Naagaarjuna and Zeno on motion

·期刊原文
Naagaarjuna and Zeno on motion

By I. W. Mabbett
Philosophy East and West
Volume 34,no.4
October 1984
P.401-420
(C) by University of Hawaii Press

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P.401

AAryadeva: Master, look out! Zeno of Elea, inspired
no doubt by jealousy of your superior arguments,
has just shot a poisoned arrow at you. Take cover!

Naagaarjuna: Never fear. The arrow will never
arrive, and he knows it. It was a mere empty
gesture of defiance. Look, he has given up waiting
for the arrow to strike me and gone home.

AAryadeva: Nevertheless, I would take cover if I
were you. See, the arrow has already traversed
half the path it has to travel.

Naagaarjuna: You have little faith in the power of
praj~naa. Why, Zeno himself has proved that an
arrow cannot move. At every moment, it is
stationary. The period of its travel is made up of
an infinite number of moments, and at every one of
them it is stationary. So how can it move?

AAryadeva: I wouldn't be so sure of that argument.
About eighteen centuries from now, there are going
to be some mathematicians and philosophers who
will exhibit fatal weaknesses in it. See, the
arrow has traversed three-quarters of its path.

Naagaarjuna: But, my friend, I have [he interrupts
himself and gestures modestly] superior arguments
based on the premises of any opponent you care to
name which prove that there can be no arrow and no
movement. If there is movement, there must be
something moving. Now, if the movement and the
thing moving are two things, the thing moving must
in itself be without movement...

AAryadeva: I agree, but meanwhile the arrow has
traversed seven-eighths of its path. Take cover!

Naagaarjuna: But this is impossible, because the
thing moving must necessarily be actuated by a
movement. So then there would be two movements,
and two things moving, which is absurd. So really
there is no arrow. [The arrow strikes
Naagaarjuna.]

AAryadeva: Oh master! Let me draw out the arrow.

Naagaarjuna: Stay! I wish to get to the bottom of
this. What sort of man can have shot this arrow at
me? What is his stature as a philosopher? Of what
race is he? From what place does he come? What
sort of bow is it that can thus defy all the laws
of dialectics? I need to know how it was made,
what sort of string it possesses, what sort of
shaft the arrow has...

AAryadeva: But, master, is it not written that the
life of one who is struck by an arrow does not
depend on whether the arrow is eternal, or whether
it is not eternal, whether it moves, or whether it
does not move?

Naagaarjuna: I'm glad you said that. I was just
going to say the same thing myself. Draw out the
arrow.(1)

It is difficult to read the kaarikaas of
Naagaarjuna's Muulamaadhyamaka`saastra, in most of
the current editions and translations, without a
feeling insinuating itself into the mind that in
some way Naagaarjuna is exercised by the same
problems as Zeno of Elea, and offers solutions which
use much the same logic, even if they are different.
Jacobi suggested that the two could be compared.(2)
Stcherbatsky commented on the parallel: "It is
noteworthy that a splendid opportunity offered
itself here [that is, in chapter 2 of the kaarikaas]
to Naagaarjuna to repeat, in some form or other,
some of Zeno of Elea's deductions of our usual
conception of motion ad absurdum. The Greek
Philosopher was also a monist, he was anxious to
prove that motion is impossible, because he followed
Parmenides in denying

P.402

plurality. There is no trace of Naagaarjuna having
known them."(3) Kajiyama has seen a resemblance
between the arguments of the two thinkers.(4) Murti
discussed them together and claimed that
Naagaarjuna's arguments are superior because (among
other things) they deny the possibility of rest as
well as motion, while Zeno denied motion only.(5)
Siderits and O'Brien devote an article to the
comparison, and suggest ways in which some of the
arguments in chapter 2 of the kaarikaas can be
interpreted as refutations of the possibility of
motion on the supposition that space or time is
either continuous or discontinuous in structure,
severally.(6)

One important question about Naagaarjuna is
whether his arguments succeed in disproving the
possibility of any coherent account of motion.
Another is whether they are similar to Zeno's. Murti
believes that they do indeed succeed in disproving
motion, and that they are rather different from, and
superior to, Zeno's. Siderits and O'Brien do not
accept them all as valid disproofs of motion, but
consider that they succeed in showing the absurd
implications of the views of Naagaarjuna's
'atomistic' opponents, which was their purpose, and
that they are very similar to Zeno's arguments. I
believe that each of these views is partly right and
partly wrong. I believe that the temptation to make
comparisons with Zeno, however natural, tends
grievously to obscure Naagaarjuna's meaning.

The two thinkers may not have thought the same
things, but there are several telling parallels
between the two men all the same. Here are six.

Zeno bent his disputation to the service of his
master Parmenides, whose philosophy, in bold
contravention of common sense, denied the plurality
of the universe's content. Perhaps this makes him a
monist, but the inference has been denied in some
quarters. Naagaarjuna similarly claimed to show that
we cannot coherently conceive of a universe of
discrete entities somehow linked together. But he
was not a monist. Indeed he denied that he was
anything.

Parmenides' philosophy was an obvious target for
mockery. Zeno sought to defend it by mocking the
mockers--not by proving Parmenides right, but by
demonstrating the contentions of his opponents to
have contradictory implications. This technique
looks like reductio ad absurdum, though it has been
denied that it was so in a formal sense.
Naagaarjuna's technique was, quite explicitly, to
adopt for the sake of argument the assumptions of
his opponents and show them to have absurd
consequences. This looks like reductio ad absurdum,
though we should beware of attributing to
Naagaarjuna a conscious acceptance of a formal logic
essentially the same as western logic.

It follows that the purpose of Zeno's arguments
was not so much to fortify a philosophical citadel
of his own as to raze the battlements of his
opponents. He should be judged, therefore, not by
the validity or profundity of his arguments, but by
his success in refuting those particular
contentions, weak or strong, which happened as a
matter of historical fact to be those of the mockers
of Parmenides. Much the same can be said of
Naagaarjuna, who claimed not to be proving a
particular view correct but to be showing the latent
absurdity of all those views

P.403

he attacked. He forbade inference from the falsehood
of the views he attacked to the truth of their
contradictories, But there is an important
difference here--Naagaarjuna was more ambitious. He
wanted to prove untenable not alone the views of
particular antagonists but all views whatsoever.

Who, precisely, were the antagonists in each
case? Our assessment of Zeno's success requires us
to identify his intended victims, but it is not at
all clear, from the scanty and second-hand fragments
of his teachings extant, exactly who they were. They
may conceivably have included atomists; this
supposition has helped some modern commentators to
make sense of various of the paradoxes. But there
are different ways of taking some of them
(particularly the Stadium), and Zeno's meaning may
have been often misunderstood, The case seems better
with Naagaarjuna, for we can recognize at many
points the schools of Saa^mkhya and Vai`se.sika, and
other opponents. But, as the present discussion
illustrates, it is not really clear at all points
what Naagaarjuna is saying against whom. Perhaps in
places he argues against atomism, but this is at
least not obvious.

