## 1. The Vaisesika System of Categories


### 1.1 Methodology and Theory of Definition



Most Nyaya-Vaisesika texts are structured in one of
two ways. They either follow a traditional Vaisesika
pattern, in which the categories and their various sub-groups are
discussed in order, or else they follow a pattern employed by the
Buddhist logician Dinnaga, and copied by
Gangesa, in which each of the sources of knowledge is
treated in turn. *The Manual of Reason*, however, adopts a
style of analysis due to Vatsyayana (the first commentator
on the *Nyaya-sutra*). Vatsyayana stated
that:



> 
> This [Nyaya] system will follow a three-fold procedure, viz.
> enumeration (*uddesa*), definition
> (*laksana*) and examination
> (*pariksa*). Of these,
> 'enumeration' means the act of referring to each object
> [to be analysed] by name; 'definition' means [citing] a
> characteristic of the named object which distinguishes it from all
> other objects; 'examination' means ascertaining, with the
> help of the *pramanas*, the appropriateness of the
> distinguishing characteristic for the object defined
> (*Bhasya* before NS 1.1.3).
> 



The heart of this method lies in the use it makes of definitions,
conceived of as differentiating marks of the thing defined. *The
Manual of Reason* (TSD 3d) refines the idea: it defines a
'definition' of a class of things as any characteristic
which is co-extensive with that class. A defining characteristic of
the class 'cow' is the property 'having
dewlap'. Note that this does not tell us what the
*essence* of the class is--it merely supplies us with a
syndrome or *trait* by means of which we can identify the thing
in question. The Naiyayikas, we might say, have a
'diagnostic', rather than an 'essentialist',
conception of definition. The purpose of the 'examination'
now becomes clear: it is to see whether the alleged defining trait
really is co-extensive with the class to be defined, or whether it is
faulty, either by 'over-covering' (cf.
*ativyapti;* applying to things outside the definiendum)
or by 'under-covering' (cf. *avyapti*; not
applying to everything within the definiendum), or both. A properly
defining characteristic has to be, to use modern terms, both a
necessary and a sufficient property of the thing to be defined. We see
the pattern of enumeration, definition, and examination repeated again
and again in Navya-Nyaya texts like *The Manual of
Reason*.


### 1.2 What is the Vaisesika System of Categories?



The Vaisesika system of 'categories'
(*padartha*) is an attempt to classify in a systematic way
all the different types of existent. Navya-Nyaya lists seven
'categories' of object: substance (*dravya*),
quality (*guna*), motion or action (*karma*),
universal (*samanya*), particularity or
differentiator (*visesa*), inherence
(*samavaya*), and absence (*abhava*). Of
these, the first six comprise the classical list of categories, found
even in the *Vaisesika-sutra*, while the
seventh (absence) is a distinctive addition by the later school. Most
of these types are themselves subject to sub-division: thus, there are
nine types of substance, twenty four types of quality, etc.



One main question concerning this list of categories is whether we can
discern any underlying structure or organising principle. This is
related with another important question: just what is a category?
*The Manual of Reason* answers this second question by giving
the etymological analysis of the term
'*padartha'* (category):
'*padartha'* is the *artha* or meaning
of a *pada* or word. The claim is that the Vaisesika
categories are in some way the metaphysical correlates of linguistic
structures. One way to make this claim more precise would be to note
the existence of striking similarities between the
Vaisesika system and Sanskrit grammar (cf. esp. Faddegon
1918). Another way is to observe a distinctive pattern of argument
employed, in which the hypothesis that a certain type of substance,
quality, etc. exists is supported on the ground that it explains some
feature of our linguistic practice (for example, the argument that
space exists as it explains our use of directional terms.)



An alternative approach would be to seek some purely *apriori*
rationale behind the list. Athalye (1930: 75) offers one such:



> 
> A notion is either positive or negative, and so the external object of
> a notion might be 'existent' (*bhava*) or
> 'non-existent' (*abhava*).
> 'Existent' things again are of two kinds, properties and a
> common substratum in which they reside. The latter is
> 'substance' (*dravya*). Of the properties, again,
> some reside in many objects conjointly, others in individual things
> singly. The first is 'universal'
> (*samanya*), while the latter class is again
> divisible into properties that are stationary and those that are
> evanescent, i.e. 'quality' (*guna*) and
> 'motion' (*karma*). The remaining two categories,
> 'inherence' (*samavaya*) and
> 'particularity' (*visesa*) are assumed
> to explain the special theories of the Vaisesikas.
> 



This reconstruction of the Vaisesika system is not quite
satisfactory, for it relies on an unexplained and perhaps
question-begging distinction between stationary and evanescent
properties, and leaves two of the categories completely unaccounted
for. Another reconstruction (also deficient) is offered by Potter
(1977). When we look at *The Manual of Reason*'s own
definitions of the individual categories, it seems to be following
this approach. *The Manual of Reason*'s definitions are
as follows:



Substance

(i)
 that which possesses the universal substance-hood;
(ii)
that which possesses qualities (TSD 3)

Quality

(i)
that which possesses universals, and isn't a substance
or motion;
(ii)
that which possesses the universal quality-hood (TSD 4)


Motion

(i)
that which causes conjunctions (between substances);
(ii)
that which possesses the universal motion-hood (TSD 5)


Universal
that which is eternal, unitary, and inherent in many things (TS
82)
Differentium
that which exists in eternal substances and functions as their
differentiator (TS 83)
Inherence
that thing which is eternal and a relation (TS 84)
Absence
[No general definition given]


There are certain problems with this series of definitions, read as an
*apriori* reconstruction of the categories. In particular, the
definitions of 'substance' and 'quality' seem
to be jointly circular, unless we take as already given universals
such as substance-hood, which make the definitions somewhat vacuous. I
will give another reconstruction, one which roughly follows the great
Nyaya-Vaisesika author Udayana (cf. Tachikawa
1981).


## 1.3 The Underlying Structure of the List



First divide things up into the existents and the non-existents, the
latter corresponding to the category 'absence'. Now take
inherence to be a primitive, fundamental relation. Given such a
relation, the following three-fold division is exhaustive:


1. things which do not inhere in others, but are inhered in,
2. things which both inhere in others, and are themselves inhered
in,
3. things which inhere in others, but are not inhered in by
anything.



We want group (a) to correspond to the category
'substance'. Unfortunately, the Vaisesikas
claim that wholes are distinct from, and inhere in, their parts. The
only substances which do not inhere in anything are the atomic
substances (which for the Vaisesikas correspond with the
eternal substances). Group (c) corresponds to the category
'universal', for universals are said to inhere in things
(substances, qualities and motions) but do not have anything inhering
in them. Group (b) comprises, the non-atomic substances, the qualities
and the motions. Let us now divide this group into two: those which
are inhered in only by universals, and those which are inhered in by
other things as well. The former corresponds to the categories
'quality' and 'motion', for substances are
inhered in, not only by universals, but also by qualities, motions, as
well as by other substances. Finally, we must find a way to sub-divide
the former group into qualities and motions. More traditional
Naiyayikas preserve the distinction by saying that motions, but
not qualities, cause the substances in which they inhere to come into
contact with (or break away from) each other. This, however, appeals
to the idea of 'contact', which cannot itself be defined
in terms of our primitive relation inherence. Some radical
Naiyayikas (especially Bhasaravajna) claim that
motions are just a kind of quality, as their properties are so
similar. The only remaining category is 'differentium'
(*visesa*), whose members reside in and individuate
the eternal substances i.e. the atoms. The point, perhaps, is that all
other things are individuated by the universals and wholes that inhere
in them, but two atoms of the same substance are in all respects
identical. But if objects are individuated by means of what inheres in
them, then there must be something inhering in each atom which
distinguishes it from the others--a 'differentium'
(see SS10.2).



This is a rough sketch, omitting many technicalities, of how the
Vaisesika philosophers tried to build their system of
categories on logical principles (for an example of such
technicalities, see TSD 3(c). *The Manual of Reason* points out
that a substance cannot be defined as the substratum of qualities,
because of the Vaisesika doctrine that substances do not
possess any qualities at the moment when they are created.)


## 2. Physical Substance


### 2.1 The Five Primary Physical Substances



Vaisesika distinguishes, among nine acknowledged types of
substance, a sub-class of five--earth, water, fire, air and
*akasa*--to which it gives the name
"*bhuta*" ('physical substance').
A *bhuta* is defined as a substance which possesses a
specific sensible quality--odour, taste, colour, touch and
sound.



