1881–1966). Dutch mathematician

known to philosophers as the founder of *intuitionism as
a philosophy of mathematics. This owes something to the
philosophy of Kant, but more to the paradoxes and con-
tradictions that beset logic and mathematics in the early
1900s. Brouwer thought that these arose because familiar
principles of reasoning were being blindly applied to an
unsuitable subject-matter, i.e. to infinite totalities. In his
view only a ‘potential’ infinity can be understood, and
consequently a statement about all numbers can be
counted as true only if we have a method of proving it for
any arbitrary number. Since there are many statements
about all numbers which we can neither prove nor dis-
prove, Brouwer inferred that the law of excluded middle
does not hold in mathematics. d.b.
*intuitionist logic; constructivism.
A. Heyting, Intuitionism, 3rd edn. (Amsterdam, 1971).
P. Mancosu (ed.), From Hilbert to Brouwer: The Debate on the Foun-
dations of Mathematics in the 1920s (Oxford, 1988).
Brownson, Orestes Augustus (1803–76). New England
social critic, political advocate, religious controversialist,
philosopher, and journalist, Brownson was for a time an
effective advocate of *New England Transcendentalism.
He was perhaps the most socially astute transcendentalist,
arguing in ‘The Laboring Classes’ (published in his Boston
Quarterly Review in 1840) that the wage system exploited
the many in favour of the few and that reform could result
only from changing the system and not simply from indi-
vidual moral improvement (the standard transcendental-
ist solution to social problems). His most radical reform
proposal was for the abolition of hereditary property: at

death one’s property reverts to the state, which is to dis-
tribute it fairly. His conversion in 1844 to Roman Catholi-
cism caused dismay among his former transcendentalist
compatriots; as a Catholic Brownson was as creative,
outspoken, and controversial as he had been as a
transcendentalist. c.c.
Arthur M. Schlesinger Jr., Orestes A. Brownson: A Pilgrim’s Progress
(Boston, 1939).
Bruno, Giordano (1548–1600). Italian philosopher who
sought to overthrow Aristotelianism and replace it with
his own eclectic and often self-contradictory philosophical
system. Combining the astronomy of Copernicus with
the metaphysics of Nicholas of Cusa and the atomism of
Lucretius, he believed in an infinite universe which con-
tained an infinite number of inhabited worlds, moving
within an uncentred space and composed of minimal par-
ticles. He rejected *hylomorphism in favour of a *monism
in which the universal, infinite, and eternal substance was
identical with both God and nature. Having been excom-
municated by the Catholic, Lutheran, and Calvinist
Churches on account of his unconventional religious
views and undisciplined behaviour, he was finally burned
at the stake by the Inquisition. He died a heretic, but in the
nineteenth century he was transformed into a martyr to
free philosophical inquiry. j.a.k.
*persecution of philosophers.
P. Michel, The Cosmology of Giordano Bruno (Paris, 1973).
Brunschvicg, Léon (1869–1944). French idealist philoso-
pher who provides a sustained neo-Hegelian answer to
the Kantian question: How is knowledge possible? Reject-

ing the Kantian project of a transcendental deduction of
the categories, Brunschvicg construes philosophy as the
historical reflection of consciousness on consciousness.
This reveals ‘the progress of consciousness’ (le progrès de la
conscience) typified by the emergence of the natural sci-
ences, the findings of which, Brunschvicg argues, are con-
sistent with his own idealism.
Brunschvicg is also known for his scholarly treatments
of Descartes and Pascal and for the extension of his histor-
ical idealism to the ethics of conscience. s.p.
*idealism; Hegelianism.
Leon Brunschvicg, La Philosophie de Léon Brunschvicg (Paris, 1949).
—— Le Progrès de la conscience dans la philosophie occidentale, 2 vols.
(Paris, 1927).
brute fact. Two related uses of this idea feature in con-
temporary analytical philosophy. The first and more com-
mon one signifies the terminus of a series of explanations
which is not itself further explicable. Thus, for example, it
is often said that while the behaviour of matter can be
explained by reference to laws of nature the existence and
character of those laws is itself a ‘brute fact’. The second
and more technical use indicates an underlying situation
partly constitutive of the truth of a claim. The expression
was first used in this sense by Anscombe to characterize
the status of facts relative to higher-level descriptions. A
set of facts S is ‘brute’ relative to a description D when the
truth of D is constituted by the holding of those facts in a
certain context and under normal conditions. Thus, the
*fact that I inscribed a piece of paper, in a context consti-
tuted by banking conventions, is brute relative to the

description ‘J.H. signed a cheque’, and the fact so
described may itself, in a given context, be brute relative to
the description ‘J.H. ran into debt’. Hence the status of
brute and non-brute facts is a relative one. j.hal.
G. E. M. Anscombe, ‘On Brute Facts’, Analysis (1958).
Buber, Martin (1878–1965). Jewish philosopher born in
Vienna and raised in the Ukraine in the home of his grand-
father, the Midrash scholar Solomon Buber. Martin Buber
studied in Vienna with Dilthey and Simmel and became a
Zionist leader in the 1890s, advocating cultural and edu-
cational activism. Attracted to the Hasidism of Nah
.
man of
Bratslav, whose tales he adapted in German, he wrote
Buber, Martin 111
novels of the Hasidic milieu and urged formation of a
Gemeinschaft in Palestine that would include Arabs and
Jews. His teaching cut off by Nazi edicts, Buber settled in
Palestine in 1938 and became a prominent advocate of a
binational (Arab–Jewish) state. His I and Thou (1923)
grounds ethics and theology in a dialogical encounter: our
fundamental attitudes of turning-toward or leaning-back
demarcate the basic relations of I–It and *I–Thou, which
constitute both self and other in radically different ways,
objectively, in terms of uses, causes, effects, and chal-
lenges to be overcome; or intersubjectively, and person-
ally, that is, morally, even aesthetically. Authenticity,
responsiveness, even genuine presentness (and thus free-
dom) are attained only in the I–Thou relationship. The
objectivity of the I–It is fixed in the past. *God is the eter-