Both Zeno and Naagaarjuna have been accused of
sophistry by some commentators. They offer arguments
which may appear at first sight (and perhaps on
further inspection) to be mere trickery, verbal
prestidigitation. Robinson sees Naagaarjuna as (the
American equivalent of) a thimble-rigger.(7) But
both have also attracted a great deal of serious
attention from modern philosophers who find that
their arguments bite on real problems.

Finally, both claimed to show the impossibility
of giving any coherent logical account of motion.

Of course, there is a major difference which,
taking the kaarikaas out of their religious context,
we may overlook. Naagaarjuna's dialectic is not mere
logic, or even mere metalogic. It is heuristic, or
therapeutic. Its function is largely to prepare us
for meditation or mystic insight.(8) I acknowledge
this, but it does not affect what follows. My
purpose is chiefly to clarify what Naagaarjuna means
when he writes about a certain topic. There may be
higher purposes, but this one is sufficient for the
moment.

First Zeno. He propounded many paradoxes
intended to elicit contradictions implicit in
commonsense pluralist thinking. Only some survive,
in often obscure fragments preserved in later Greek
writings. Of those surviving, some (four or five)
concern the possibility of motion. The modern
literature on Zeno is so abundant and technical, and
the problems of interpretation are so complex, that
a bare summary, rather than any serious discussion,
must serve here.

The paradoxes of motion are best introduced by
one that does not itself concern motion but which
well illustrates Zeno's general approach to the
problem of motion, or at least the approach which,
attributed to Zeno, has been used as a term of
comparison for Naagarjuna's approach. This is the
argument about infinite and nil magnitude. If a
thing has any magnitude at all, it must have either
no magnitude or infinite magnitude. As Aristotle
phrases it, "If there exist many things, the things
that exist are unlimited. For there are always other
things in the

P.404

middle of the things that exist, and again others in
the middle of these."(9) That is, any thing is
infinitely divisible. It therefore has an infinite
number of parts (scilicet: parts of equal size). If
each of these has no magnitude, then it does not
exist, and the whole which is the sum of them also
does not exist, since zero multiplied even by an
infinite number is still zero. But if it has any
positive magnitude at all, then the whole has
infinite magnitude. Both results are unwelcome.

This paradox invites us to contemplate a
continuum of space which is divisible into an
infinite number of parts, and elicits difficulties
confronting the addition of divisions of the
continuum. Similarly, the paradoxes of motion invite
us to contemplate continua of space and time which
are divisible into an infinite number of points or
instants.

The Dichotomy argues for the impossibility of
getting anywhere. Before a body can cover a half of
any distance, it must cover the first quarter;
before this, it must cover the first eighth, and so
on infinitely. Before it can cover any positive
distance at all, it must first perform an infinite
number of tasks. So it cannot start. A fortiori it
cannot arrive anywhere, for, supposing that it gets
halfway, it still has to reach the three-quarter
mark, and after that the seven-eighths mark, and so
on, so that it must perform an infinite number of
tasks before it reaches its goal.

The Achilles paradox is, for most purposes,
reducible to the Dichotomy. Achilles, as every
schoolboy knows, raced against the tortoise, which
was given a start. First Achilles had to run to the
tortoise's starting point. While he did so, the
tortoise covered a certain distance. Achilles'
second task was to run to the point reached by the
tortoise while he was performing his first task; his
third task was to run to the point reached by the
tortoise while he was performing his second task:
and so on. Achilles had to accomplish an infinite
series of runs converging upon, but never finally
reaching, the overtaking point. Therefore he never
overtook the tortoise.

The Stadium paradox is the most obscure, and it
is not at all clear what proposition it was intended
to refute. The contradiction said to result from it
is that "half the time is equal to its
double".(10) The explanation given can be construed
in different ways, and considerable ingenuity has
been directed to its interpretation. To be brief,
let us suppose simply that two bodies A and B pass
each other, moving in opposite directions at the
same speed. If this speed is x, then the speed of
each in relation to the other is 2x. Therefore each
is moving both at x and at 2x, which must seem
absurd to anybody who has not grasped that speed is
relative. On this view of the matter, Zeno was
eliciting the inconsistency of an absolute
definition of motion. It is a plausible view if we
suppose that his contemporaries had not clearly
grasped the relativity of speed.(11)

But much of the discussion of the paradox has
rested upon the supposition that Zeno's target was
atomism--the notion that space and time consist of
indivisible ultimate units. Thus, when A has
traveled a distance of one indivisible unit of space
along B which is passing it, it has traveled half a
unit along the

P.405

earth's surface; but by definition there is no such
distance as half a unit, so the result is absurd.
Similarly, if in one indivisible unit of time A has
traveled a distance d over the earth's surface, it
has traveled 2d along B; but there was no time at
which it had traveled d along B, for if there
existed such a time it would have to be half an
indivisible unit, which is absurd.

Finally, the Arrow paradox. A traveling arrow
is motionless. The argument can be reconstructed
something like this: if the arrow is moving during a
period, it is moving at every particular instant
during the period; at any particular instant, it
must occupy a volume of space exactly equal to
itself, no greater; while it occupies this volume,
it has no room to move and so must be at rest;
therefore, while it is moving, it is at rest.(12)

All these paradoxes, except apparently the
Stadium, turn on the problem of infinite division. A
space or line or period of time has an infinite
number of parts, mathematically speaking. Each part
has no room in it for substance or motion; it is
empty (`suunya, we are tempted to say). Therefore
the whole has no room in it either. There are places
where Naagaarjuna has been taken to be denying the
possibility of transition from one part of a
continuum to another because of the emptiness of the
stages that must be traversed. Therefore the two
philosophers may seem to be cooking in the same
kitchen.

What of infinity? It is unfinished, has no
limits. An infinitely large number is not an actual
number, like the number of gods supposed to be on
Mount Meru. For any actual number of parts into
which a continuum may in thought be divided, an
infinite number is larger. So the infinitely small
part is not actually there. To ask of it whether it
has any positive magnitude or not is like asking,
"If I were a completely different person from the
person I am, would I have black or brown hair?" (The
problem of counterfactuals is involved. "If what
does not actually exist actually existed....") The
answer, presumably, is "Whatever you like." We are
in Zen country,

The first part of an unfinished series may
actually exist, but the finish of it does not. So.
even if we can say that there are infinitely many
sets of equal parts into which a continuum can be
divided (the first set containing two equal parts,
the second three, and so on), there is no such set
containing an infinite number of parts.(13)
Therefore Zeno's arguments rest on false premises
and fail to get started. This is true of the Arrow
as well as the others. What is wrong with the Arrow
is not that it conceives of the possibility of
motion at an instant, for this conception is normal
both to ordinary speech and to mathematics. What is
wrong with it is its false assumption that, in order
to be moving at an instant, a body must traverse a
positive distance at that instant. All that is
necessary is that the instant should fall within a
period during which the body is moving. (This has
been shown by Barnes in the place cited.)