It was, perhaps, originally thought that the five physical substances
and the five sensible qualities are directly correlated, each quality
residing in one and only one substance, odour just in earth, taste
just in water etc. (such a view is reported by Vatsyayana
under NS 3.1.65-6). This may give some insight into the origins
of the 'five physical substances' theory, but it was
realised very early on that it is extremely implausible to maintain
that earth, for example, is invisible, or else that its colour is
always due to intermixture with fire (Bhaduri 1947: 133). The set of
correlations between physical substances and sensible qualities is
more complex in the *Vaisesika-sutras* and
later texts, and is indicated in the following chart:




|  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- |
|  | odour | taste | colour | touch | sound |
| earth | x | x | x | x |  |
| water |  | x | x | x |  |
| fire |  |  | x | x |  |
| air |  |  |  | x |  |
| *akasa* |  |  |  |  | x |



The orthodox Vaisesika view is that each physical substance
is characterised by the possession of a particular type of sensible
quality and the absence of certain others. Thus, earth is the
substance endowed with odour, water with taste but not odour, fire
with colour but not taste or odour, etc. A drawback of such
definitions is that we cannot infer, from the detection of a sensible
quality, which type of substance is present. Later
Vaisesika therefore looks for a diagnostic set of
definitions, one which seeks to find, for each substance, a particular
sensible quality whose presence is indicative of that substance. The
*Manual of Reason* (TS 10-14):



> 
> Earth is (specifically) endowed with odour
>   
> 
> Water is (specifically) endowed with cold touch
>   
> 
> Fire is (specifically) endowed with hot touch
>   
> 
> Air is (specifically) endowed with touch without colour
>   
> 
> *akasa* is (specifically) endowed with sound.
> 



Thus, although earth, water, and fire are all tactile, only water
allegedly has cold touch. It seems that it could find no positive
distinguishing trait for air, and thus reverted to the older style of
definition.



It is perhaps surprising to find a 'five elements' theory
defended still in the seventeenth century. Some modern writers have
tried to represent these substances as metaphors for different
'states' of matter--solid (earth), liquid (water),
gas (air), and temperature (fire). This is, however, improbable, for
it is nowhere said that a particular substance can turn from earth to
water to air. Perhaps it is a mistake to see the theory as belonging
to physics at all; instead, bearing in mind the way the substances are
defined in terms of their sensible qualities, we might see it as an
exercise in the logical analysis of the data presented by the various
sense modalities to construct a (metaphysical) theory of the world.
Such a theory would, for example, explain the fact that there are
correlations between what we see and what we touch by positing that
there must be types of things which can be both seen and touched.
Likewise, the occurrence of tactile sensations with no correlated
visual sensations leads us to postulate the existence of substances
which can be felt but not seen (air), and so on for the other
substances. It is, after all, the existence of such correlations
between different sense modalities which grounds an objective
conception of the world (phenomena accessible only by one sense are
more likely to be thought of as subjective in origin).


### 2.2 Vaisesika Atomism



*The Manual of Reason* (TS 10-14) repeats the
conventional Vaisesika theory that the first four
substances (earth, water, air, fire) are each of two types, atomic and
composite. An atom (*paramanu*) is indestructible
(*anitya*), indivisible (i.e. non-composite), and has a special
kind of dimension, called "small" (*anu*).
The Vaisesikas' standard argument for atomism is as
follows. It is an empirically established truth that whatever is
perceived is composite. Thus even the smallest perceptible thing,
namely, a fleck of dust in a sun-beam, has parts, which are therefore
invisible. The Vaisesikas call the smallest perceptible
thing a "triad" (*tryanuka*) and claim that
it has three parts, each of which is called a "dyad"
(*dyanuka*). Does each of these parts itself have parts?
Yes--for it is another empirically established truth that the
parts of a visible thing themselves have parts (e.g. a piece of cloth,
whose parts, the threads, are themselves composite). The
Vaisesikas say that a dyad has two parts, each of which is
an atom.



This argument establishes that there are objects too small to be seen,
but it does not demonstrate that some of them are non-composite. Why
cannot the process of sub-division be continued ad infinitum? *The
Manual of Reason*'s intriguing answer is that if such were
the case then Mount Meru and a mustard seed would have the same size,
as each would have the same (infinite) number of constituent parts! An
implicit premise here (articulated by other Vaisesikas) is
that the size of a whole is a function of the size, number and spatial
arrangement of its parts.



The argument seems to be question-begging, for the implicit premise is
only true if atomism is already accepted. A non-atomist will say that
the size of an object is determined, not by its constituents, but by
the spatial boundaries of the 'stuff' it is made of.


### 2.3 The Metaphysics of Number (*samkhya*)



The Navya-Nyaya account of number has been likened in content and
sophistication to that of Frege, and is indeed fascinating. *The
Manual of Reason* says only that numbers are qualities
(*guna*-s), that they are the ground for numerical
judgements, and that they range from 1 to a very high number called
*parardha* (1014. Note here again discomfort with the idea
of infinity). The view that numbers are qualities is in fact
associated with old Vaisesika, and turned out to be
irreconcilable with the structure of the Vaisesika
ontological system. We may speak of there being three horses in the
field, but also of there being 24 qualities in the
Vaisesika system. Yet a quality cannot by definition reside
in another quality--hence numbers cannot be qualities. This
problem led the Navya-Naiyayikas to develop a new account of
numbers, based on a new type of relation called the
*paryapti* or 'completing' relation.



Here is a summary of their theory. Consider the following pair of
sentences:


1. The table has wooden legs
2. The table has four legs.



The similarity between (1) and (2) suggests that we think of
number-words as akin to other adjectives, i.e. as attributing some
property to the object/s they qualify. The Nyaya say that, in
(1), the property of being wooden resides in the legs of the table by
the relation of inherence. Can we analyse (2) the same way, as stating
that a universal property four-hood inheres in the legs? The new
Nyaya (esp. Raghunatha and Jagadisa) answer in the
negative. For note that (1) entails


3. Each leg is wooden.



However, (2) does not entail,


4. Each leg is four.



The solution offered is to postulate a new relation,
'completion', which relates the property fourhood to the
four legs *jointly*, but not to each leg individually.
Raghunatha remarks that "the 'completion'
relation, whose existence is indicated by constructions such as
'This is one pot' and 'These are two', is a
special kind of self-linking relation." His commentator
Jagadisa adds:



> 
> It might be thought that the 'completion' relation is
> nothing but inherence...So Raghunatha states that
> 'completion' is a another relation....In a sentence
> like "These are two pots", 'completion'
> relates the property two-hood by delimiting it as a property which
> resides in both pots. Otherwise, it would follow that there is no
> difference between saying "These are two" and "Each
> one possesses two-hood".
> 



The proposal is that number properties are related jointly to objects
by the many-one relation 'completion'. I think we can
simplify this proposal a little without losing its essential
structure. Rather than saying, in a sentence like "Mars is a
planet", that the property planethood resides in Mars by the
inherence relation, we would now say that the predicate
"...is a planet" is true of Mars, so to speak
building the inherence relation (or copula) into the predicate. In an
entirely analogous way, we can build the completion relation into the
number-predicate, which then becomes, if the number is *n*, an
*n*-place relation. Thus the sentence "Venus and Mars are
two" asserts of Venus and Mars that they stand in a certain
2-place relation, the relation which is the number 2. The Nyaya
idea, then, is that number-adjectives are *n*-place relational
predicates, and that numbers are *n*-place relations holding
jointly between *n* distinct objects. It in no way follows from
the statement that the relation 2 holds between Venus and Mars, that
it holds just with Venus, any more than it follows from the statement
that *X* is to the left of *Y*, that *X* is to
the left, full stop. On the Nyaya proposal, then, it looks as
though the troublesome inference is blocked because its conclusion is
not even well-formed, since the phrase "Venus is two",
like the phrase "*X* is to the left", is an
incomplete or unsaturated expression.



The Nyaya, we have seen, distinguish two relations, the inherence
and completion relations. Their motive is, as we might now say, to
account for the distinction between collective and distributive
properties. For the recognition that the inference from "These
are two pots" to "Each pot is two" is invalid is
just the recognition that the predicate two does not distribute over
plural subjects. The Nyaya idea is to analyse collective
predicates like '...are two', not as one-place
predicates of aggregates or sets, but as n-place relational
predicates, true of n objects jointly. But since such relational
predicates still take objects as subjects, this indeed shows that
recognising the distinction between distributive and collective
predicates does not force us to abandon the adjectival view. The
Nyaya, indeed, have a term for collective properties: they call
them *vyasajya-vrtti-dharma* or 'properties
which occur jointly'.