nal Thou, never transformed into an It by spiritual ennui
or fatigue, but glimpsed through our encounters with
others, with nature and with works of art. It is when we
speak to him, not of him, that we encounter the living
God. Even those who hate God’s name can do this, when
they address their lives in terms of a subjecthood that
cannot be limited by another. Revelation is humanity’s
continuing response to the eternal Thou, epitomized in
God’s covenant with Israel. l.e.g.
P. A. Schilpp and M. Friedman (eds.), The Philosophy of Martin
Buber (La Salle, Ill., 1967).
Buddha, the ( fl. fifth century bc). The Sanskrit word ‘bud-
dha’ refers to any enlightened person, but ‘The Buddha’
refers specifically to Siddha¯rtha Gautama, son of a ruler of
Sa¯kya in what is now Nepal. Modern scholarship places
him rather later than the traditional dates of c.560–480.
The Buddha founded a non-theistic religion and articu-
lated the foundations of *Buddhist philosophy—the Four
Noble Truths concerning suffering, its causes and its ces-
sation, the theory of ‘dependent origination’, and the
denial of substantial selfhood.
According to tradition, the twenty-nine-year-old Gau-
tama, troubled by the sickness and death he witnessed, left
Sa¯kya in search of an understanding of suffering. After
several unsuccessful years of ascetic and spiritual practice,
he found enlightenment, at thirty-five, while meditating
beneath a fig-tree. He then delivered the first of many dis-
courses (suttas) that, after centuries of oral transmission,
were recorded in the Pali Canon. The Buddha was a man
of great physical presence, compassion, and serenity.

This, allied to his dialectical skills, ensured that before his
painful but dignified death he had already gained a large
following of monks and lay people.
Unlike the founders of other religions, the Buddha
grounded his teachings on rational reflection, not divine
revelation, and adumbrated a philosophically sophisti-
cated account of reality, mind, and the human condition.
His philosophical temper was decidedly *empiricist, for
‘right view’ is vouchsafed by clear-headed experience of
the world and oneself. He criticizes Brahmanism for pos-
tulating such transcendent entities as an absolute Self
(a¯tman), and rejects so-called unanswered questions
(e.g. ‘Is the world eternal?), not only because they are irrele-
vant to obtaining ‘release’ from suffering, but because,
enquiring beyond the limits of experience, they are sense-
less. The truths he himself advances are available to any-
one fully ‘mindful’ of the world around him and the
workings of his own mind. Indeed, mindful experience is
essential to proper understanding of these truths. One
who grasps that there is only ‘not-self’, for example, does
not simply assent to the Buddha’s propositions, but experi-
ences the world and himself in a new key. The Buddha’s
moral philosophy is equally empiricist in character, experi-
entially based reflections on the integral role of such
virtues as compassion and equanimity in a life liberating
itself from the causes of suffering. d.e.c.
M. Carrithers, The Buddha (Oxford, 1983).
S. Hamilton, Early Buddhism: A New Approach (Richmond, Surrey,
2000).
Buddhism: see Buddhist philosophy.

Buddhist philosophy. Ethical, metaphysical, and epi-
stemological views held by an Indian prince turned ascetic,
Siddha¯rtha Gautama (said to have been born 563 bc), and
by subsequent schools of thought claiming allegiance to
him. Siddha¯rtha was called ‘Buddha’, which means ‘the
awakened one’.
Buddha’s teachings. Facing the fragility of life, and the facts
of disease, decay, and death, young Siddha¯rtha left his
family in search of peace and enlightenment, which came
not through extreme austerity or philosophical wrangling
but through meditating along ‘the middle way’. On finally
becoming ‘awakened’ he preached Four Noble Truths:
1. Life is suffering.
2. Suffering involves a chain of causes.
3. Suffering can cease.
4. There is a path to such cessation.
The first truth, equating existence with suffering, was
buttressed by a reductionist metaphysics of universal
impermanence and soullessness. We suffer because we
expect a substantial core in things, when in fact there is
none either inside or outside us. Apparent *substances are
reducible to groups of ephemeral parts, *persons to
streams of causally interdependent collections of five psy-
chophysical aggregates, an ‘essence’ like catness to mere
exclusion from the mixed set of non-feline individuals.
Since selves and things are so unstable and essenceless,
our inborn wish to retain our identity and to cling to an
essence of what we desire leads to frustration. The truth of
universal pain ultimately becomes an evaluative rather
than descriptive judgement. Buddha urges that life should

be looked upon as agony through and through.
The second truth concerning the cause of suffering was
fleshed out as the twelve-link causal chain of dependent aris-
ing: ignorance → karma-propensities → embryonic sen-
tience → body and psychoses → five senses plus an
introspective faculty → sense–object contact → experience
→ thirst →clinging→rebirth →decay→death.
112 Buber, Martin
This, called the ‘Wheel of Becoming’, obviously con-
nects with the *karma-based theory of metempsychosis.
But if there is no self, what is reborn? In answer, Buddha
draws a Ryle-like analogy between ‘The individual gets
reborn’ and ‘The news travels’. It is ignorance to think of
the news as an entity doing the travelling. To conceive a
continuing agent is equally mistaken, and propels us
towards egoistic actions—we find ourselves enmeshed in
the causal chain of becoming. The so-called person is in fact
just a bundle of five psychophysical factors. These five
aggregates (physical forms, sensations, feelings, judge-
ments, and latent dispositions) constituting the individual
at the dying moment cause another, subtler, fivefold
replica, which causes yet another—and so on until the new
physical form of a foetus is produced, to which all the crav-
ings, traces, and the illusory sense of identity of the dying
bundle have been bequeathed. ‘The soul’ is the name of a
causally bound bundle which spans countless deaths and
births. This reductionist set-and-series concept of a person,
called the doctrine of anatta¯ in Pali, has recently received
some publicity among English-speaking philosophers
through the work of Derek Parfit.