On one level of discourse, the language of
ordinary speech applied to mathematical problems
('lower mathematics', let us say) , such
considerations may furnish satisfactory means of
dealing with the problems which the historical

P.406

Zeno is actually likely to have had in mind. We may
notice that these considerations do not attribute to
Zeno, or require for the solution of his conundrums,
any particular theory about the structure of space
and time, nor is it necessary to suppose him to have
been attacking any such theory. To be sure, it is a
useful philosophical exercise, in discussing some
paradoxes, to refer to the theory that space or time
is either continuous or discontinuous in order to
see how it fares under Zeno's broadside. But to say
that much is not to say that Zeno was actually
talking about these particular theories, or even
that it is impossible to discuss the things he
actually said without referring to them.

There is an irony in this, because Zeno and
Naagaarjuna can be made to fit into the same slot
only to the extent that they may be supposed to have
aimed specifically at the continuous and granular
theories. It may yet turn out that both were
innocent of such intentions.

But of course the story does not end there. On
another level of discourse, the level of serious
mathematics, it is not possible to deal so
cavalierly with the problem of infinite division.
For the mathematician, it is indeed normal to treat
a line as if it consisted of an infinite number of
extensionless points. To his habits of thought, the
points are actually there. Therefore, a much more
sophisticated apparatus must be brought to bear if
he is to provide a solution to Zeno's puzzles in
properly mathematical language. Perhaps it was not
until the nineteenth century that mathematics began
to be able to cope with Zeno. A mathematical
meditation on the paradoxes elicits a whole series
of really meaty problems that provide stimulating
exercise for the intellect. As each is solved,
another arises. Salmon writes: "As one peels away
outer layers by disposing of the more superficial
difficulties, new and more profound problems are
revealed."(14) Zeno is an onion. The coherent
conception of an infinite series of terms with a
finite sum, of the performance of an infinite number
of tasks, of a continuum composed of extensionless
points--all these challenges, and more, must be met
before we can get to the bottom of the paradoxes.

So, in the language of ordinary speech, Zeno is
not entitled to speak of an infinite number of
actual parts constituting a whole, and his
juggernaut is quickly stopped; in mathematical
language, he is so entitled, and many technical
problems arise. Is ordinary language right, or is
mathematical language right, or both. or neither? My
feeling is that the question is empty. If there are
to be two rival answers to a question, the answers
and the question must be all in the same language.
If not, they are neither rivals nor allies--they are
not related.

A language is a symbol system. If a symbol
system is to be useful for describing the real
world, it must be internally consistent and it must
be isomorphic with the real world at certain
critical points, but we cannot demand that it be
totally isomorphic everywhere. Therefore a language,
pedantically exploited, is likely to yield fictions
or paradoxes sometimes when it is translated into
practical experience or some other language. The
propositions of high-energy physics

P.407

produce many paradoxes when they are translated into
lay terms. Complex conditional statements in a
highly inflected language like Sanskrit may yield
nonsense when translated literally into Chinese,
That mathematicians use the proposition that a
continuum is composed of infinite numbers of
extensionless points is a fact about the way
mathematical language works rather than a fact about
the real world.

Whether this feeling is correct does not matter
here. What matters is simply that Zeno's
propositions have been read in different
ways--sometimes conceptual, sometimes mathematical,
and perhaps sometimes confused. The same distinction
can be applied to Naagaarjuna.

Let us turn now to Naagaarjuna. The second
prakara.na (chapter) of his
Muulamaadhyamakakaarikaas is presupposed by much or
most of what follows and pivotal to the whole work.
It contains arguments or argument schemata which
later chapters frequently cite as authority for
their own conclusions. It also contains most of the
verses which have lent themselves to the
interpretation that they embody arguments like
Zeno's or are addressed to the same questions as his
paradoxes of motion. Therefore it is necessary to
look closely at this chapter if we are to achieve a
proper comparison between Naagaarjuna and Zeno.

Our troubles begin with the first verse, II. 1:

Gata.m na gamyate taavad agata.m naiva gamyate
gataagatavinirmukta.m gamyamaana.m na gamyate(15)

Here, gata means 'gone' and agata 'not gone'.
Gamyate and gamyamaana have inspired a variety of
translations. S. Yamaguchi, cited by K. K. Inada,
"enlightens us that the final na gamyate refers to
the fact that a certain condition is unknowable or
inconceivable."(16) For gamyamaana, Inada has 'the
present passing away',(17) Streng has 'the present
going to',(18) Sprung has 'what...is just being
traversed', (19) Siderits and O'Brien have
'present-being-gone-to', (20) and May has 'un
mouvement actuel'.(21)

The final gamyate is particularly problematic,
for the verb may be taken either in its normal sense
of 'go' or in the sense of 'observe, understand,
guess'.(22) Monier-Williams attributes this second
sense especially to the passive--'to be understood
or meant'.(23) Translators agree in taking gamyate
upon its first two occurrences in the first sense;
the gamyate at the end of the verse is taken
sometimes in the first sense and sometimes in the
second.

The case for understanding the final gamyate in
the sense of 'observe' or 'understand' rests
ultimately upon the later commentators, for
instance, Candrakiirti, who unambiguously glosses it
as praj~naayate, immediately after paraphrasing
gamyamaana.m na gamyate as na... t.rtiiyam aparam
adhvajaata.m pa`syaamo gamyamaana.m naama.(24)
Candrakiirti explains the double entendre clearly in
his commentary on verse 2.(25) Both Buddhapaalita
and Bhaavaviveka, as cited by Hopkins, had also
followed this interpretation, the first explaining
na gamyate as

P.408

"is not correct because of not being apprehended,"
the second explaining it as "is not
apprehended."(26) A. Saito adds the authority of the
Akutobhayaa for this interpretation, as embodied in
the Tibetan translations.(27)

The case for understanding gamyate in the sense
of 'go' rests upon its contexts. Verse 1 is
concerned, in the first line, to deny the predicate
gamyate of two entities, gata.m and agata.m. In
these two cases, Candrakiirti and translators agree
in taking gam in the sense of 'go'. In the second
line, it is said that a third entity, gamyamaana,
lacks the predicate gamyate. What could be more
natural than to suppose that it is the same
predicate? Otherwise, Naagaarjuna must be supposed
to be making a pun which he cannot be proved to be
making.