## 3. Space, Time and Motion


### 3.1 Space (*dik*)



*The Manual of Reason*'s remarks on the nature of space
and time are sketchy in the extreme. We must supplement them with
details from other Vaisesika and Nyaya authors. Even
then, the theories of space and time found in
Nyaya-Vaisesika texts have been studied very little,
and we can only form a rough and inadequate picture at the present
time. *The Manual of Reason*'s observations concerning
the notion of space are as follows:


1. Space is a substance (TS3)
2. Space is the 'ground' for statements such as
"this is east of that" etc. (TS 16)
3. Space is unique, ubiquitous, and eternal (TS16).
4. Space is an instrumental cause of every effect (TSD16).
5. 'Nearness' (*aparatva*) and
'farness' (*paratva*) are spatial qualities of
objects.



Space is conceived of as that substance in virtue of which statements
attributing distance and direction, such as "*A* is to
the east of *B*" (or "*A* is near to
*B*", "*A* is nearer to *B* than to
*C*", etc.) are objectively true or false. Space is thus
an explanatory postulate: it is argued that we must postulate the
existence of a new (spatial) substance to explain the fact that
objects stand in spatial relations with one another. The problem is to
make sense of this claim. Bhaduri (1947: 216-7) does so as
follows (I paraphrase his account):



> 
> Imagine a sequence of objects *A*, *B*, *C*,
> *D*, ..., *F*, each in contact with the next,
> arranged in a line. Now *A* is to the left of *B*, and
> *B* is to the left of *C*, and since "being to the
> left of" is a transitive relation, *A* is to the left of
> *C*, etc. But, although *A* is in contact with
> *B*, and *B* is in contact with *C*, it is not
> true that *A* is in contact with *C*--contact is
> atransitive. Thus contact cannot be what spatially relates objects.
> What then? "According the Vaisesika, it is space
> which brings [*A* and *C*] into relation. Both are in
> conjunction with space and thus with each other through its mediation.
> Space is that which turns the relation of conjunction into a
> transitive relation" (Bhaduri).
> 



This explanation has a problem. It assumes that between any two bodies
there is a chain of touching material objects. But, given this
assumption, we do not need to postulate a new substance with which
everything is in contact, in order to create a transitive relation
from contact. For we can define "being to the left of"
thus: *x* is to the left of *y* iff there are distinct
objects *p*, *q*, *r*,...*t* such
that *x* is in contact with *p*, *p* is in
contact with *q*, ..., *t* is in contact with
*y*.



Potter (1977: 92) refines the argument. We say that *A* is
nearer to *D* than to *F* because there are more
intervening objects between *A* and *F* than there are
between *A* and *D*. Suppose however that between
*D* and *F* there is no chain of material objects. How
is it that we can still say "*A* is nearer to *D*
than to *F*"? Potter answers: "In order to provide
the material to explain this comparative judgement we must postulate
an intervening series of entities, and these must be spatial".
Note that this explains, not the transitivity of directional relations
like "to the left of", but rather the magnitude of
distance relations like "near to". "Near to"
is not a transitive relation. It accepts the basic premise that the
distance between two objects is measured in terms of the number of
intervening entities, and postulates a series of "spatial
entities" when there are no material ones present.



This explanation also has a problem, for space is supposed to be a
single entity. Perhaps it should say that the two objects are in
contact with a 'segment' of space, and spatial segments
have magnitude.



Perhaps the best way to construe the argument is as offering an
explanation of spatial separation *without* having to postulate
a series of mediating bodies. Thus, if *A* is nearer to
*D* than *F*, and there is nothing either between
*A* and *D* or between *A* and *F*, the
best explanation is that *D* is in contact with a nearer part
of space than *F*.



*The Manual of Reason* says that space is
'ubiquitous' (*vibhu*), which it defines as
'being in contact with every sample of earth, air, fire, water
(and 'mind') (TS14). This raises the question: is space
infinite in dimension, or the same size as the cosmos? If space is
defined in terms of the relations between physical objects, then it
would seem to have the same size as the cosmos. There are however
Vaisesika arguments that it is infinite. The
Vaisesikas say that most bodies are either
'long' (*dirgha*) or 'short'
(*hrasva*) in dimension (TS25, Bhaduri 1947: 118), but that a
body's having 'long' or 'short'
dimension is unintelligible unless it has bounding, perimeter parts.
Space, however, has no parts and hence no boundary. Some
Vaisesikas conclude that space has no finite dimension
(i.e. is infinite); others that it has a special dimension called
'*paramadirgha*' or 'maximal
length'.


### 3.2 Time (*kala*)



*The Manual of Reason* says of time that it is the ground for
statements about the past, present and future, that it is unique,
eternal and ubiquitous, and that it is the container of everything and
a instrumental cause of every effect (TS15+D). The conception of time
mirrors that of space: it is that in virtue of which statements of the
form "A is earlier than B" are objectively true of false.
Time is said to differ from space, and thus not be identical with it,
in the following respect: whereas what is spatially near or far varies
from person to person, what is temporally near or far is the same for
all persons (cf. Bhaduri 1947, Mohanty 1992). But why should we
restrict our attention only to presently existing persons?



In the *Nyaya-sutra*, Gautama mentions an argument
against the possibility of present time remarkably similar to (and
perhaps even derived from) Nagarjuna's arguments
against motion. NS 2.1.39 (paraphrased): There is no such thing as the
present time, because, when an object is falling to the ground, each
point on its descent belongs either to the already-traversed sector or
to the yet-to-be-traversed sector. There is therefore, no point on the
trajectory to which the present time can be attributed. The present
time is an imaginary point of demarcation between the past and the
future. Gautama replies (NS 2.1.40-42) to this by saying (i)
that the concepts of 'past' and 'future' are
relative to that of the 'present', and not to each other,
and (ii) that the denial of the present has an absurd consequence,
that nothing can be known perceptually, as perception functions in the
present. The point of (i), perhaps, is that even if the present is
just a boundary, it is not thereby imaginary.


### 3.3 Vaisesika Dynamical Theory: The Nature and Causes of Motion



Beginning with Prasastapada (6th century C.E.),
the early Vaisesika authors took a rational and scientific
interest in the behaviour of projectiles and other moving bodies.
Their theory bears comparison with Philoponus'
"impetus" theory, which was responsible for a paradigm
shift in Western scientific thought. *The Manual*'s
account substantially agrees with that already found in
Prasastapada, which is partially traceable to the
*Vaisesika-sutra* itself. The content of the
relevant stanzas can be summarized as follows:



> 
> 
> Motion is the non-inherent cause of conjunction and disjunction. It is
> of five types, four volitional (throwing upwards, throwing downwards,
> contraction, expansion) and the fifth comprising all non-volitional
> motion (including falling, rotating, flowing, etc.) (TS 5, 81).
> 
> 
> 
> Weight (*gurutva*) is the non-inherent cause of the initial
> falling motion of a body (TS 30).
> 
> 
> 
> Fluidity (*dravatya*) is the non-inherent cause of (initial?)
> flowing (TS 31).
> 
> 
> 



'Impetus' (*vega*) is a dispositional property
(*samskara*), as is 'elasticity'
(*sthitisthapaka*) (TS 80). 'Impetus' is the
non-inherent cause of the second and subsequent falling motions of a
body (TS 30). Elasticity is that which restores something to its
original state after it has been distorted.



Here is a brief summary of the theory. A moving body possesses, at
each moment in time, a particular 'motion', which is to be
thought of as a momentary, quality-like property of the body. Motions
are defined to be the cause of conjunctions or disjunctions. A
conjunction with a (stationary) body is brought about by displacement
in space. We are thus to think of the motion of a body as being either
identical with, or else the cause of, its displacement in space
between two moments in time. A motion cannot be caused by another
motion (as that would lead to perpetual motion). A body is set in
motion by its possession of a quality like 'weight' or
'fluidity'. It persists in motion by having a
dispositional property, 'impetus' or
'elasticity', which is the continuous cause of subsequent
motions. It is brought to rest by coming into contact with other
objects.



The role of 'impetus' in this account is particularly
interesting. It is illustrated with reference to two examples: (i) a
fruit falling from a tree; (ii) a javelin thrown obliquely
upwards.