The third noble truth sets up *nirvana as the final liber-
ation from the pain of repeated embodiment, which can
only happen if the ignorance of regarding oneself as a sub-
stantial permanent ego is dispelled. Ultimate and unend-
ing calm is attained when all cravings—even the craving
for extinction—cease without leaving behind any seed.
Since such a state is attainable by every thinking being,
irrespective of class, gender, caste, or even species, Bud-
dhism is not pessimistic or discriminatory.
Finally, the fourth noble truth of the way to the
summum bonum of nirvana gives the ethics. This is the eight-
fold path: ethically correct views, right resolutions, right
speech, right action, right livelihood, right effort, proper
mindfulness, and regular practice of concentration. These
intellectual, social, and meditational virtues promote the
overarching moral qualities of clarity, desirelessness, uni-
versal friendliness, and compassion. Suffering ceases
through selflessness, metaphysical and moral. Using a uni-
versalizability criterion the Buddha preached: ‘All men
tremble at punishment, all men fear death. Likening others
to oneself, one should neither slay nor cause to slay.’
The Subsequent Schools. Although all Buddhists owed alle-
giance to the three scriptural ‘baskets’ into which the doc-
trines, codes of conduct, and philosophical utterances of
Buddha were collected, there arose a major theoretical rift
between the so-called ‘Lesser Vehicle’ (Hı¯naya¯na) and
‘Greater Vehicle’ (Maha¯ya¯na) within 200 years of the Mas-
ter’s death. The former faction now survives in Sri Lanka
and Burma, and the latter in Tibet, China, Korea, and
Japan. The latter faction of Buddhism may have been

called ‘greater’ because in it the aim of life is not only to end
one’s own suffering but to strive, even after one’s own
personal nirvana, for the enlightenment and happiness of
others. Hence the ideal of an altruistic enlightened man
who caringly resolves ‘May the fruits of my austerities and
meditations alleviate the sufferings of all sentient creatures,
even of women giving birth!’ This is supra-moral kindness.
The Lesser Vehicle. The Lesser Vehicle itself branched into
two schools, the first being the realist Vaibha¯s
.
ika. Postu-
lating some seventy-two types of composite elements and
even a few eternal entities like space and the state of peren-
nial painlessness, this school earned the title ‘the every-
thing-exists school’. Some members offered detailed
accounts of how atoms combine to form directly perceiv-
able matter. Acute in-house debates regarding the reality
of the past and the future led to observations like this:
‘Past’, ‘present’, ‘future’ are equally objective descriptions
of the same bit of reality, just as the same woman is cor-
rectly described as ‘mother’, ‘wife’, and ‘daughter’.
The second school of the Lesser Vehicle, representa-
tionalist–realist Sautra¯ntika, criticized the first for eternal-
ist heresies and gave the following sorts of argument for
strict impermanence: If A endures for more than a
moment, say over t
1
, t
2
, t

3
, then, given the Buddhist defin-
ition of reality, it can be real only by being causally product-
ive at t
1
, t
2
, and t
3
. Now, either A produces some effect at
each moment or it lies capable but fallow at t
1
and t
2
and
actually fructifies at t
3
, when operating auxiliary condi-
tions join A. If it produces effects at each moment, then it
must have three different effects because the same effect
cannot be produced thrice. Accordingly A disintegrates
into three momentary realities, corresponding to three
distinct causal capacities. If it remains fallow at t
1
and t
2
waiting for some auxiliary conditions, as the seed in the
granary waits for soil and rain, it is only the terminal entity
A-at-t
3

which qualifies as real, the previous temporal parts
being non-entities, or distinct entities, one generating
the other. This is the heart of the famous doctrine of
momentariness.
Given such strict momentariness, the really real is
accessible only to pure sensation, which grasps these
instantaneous propertyless particulars. Sautra¯ntika episte-
mology is thus at best a critical realism about tables and
chairs where the macroscopic world is a construction of
inference. Any verbalizable perception invoking classifica-
tory concepts is analysed as inference and imagination.
Later Sautra¯ntika Buddhists like Jña¯nas´rı¯ attack all
word-generated awareness as fiction-loaded. Words refer
to objects through modes of presentations which are gen-
eralities—they never capture particular objects in their
vivid singularity. This goes by the name of the exclusion
theory of meaning, which is at the heart of Buddhist
nominalism. Even an expression like ‘that cow’ serves
only to distinguish the referent from dogs, horses, asses,
and other cows further away. Apart from this network
of mind-made distinctions, there is no natural kind called
‘the cow’.
The Greater Vehicle. This nominalistic representationalism
of Sautra¯ntika inevitably led to a Berkeleian idealism of the
first school of the Greater Vehicle. Yoga¯ca¯ra, also named
‘the mind-only school’ seeks to refute atomists and critical
realists by four major arguments.
Buddhist philosophy 113
1. Many intricate considerations are put forward against
the existence of bodies in space. If, as the realistic