Further, in verse 2, Naagaarjuna introduces a
possible objection to his argument, an objection
which asserts that, because activity is in the
gamyamaana, there is really motion (gati) in the
gamyamaana after all. The point is not that
therefore the gamyamaana is perceived; it is that
therefore it has motion. Other things being equal,
it is obviously more natural to regard the objection
in verse 2 as a precise contradiction of the
proposition gamyamaana.m na gamyate; since it says
that there is motion in the gamyamaana, this
suggests that na gamyate denies motion.

Again, as May points out, verse 8 is analogous
in structure to verse 1: it denies the predicate
gacchati firstly to the entity 'goer', and secondly
to the entity `nongoer'; then it asks what third
entity there is apart from these two to which one
could apply the predicate gacchati. Here, fairly
obviously, gacchati means the same ('go') in all
three cases, and is so interpreted by Candrakiirti.
As May says, the double meaning of gam embarrassed
the Tibetan translators of the Prasannapadaa where
`ses pa ('known') is used at verse 1 and `gro ba
('gone') on later occasions.(28)

The authority of Pi^ngala can be added for the
translation 'go'; the zhong-lun translates the last
part of verse 1 as qu shi yi wu qu.(29)

May says that the translation of gam as 'go'
"semble plus naturelle."(30) It will be followed
here.

Only now is it possible to return to the
beginning and consider how the relevant verses
should be translated. Verse 1 denies the single
predicate gamyate to the three entities gatam,
agatam, and, separate from these two, the
gamyamaana.m. That is, literally, it is false to
say, of what has been gone, what has not been gone,
or what is now being gone, that it is gone. How are
we to understand this?

Throughout the kaarikaas, Naagaarjuna is
concerned essentially with the relationship of
dependence. A predicate, characteristic or effect
may be said to depend upon its subject, entity or
cause. The difficulties in defining this dependence
seem to Naagaarjuna, in every case he examines, to
be insoluble.

In the present chapter, the dependence of the
predicate gamyate upon its subject is taken as a
paradigm case. In this first verse, Naagaarjuna is
not thinking of a movement as an event dependent on
a cause or instigator, an agent or 'goer', for that
is a different example considered later on in the
chapter. He appears to be

P.409

thinking of a movement, independently of any cause
or agent, as a change in state. It is a field event.
A movement is the alteration of the field from one
state to another. The field is the space in which
the movement occurs--adhvajaata, according to
Candrakiirti. Of course, Candrakiirti does not have
to be right in taking gamyamaana in this way. There
may be a better way of interpreting the expression,
but until a better way has been established it seems
reasonable to adopt the present one.

It does not, in fact, matter enormously to the
immediate argument how we translate gamyamaana; what
matters is only that it, along with gata and agata,
is an example of a thing ostensibly depended upon,
and Naagaarjuna is concerned to explore the meaning
of the dependence of one thing or property (such as
gamyate) upon another (such as gata, agata or
gamyamaana). For convenience in this case, we can
describe the thing depended upon as the field or
locus of a movement. So the problem is to define the
relationship between the field or locus, the space
in which a movement occurs, and the movement which
represents a change in it or characterizes it. Let
us render the sense of verse 1 as follows:

A field or locus of past motion is not
characterized by movement; similarly a field or
locus without motion is not characterized by
movement either. When the locus with or without
motion is eliminated, the locus of present motion
(also) is not characterized by movement.

The field which is a locus of past motion or
without motion is obviously not characterized by
movement; this much can be accepted at once.
Further, Naagaarjuna announces, the locus of present
motion cannot be said to be characterized by
movement. This more contentious claim he proposes to
establish in what follows.

There are two reasons why this verse might
encourage us to read Zeno's problem mistakenly into
the argument. The first is that it is tempting to
treat gata, gamyamaana, and agata as past, present,
and future conditions, respectively. Thus we imagine
Naagaarjuna to be contemplating a time continuum
which (we immediately suppose) can be exhaustively
divided into past and future, leaving no room for
the invisible present in which movement is now
occurring. But this is not what the text says, and
we must not jump to conclusions.(31)

The second reason is Candrakiirti. On this verse
Candrakiirti offers two comments, of which the first
looks Zenonian but in fact leaves open the central
question. and of which the second undoubtedly is
Zenonian.

What he says first is that, because present,
past, and future are mutually exclusive, a present
movement cannot inhere in the path of a past or
future motion, and we do not observe (na
pa`syaama.h) any third sort of path, where present
motion might occur, besides one characterized by
completed or past motion (gata) and one
characterized by absent or future motion (anaagata).
The question is why we do not observe any such path.
Zeno's answer springs to our minds, but not
necessarily to Naagaarjuna's; in fact in later
verses he will give a different answer.

P.410

But Candrakiirti's further comment clearly
suggests Zeno's answer, and it is this especially
that is liable to prejudice the modern reader of the
kaarikaas. He explains the invisibility of a locus
for present motion by attacking the claim that the
place occupied by a walking foot surely constitutes
a path of present motion. For any particle of matter
within the foot, the place occupied by the whole
foot is already traversed and hence gata (if the
particle is at the tip of the toe), or not yet
traversed and hence agata (if it is at the back of
the heel). We might add, though Candrakiirti does
not say it, that the place is divisible into two
sections (if the particle is in the middle). Since
each particle can in turn be subdivided, it is not
possible to discover a part of the foot which
occupies a path of present motion. (Siderits and
O'Brien, apparently relying on Yamaguchi, offer a
confused account of this passage.
A^ngulyagraavasthitasya paramaa.nor ya.h puurvo
de`sa.h sa tasya gate 'ntargata.h is accurately
translated by Sprung as: "A place which is earlier
for a minute particle located in the tip of the toe
falls for it within the sector of the
traversed."(32) There is no need to invoke scribal
error.) This argument can be made to appear cogent
only with the help of Zeno's approach to the problem
of infinite divisibility.

But Naagaarjuna must be allowed to speak for
himself. In verse 2, leaving aside the ground or
locus of completed and the ground of absent motion,
he takes up the claim that there is indeed movement
inhering in the ground of present motion, since,
after all, movement is where activity (ce.s.taa) is
and activity is in the ground of present motion. In
verse 3 he launches his attack on this claim:

Gamyamaanasya gamana.m katha.m naamopapatsyate
gamyamaana.m vigamana.m yadaa naivopapadyate
How can movement occur as a characteristic of the ground
of present motion, when the ground of present motion does
not occur without movement?

