The Oxford Companion to Philosophy Part 100 ppsx

properties of change to demonstrate that change is impos-
sible. (a) The ‘race-course’ (also known as the ‘stadium’ or
‘dichotomy’). A runner has to run a given length. Before
running the whole length, he must have run half of it.
Then, before running the second half, he must have run
half of that half. And so on. Since the division again never
terminates, the whole stretch is composed of infinitely
many successive pieces, each of some length. But the run-
ner cannot finish the task of traversing infinitely many
substretches in succession. (b) The ‘Achilles’. A slow run-
ner is given a start by a fast runner. The fast one can never
catch up: again he has to traverse infinitely many succes-
sive stretches, first to the slower runner’s starting-point,
then to the point the slow runner has reached by then, and
so on. (c) The ‘arrow’. In any indivisible instant of its flight,
is a flying arrow moving or at rest? If the former, how can
it move in an instant? If the latter, it is never moving, and
therefore is at rest. (d) The ‘moving rows’ (also known as
the ‘stadium’) A paradox involving relative motion; the
details are unclear.
(3). Other arguments recorded are: (a) one about
‘place’, again constructing an infinite progression (if
everything that is is in a place, and place is, then a place is
in a place, and so ad infinitum); (b) possibly the first sorites
argument (about the smallest *heap of grain to make an
audible noise when dropped; details unreliable). e.l.h.
G. E. L. Owen, ‘Zeno and the Mathematicians’, Proceedings of the
Aristotelian Society (1957–8).
W. C. Salmon (ed.), Zeno’s Paradoxes (Indianapolis, 1970).
G. Vlastos, ‘Zeno of Elea’, in P. Edwards (ed.), The Encyclopedia of
Philosophy (New York, 1967).

zombies. The zombies of Haitian voodoo lore and horror
movies are the ‘living dead’, but the philosopher’s zom-
bies are merely the stuff of *thought experiments. A zom-
bie, if there could be such a thing, would be a living
creature that was indistinguishable in its physical constitu-
tion and in terms of its outward appearance and behaviour
from a normal human being, but in whom the light of
*consciousness was completely absent: a being with no
inner, conscious mental life, no first-person point of view,
no *qualia—in short, a being such that there would be
nothing it was like to be that being. But could there be such
a being? It is not enough to point out that we can imagine
there being zombies, because not everything that we
can imagine is really possible (*time-travel may be an
example). It may be difficult to determine whether
zombies really are possible, but the issue undoubtedly has
far-reaching implications for the metaphysics of mind.
e.j.l.
D. J. Chalmers, The Conscious Mind (Oxford, 1996).
Zoroastrianism. An ancient Persian religion, most likely
to be known to philosophers either in connection with
Nietzsche’s naming the central character of Thus Spoke
Zarathustra after its founder or because Pierre Bayle in his
Dictionary (1697) presented it as a key to the problem of
evil. Zarathustra is now thought to have flourished in the
middle of the second millennium bc. In an audacious
transvaluation, he proclaimed the gods (daevas) wor-
shipped by the very ancient Persians to be evil. The leader
of the daevas is the eternal opponent of the one good God,
Ahura Mazda. The feature of Zoroastrianism that

attracted Bayle is that the forces of good and evil are about
equally matched. At the end of time Ahura Mazda will
score a final victory, but until then he often fails to control
events. Consequently Zoroastrianism, unlike Christian-
ity, Judaism, and Islam, escapes the paradox of an all-
powerful God who is responsible for what many people
take to be unnecessary *evil. j.j.k.
Mary Boyce, Zoroastrians: Their Religious Beliefs and Practices
(London, 1979).
970 Zeno of Elea
APPENDIX
Logical Symbols
A book like this cannot define the logical symbols precisely, both because they
may have somewhat different definitions in different logical systems, and
because the methods of definition used by logicians cannot be explained in a
few words. The following list merely offers rough equivalents in English for
symbols and letters that are used in the Companion, with a few comments. For a
more generous list of some of the alternatives see the entry ‘notations, logical’.
And do note that any explanation given within a particular article overrides
what is said here.
~ or ¬ or – or N not
· or & or and
∨ or
⊃ or → if (i.e. ‘P ⊃ Q’ and ‘P → Q’ mean ‘If P, Q’; signs for material
implication)
—
3
if (similarly; a sign for strict implication)
≡ or ↔ if and only if (material equivalence)
= is the same as, or if and only if (strict equivalence)