Vaibha¯s
.
ika school maintained, six atoms join the seventh
from six sides, either the central atom falls into six parts,
which goes against its indivisibility, or the contacts all
happen at one point, which fails to explain any increase of
size. So the very idea of extension is incoherent.
2. No external object—macroscopic or atomic—has
both the causal and phenomenological features of a real
object of awareness. That which both causes and bears the
manifest form of a piece of awareness can count as its real
object. If I see glistening water but my seeing is caused by
hot air refracting sunlight, I call that a mirage. But, upon the
critical realist theory, the actual cause and the phenomeno-
logical content of perception fall apart. Awareness is caused
by imperceptible atoms while it assumes the felt form of
chairs and cherry blossoms.
3. Thus, as awarenesses, wakeful and veridical ones are
indistinguishable from dream and erroneous ones, and
equally devoid of any extra-mental object.
4. Finally, if x and y are not the same they could be iso-
lated from each other, but blue can never be isolated from
awareness of blue; hence they must be the same.
These idealistic arguments offered by Vasubandhu
(fifth century ad) were vigorously attacked by realists of the
Jaina, Mı¯ma¯msa¯, and Nya¯ya schools. Even S
´
an
.
kara, himself

an absolute idealist, scoffed at the mind-only Buddhist: ‘If
externality is such an impossibility, how come things even
appear to be external? No one is even mistaken for a barren
woman’s son!’ Anticipating G. E. Moore, philosophers of
the Nya¯ya school appealed to *common sense, and isolated
formless awareness as the common element in awareness
of blue and awareness of yellow, thereby questioning the
inseparability of objects and perception. Jaina opponents of
Yoga¯ca¯ra claimed that perception itself points to the
act–object distinction, but Yoga¯ca¯ra stuck to treating the
‘of’ of intentionality after the fashion of ‘City of Rome’, as
if the distinction was verbal and spurious.
The last and currently most influential school of the
Greater Vehicle—thanks to the present Dalai Lama—is
Voidism or Ma¯dhyamika, which was fully developed by
*Na¯ga¯rjuna with the help of such sceptical arguments as
the following. The reliable means of knowledge are estab-
lished by appeal to the reality of the objects they make us
know; but the reality of the objects, in turn, is established
upon the authority of the means of knowledge. Since the
criterion of knowledgehood itself is so hopelessly circular,
how can anything be known to have this or that deter-
minate nature? Excelling in negative dialectics, anti-
realism reaches its mystical climax in Voidism. This
mysticism, of course, has nothing to do with faith in God.
In chapter 10 of his Twelve-Gate Treatise Na¯ga¯rjuna argued,
God could not be our father because children should have some
resemblance with their father, but in our suffering we are most
ungodly. Being self-existent, God should also have no needs, yet
obviously he needed to create, otherwise he would be whimsical

like an infant. As omnipotent, God should not have any obstacles
to his desire, so what explains the gradual unfolding of creation
instead of creation of everything all at once? Finally, if God is the
maker there should be no evil or ugliness in things, but obviously
there is.
Suffering, causation, and temporal succession are all
shown to be uncharacterizable in any determinate man-
ner, because all characterizations are equally empty. It is
this insistence on the emptiness of all things which makes
Na¯ga¯rjuna a ‘Voidist’. Since all things are empty, so is the
doctrine of emptiness. Far from being self-refuting, such
absolute epoche¯ is said to be irrefutable. ‘If I had a view I
could have had a flaw, but, emptied of all views, I am flaw-
less.’ So says the Voidist, enjoying tranquillity. a.c.
*Indian philosophy; Hindu philosophy.
M. Carrithers, The Buddha: A Very Short Introduction (Oxford,
2001).
A. K. Chatterjee, The Yogacara Idealism (Benares, 1976).
E. Conze, Buddhist Thought in India (Ann Arbor, Mich., 1970).
S. Mookherjee, The Buddhist Philosophy of Universal Flux (Delhi,
1980).
T. Stcherbatsky, Buddhist Logic, 2 vols. (Paris, 1958).
Bultmann, Rudolf (1884–1976). German theologian who
gives a Heideggerian interpretation of the New Testament
which is both anti-metaphysical and existentialist. Bult-
mann argues that it is the awareness of death as an imme-
diate possibility which produces the need for Christianity,
and claims that a life without Christ is inauthentic but a life
lived in Christ is authentic. His ‘demythologizing’ of the
New Testament construes its historical and theological

doctrines as descriptions of the human condition in so far
as this is a condition of need for God. Bultmann’s readings
are controversial because they might be logically consist-
ent with atheism. s.p.
*existentialism; authenticity.
Rudolf Bultmann, Theologie des Neuen Testaments (Tübingen,
1948–53); tr. as Theology of the New Testament, 2 vols. (New
York, 1952).
Ronald W. Hepburn, ‘Demythologizing and the Problem of
Validity’, in A. G. N. Flew and A. MacIntyre (eds.), New Essays in
Philosophical Theology (London, 1955).
bundle theory of the self. Empiricist theory of *personal
identity particularly associated with David Hume.
Hume’s view—that we are never aware of our *self as a
substance, but only as a ‘bundle or collection of different
perceptions’—has been interpreted as a sceptical denial of
personal identity. More plausibly, Hume can be taken to
be meaning that the peculiarly complex unity or identity
of the self should be interpreted in terms of constantly
changing causal relations, more like the identity of a com-
plex play than a simple material object. A Humean theory
of the self was developed by William James. r.s.d.
David Hume, A Treatise of Human Nature, i. iv. 6.
William James, The Principles of Psychology (New York, 1890).
Burali-Forti’s paradox, due to Cesare Burali-Forti, arises
from the assumption that there is a series S
1
consisting of
all ordinal numbers and that this series is well-ordered.
114 Buddhist philosophy