1. At time *t*0 the fruit is stationary at place
*s*0. Its weight is counterbalanced by its contact
with its stalk. At *t*1, its stalk breaks and its
weight causes it to move to point *s*1. At this time
too there is produced in the fruit a dispositional
'impetus'. At *t*2, the impetus in the
fruit causes a second motion, from *s*1 to
*s*2, and so on for all subsequent times. Note that
the 'weight' of the fruit is the cause of its initial
motion, but then ceases to be operative. The cause of all subsequent
motion is the 'impetus' impressed into the fruit by the
initial motion. It is this idea, that the subsequent motion of the
fruit is the result, not of an external force, but of the internally
impressed *vega*, which licenses us to describe the
Vaisesika account as an impetus theory.
2. When the javelin is thrown, the initial volitional push imparts
into the javelin an initial motion and an impetus. The upwards impetus
counteracts the javelin's weight and causes its upwards motion.
When this impetus is exhausted by contact with the air, the
javelin's weight imparts a downwards impetus and the javelin
falls. The horizontal motion of the javelin is caused by its having a
horizontal impetus which again decreases as a result of contact with
the air. The amount of impetus initially acquired by the javelin is
proportional to the applied volitional push. Once again, its is the
javelin's having impetus, rather than the action of some
external force, which accounts for its continued motion through the
air.



The Vaisesikas extend this model to explain certain other
kinds of motion. (1) The initial cause of the flowing of water is
alleged to result from a force called 'fluidity' (rather
than the weight of the water). The subsequent flowing is the result of
the water's acquired impetus. (2) Interestingly, the impetus of
a body moving in a straight line was thought to be ontologically of
the same type as the elasticity of a bent stick--a fact which
reveals that impetus was thought of as a kind of internal force, not
as inertia. (3) The Vaisesikas mention various other kinds
of motion: the movement of an iron needle towards a magnet, the upward
motion of flames, the movement of air, and the initial motion of the
atoms at the beginning of creation. Given the above model, there must
be some 'force' which initially gives rise to each of
these motions, yet none of the 'forces' so far isolated
(weight/gravity, fluidity, elasticity) will do. The
Vaisesikas therefore speak of a new force,
'*adrsta*' (the
'unseen' force), alleged to account for such motions.


## 4. Selves: Human and Divine



The eighth of the nine Vaisesika types of substance is
'self' (*atman*), defined as the substratum of
mental states such as believing, knowing, etc. (The ninth is
'mind' (*manas*), a distinct element in the
ontology of the mental.) Selves are divided into two types--human
(*jiva*) and divine (*paramatman;
isvara*). *The Manual of Reason* supplies
arguments (all traceable back to earlier authors) for the existence of
both types of self.


### 4.1 A Causal Argument for God's Existence



A properly formulated Nyaya argument has three components:
thesis, reason (*hetu*) and example
(*drstanta*). The thesis, again, has two
components: the 'locus' (*paksa*) or place of
the inference, and a property (*sadhya*) whose presence in
the locus is to be inferred. Thus every Nyaya argument exhibits
the same pattern: *p* has *S*, because it has
*H*; e.g., *d*. (For example: "The mountain ( =
*p*) has fire (= *S*), because it has smoke ( =
*H*); e.g. the kitchen ( = *d*)". See further SS8). A
sound argument must fulfil at least three criteria: (i) the reason
property must be uncontroversially present in the locus; (ii) the
reason property and the inferred property must be appropriately
related, roughly such that wherever the reason is present, so is the
inferred property; (iii) the example must be an uncontroversial place
where both the reason property and the inferred property are
present.



With this in mind, let us consider *The Manual of
Reason*'s argument for the existence of God:



> 
> A dyad of earth etc. has a maker, because it is an effect; e.g. a pot
> (TSD 17b).
> 



Here, the locus of the inference is a dyad, the smallest composite
entity. The reason is "being an effect"
(*karyatva*), and the inferred property is "having a
maker" (*kartr-janyatva*). *The Manual of
Reason* carefully defines what it means by a 'maker':
a thing which is non-inferentially aware of the inherent or material
cause of the thing to be made, has a desire to make it, and acts
accordingly. In this sense, the potter, but not the potter's
wheel or the clay or any other causally relevant feature, is the maker
of the pot, for it is the potter who sees the clay (= material cause
of the pot), desires to make a pot, and acts accordingly by using the
wheel and stick.



Comments: (1) Why does *The Manual of Reason* take dyads to be
the locus of the inference? This is, in fact, a clever move.
Obviously, we cannot take God to be the locus (e.g. God exists,
because...), for then the first criterion on a sound inference
will not be met--the reason property, whatever it is, cannot be
uncontroversially present in a locus whose very existence is
controversial. We can't take the locus to be "everything
in the world", for many such things are not effects (e.g. atoms,
space) and so *The Manual of Reason*'s desired reason
will again not be unequivocally present in the locus. Hence, we must
pick some particular thing. We had better not choose a human artefact,
for the inference, even if sound, would then establish nothing about
God. From the class of non-artefacts, the choice of dyads is a good
one here, for (a) they are the most basic things made out of the
atoms, and hence out of which everything else is made, and (b) if
*The Manual of Reason* can show that these have a maker, then
it follows that the maker is aware of everything (from the definition
of a maker and (a) above). Thus, God's omniscience will be a
corollary of the proof of his existence.



(2) The argument takes the picture of causation used in the
"potter-pot" example and extends it to cover all natural
phenomena. God's function is to make things out of the given and
uncreated ingredients (the atoms, cf. the clay), which are the
products' material cause. Matilal accordingly describes the
Nyaya as having a "potter model" of God, in contrast
with a "spider model", in which God spins the world out of
his own essence, or a "magician" model, in which the world
is an illusion conjured up by God. The argument, however, rests upon
an anthropomorphic and agentive view of causation. The Buddhist
Dharmakirti ridiculed the argument by likening the pot to an
anti-hill (another thing made of clay): should we say that this
admittedly complex and intricate construction is the product of
intelligent agents? And even if we do, why should not the world, like
an ant-hill be a product of collective agency, rather than produced by
a single agent?



(3) The argument might be thought of as an argument based on
induction, induction from the class of artefacts to the class of
natural products. What licenses the induction from things seen to have
a maker to things not so seen? Dharmakirti (cf. Vattanky 1984:
56-8) says that we are licensed to infer that an object has a
maker only if we have seen other objects of the same type being made.
Thus, we can infer that the Pyramids had a maker, not because we can
see that maker, but because the Pyramids belong to a type (buildings)
other instances of which we have seen made. The Naiyayika makes a
bolder inductive claim, that two object belong to the same
'type', in this sense, if they are both effects.


### 4.2 An Argument for the Existence of the Human Self



Vaisesika defines the human self as the substratum of such
psychological qualities as believing, etc., as well as of happiness
and other emotions, which God does not have. There is an implicit
appeal, here too, to the "potter" model of causation: just
as, in the sentence "The potter makes the pot", the
property "....making the pot" resides in the potter,
so too in "I believe that *p*", the property
"....believes that *p*" resides in me. Given
that the self is defined as that substance, whichever it is, in which
a person's psychological qualities reside, the question is
whether we can identify this substance as a physical one, for example,
the person's body or their senses, or whether we must postulate
some new type of substance. Vaisesika's argument for
the existence of the self as a new substance is by elimination of two
rival candidates.



(1) The substratum of beliefs, etc. is the person's body.
*The Manual of Reason* makes the case for this as follows: If I
say, "I am cold", "I am running", it is my
body to which the predicate applies. Therefore, when I say "I
believe that *p*", the subject likewise is my body.
*The Manual*'s reply is that if this were true, then



> 
> there would be the difficulty that with the destruction of a hand, a
> foot, etc., there will be the destruction of the body and it will
> follow that there will also be the destruction of the self.
> 



Clearly, I can lose part of my body without ceasing to believe and
know things. But losing part of my body does not entail losing my
body, as a whole. So this argument fails. A better argument is found
in the *Nyaya-sutra*: the very phrase "my
body" shows that I am not identical with my body. But this
doesn't work either, for I can also say "my soul"!
There is no clear argument against physicalism here.