∀ all (‘∀x’ etc. are sometimes written ‘(x)’ etc.)
∃ some, at least one, there exists, i.e. not ∀ not
ٗ or L necessarily
◊ or M possibly, i.e. not ٗ not
∈ is a member of (a set or class)
∉ negates ∈
≠ negates =
∩ indicates intersection
∪ indicates union
Letters are very variously employed, and the following is no more than a guide
to usage in the Companion.What are here called schematic letters (*schema) are
sometimes brought under the general label *‘variables’.
P, Q or p, q, etc. schematic letters for replacement by indicative sentences, or
by names of such sentences
F, G, etc. schematic letters for replacement by predicates (e.g. ‘is a
swan’, ‘laughs’, ‘is to the left of’), or by terms (e.g. ‘swans’,
‘black things’)
∨
R schematic letter for replacement by two-place predicates
(e.g. ‘is to the left of’), or by indicative sentences
S, P schematic letters for replacement by terms
a, b, etc. or X, Y schematic letters for replacement by singular names or refer-
ring expressions (in predicate logic these are written after
predicate letters, e.g. ‘Fa’, ‘Rba’), or by terms
x, y, z, etc. individual variables
α, Γ, ∆, etc. variables used informally, i.e. not as parts of a logical lan-
guage, for talking about—usually generalizing over—
expressions of a logical language, or sets of them
n, m the same for talking about numbers
t, t

1
, etc. the same for time instants
w, w
1
, etc. the same for possible worlds
E, F the same for events
φ, ψ like α, Γ, ∆ etc. or general like x, y, z,etc.
A, B, etc. very general—used either like S, P, etc. or like α, Γ, etc. or like
a, b, etc. or even like P, Q, etc.
Other letters are explained in their places in the book, or are self-explanatory.
c.a.k.
972 Logical Symbols
APPENDIX
Maps of Philosophy
Mapping philosophy is as difficult as mapping the world. Asia and Alaska are
likely to be a whole map-width apart, despite the mere 56 miles that really sep-
arates them. On one projection Africa will look like a squashed-up kidney bean,
on another like a woebegone banana. On one the world itself will appear as an
ellipse, on another as two circles. The world has two hemispheres (east and
west) but also two other hemispheres (north and south). Equal-area and equal-
population maps (where equal areas on the page represent equal areas on the
ground, or equal populations, respectively) may be almost unrecognizable as
Aesthetics
Philosophy
of education
Social
philosophy
Moral philosophy
Epistemology
Logic and

philosophical
logic
Political
philosophy
Philosophy
of language
Philosophy
of history
Philosophy
of science
Metaphysics
Philosophy
of mind
Philosophy
of law
Philosophy of
religion
Philosophy of mathematics
Inner and outer circles of philosophy
referring to the same planet. Yet maps are made and are useful. Most normal
maps (though not all possible ones) will show London as between Cambridge
and Brighton. The situation is the same in philosophy. There is no one way of
mapping it. Different, perhaps overlapping, perhaps inconsistent, maps may be
used for different purposes, and will all be horribly misleading unless used
merely as over-simplified rough guides. It is essential that the reader remember
these points when looking at the following pages.
Inner and Outer Circles of Philosophy
Philosophy can be thought of as concerning what in the most general sense
there is, what we can know and how, and the most general conditions that must
be satisfied by any coherent thought. This gives us the three items in the central

circle. The items in the outer circles are less general and concern limited areas.
They also tend to depend on the central items in ways that those do not depend
on them in return. For instance, moral philosophy often depends on theories of
implication, which belong in logic and philosophical logic, but logic and philo-
sophical logic do not themselves depend for their tools on moral philosophy.
The relation between the two outer circles is somewhat similar, though less
markedly so. Political philosophy, for instance, seems to presuppose moral
philosophy without being presupposed by it. No doubt for these reasons
philosophers have given more attention to the more central items, so that the
diagram also to some extent maps popularity. However, both the circles them-
selves and the regions within them should be thought of as only rather vaguely
delimited. There are multiple overlaps, and in particular no attempt has been
made to order the items within each ring, which are arranged alphabetically,
reading clockwise from the top; no significance attaches to co-radiality.
Groups of Parts of Philosophy
Any grouping is bound to be somewhat arbitrary and roughshod, but the reader
may find it helpful for certain similarities to be pointed out, bearing in mind
974 Maps of Philosophy
I
Epistemology
Philosophy of science
III
Aesthetics
Moral philosophy
Political philosophy
V
Philosophy of education
Philosophy of history
Philosophy of law
Social philosophy

II
Metaphysics
Philosophy of mind
Philosophy of religion
IV
Logic
Philosophical logic
Philosophy of language
Philosophy of mathematics
always that the grouping presented here, though it has the rationale explained
below, is certainly not unique.
Group I has in common a concern with the conditions under which we can
know something, the justifications that we can offer for claims to know it, and
the methods that may help us to come to know it.
Group II asks primarily about what there is, either completely generally or in
certain obviously important spheres such as that of beings as developed as our-
selves or that of the ultimate power, if any, behind the universe. It then asks
about the nature of these various things.
Group III combines various questions concerned in one way or another with
value: what sorts of value there are, what things are valuable in these various
ways, and what connection there is between value and a duty to produce it, as
well as the question what alternatives, if any, to value can be offered as a foun-
dation for our duties.
Group IV mainly concerns abstract structures, and in particular the structure
of any coherent thinking and the tools that are essential for such thinking—
since presumably we could not think in any effective way without language.
Group V, finally, is a bit of a ragbag since it consists of philosophical problems
directed at various particular subject areas. The list could be extended almost
indefinitely, since there are usually at least some philosophical problems
attached specifically to each of the special sciences or other major areas of