The term vigamana.m ("without movement") in the
second line is not the only reading, but it has been
shown to be correct. The text published by de La
vallee Poussin has dvigamana.m ("double
movement") , probably an error.(33)

Siderits and O'Brien have ingenious Zenonian
interpretations for both meanings. First 'double
movement'. Imagine that both time and space are
granular, composed of ultimate indivisible but
extended units. Suppose that in one such unit of
time, an object moves through two such units of
space. It has arrived at the second of them, but
there was no actual time when it was located at the
first, for such a time would have to be a division
of the ultimate indivisible time unit. So there are
two movements, one proceeding directly to the second
unit of space (required by the premises) and one
passing though the first en route (required by
common sense); but in fact there can be only one
movement, so the theory of granular space and time
is absurd. Now 'without movement'. Imagine that time
is granular or discontinuous but space is
continuous. Thus an object does not move along a
line; at each indivisible instant it is at a new
point, without having

P.411

traversed the preceding interval. So there is no
movement; but in fact there is a movement, so the
theory of granular time is absurd.(34)

These arguments are what Zeno might have meant
if he had said what Naagaarjuna said. However,
Naagaarjuna was not Zeno. It remains to be
discovered what Naagaarjuna meant, and in the next
two verses he goes on to explain his meaning.

Gamyamaanasya gamana.m yasya tasya prasajyate
.rte gater gamyamaana.m gamyamaana.m hi gamyate

If you claim that there is movement of the ground of
present motion, you are committed to the fallacious
consequence that there is a ground of present motion
without movement, for the ground of present motion is
characterized by moving.

Gamyamaanasya gamane prasakta.m gamanadvayam
yena tad gamyamaana.m ca yac caatra gamana.m puna.h

In the movement of the ground of present motion is
fallaciously entailed a double movement: that by which
the ground of present motion is what it is, and that
which is the present motion itself.

In these verses, Naagaarjuna introduces an
argument schema that is fundamental to the main
thrust of his philosophy. It is a trusted friend
through later chapters. And it has nothing to do
with Zeno.

How then are we to understand the argument of
verses 2-5? First let us look at the proposal of
Murti, who paraphrases it thus:

It would be pointed out that there is some such
space as the 'being traversed'; for that is the
place where the activity is present; and this
activity does not pertain to the traversed or that
portion yet to come. But as the activity belongs to
the moving body and not to the space, this
consideration also will not help us to distinguish
that space. It is not possible to ascribe motion to
both, to the space covered and the moving body.(35)

Now let us take Candrakiirti as a guide. Here is
Sprung's translation of the commentary on verse 4:

The one arguing the view that what is in
traverse [i.e. gamyamaana] has motion must think
that, as what is in traverse is a mere name devoid
of motive activity, motive activity is adventitious
to it. According to this view it must follow that
what is in traverse is devoid of motion; that is,
movement would be without motion! For such a one,
what is in traverse moves.... As what is in traverse
lacks motion entirely, for one of such view it
follows that it moves, because the activity Of
motion is fully appropriated by the 'it moves'. The
undesirable consequence follows, therefore, that
what is at present in traverse lacks motion.(36)

Sprung's translation of the commentary on verse
5 is less happy; here is a fresh translation:

One movement is that in relation to which the
locus or path (adhvaa) receives the designation
'ground of present motion'. The second is that
whereby, on the

P.412

basis of that ground of present motion, that locus
or path is characterized by movement. This double
movement is fallaciously entailed if there is
movement of the ground of present motion.

How are we to make sense of this?

Gati and gamana mean "movement," not "moving
body," and Murti's distinction does not seem to be
helpful. We must return to the distinction made
above between the field or locus, adhvajaata, within
which the motion occurs, and the motion itself. The
first is conceived of as the ground or substrate of
the motion, and the motion is conceived of as the
property or characteristic dependent on it.
Candrakiirti correctly understands Naagaarjuna to be
saying that the attribution of movement to the field
in which it occurs entails the absurdity of two
movements. The argument runs thus: the field
(adhvajaata) is one thing, the movement another. The
first movement is the movement which the field
possesses by definition as the "ground of present
movement" (gamyamaana). It possesses the movement a
priori. This first movement is entailed by the very
existence of the field of movement. But the movement
which actually takes place is not an a priori
property; it is contingent and separate. Being a
separate entity, it is added to the field from
outside, so to speak. But the field already
possesses movement by definition; therefore the
movement which is added to it is a second movement.

This argument, whatever we may think of it, is
not like Zeno's. Zeno sought, on mathematical
assumptions, to show the impossibility of analyzing
space, time, and motion. Naagaarjuna sought, on
metaphysical assumptions, to show the impossibility
of analyzing ground and consequent, substance and
attribute.

His argument is made clearer in the following
verses, 6-11, which apply the same schema to the
relationship between subject and verb. As for
substrate or locus of motion and the movement which
characterizes it, so for the agent of motion, the
mover, and its action, the moving. The anomalous
double moving (gamanadvayam) entailed by the
previous analysis of locus and characteristic cannot
be tolerated, because this would entail the
absurdity of two agents, two separate movers, for
there is no moving without a mover (verse 6). A
moving entails a mover and vice versa (verse 7). But
now it is to be shown that the concept of moving is
incoherent. A moving must have a subject, and the
subject must be either a mover or a nonmover.
Obviously it is not a nonmover (verse 8). But it is
not a mover either; "the mover moves" does not make
sense, for there is no mover without moving (verse
9). But the statement "the mover moves," intended to
attribute moving to the mover, in fact implies the
possibility of a mover without a moving (verse 10).
For, if the mover moves, there are two movings: that
by which the "mover" is realized(37) in its capacity
as a mover and that which (in fact, contingently)
moves (verse 11) . That is, "the mover moves"
absurdly entails two movers and two movings. The
subject, the mover, must a priori move if it is to
be designated in the first place as the subject; to
this must be added a second, contingent movement
which is comported by the verb, and this being a
second

P.413

movement must have a second mover. This argument is
sufficiently clear, and the version just given is in
agreement with those of most modern commentators.(38)

So far, then, there appears to be no evidence
that Naagaarjuna was addressing the same problem as
Zeno. One paragraph only of Candrakiirti's
commentary has suggested an approach like Zeno's. It
would be improper to reject Candrakiirti at this
point, and accept his authority at others, if the
kaarikaas themselves bore out the Zenonian
interpretation. But they do not.

Verses 12-14, which argue against the
possibility of any movement getting under way, raise
problems for us.

Gate naarabhyate gantu.m gantu.m naarabhyate 'gate
naarabhyate gamyamaane gantum aarabhyate kuha

Where motion is completed, movement cannot be initiated.
Where there is no motion, movement cannot be initiated.
Where motion is (already) under way, movement cannot
be initiated. Where is movement initiated?