(2) The substratum of beliefs etc. is the person's
sense-faculties [recall that every physical substance was divided into
three: pertaining to body, sense-faculty, and (inanimate) object].
This rather strange claim might be taken to include the view of the
Buddhists, that a person is reducible to a stream of momentary mental
events, including sense-data etc. *The Manual of
Reason*'s argument against such a view (a repetition of an
argument already found in the *Nyaya-sutra*) is a strong
one:



> 
> Were this the case, there would be no re-identifying awareness
> (*anusandhana*), e.g. "I who saw that pot am now
> touching it", for there cannot be any recognition by one of what
> is apprehended by another.
> 



The idea here is that the possibility of recognitive experience
presupposes the existence of a unitary enduring self. There are really
two arguments compressed here. One is this: I cannot *remember*
an object unless I have seen it earlier--I cannot remember what
you have seen (cf. Locke's account of personal identity in terms
of a continuity of memory experiences). The other argument is more
intricate. The Abhidharma Buddhist claims that a person is just an
aggregate of experiences, some visual, some tactile, etc. The problem
raised for such an account by the Naiyayika is that it is
possible to make trans-modality judgements, in which the deliverances
of one sense-faculty are compared with another. Suppose that
*V*(*o*1) is a visual experience of an object
*o*1, and *T*(*o*2) is a
tactile experience of an object *o*2. It is possible
to judge "*o*1 =
*o*2", but this judgement does not belong to
the sphere of any one sense-faculty. Hence, it must be located in some
other substance. The self is here conceived of as that which collates,
organises and compares the deliverances of the individual senses. See
Ganeri 2012, chapters 11, 15, 16 for an expanded discussion.



This is a convenient place at which to introduce the last of the nine
substances, the 'mind' (*manas*). It is defined by
*The Manual of Reason* (TS18) as a sixth sense-faculty, one by
which a person 'perceives' their inner mental objects
(beliefs, pleasure sensations etc.) In other words, it is a faculty of
introspection. Naturally, we need an argument why this faculty cannot
be identified as belonging to the self, and the usual Nyaya claim
is that the self is the agent of cognising, while the mind is an
instrument for cognising, just as we must distinguish between the
axe-man, who is the agent chopping the tree, and the axe, which is the
instrument for chopping. The Nyaya also claim that the mind has
another function, which is to 'switch' between the
different sense-faculties, it being assumed that, while we are being
subjected to sense-impressions from different faculties
simultaneously, we only attend to one at a time.



*The Manual of Reason* (TS 79) says that eight of the
Vaisesika qualities reside only in the self, and in no
other substance. They are cognition, memory, pleasure or happiness
(*sukha*), pain or unhappiness (*duhkha*), desire
(*iccha*), aversion (*dvesa*), merit
(*dharma*) and demerit (*adharma*) (TS 73-78). The
first two we will discuss later (SSSS 5.2-3). As regards
happiness and unhappiness, Matilal (1986: 301), summarizes the
Vaisesika view when he says that "the essential
characteristic of pleasure or happiness consists in its being
experienced as favourable to us or being in accord with us, i.e. with
our body or mind or our very existential situation
(*anukula*)", which makes it distinct from knowing
or perceiving or apprehending something, and that it is an
"inner disposition on account of which the external world
becomes agreeable or desirable". Desire is the state of craving
for something. Merit is that which is produces by meritorious action
(*karma*). See further Ganeri 2012, chapters 13, 14.


## 5. Philosophical Psychology


### 5.1 Overview of Philosophical Psychology



Study of the nature, content and causes of cognition (*buddhi,
jnana, upalabdhi*) lies at the very centre of the
Nyaya philosophical method. In epistemology, the question asked
is: how do we distinguish between true and false cognitions, and under
what conditions does a true cognition arise? In logical theory, the
issue is: when does one cognition 'follow' from another,
in some suitably articulated sense. In philosophy of language, the
assumption is that sentence structure mirrors cognitive structure, and
hence that an inquiry into sentence meaning proceeds via an analysis
of the cognitions sentences 'express'. The importance of
this topic is reflected by *The Manual of Reason*, for although
'cognition' is technically just one of twenty-four types
of quality in the Vaisesika schema, its analysis accounts
for nearly half of the book (TS 34-74).



The term 'cognition' is used by the Naiyayikas to
refer to any intentional (*sa-visayaka*; object-directed)
mental state, including states of perceiving, inferring, doubting,
guessing, remembering, etc., but excluding desiring, hoping,
suffering, etc. (cf. Matilal 1968: 7-8). Because we say that the
subject has such states, they are thought to be
'qualities' (in the technical Vaisesika sense)
of the soul. *The Manual of Reason* states that a cognition is
the "ground for all linguistic practice" (TS 34),
reflecting the Nyaya conception of language as primarily an
instrument for transmitting true thoughts from speaker to hearer.



From the point of view of epistemology, the most important division,
within the class of cognitions, is between those which are true and
the rest. However, the standard Nyaya classification of the
species of cognition, repeated by *The Manual of Reason*,
begins with another division, between memory cognitions
(*smrti*) and the remainder (*anubhava*;
nonrecollective cognition). The full classification is as follows:




|  |
| --- |
| cognition |
|  |  |  |
| nonrecollective
 (*anubhava*) |  | memory
 (*smrti)* |
|  |  |  |  |  |
| true (*prama*)
 perceptual 
 inferential 
 comparison-based 
 testimony-based | not true (*aprama*)
 false (*viparyaya*; 4 types)
 doubt (*samsaya*)
 *tarka* |  | 'true' (*yathartha*) | 'not true' (*ayathartha*) |
|  |  |  |  |  |  |  |  |  |



Nyaya epistemology is in effect a theory of the true
nonrecollective cognitions, and their division into four types on the
basis of the different accredited epistemic means
(*pramana-s*) by which they are produced. (What
about accidentally true cognitions, e.g. the result of a lucky guess?
There are well-discussed problems with incorporating them into the
above schema). It is clear that, no matter how generally reliable are
our epistemic methods, it will always be possible for misfires to
issue occasionally in false cognitions (e.g. perceptual illusions,
beliefs resulting from a reporting error, etc.). *The Manual of
Reason*'s example (TS 72) is of the false pseudo-perceptual
judgement "This is a piece of silver" on seeing an
oyster-shell. I will discuss the epistemology of perception, inference
and testimony in SSSS 7, 8 and 9 respectively. Here, I will
examine in more detail three types of cognition which, though very
important within the Nyaya framework, are subsidiary to its
epistemology. They are: memory, 'doubt' and
*tarka*. (Where do dreams fit in the schema? TS 70 states that
they belong in the category of 'false' cognitions. This,
however, is odd, since they are not the product of any of the four
*pramana*s misfiring. Neither are they memories or
states of doubt. According to Prasastapada, dreams are the
result of the free movement of the 'mind' when it is not
connected with the external sense-faculties, influenced by
*adrsta*, 'unseen' forces.)


### 5.2 Memory



Memory is considered in the western tradition to be an important means
by which an individual can justify her beliefs about the past. It is
striking then to note that the Nyaya at the outset separate
memory states from knowledge-yielding beliefs and deny to them the
status of knowledge-hood. *The Manual of Reason* has the
following to say about memory:



> 
> 
> A memory state is one which results solely from a 'mental
> disposition' (*bhavana*) (TS 35).
> 
> 
> 
> A 'mental disposition' is a quality of the soul which is
> caused by a nonrecollective cognition and causes a memory cognition
> (TS 80).
> 
> 
> 
> Memories are either 'true' or 'false', as the
> originating cognition is true or false (TS 74).
> 
> 
> 



The general theory is that an initial cognition, e.g. a perceptual
experience of an object, generates a dispositional mental state, which
has the capacity, when certain other causal factors are present, to
trigger an active memory of that object. (The whole process might be
likened to that of someone who, having learned to swim, has a
dispositional capacity to swim, which they exercise on certain
occasions.) The resultant memory state has the same content as the
originating perceptual experience, and can be said derivatively to be
'true' or 'false', depending on whether the
original perception was veridical or not. Memory, on this account is
represented as an entirely infallible faculty: there is no mention of
the possibility of what is called "false memory", i.e.
having memories without any originating experience, or of
"faulty memory", in which the content of the memory does
not exactly match that of the originating experience.



Given this account, in which memory is seen merely as reproducing a
past knowing experience, there is perhaps a sense in which the memory
does not itself count as knowledge, any more than an exact
reproduction of a Picasso counts as a Picasso. The Naiyayikas
state that memories lack 'independence'. The idea,
perhaps, is this. In general we establish the veracity of an
experience by examining the way in which it was caused (my perception
of the table is veridical, because my eyesight is good, the lighting
is adequate, etc.). In the case of a memory, however, we must go via
the originating experience. Memory is conceived of as a mere surrogate
for the original experience, and its veracity is
'dependent' on that of the original. We might think,
however, that memory in fact does more than merely reproduce the
original experience. It may represent the experienced event as
happening in the past, and thus have a different content.