human activity. Those mentioned have achieved a certain entrenchment, pre-
sumably because, although each of them has connections with various items in
the other four groups, they are thought to raise more problems of their own
than the philosophies of, say, physics or economics. One special case deserving
mention is the subject often called philosophy of action: its subject is quite gen-
eral and not a particular sphere of human activity; but in fact it is usually
regarded as a branch of philosophy of mind.
Parts of Philosophy and Philosophical Positions and Doctrines
In what follows, those diagrams headed ‘Epistemology’, ‘Metaphysics’, ‘Logic
and philosophical logic’, ‘Philosophy of mind’, ‘Moral philosophy’, ‘Political
philosophy’, ‘Philosophy of language’, and ‘Philosophy of science’ represent
the parts of philosophy, or questions that can be asked, while the others repre-
sent philosophical positions and doctrines, or answers that might be given.
Solid lines represent relations in a tree diagram. Dotted lines represent connec-
tions, as when in the former group the ‘main related subjects’ are listed, or else
emphasize that the items they connect share a greater than usual degree of
overlap, or merge into each other and cannot be sharply distinguished. For
instance, in ‘Theories on mind and body’ property dualism, though presumably
to be classified under dualism, is closely bound up with certain monist views.
The lists of ‘main related subjects’, and items linked only by dotted lines to
the main subject, are not always limited to subjects within philosophy
itself. The few attributions of views to named figures should be regarded as
approximate, sometimes controversial, and of course not exhaustive. There
are more philosophers who might be mentioned in connection with each view.
a.r.l.
Maps of Philosophy 975
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Maps of Philosophy 977
Epistemology Main related subjects
1

See scepticism; fallibilism.
2
See scepticism; common sense; arguments from illusion.
3
See reliabilism.
4
See epistemological justification.
5
See epistemological justification.
6
See holism; epistemological relativism.
7
See the given.
8
See scepticism; fallibilism; epistemological relativism; epistemological justification; foundationalism.
Relations of knowledge
to other notions
Knowledge Knowledge
and certainty
1
and belief
Knowledge Knowledge
and doubt
2
and causation
3
Knowledge and Knowledge Knowledge and
justification
4
and evidence

5
revisability
6
Types of knowledge
Of objects Of concepts Propositional
A priori Empirical A priori Empirical
Innate Intuition Direct Indirect
Philosophy of language Perception Memory
Testimony Inference Abduction
Philosophy of mind
Philosophy of psychology
Evolutionary
epistemology
Philosophy of biology
Anthropology
Naturalized
epistemology
Philosophy of science
Sociology of
knowledge
Moral
epistemology
Moral philosophy
Objects of knowledge
External The The Values Abstractions Minds Philosophy
world past future of mind
Our own Our own Other minds
experiences
7
inner states

Sources of knowledge
Perception Memory Reason Introspection Other alleged
sources
Deduction Induction Other Intuition Telepathy Clairvoyance Precog-
nition
Possibility of knowledge
8
978 Maps of Philosophy
Empiricism
As psychological
doctrine: about
origin of concepts
or knowledge
(locke, hume)
As epistemological doctrine
Of concepts Of propositions
Extreme or Moderate or Extreme: Less extreme: Weak:
strong: all weak: some all knowledge all knowledge some knowledge
concepts are concepts are is of depends on is empirical
empirical empirical sense-data sense-data (locke)
(locke)
As semantic doctrine:
logical empiricism/logical positivism
Re meanings Re meanings
of words: of sentences:
operationalism verificationism
Anti-realism
Conclusive Weak: experience
must be relevant
(ayer)

In practice In theory
(schlick)
Constructive
empiricism
(van fraassen)
Philosophy of
science
Maps of Philosophy 979
Rationalism
As psychological doctrine
(about the origin of our
ideas and beliefs)
Innate Instinctive
ideas ideas
Cartesian Linguistic
(descartes (chomsky)
held both the
versions below)
Strict: Loose:
all ideas some ideas innate
innate (hume’s ‘impressions’)
As epistemological doctrine
(about the justification of
our beliefs)
Innate Intuitions Inescapable
knowledge conceptual
apparatus
(kant; cf.
chomskyan
linguistic

rationalism)
Extreme: Moderate:
senses senses
totally partly
rejected accepted
(eleatics)(descartes,
leibniz)
In moral philosophy
Reasoning Intuition
as basis as basis
of morality of morality
(kant)(kant)
Intuition Intuition
of general of particular
principles moral facts
In religion
Rejection of Rejection of
revelation religion as
such (the
usual meaning
of ‘rationalism’
here)