From this it follows that S
1
has an ordinal number X. From
this it follows that there is a series S
2
of ordinals up to and
including X which has the ordinal number X+1. This con-
tradicts the assumption that S
1
has all the ordinal num-
bers. This contradiction about ordinals is not usually
taken up in popular discussions because the notion of a
transfinite ordinal is more difficult to explain than that of a
trans-finite cardinal. In this sense all transfinite ordinals
are inaccessible. j.c.
*number.
Cesare Burali-Forti, ‘Una questione sui numeri transfiniti’, Rendi-
conti di Palermo (1897); Eng. tr. in J. van Heijenoort (ed.), Source
Book in Mathematical Logic 1879–1931 (Cambridge, Mass., 1964).
Burckhardt, Jakob Christoph (1818–97). A historian who
lived for most of his life in his native Basle. Although a
pupil of Ranke, he was less concerned to discover object-
ive facts than to explore European *‘culture’ (one of the
three great ‘forces’, along with religion and the state, that
govern history), often by way of an anecdote that enabled
him to ‘discern and feel the general in the particular’. His
influential works include The Age of Constantine the Great
(1852; tr. London, 1949) and The Culture of the Renaissance
in Italy (1860; tr. London, 1878). His main philosophical
work, consisting of lectures (which Nietzsche attended) at

Basle between 1868 and 1871, was published as Reflections
on History (1906; tr. London, 1943). Like Schopenhauer
(whom, to Nietzsche, he called ‘our philosopher’), he
despised Hegel’s rationalist and teleological view of his-
tory; denied that man makes significant progress, and thus
preferred to focus on what is ‘recurrent, constant and typ-
ical’; and regarded democracy and industrialization as
threats to liberty and culture. m.j.i.
K. Löwith, Jakob Burckhardt: Der Mensch inmitten der Geschichte
(Lucerne, 1936).
Burge, Tyler (1946– ). American philosopher based at the
University of California, Los Angeles. Burge has worked
largely in the philosophies of mind, language, and logic.
His earlier work on singular terms and demonstratives
was within the context of Davidson’s theory of meaning.
He is also known for a series of papers, beginning in 1979,
in which he argues for *anti-individualism: the thesis that
the contents of thinkers’ intentional states cannot be fixed
by facts about those thinkers taken in isolation from the
rest of their community. Burge argues for this through an
ingenious variation on Putnam’s Twin Earth thought
experiment (*arthritis in the thigh). Burge claims that only
by appreciating the social determination of the contents of
thinkers’ thoughts can we account for the irreducibly nor-
mative character of intentional mental states. t.c.
*externalism.
Tyler Burge, ‘Individualism and the Mental’, Midwest Studies in
Philosophy, iv (1979).
Buridan, John (c.1295/1300–c.1360). Student, and then
teacher, at Paris, he was twice rector of the university, in

1328 and 1340. Generally classified as a nominalist, he was
one of the great logicians of the Middle Ages, but also a
philosopher and theologian. He wrote commentaries on a
number of works by Aristotle, his Commentary on the
Physics of Aristotle being particularly well known for its
discussion of impetus, in which Buridan attempts to
explain how it happens that when a projectile leaves the
projector (for example, when a stone leaves the thrower’s
hand) it does not promptly fall to earth as a heavy object
surely would but instead continues upward. Buridan
solves the problem by arguing that the projector imparts
an impulse, or impetus, to the projectile, and that it is the
impetus that maintains the projectile in motion until
countervailing forces, in particular air resistance and the
projectile’s weight, prevail and the body finally falls to
earth. In the course of his discussion Buridan develops
the concept of inertia at least in respect of celestial bodies
and in so doing makes a clean break with Aristotelian
physics. a.bro.
*ass, Buridan’s; Aristotelianism.
E. A. Moody, ‘Jean Buridan’, in Studies in Medieval Philosophy, Sci-
ence and Logic: Collected Papers 1933–1969 (Berkeley, Calif.,
1975).
Burke, Edmund (1729–97). Irish-born political writer
noted for literary style, and English MP believed to be an
important source of *conservatism.
In describing the work of Burke it is accurate to call him
a ‘political writer’ rather than a political theorist or
philosopher. He was suspicious of the abstract and his
writings predominantly exemplify rhetoric at the expense

of reasoned argument. He was a master of prose style,
although he was never noted for skill in oratory, and some
of his best speeches were said to have emptied the House
of Commons. Burke is not and would not have wanted to
be considered a great political philosopher, but he satisfies
one criterion of greatness—his thought appeals to succes-
sive generations of political thinkers.
For one who was later to dismiss abstract philosophiz-
ing with some contempt Burke rather oddly began his lit-
erary career with two successful works in that genre. The
first was A Vindication of Natural Society (1756; 2nd edn.
1757), in which he attacked social philosophy, especially
that of Rousseau. In 1757 he published a second philo-
sophical essay which, like the first, was very successful—A
Philosophical Enquiry into the Origin of our Ideas of the Sublime
and Beautiful. As a result of his success he was taken up by
the literary and artistic circles of London, and was encour-
aged by his publisher to try his hand at history. His histor-
ical work was not published in his lifetime. Thereafter
began his political life, in which he was to continue until
his death in 1797.
In his political life he devoted himself (as he says) to five
‘great, just and honourable causes’: the emancipation of
the House of Commons from the control of George III
and the ‘King’s friends’; the emancipation of the American
colonies; the emancipation of Ireland; the emancipation
Burke, Edmund 115
of India from the misgovernment of the East India Com-
pany; and opposition to the atheistical Jacobinism shown
in the French Revolution. Successive generations have