### 5.3 Doubt (*samsaya*)



The concept of doubt has an important theoretical role in Nyaya,
for a state of doubt is claimed to be a necessary precondition for any
philosophical enquiry. Doubt is one of the sixteen topics listed under
*Nyaya-sutra* 1.1.1, which determine the content of
the entire text. In particular, a doubt is the first step in a
properly formulated inference: is there a fire on the
mountain?--Yes, because there is smoke there. *The Manual of
Reason* gives a very precise definition of a doubt (TS 71): a
cognition of two incompatible qualifiers in the same qualificand, for
example the cognition "Is this (dimly perceived or distant
object) a person or a tree-stump?" Schematically, then, a doubt
is a cognition whose content is of the form "*x* is
*F* or not-*F*?".



Two points are worth noting. (i) Although doubts are classified as
non-true (*aprama*) cognitions, they are not false. A
false cognition is one whose content is "*x* is
*F*" when in fact *x* is not *F*. (ii)
Doubts are distinguished from other cognitions by virtue of having a
special type of content, rather than by being propositional attitudes
of a special kind. The Nyaya do not here say that we can take one
of a series of attitudes towards the same proposition, believing,
disbelieving, doubting, etc. Yet if the only thing which distinguishes
a doubt is its having a content of the form specified in TS 71, then
what differentiates the doubt that *x* is *F* from the
belief that *x* is both *F* and not-*F*?
Vardhamana replies by drawing a distinction between actually
having a contradictory belief and merely believing that one has a
contradictory belief. The former is supposedly impossible, the
supposedly contradictory belief that *x* is both *F* and
not-*F* is really a belief that I have a belief whose
qualificand is *x* and whose qualifiers are *F* and
not-*F*. Since there are no genuine contradictory beliefs,
there are no beliefs with the same content as doubts.


### 5.4 *Tarka "*Suppositional Thinking"



The term '*tarka'* is often used loosely in the
sense of hypothetical or reductio-ad-absurdum reasoning, but *The
Manual of Reason* gives it a much more precise and technical
sense:



> 
> *Tarka* is the 'ascription' (*aropa*)
> of the 'pervader' (*vyapaka*) by the
> ascription of the 'pervaded' (*vyapya*). For
> example, 'if there is no fire, then there is no smoke'(TS
> 73).
> 



The terms in this definition require explanation. The technical sense
of 'ascription' (*aropa*) is
'counterfactual or suppositional cognition'
(*aharyaropa*), defined as a cognition whose
qualifier is an property the opposite of which is known to reside in
the qualificand. In other words, it is a counterfactual assumption.
'Pervader' and 'pervaded' are notions taken
from the Nyaya theory of inference. When we say that wherever
there is smoke, there is fire, this can be re-expressed as that fire
pervades smoke, i.e. that the property of being a
smoke-possessing-thing has a narrower extension than the property of
being a fire-possessing-thing. So here, fire is the pervader and smoke
is the pervaded. Thus, *tarka* consists in a cognition of
smoke's absence given the counterfactual assumption that fire is
absent. It is the cognition of a conditional "if *p* then
*q*", or "were *p* to be true then
*q* would be true", assuming that
'*p*' is false.



One main function of *tarka* is said to be the elimination of
doubt. Suppose one has the doubt "Is *x*
*F*?". One might then judge "if *x* is not
*F* then *x* is not *G*", and if one also
knows that *x* is *G*, it will follow that *x* is
*F*. The Naiyayikas recognise this function but deny
nevertheless that *tarka* is a source of knowledge
(*pramana*). Their reason, it seems, is that there
is a distinction between citing positive empirical evidence for a
thesis and merely eliminating the contrary possibility by a priori
methods. This is reflected, perhaps, in the fact that no example is
cited in arguments based on *tarka* to buttress the inference.
*The Manual of Reason*, it seems, goes even further and denies
that the counterfactual conditional is a true cognition, which
implies, since they are not false either, that counterfactual
conditionals do not have a truth-value.



Udayana claims that *tarka* is of five types, namely
'self-dependence' (*atmasraya*),
'mutual dependence' (*anyonyasraya*),
'circle' (*cakraka*), 'infinite
regress' (*anavastha*), and 'having an
undesirable consequence' or reductio-ad-absurdum
(*anistaprasanga*). These are basically
self-explanatory - the fifth,
'*prasanga*' is the one used to great effect
by Nagarjuna and other Madhyamika Buddhists. Other
authors give slightly different lists (see S. Bagchi 1953 for
details).


## 6. Causation and the Causal Theory of Knowledge


### 6.1 Overview of Causation



The study of causation is an important part of Indian philosophical
thought. One reason for this is the early interest in cosmological
speculation: "We should remember that philosophic activity in
India arose out of the cosmogonic speculations of the Vedas and the
Upanisads. The all-important business of philosophy was to
attempt to discover some simple, unitary cause for the origin of this
complex universe" (Matilal 1985: 287). Another reason is that
Indian linguistics (especially the Paninian system of
'*karakas*' or relations between verb and
noun, which greatly influenced Nyaya,
Mimamsa and Buddhist thinkers) is based on an
underlying causal model, in which the verb in a sentence designates an
event, for the production of which each such object as is designated
by a noun has a particular causal role. This same model informed and
influenced Indian epistemology, and led to the development of the
theory of '*pramanas*', the causal means
or processes leading to an epistemically accredited awareness-event
(*prama*). In the Nyaya tradition, four such
*pramanas* are recognised: perception
(*pratyaksa*), inference (*anumana*),
'analogical identification' or 'comparison'
(*upamana*) and testimony (*sabda*). The
accounts given of each of these employ an extremely causalistic idiom,
typical questions being 'what causes a perceptual
experience?', 'what are the distinguishing causal factors
of true and false perceptual experiences?', 'under what
conditions does knowledge of the premises of an argument cause
knowledge of the conclusion?', etc.



The choice of examples undoubtedly influences one's causal
theory. The Naiyayikas almost invariably illustrate their
discussions with one of the following three examples: (i) *The
potter-pot example*. The effect is the finished pot. Some of its
causes are the pot-halves (which the potter joins to form the pot),
the potter, his wheel and stick, the contact between each of the
pot-halves, and between them and the stick, etc. (ii) *The
thread-cloth example*. Here the effect is the piece of cloth.
Among its causes are the threads from which it is woven, the weaver,
the shuttle, the loom, various contacts, etc. (iii) *The axe-tree
example*. The effect, i.e. the felling of the tree, is caused by
the axe, its contact with the tree, the axeman, etc. Some of the
questions we would like to ask here are these. Can all instances of
causation be fitted into the general pattern illustrated by these
examples (e.g. is there always an 'agent')? Do the
Naiyayikas have an adequate account of causation even for these
examples (i.e. can they distinguish between those factors which are,
and those factors which are not, causes of the effect)? Can both
objects and events be causes? Are causal relations singular or based
on repeatable regularities? Attempts to answer such questions as these
led to increasingly sophisticated accounts of causation as the
Nyaya school evolved.


### 6.2 The Three Types of Cause



The Nyaya-Vaisesikas traditionally held that, within
the total collection (*samagri*) of causal factors
leading to an event, there are three distinguishable types of cause,
namely 'substrate' or 'inherence' causes
(*samavayi-karana*), 'non-substrate' or
'non-inherence' causes
(*a-samavayi-karana*), and
'instrumental' causes
(*nimitta-karana*). This classification is repeated
by *The Manual of Reason* (TS 43). A substrate cause is a
substance in which the effect inheres. The substrate cause of a pot
would be the pot-halves; of a cloth, the threads. This is because the
Nyaya say that a whole inheres in its parts, and, so, if the
effect (e.g. the pot) is a whole, its substrate causes are the parts
in which it inheres. If the effect is an object's coming to have
a new property (e.g. the tree's being felled), the substrate
cause is the object (the tree). Note that, in spite of a certain
similarity, the notion of a substrate cause is not the same as
Aristotle's "material" cause, for (i) the parts of
an object are not necessarily identical with the material from which
it is composed, and (ii) even an immaterial substance can be a
substrate cause, for example the soul, which is the substrate cause of
epistemic events.



All other causal factors are either 'non-substrate' causes
or 'instrumental' causes. A non-substrate cause is one
which inheres in the substrate cause. Thus, though not being the
substrate, it is closely connected with it. The conjunction of threads
is said to be a non-substrate cause of a piece of cloth. Another
example is often cited. The non-substrate cause of the colour of a
piece of cloth is the colour of the threads (which colour inheres in
the threads, in which inheres the effect, the colour of the cloth).
Any other causal factor is called an instrumental cause, for example,
the weaver's shuttle or the weaver herself. Why did the
Naiyayikas distinguish between non-substrate causes and the
remainder? Perhaps it was an attempt to differentiate between those
causes which must continue to exist for the effect to exist, and those
which need not. If the threads were to lose their colour, then the
cloth would lose its, and if the threads were to become disjoint, the
cloth would cease to exist altogether. If, however, the weaver dies,
having already woven the cloth, or if the shuttle is subsequently
destroyed, it will not affect the continued existence of the
effect.