Na puurva.m gamanaarambhaad gamyamaana.m na vaa gatam
yatraarbhyeta gamanam agate gamana.m kuta.h

Before movement is initiated, there is no locus of present
or completed motion where movement might be initiated.
And how could there be movement where there is no motion?

Gata.m ki.m gamyamaana.m kim agata.m ki.m vikalpyate
ad.r`syamaana aarambhe gamanasyaiva sarvathaa

What can be the meaning of a locus for completed motion,
a locus for present motion and a locus devoid of motion,
when we can in no way discover any initiation of movement?

In the verses we might again imagine Zeno's
argument, which contemplates a time continuum and
divides it into past and future sections which
exhaust it. There is no space left for the
durationless present in which something might
happen. In this case, the argument would be that
there is no space between the earlier period of no
movement and the later period of movement in which
the beginning of movement could happen.

Siderits and O'Brien offer two interpretations
of Naagaarjuna's argument, one mathematical (like
Zeno's) , much as the preceding paragraph here
describes, and the other conceptual. They then
reduce the conceptual argument to the mathematical,
thus securing a close analogy to Zeno.

Their conceptual version of Naagaarjuna's
argument appears to be that the concept of the
beginning of motion involves a vicious circle. Gata,
gamyamaana and agata are three moments of time,
past, present, and future, and they are conventional
constructs which cannot be defined except in
relation to the event in question, the movement.
Before the movement begins, therefore, the three
moments cannot be identified. But the beginning of
movement must by definition take place in one of the
three moments, and can be identified only in
relation to them. The moments and the beginning of
movement can be identified only in

P.414

relation to each other. Before the movement begins,
the moments cannot be identified; therefore the
beginning itself cannot be identified.(39)

This is then collapsed into the mathematical
version with the claim that the argument must be
directed against the view of time as an infinitely
divisible continuum. On this view, any attempt to
identify a first instant of motion (which would
qualify as the beginning of movement) must fail,
for, between any instant during the period of
motionlessness before movement, however late, and
any instant during the period of movement, however,
early, there is an infinite number of other
instants, and no one of them can be identified as
the first during the period of movement.(40) This is
the reason the beginning of movement cannot be
identified, and why the three moments cannot be
identified.

Again, it is easy to countenance the proposition
that if Zeno had said what Naagaarjuna said, this is
very likely what he would have meant. Naagaarjuna's
actual meaning, though, may be different.

Prima facie, we would expect to find Naagaarjuna
presenting another phase of his argument for the
unintelligibility of ground and consequent,
substance and attribute, subject and predicate, for
this is the gravamen of his thesis. We must
therefore interpret the beginning of movement as the
attribute whose substance he professes to seek in
vain.

This suits the text very well. In earlier verses
he has argued for the impossibility of linking
movement to a ground or locus. In later verses he
will argue for the impossibility of linking the end
of movement to a ground or locus. Here he is
concerned with the ground for the beginning of
movement. Implicitly, it is an argument against
change.

For a particular change, he considers, cannot
occur in the abstract; it must occur in a particular
physical field identifiable in time and space. It
must be a characteristic of some particular locus.
In the case of the change constituted by the
beginning of movement, it is clear, firstly, that
this locus cannot be the locus of completed
movement, for what is now beginning is by definition
not what is completed. Substance and attribute,
characterized and characteristic, must exist at the
same time. A property cannot be a property of an
entity that has ceased to exist. (This is an
important theme elsewhere in the kaarikaas.)
Secondly, and for analogous reasons, the locus of
the beginning of movement cannot be a locus that is
devoid of motion. Change cannot be a characteristic
of a field that has not begun to change. So perhaps
the locus is a locus of present motion.

Now, the previous paragraph was a loose
paraphrase and elaboration of what Candrakiirti
begins to say under verse 12. It is interesting to
see how he continues. The beginning of movement
"also does not characterize the locus of present
motion because that locus does not exist, (and this
in turn is) because (the existence of the locus of
present motion) would entail the fallacy of two
originations and two originators'' (naapi gamyamaane
tadabhaavaat kriyaadvayaprasa^ngaat
kart.rdvayaprasa^ngaac ca).(41) Here we meet again
the logic of two movings and two movers. If there is
a change, there must be a locus of change; in order
to be

P.415

identified as a locus of change, it must a priori be
characterized by change; if a change occurs in this
locus, which by definition is already characterized
by change, then there are two changes; therefore
there are two entities which change.

The reason why the beginning of movement cannot
be identified is that there is no locus for it. If
there were a locus at all, there would have to be
two loci and two beginnings of movement. The reason
is not that a locus cannot be discovered at any
point along an infinitely divisible time continuum.

It might be said that Zeno's argument against
the possibility of motion getting under way is
better than this one, and that this one needs to be
supplemented by Zeno's. But that does not mean that
Naagaarjuna's argument actually is Zeno's. Siderits
and O'Brien say: "Indeed on this interpretation the
argument seems specious unless we make the
additional assumption that its target includes a
'knife-edge' picture of time."(42) But perhaps it is
specious. There is no necessary disrespect to
Naagaarjuna in saying this, for the whole of the
kaarikaas is supposed to be in inverted commas, as
we shall have occasion to notice again below.

There is nothing else in the remainder of the
chapter which raises any fresh reason for
attributing Zeno's interests to Naagaarjuna. Rather,
there is further evidence of his concern with the
metaphysical question of how substance can be
related to attribute, entity to property, and so
forth. Just as a movement cannot begin in a field
where motion is completed, absent or present, so
too, he argues, it cannot end there (verses 15-17).
Here the argument is precisely analogous to the one
in verses 12-14 about the beginning of movement. It
is impossible to specify the relationship between
entity and property or subject and predicate, such
as mover and movement, for they are neither two
separate things nor one and the same (verse 18. They
are distinguishable, so they cannot be the same
(verse 19), but if they were separate the entity
(mover) could in principle exist without its
property (movement), which is absurd (verse 20).
Therefore we cannot coherently conceive of either
(verse 21). The mover does not carry out the
movement that realizes it, or any other sort of
movement (verses 22-23), neither an existing nor a
nonexisting mover moves, so there is no movement,
mover or locus of motion (verses 24-25).

The whole chapter thus betrays a deep
preoccupation with the logic of the relationship of
dependence. Many arguments can be read into the
kaarikaas severally, but they have a single essence:
the unintelligibility of the dependence of one thing
upon another, of epiphenomenon upon substrate.

How valid is this argument? What assumptions
made Naagaarjuna's argument seem plausible to
anybody? Did it seem plausible to him?

Naagaarjuna's argument assumed the equivalence
of analytical and empirical statements referring to
the same thing. The statement "Devadatta runs," if
true, is true contingently. The statement "The
runner runs" is true analytically. For us, there is
an important distinction to be made between the two
types of statement.