reacted in different ways to Burke’s position on all these
questions, if indeed he has a consistent position. For
example, his stand against the French Revolution was
attacked by the early Utilitarians such as Paine, Bentham,
and James Mill, on the ground that he had betrayed his ear-
lier championship of political *liberty. He himself
regarded his defence of the Indian people against the East
India Company as his greatest achievement, yet it has
been argued that he was lacking in historical knowledge of
India and that he did not really understand the difficulties
facing Warren Hastings in dealing with a totally different
social order. His greatest contribution to political thought
is summed up by Wordsworth in The Prelude. Words-
worth says of Burke that he ‘declares the vital power of
social ties Endeared by custom’. In other words, Burke
thought of all political power as a trust, and in the case of
Britain politicians were entrusted with the preservation of
a traditional hierarchical social and political order.
Burke’s belief that society depends on what he called
‘prejudice’, that is, on instinctive feelings of love and loy-
alty, plus his rejection of the central place which revolu-
tionary thinkers had given to reason, led to his critique of
natural law and natural rights. Basically he seems to be
saying that communities are held together not by self-
interest but by the feeling that we are members one of
another; communal feeling is everything and reason is
insignificant. Hence, he rejected the appeal made by the
revolutionaries to abstract individual rights. For Burke the
important contrast is not between repressive govern-
ments and the abstract rights of the rational individual, but

between the beautiful order of society bonded by loyalties
and ‘prejudice’, and ‘a disbanded race of deserters and
vagabonds’. In rejecting natural law he shared the conser-
vatism of Hume, but his reverential attitude to the state is
much more like Rousseau than Hume. r.s.d.
*sublime; revolution.
Edmund Burke, Reflections on the Revolution in France (1790), ed.
Conor Cruise O’Brien (Harmondsworth, 1968).
—— Pre-Revolutionary Writings, ed. I. Harris (Cambridge, 1993).
C. B. Macpherson, Burke (Oxford, 1980).
Burnyeat, Myles Frederic (1939– ). Laurence Professor
of Ancient Philosophy, University of Cambridge in the
1980s and 1990s, thereafter Fellow of All Souls College,
Oxford. Noted chiefly but not solely for his work on the
history of epistemology, he has produced important stud-
ies of Plato, and has played a significant role in the redirec-
tion of scholarly attention to *Hellenistic philosophy, in
particular to the ideas of the *Sceptics. n.c.d.
Myles Burnyeat, The Theaetetus of Plato (Indianapolis, 1990).
——(ed.), The Skeptical Tradition (Berkeley, Calif., 1983).
——(co-ed.), Doubt and Dogmatism: Studies in Hellenistic Epistemol-
ogy (Oxford, 1980).
——(co-ed.), Science and Speculation: Studies in Hellenistic Theory
and Practice (Cambridge, 1982).
business ethics. One of the areas of *applied ethics.
Although the application of morality to business is as old
as business and morality themselves, the rise of business
ethics as an identifiable subject of study took place in the
1970s in the United States, and since the late 1980s in
Europe, Australia, and a number of countries in Asia,

Africa, and South America.
Business ethics as an academic area is defined by
the interaction of business and ethics, and the set of
related problems thus generated. At its broadest, it studies
the moral justification of economic systems, whether
national or international. Within a given system it studies
the moral justification of the system’s structures and
practices. Since corporations are a dominant feature of the
free-enterprise system, a good deal of work has focused on
the structures, governance, responsibilities, and activities
of corporations. Within the corporation business ethics
deals with the moral responsibilities and rights of indi-
vidual managers and employees—the more traditional
focus of previous work on ethics in business.
Those who work in business ethics tend to engage in
four types of activity. The first and most common is the
development and discussion of case-studies that raise
some moral issue in business. These are used to sensitize
students, those in business, and the general public to the
need for ethical considerations in business. Although at
first these cases tended to illustrate unethical behaviour
on the part of large corporations, in recent years there has
also been a growing literature on positive cases presenting
exemplary corporate or individual activity. Cases-studies
in turn have led to the investigation of the morality of par-
ticular practices, to the responsibility of corporations with
respect to consumers and the public, product safety, the
rights of workers, environmental degradation, and similar
issues. A third kind of research considers how corpor-
ations might be structured so as to reinforce ethical behav-

iour and discourage unethical behaviour on the part of
both workers and managers. A fourth kind of activity can
be called meta-ethical. This looks at the appropriateness of
applying moral language to entities other than human
beings, e.g. to corporations, corporate structures, economic
systems. There has been lively discussion of whether corpor-
ations can rightly be said to have moral *obligations or
responsibilities. Terms such as *‘responsibility’, *‘con-
science’, *‘rights’, *‘virtue’, mean something diferent when
applied to corporations than when applied to human indi-
viduals, as do notions of praise and blame, reward and pun-
ishment.
The importance of international business has led to dis-
cussions of international business ethics and to a reconsid-
eration of moral and cultural relativism, which take on
special significance when considering doing business in
societies with corrupt governments and in the absence of
many traditional restraints. Work in international busi-
ness ethics has called into question whether Western-type
approaches to ethical theory actually enjoy the universal-
ity which they claim or to which they aspire. The primary
focus of international business ethics has been on the
116 Burke, Edmund
actions of multinational corporations from developed
countries operating in less developed countries. Issues
include bribery, the use of child labour, the degradation of
the environment, the exploitation of workers, and the
increasing gap between rich and poor countries. Global
issues involve the justice or fairness of policies of global
institutions such as the World Trade Organization and the

World Bank, the depletion of the ozone layer, and the
appropriate role of corporations and nations in halting or
reversing the process, and the depletion of non-renewable
natural resources. The growth of the Internet as a medium
of commerce that easily crosses national boundaries has
also generated new concerns about the ethical dimensions
of privacy violations by businesses, control of commercial
pornography, and protection of intellectual property avail-
able in digitalized form.
Business ethics has developed into a significant area of
research and teaching with its own texts, journals, and
professional societies. But it has gone beyond the aca-
demic setting in which it developed. It has become some-
thing of a movement, in which corporations have adopted
codes of conduct or statements of values and beliefs, have
introduced the position of corporate-ethics officer, insti-
tuted in-house training programmes in ethics, established
ethics hotlines, and appointed ethical ombudsmen. The
corporate movement is mixed: sometimes salutary, pro-
viding positive promotion and reinforcement of ethical
norms; sometimes self-serving, emphasizing ethics for
employees towards the corporation, but exempting the
corporation itself (and its top officers) from ethical assess-
ment; and sometimes negative, serving simply as ‘win-
dow-dressing’ to mask amoral corporate activity. The
movement can be distinguished from the academic area
with which it is related, but which continues to have a crit-
ical (although not necessarily antagonistic) component
with respect to business, and which interacts with stand-
ard normative and meta-ethical theory. r.de g.