It does not follow from these definitions that anything which inheres
in the substrate is a non-substrate cause, or that anything which does
not is an instrumental cause. In other words, we still need to define
"being a cause". First, however, two more types of causal
factor are distinguished by the Nyaya. These are the
'special' instrumental cause (*karana*) and
the 'operating condition' (*vyapara*) We
often speak of *the* cause of an effect, and in doing so pick
out one factor from the total collection of causal factors as being
particularly salient or important in bringing about the effect.
Intuitively, the idea is that, even if we have the substrate cause
(the pot-halves), the non-substrate cause (the contact between the
halves), and even some of the instrumental causes (the potter, etc.),
we will not get the effect (the pot) unless the potter acts or
'operates' to bring it about. In a sense, then, it is the
potter's actually using his stick which is *the* cause of
the pot. The Naiyayikas try to capture this idea by saying that
one of the instrumental causes is the 'special'
(*asadharana*) cause of the effect, and they
call it the '*karana*'. This notion is
particularly important to the Nyaya epistemology (see below).
What constitutes the 'special' nature of this cause? The
Navya-nyaya (cf. TS 54) answer is as follows. They introduce
first the notion of an 'operative condition'
(*vyapara*), defined as that cause which immediately
precedes the effect. For example, the operative condition for a pot is
the conjunction of the pot-halves; for the felling of a tree, it is
the final contact between axe and tree before the tree falls. The
'special' cause is defined as that factor which
'brings about' this operative condition. In other words,
it is the factor whose operation directly brings about the effect. In
the examples, it would be the axe or the potter's stick. These
objects are, for the Nyaya, the true instruments by means of
which the effect is produced.


### 6.3 What is a Cause?



The Naiyayikas build up in this way a model of causation, in
which different causal factors have different types of causal role.
The model reflects (or is reflected in) the Indian grammatical
analysis of causal statements, such as "The potter throws a pot
with her stick", "The lumberjack fells a tree with her
axe", in which one distinguishes, apart from the verb
designating the event, an agent (*kartr*), object
(*karman*), instrument (*karana*), and so on. We
do not yet know, however, how to distinguish between causes and
non-causes. *The Manual of Reason* (TS 41) provides the
Navya-Nyaya answer. Given two entities, *c* and
*e*,



*c* is a causal factor for *e* iff
1. *c* exists before *e*,
2. *c* exists 'regularly'
(*niyata*) with *e*, and
3. *c* is 'relevant'
(*ananyathasiddha*) to *e*.




The first clause is to prevent self-causation. The import of the
second condition is that entities similar to *c* must always
exist with entities similar to *e*. There must be an invariable
or constant conjunction between *c*-type entities and
*e*-type entities. This rules out objects which just happen to
be there, such as, to give the Naiyayikas' example, a
donkey happening to wander past the pottery just as the potter goes to
work. This feature of the account, the insistence that a causal
relation instantiates a regularity, resembles a Humean account of
causation. The Naiyayika, however, recognised the possibility of
'accidental', non-causal regularities, such as day always
preceding night, or (the example given by *The Manual of
Reason*), the colour of the thread always preceding the cloth.
Although the occurrence of a cloth is invariably preceded, not just by
threads, but by the presence of thread-colour as well, we would not
want to say that thread-colour is a cause of cloth. The third clause
is their attempt to eliminate such accidental regularities. The same
clause is supposed to stop the cause of a cause (e.g. the
potter's parents) from being a cause. Its meaning, however, is
not quite clear. Literally, it states that a cause must be 'not
established otherwise'. Kalidas Bhattacharya says that "an
invariable antecedent is irrelevant if knowledge of it is not required
for any anticipative knowledge of the origination of the effect"
(see Potter 1977: 67). Matilal says that an antecedent is irrelevant
if "it is possible to find a reasonable explanation of its
appearance" (1985: 290). *The Manual of Reason* states
that an antecedent is irrelevant if its antecedence is only
established along with some other entity. We know that thread-colour
precedes cloth only because we know that it occurs with the thread
(which we know to precede cloth); hence the thread-colour is
irrelevant in this sense. This highlights an asymmetry between the two
regularities, the threadcolour-cloth regularity and the thread-cloth
regularity. For while we can establish the latter directly by
observing correlations between thread and cloth, we establish the
former by observing the correlation between threadcolour and thread.
Thus the former supposedly depends on the latter but not vice versa.
It is not clear, however, that the dependence does not run the other
way too. In any case, in using this criterion to block transitivity,
the Naiyayikas seem to seeking a definition not of causality per
se (which most regard as a transitive relation), but rather an
epistemic notion of 'causal explanation' or 'causal
salience'.


### 6.4 Causation and Knowledge



Cognitions that are not memories are classified under two headings:
true and false. If we can find factors invariably preceding
*true* cognitions, then we will have the beginnings of a causal
theory of knowledge. We will be able to say that a cognition is a
knowledge-episode iff it is (i) true and (ii) preceded by a causal
factor which invariably precedes true cognitions (i.e. its truth will
not be an accident). The Nyaya (TS 39) claim to find four, and
only four, invariable correlations: perception, inference, comparison,
and testimony. To each they apply the model of causation outlined
above. In particular, they isolate, in each case, a
'special' instrumental cause (*karana*), to
which they give the name '*pramana*'. In
the case of perception, for example, it is the senses. Note that an
invariable correlation between two entities, in the sense defined
above, does not entail that whenever the first is present, so is the
second--the potter is invariably connected with a pot, but only
causes a pot when he is actually 'operating'. Similarly, a
*pramana*, e.g. the eyes, only causes a true
cognition when it is actually operating. In other words, the
*pramana* is a necessary but not a sufficient cause
for true cognitions. To get a sufficient cause, the Nyaya (TSD 69
iii) says:



> 
> The causal condition that is 'special' to true cognition
> is called a '*guna*' [an epistemic
> excellence]; the causal condition that is 'special' to
> false cognition is called '*dosa*' [an
> epistemic defect]. In the perceptual case, the *guna* [of
> a true cognition '*x* is *F*'] is the
> sensory connection with an object [*x*] possessing a property
> [*F*], etc.
> 



This is, in effect, the operative condition for true perceptual
cognitions. Thus, the occurrence of all the usual factors (substrate
causes, non-substrate causes, general instrumental causes, etc.)
together with an epistemic excellence (*guna*) is a
necessary and sufficient causal condition for the occurrence of a true
cognition (see also Philips and Tatacharya 2003).


## 7. Perception, Concepts and Sense-Object Relations



Noticing something coiled up in the corner of the room, I perceive it
to be a piece of rope. Looking out of the window, I see that the sky
is blue and see also, perhaps, the blueness of the sky. I see too that
the air is cold, and that there is nobody on the street. What do all
these experiences have in common, in virtue of which they are all acts
of perception? *The Manual of Reason* (TS 46) gives the
classical Nyaya answer:



> 
> **Principle 1**: In each case of perceptual experience,
> the experience has as its special instrumental cause a
> 'connection' (*sannikarsa*) between the
> object perceived and the perceiver's sense-faculty.
> 



All seeings are the product of a sensory connection (of a type to be
specified) with the thing seen. This basic idea must be embellished in
two ways before it is can serve as a proper a theory of perception:
(i) some account must be given of the fact that, in all the cases
cited above, the content of perception is semantically structured
(e.g. that the thing in the corner is a piece of rope), for otherwise
perceptual experiences would not be capable of being true, and hence
fail to qualify as knowledge-episodes; (ii) an account must be given
of the type of 'connection' involved here. Only then can
we evaluate the merits of the Nyaya theory.


### 7.1 'Qualificative Perception' and the Role of Concepts



A structured perception, of an object a as having a certain property
*f* (e.g. seeing the thing in the corner as being a piece of
rope), is called by the Naiyayikas 'qualificative'
(*savikalpaka = saprakaraka*), for it a perception of an
object, the 'qualificand' (*visesya*) as
having a certain feature or 'qualifier'
(*prakara*; *visesana*) (cf. TS 47). It
is alleged by the Naiyayikas that any piece of perceptual
*knowledge* must be of this form, and further that most cases
in which we claim just to be seeing an object (e.g. "I see the
car") are really cases of seeing something as a car. In a
'qualificative' perception, it is the qualificand which is
in sensory connection with the perceiver. How then does the qualifier
enter the picture? The Nyaya claim that:



> 
> **Principle 2**: In every case of perception, the
> qualifier is a previously perceived entity (substance, quality, motion
> or universal) which is recalled by the perceiver and
> 'superimposed' upon the qualificand.
> 



The intuitive idea is that the qualifying feature is a concept,
empirically acquired by the perceiver, and now used to categorise the
object perceived. To see that the passing animal is a horse, one must
first possess the concept *horse*, by means of previous
acquaintance with the type. (Use of the term 'concept'
here does not imply that the features are in any sense
subjective--for the Nyaya they are objective entities or
constructions out of objective entities). The Nyaya thus use
their theory of memory (initial experience causing dispositional trace
causing memory event) as a theory of concept-possession.