P.416

Naagaarjuna's argument made no such distinction.
According to it, therefore, whatever can be said
correctly about one type can be said correctly about
the other. Therefore, in Naagaarjuna's thinking, if
an entity has a property as a matter of contingent
fact, that is the same as having it by definition,
and having it by definition is the same as having it
as a matter of contingent fact. If a subject has a
predicate, it makes no difference whether it has the
predicate contingently or a priori.

Let us pause to notice the importance of this
distinction. The words that we use are taken to
refer to entities and events. Events and entities
can be analyzed into progressively more basic
constituents. Any entity or event is a more or less
complex cluster of constituent entities or events. A
word for a particular thing is intended to identify
a more or less loosely defined cluster, of which it
should be possible to say what subordinate events or
entities are inside it, constituents of it, and what
others are outside it, separate from it.

It is for the creators and users of language to
determine by stipulation where the boundaries of a
cluster lie. According to purpose and usage, it may
be appropriate, for example, in speaking of a
particular red-painted ball, to treat the cluster
"ball" either as including or not including its red
paint. "I am going to take this ball and paint it
red"--the ball exists whole apart from its paint. "I
mistook the ball for a tomato"-the ball includes its
paint. In each case, being red is a property of an
entity, the ball. In the one case, the property is
attached from outside: in the other, it is a
constituent of the entity. For many purposes and on
many occasions, it does not matter where the
boundary lies, and usage is vague. Sometimes it
matters, and we must stipulate.

"The runner runs." Here the property of running
is clearly a constituent element within the cluster
identified by 'runner'. That is why it is an
analytical statement. "Devadatta runs." Here the
property is attached to the cluster from outside,
for the word 'Devadatta' draws the boundary in a
different way. So it is an empirical statement; it
points to a merely contingent relationship.

Naagaarjuna's argument cannot admit that
different words draw different boundaries. There is
a unique individual running, and it has unique
boundaries. Therefore with seeming plausibility the
argument can proceed. "Devadatta runs." Since we can
distinguish between the person, Devadatta, and the
property of running, they cannot be numerically
identical. The property of running is separate and
attached from outside. But what is this Devadatta to
which the property is attached? In order to have the
property attached to him, he must be a runner.
Therefore (by definition) the property of running
must be part of what we identify when we identify
Devadatta. His running is a constituent of his
identity. Yet the running was originally supposed to
be attached from outside, so that in himself he
lacks running. So we find that he both possesses and
lacks running. and that there are two runnings--the
one that is constituent of him and the one that is
contingently attached from outside.

This is putting words into Naagaarjuna's mouth,
but they are very close to his

P.417

own. Dwarfs climb on giants' shoulders, and can see
farther: with the advantage of modern thought we can
see the fallacy clearly enough.

Was Naagaarjuna taken in? Ostensibly, of course,
this is a mistaken or at least trivial question.
Maadhyamaka dialectic did not espouse any views, we
are told; it merely sought to expose the absurdity
of others' views by accepting their premises for the
sake of argument and drawing out the contradictions.
In the case of the arguments considered above, the
opponents under assault were those who (a) believed
that it is possible to speak coherently of the
dependence relationship between substance and
attribute, subject and predicate, and (b) failed to
distinguish between analytical and empirical
statements.

Yet it may be that, in showing the absurdity of
the dependence relationship upon premises that
confuse analytical and empirical statements,
Naagaarjuna really believed that he had shown the
absurdity of the dependence relationship upon any
premises whatsoever. After all, his arguments do not
so much explain the confusion responsible as
manifest it. This is another matter. There is no
need to explore the question here.

There were indeed people who debated whether
space or time is granular or infinitely divisible,
but there is no evidence that these were
Naagaarjuna's targets. Therefore there is no
evidence that he was concerned with zeno's problems.

Yet, indirectly, there may be some consonance
between Zeno's problems and Naagaarjuna's. Those who
failed to distinguish properly and consistently
between the analytical and the empirical found
themselves unable to account satisfactorily for
change. If a thing has a property at all (it seemed
to them), it has it essentially, necessarily, and a
priori. Therefore it has it as lone as it lasts. If
anything exists at all, whatever is true about it
must be eternally true about it. Hence it was
natural for the word "exist" to acquire the meaning
"exist eternally." The problems raised by these
assumptions were a constant stimulus and irritation
to Indian philosophers, like the grain of sand
around which the oyster builds its pearl; major
doctrines were addressed to these problems,
especially the problem of svabhaava which is a
refrain of the kaarikaas. For debaters confronted by
the problem of the eternity of what exists, the most
urgent issue of all was between an unchanging
universe and an unreal one. (Both the Buddha and
Naagaarjuna, in their different ways, sought to
avoid the issue; but they could not help being
exercised by it.)

Now, Heraclitus, like a good Hiinayanist,
believed in a universe in constant flux, with
nothing solid and lasting in it. You cannot cross
the same river twice. Parmenides, Zeno's master,
took an opposite view: there is no plurality, no
change. In the words of the kavir.si Hector Monro:

According to the views of Heraclitus
The universe is one eternal fidget,
Wriggling and writhing like the village ijjit,
Or any of the pop groups that now blight us.
The river flows with nothing firm to bridge it,

P.418

The variable denotes no constant digit,
The candle burns in honour of saint Vitus.
Parmenides, a far more stable character,
To this continual shimmying remonstrant,
Protested at a Cosmos so inconstant.
Penelope, when all the suitors barracked her,
Not Hollywood's promiscuous animality,
He thought the proper model for Reality.(43)

Zeno attacked motion and plurality in the
service of his master's radical antipluralism. So
did Naagaarjuna, from a different point of view.

Now, as it turns out, we can transform each of
them into the other by turning him back to front.
For one, there is no motion because it never starts;
for the other, there is no motion because it has
eternally ended.

Imagine that they are in competition to woo
Penelope. Both set out at the same time to press
their suit upon her. Zeno, by his own account, will
never get past his own front door, so he is out of
the running.

The case is quite other for Naagaarjuna. If one
who sets out has the property of arriving, it is
obvious that the setter-out and the arrival must
exist at the same time. Otherwise there is no way of
bridging the gap between substance and attribute.
The entity has its property a priori. Of course,
Naagaarjuna's main conclusion is that entities
cannot coherently be said to have properties at all.
But if, on the level of conventional truth, we wish
to speak of entities having properties, we are
committed to regarding them as having those
properties by definition (verse 3: gamyamaana.m
vigamana.m... naivopapadyate) . Therefore, if
Naagaarjuna is a setter-out who has the property of
arriving, the setter-out has that property by
definition.