*capitalism; markets and the public good; professional
ethics.
Tom L. Beauchamp and Norman E. Bowie (eds.), Ethical Theory
and Business, 6th edn. (Upper Saddle River, NJ, 2001).
Richard T. De George, Business Ethics, 5th edn. (Upper Saddle
River, NJ, 1999).
—— Business Ethics Quarterly, 10, no. 1 (2000).
G. Enderle (ed.), International Business Ethics: Challenges and
Approaches (Notre Dame, Ind., 1999).
Butler, Joseph (1692–1752). Anglican divine, Bishop of
Durham. His Fifteen Sermons (1726), perhaps the finest eth-
ical work in English, brilliantly attacks psychological and
ethical *hedonism and provides a via media between a
moral-sense approach to ethics and a rationalist one. Since
pleasure is the satisfaction of an impulse, the desire to
maximize one’s own (self-love) requires impulses with
other objects, e.g. particular passions (like hunger) and
*benevolence. Self-love is not peculiarly ‘natural’. Life is
‘natural’ when the influence of each motive accords with
its intrinsic authority. Conscience should adjudicate
between the two high-level principles of self-love and
benevolence and these should control the particular pas-
sions. Butler’s book The Analogy of Religion (1736) defends
Christianity against *deism. The analogy is between the
Bible and nature, which bear the marks of the same author.
In a famous appendix Butler defends the absoluteness of
*personal identity against Locke’s empiricist treatment.
t.l.s.s.
Austin Duncan-Jones, Butler’s Moral Philosophy (Harmondsworth,
1952).

Terence Penelhum, Butler (London, 1985).
Butler, Samuel (1835–1902). Satirist, novelist, metaphys-
ical biologist, anti-Christian. Erewhon (1872), and Erewhon
Revisited (1901), satirize Victorian values. In Erewhon
(‘nowhere’ backwards—almost) there are two currencies,
one issued by commercial banks and used for all practical
purposes (the decencies of ordinary and business life) and
another issued with great solemnity in magnificent build-
ings, but commercially useless (Christianity). Erewhonian
thought also includes elements of his own striking specu-
lations, for example on machines as extensions of the
human organism which may threaten us by a rival evolu-
tion of their own and on the invalidity of a distinction
between an individual and his influence (so that there is a
genuine afterlife as long as this continues). In several anti-
Darwinian works Butler propounds his Lamarckian the-
ory of creative *evolution by inherited memory, as he
does also in his novel of generational change The Way of All
Flesh (1903). His satirical (and sometimes perversely per-
suasive) defence of the Resurrection in The Fair Haven
(1873) was quoted in pulpits until its disguised authorship
was discovered. t.l.s.s.
Peter Raby, Samuel Butler: A Biography (London, 1991).
Byzantine philosophy. ‘Byzantine philosophy’ would
seem to refer, straightforwardly, to philosophy written in
the Byzantine Empire. In fact the reference is anything but
straightforward. There is, for example, no clear chrono-
logical line separating late ancient from Byzantine phil-
osophy. There is, again, no responsible way to extricate
Byzantine philosophy from Byzantine theology or Byzan-

tine literature. The best that can be done is to depict some
features in authors who have as good a claim as any to the
label ‘Byzantine’.
The most obvious feature is a continuity of learning.
Byzantine writers who disagreed about much else under-
stood themselves to share at least two kinds of tradition.
They shared a tradition of Greek literacy, including a
legacy of Greek philosophical texts considerably larger
than that available in Latin translation before the Renais-
sance. Byzantine writers shared next a set of theological
authorities. These authorities included the seven ecu-
menical councils of the Church (325–787), but also Chris-
tian writers who combined fervent piety with formidable
learning in Greek letters, including philosophy and nat-
ural science. Chief among these were Gregory Nazianzen
Byzantine philosophy 117
(323–89), Basil of Caesarea (c.330–79) and his brother
Gregory of Nyssa (c.335–95), and John Chrysostom
(347–407). Later Byzantine writers looked back to these
four, and especially to Basil and John, as the ‘fathers’ of
right belief and holy practice.
Byzantine writers were further able to appropriate the
last works of non-Christian Greek philosophy. The intri-
cate *Neoplatonism of Proclus (c.410–85) was taken over
by a Syrian who took as pseudonym ‘Dionysius the
Areopagite’. The writings of this pseudo-Dionysius (active
c.500) present a thoroughly Christian adaptation of
Procline philosophy to questions about the intelligibility
and accessibility of God. In the same years, Proclus’ pagan
successors in Athens continued his reinvigoration of the

old practices of philosophical commentary. Among their
most remarkable expositions were the extensive com-
mentaries on Aristotle by Simplicius. The fact of expert
Aristotelian commentaries by Neoplatonists illustrated
another kind of adaptation, as it seemed to fulfil the ancient
wish for a reconciliation of Plato and Aristotle.
The shared sources, Christian and pagan, and the
models of adaptation inspired various Byzantine works in
or about what seems to us philosophy. John Damascene
(died c.751) composed a Fount of Knowing that contains: (1)
a dictionary of technical terms ranging from Aristotelian
logic to Trinitarian theology, (2) a critical history and doc-
trinal analysis of Christian heresies, and (3) a compendium
of orthodox theology comprising, among much else,
elementary lessons in Aristotelian and Galenic natural
philosophy. Michael Psellos (1018–c.1096) wrote a Teach-
ing of All Sorts that displays an unusual knowledge of pagan
Neoplatonism and even an interest in philosophical
astrology and magic. By contrast, the Philosophy of George
Pachymeres (1242–1307) is a sequential paraphrase of the
principal works of Aristotle, from the Categories to the
Nicomachean Ethics.
Of course, the simultaneous inheritance of pagan and
Christian sources brought deep tensions. Even those
friendliest to ancient philosophy, such as Psellos, were
careful to note its discrepancies with Christianity. Other
Byzantine authors viewed these discrepancies as evidence
for the bankruptcy of pagan learning. So, for example, the
150 Chapters of Gregory Palamas (1296–1359) rejects the
errors of prideful reason, and especially the errors of Plato

and Aristotle, in favour of Christian revelation grasped by
the prayer of the heart.
No one can know how these controversies would have
developed if Byzantine life had not been disrupted by the
fall of Constantinople in 1453. What can be known is the
influence of visiting or exiled Byzantine scholars on West-
ern Europe. George Gemistos Plethon (1355/60–1452),
for example, electrified Florentine humanists with his
teaching of Plato. John Bessarion (1403–72), who died a
Roman cardinal, not only defended Plato against the
attacks of Aristotelians, he left his valuable Greek library
to the Venetians. Much of *Renaissance philosophy is the
afterlife of Byzantine philosophy. m.d.j.
Milton V. Anastos, The Mind of Byzantium (New York, 1966).
K. Ierodiakonou (ed.), Byzantine Philosophy and its Ancient Sources
(Oxford, 2002).
G. Podskalsky, Theologie und Philosophie in Byzanz (Munich,
1977).
Basile Tatakis, La Philosophie byzantine (Paris, 1949; English trans-
lation, Indianapolis, 2004).
118 Byzantine philosophy
cabbala: see Kabbalah.
Cajetan, Cardinal Thomas de Vio (1468–1534). General of
the Dominicans and, as Cardinal-legate to the Empire in
1518–19, involved in unsuccessful dialogue with Luther,
Cajetan was an influential commentator on Aristotle and
Aquinas. More pessimistic of the powers of human reason
than previous Thomists, Cajetan denied in particular that
the immortality of the soul could be established independ-
ently of revelation. Cajetan also developed the Thomist

theory of analogy, and so of how terms such as ‘good’
could be applied without equivocation both to *God and
to finite creatures. Cajetan argued that when we describe
both God and finite creatures as good, we employ an ana-
logy of proportionality: the same quality is attributed to
God as is attributed to creatures—but proportionately to
their differing natures. t.p.
*Thomism.
M. McCandles, ‘Univocalism in Cajetan’s Doctrine of Analogy’,
New Scholasticism (1968).
calculus. A calculus is a formal language and rules for
manipulating expressions of the language. For example,
by applying *algorithms to arabic numerals one can deter-
mine the values of arithmetical functions. A logical calcu-
lus is used to construct valid *arguments. It can be
described as the syntax of a logic where syntax has to do
only with the shapes and structure of expressions, not
their meanings.
The syntax of a logic has two parts: the grammar and
the deductive system. The grammar is a list of symbols or
rules for constructing symbols of the logical language, and
a specification of which finite strings of symbols are to
count as sentences or well-formed formulae. The deduct-
ive system of a logic consists of axioms and rules of infer-
ence which are used to construct proofs of sentences of
the logical language. Axioms can be written at any line of
a proof and do not rest on any premisses; rules of inference
permit the writing of a sentence at a line of a proof given
that appropriate conditions are met. A deductive system
must have at least one rule of inference but need not have

any axioms; a deductive system is an axiomatic system if it
contains axioms, a natural deduction system if it does not.
A proof of a sentence A from a set of premisses Γ is a finite,
non-empty sequence of sentences such that the last mem-
ber of the sequence is A and each member of the sequence
is either a member of Γ or an axiom or follows according
to a rule of inference from one or more sentences that pre-
cede it. One can mechanically determine whether any
given finite sequence of sentences is a proof.
Although logical calculuses can be objects of study in
their own right, it is their application to the construction
and criticism of arguments that gives calculuses their ori-
ginal point. An argument in English is valid just in case it is
not possible for all the premisses to be true and the con-
clusion false. Valid arguments can be grouped according
to their shapes or form. For example, it is easy to see that the
following arguments share their form, despite their differ-
ent content or subject-matter. If Wales wins, then England
loses; Wales wins; therefore, England loses. If John is tall,
then John is heavy; John is tall; therefore, John is heavy.
Logical calculuses differ according as they concentrate on
different kinds of valid argument forms. For example, the
*propositional calculus is concerned with arguments,
such as the pair just given, which depend for their validity
on the meanings of the truth-functional connectives, here
the meaning of ‘if . . . then’.
Arguments in English are often hard to make out. Bet-
ter to translate English arguments into a logical calculus
which is brief and unambiguous and then determine
whether the translation is a *proof or can be made into a

proof by inserting extra steps. For example, we can trans-
late the simple argument that establishes the defeat of
England into the propositional calculus: let ‘P’ represent
‘Wales wins’, ‘Q’ represent ‘England loses’, and ‘P → Q’
represent ‘If Wales wins, then England loses’. Then we
can make a proof of the translated argument by employ-
ing the rule of inference known as modus ponendo ponens,
which permits the move from a pair of sentences of the
form A and A → B to the sentence of the form B and,
hence, justifies the move from ‘P’ and ‘P → Q’ to ‘Q’ in our
translated argument.
To guarantee that the existence of a proof entails that
the original English argument is valid the rules of infer-
ence must be truth-preserving. A semantics for the calcu-
lus explicates, using the notion of an interpretation, the
idea of a possible situation in which sentences are true or
C