So, if he arrives at all, he arrives
instantaneously. This is not as good a performance
as that of the celebrated lady in the limerick about
another sort of relativism, but it is sufficiently
impressive.

But there is more. The arriver who arrives not
only possesses the property of arriving that
actually arrives; he possesses also the property of
arriving that realizes him as an arriver. So there
are two arrivings; therefore there are two arrivers.
Two Naagaarjunas appear at Penelope's house, and she
will be able to conduct a small svaya.mvara. As
Murti says, Naagaarjuna is the master dislectician.
He has it all over Zeno.

NOTES

1. This dialogue is inspired in part by the one
by A. Shimony in W. C. Salmon, ed., Zeno's Paradoxes
(Indianapolis, Indiana: Bobbs-Merrill, 1970), pp.
1-3, in which Zeno is eaten by an escaped menagerie
lion. "A real lion, perhaps; but really running,
impossible, and really arriving here, absurd!"

2. H. Jacobi, "The Dates of the Philosophical
Suutras of the Brahmans," Journal of the American
Oriental Society 31 (1911): 1-29.

p.419

3. Theodore Stcherbatsky, The Conception of
Buddhist Nirvaa.na, ed. J. Singh (Delhi: Motilal
Banarsidass, 1968), p. 147, n. 4.

4. Kajiyama Yuichi, Kuu no ronri (Tokyo:
Kadokawa Shoten, 1970), cited in Mark Siderits and
J. Dervin O'Brien, "Zeno and Naagaarjuna on Motion,"
Philosophy East and West 26, no. 3 (1976): 281-299;
hereafter cited as Siderits and O'Brien, "Zeno and
Naagaarjuna."

5. T. R. V. Murti, The Central Philosophy of
Buddhism (London: George Allen and Unwin,
1955/1980), pp. 178-184; hereafter cited as Murti,
Central Philosophy.

6. Siderits and O'Brien, "Zeno and Naagaarjuna.

7. Richard H. Robinson, "Did Naagaarjuna really
Refute All Philosophical Views?" Philosophy East and
West 22, no. 3 (1972): 325-331.

8. See Edward Conze, Buddhist Thought in India
(London: Allen and Unwin, 1962), pp. 241-244; J. W.
de Jong, "Emptiness," Journal of Indian Philosophy 2
(1972): 7-15.

9. Cited by Jonathan Barnes, The Presocratic
Philosophers, vol. 1 (London: Routledge and Kegan
Paul, 1979), p. 239.

10. Ibid., p. 286.

11. Ibid., pp. 291-294.

12. Ibid., pp. 276-278.

13. The last sentence represents the conclusion
argued in ibid., pp. 245-252.

14. W. C. Salmon, ed., Zeno's Paradoxes
(Indianapolis, Indiana: Bobbs-Merrill, 1970), p. 43.

15. Except where otherwise specified, quotations
are from the text edited by J. W. de Jong,
Muulamaadhyamakakaarikaa.h (Adyar: The Adyar Library
and Research Centre, 1977).

16. Naagaarjuna, A Translation of His
Muulamadhyamakakarikaa, Kenneth K. Inada, ed.
(Tokyo: The Hokuseido Press, 1970), p. 44; hereafter
cited as Inada, ed., A Translation.

17. Ibid.

18. Frederick Streng, Emptiness: A Study in
Religious Meaning (Nashville, Tennessee; Abingdon
Press, 1967), p. 184.

19. Candrakiirti, Lucid Exposition of the Middle
Way: The Essential Chapters from the Prasannapadaa
of Candrakiirti, M. Sprung, trans. and ed. (London
and Henley: Routledge and Kegan Paul, 1979), p. 76;
hereafter cited as Sprung, trans., Lucid Exposition.

20. Siderits and O'Brien, "Zeno and
Naagaarjuna," p. 289.

21. Candrakiirti. Prasannapadaa
Madhyamakav.rtti, trans. J. May (Paris: Adrien
Maisonneuve, 1959), p. 52; hereafter cited as May,
trans., Prasannapadaa.

22. Sir Monier-Williams, A Sanskrit-English
Dictionary (Oxford, 1899/1976), s. v. gam.

23. Ibid.

24. Candrakiirti, Prasannapadaa naama
madhyamikav.rtti, ed. L. de la Vallee Poussin (St.
Petersburg: Bibliotheca Buddhica, no. 4. 1903-1913),
p. 43, lines 7, 8; hereafter cited as Poussin, ed.,
Prasannapadaa.

25. Candrakiirti p. 94 line 4; cp. May, trans.,
Prasannapadaa, p. 57, and J. Hopkins, trans.,
Analysis of Going and Coming. The Second Chapter of
Candrakiirti's 'Clear Words', a commentary on
Nagarjuna's `Treatise on the Middle Way'
(Dharamsala: Library of Tibetan Works and Archives,
1974), from p. 26, no. 10.

26. Hopkins, trans., Analysis, p. 25, no. 4.

27. "The same interpretation about 'na gamyate'
is also found in Akutobhayaa, Buddhapaalita, and
Praj~naapradiipa, which Tibetan translators
correctly rendered into Tibetan: ses par mi.hgyur ro
[ABH D Tsa 35a7, BP D Tsa 168b5, PP D Tsha 64a7] in
accordance with the commentators' understanding" (A.
Saito, personal communication).

28. May, trans., Prasannapadaa, p. 55, no. 17.

29. Taisho Tripi.taka, vol. 30, no. 1564, 3c.

30. May, trans., Prasannapadaa, p. 55, no. 17.

31. Cp. Kenneth K. Inada, ed., A Translation, p.
43, which also points out that agata is not
necessarily 'future' and cites Kumaarajiiva's
accurate Chinese translation.

32. Siderits and O'Brien, "Zeno and
Naagaarjuna," from p. 289; Sprung, trans., Lucid
Exposition, p. 77.

33. Poussin, ed., Prasannapadaa, p. 94. Cp. J.
W. de Jong, "Textcritical Notes on the
Prasannapadaa," Indo-Iranian Journal 20(1978): 25-59
at p. 36.

P.420

34. Siderits and O'Brien, "Zeno and
Naagaarjuna," from p. 290.

35. Murti, Central Philosophy, p. 179.

36. Sprung, trans., Lucid Exposition, p. 79.

37. This follows de Jong's reading, caajyate,
not the alternative, cocyate.

38. E.g., Murti, Central Philosophy, from p.
179.

39. Siderits and O'Brien, "Zeno and
Naagaarjuna," from p. 295.

40. Ibid., p. 296.

41. Poussin, ed., Prasannapadaa, p. 100.

42. Siderits and O'Brien, "Zeno and
Naagaarjuna," p. 296.

43. H. Monro, The Sonneteer's History of
Philosophy (Clayton: Ancora Press, 1981), p. 8.