Principle 2 has a number of consequences:


1. If every case of seeing an object *a* as *f* is
preceded by a prior perception of *f*, and if that prior
perception were itself of *f* as qualified by some qualifier
*g*, we would get an infinite regress. The Nyaya (cf. TS
47) therefore state that, in addition to qualificative perceptions,
there are also 'non-qualificative' (*nirvikalpaka =
nisprakaraka*) perceptual experiences. In such
experiences, on sees both the object and its qualifier, but not as
being qualified by the qualifier.
2. To illustrate the general theory, suppose I perceive for the first
time a vase having a particular shade of blue which I have never
before seen. The theory states that, prior to seeing the vase as being
qualified by that shade, I first see the vase, together with (but not
qualified by) the shade, and then, recalling that shade, impose it
upon the vase.
3. Perceptual illusions, hallucinations, etc., are all explained as
cases in which a wrong feature is recalled from memory (or the concept
bank). Suppose I misperceive the coiled object in the corner as being
a snake. The account given by the Nyaya is that I recall and
superimpose the feature snakehood, on the basis presumably of its
close similarity with the true feature ropehood. Similarly, if I
hallucinate a dagger, the account entails that I am superimposing the
memory of some previously encountered dagger upon the region of space
in front of me (there must be *some* qualificand, by Principle
1). This is called the 'mislocation'
(*anyathakhyati*) theory of perceptual error. Note
that, if all error is a product of qualifier-mislocation, then no
error is possible with respect to the qualificand with which one is in
sensory connection. Note too that the Nyaya make no appeal to
'images', 'ideas' or any other subjective
content to explain illusion--it is an externalist account of
error. This shows that the so-called argument from illusion, from the
phenomenal indistinguishability of veridical and non-veridical
perceptual experiences to their having a shared subjective content, is
false. It is not clear, however, that one can always find a suitable
qualificand (is a region of space really perceived in a
hallucination?) or a suitable qualifier (e.g. when one sees a stick as
bent, because partially submerged in water, where does the feature
'being bent thus' come from?--the Nyaya actually
claim that it is an objective feature causally produced by the act of
perceiving!)
4. This theory allows the Nyaya to say that locutions like
"I see (visually) that the air is cold" or "I see
that the mango is sweet", in which the qualifier, though
perceptible is not a visible property, are genuine cases of
perception. They classify them as a type of
'extra-ordinary' perception, called
*jnana-laksana-pratyasatti*.
(The other types of extra-ordinary perception sometimes admitted are
'*samanyalaksana*', in which
all the bearers of a property are perceived by perceiving the
property, and yogic perception.)
5. The Nyaya state that experience amounts to a
knowledge-episode when and only when it is true, i.e. when the
qualifier actually qualifies the qualificand. *The Manual of
Reason* (TS 69 iii) says that the *guna* or special
causal factor for perceptual knowledge when the qualifier imposed by
the perceiver onto the sensorily connected qualificand is actually
present in the qualificand. There may, however, be scope for
Gettier-style counter-examples to this definition.


### 7.2 Types of Sense-Object Relation



*The Manual of Reason* (TS 48) reports the standard Nyaya
view, which is due to Uddyotakara, that there are exactly six types of
sense-object relation which ground perceptual experiences:


1. Contact or conjunction (*samyoga*). Ordinary
perceptions, e.g. of a pot. If by 'contact' we understand
some sort of causal relation, then the Nyaya can be said to have
a causal theory of perception. However, they may mean that the eye is
in contact with the object in some more literal sense.
2. Inherence-in-the-conjoined
(*samyukta-samavaya*). We noted above that, in
'non-qualificative' perception, one sees the object and
its feature together. The relation between the feature and the
perceiver is an indirect one--the feature inheres in the object,
with which the perceiver is in contact.
3. Inherence-in-the-inherent-in-the-conjoined
(*samyukta-samaveta-samavaya*). If the feature in
(2) is a quality (*guna*), e.g. a particular shade of
blue, then inhering in it is a universal, blueness, which can itself
apparently be perceived.
4. Inherence (*samavaya*). The
Nyaya-Vaisesikas have a rather strange doctrine, that
each sense-faculty is made out of the type of substance with which it
is particularly associated. The auditory faculty is thus made out of
*akasa*, and, as sounds inhere in
*akasa*, the relation between the hearer and the
sound is inherence.
5. Inherence-in-the-inherent (*samaveta-samavaya*). By
this indirect relation, the hearer is related to properties such as
sound-hood inhering in sound.
6. Qualifier-qualificand relation
(*visesana-visesya-bhava*).
This is an important one. The Nyaya believe that absences are
'real' objects, e.g. the absence of an elephant in the
room now, and that they can be perceived. Absences are said to qualify
their substrata, and are perceived indirectly, by the perceiver seeing
the substratum. The Buddhist Dharmakirti argued that this is
really an inference from non-apprehension (*anupalabdhi-hetu*)
running thus: "I perceive the walls of the room; if there were an
elephant, I would not see it, and my perceptual faculties are working
normally; therefore, there is no elephant".


### 7.3 Gangesa's Criticisms and New Definition



Gangesa criticises Principle 1 on three grounds: (a) it
entails that every awareness is perceptual since every awareness is
produced by the instrumentality of the 'inner' sense
faculty or *manas*; (b) it fails to include divine perception,
which involves no sensory connection; and (c) there is no one type of
sensory connection, nor anything obviously in common to the ad hoc
list of six types. Gangesa therefore offers a new
definition:



> 
> **Principle 3**: A perceptual experience is a cognition
> which has no other non-mnemonic cognition as its 'special'
> instrumental cause (*karana*).
> 



Two objections to this definition are countered. Objection 1: Since
every qualificative cognition is produced by a prior awareness of the
qualifier, the definition under-extends. Reply: No. The awareness of
the qualifier is merely an auxiliary causal factor, the
'special' instrumental cause is a sense-object contact.
Objection 2: Since recognition, which is a type of perception, does
have the prior awareness of the qualifier as its 'special'
instrumental cause, the definition under-extends. Reply: No. The
'special' causal factor is the memory of the qualifier
triggered by the dispositional trace produced by the prior awareness,
not the prior awareness itself.



Gangesa's definition has the virtue of capturing the
sense in which perceptual experience is more 'immediate'
than other types of experience, and is also applicable both to human
and to divine perception. Restricted to human perception, it turns
into the previous definition (Gangesa says that the
'inner' sense should not be regarded as perceptual after
all).


## 8. Logical Theory and Gangesa's Analysis of Inferential Warrant (*vyapti*)


### 8.1 Overview of Logical Theory



Gangesa's *Tattvacintamani* is
divided into four parts, one for each of the four knowledge-sources or
*pramana*s recognised by the Nyaya school. The
post-Gangesa scholars focused more and more exclusively on
the second part, concerning inference, and wrote increasingly detailed
commentaries on a comparatively small portion of the book, namely the
part where Gangesa examines the relation between
inferential sign and property-to-be-inferred, which is called the
*vyapti*, 'pervasion' or
'inference-warranting' relation (Ingalls 1951, Goekoop
1977, Wada 2007). Even today, in a traditional Indian education, study
of these sub-commentaries on various subsections of the
*vyapti* section of Gangesa forms an essential
part of the curriculum.



The general structure of a properly formulated Nyaya inference
has three components: thesis, reason (*hetu*) and example
(*drstanta*). The thesis, again, has two
components: the 'locus' (*paksa*) or place of
the inference, and a property (*sadhya*) whose presence in
the locus is to be inferred. Thus every Nyaya argument exhibits
the same pattern: *p* has *S*, because it has
*H*; e.g. *d*. For example, "The mountain ( =
*p*) has fire (= *S*), because it has smoke ( =
*H*); e.g. the kitchen ( = *d*)". A sound argument must
fulfil at least three criteria: (i) the reason property must be
uncontroversially present in the locus; (ii) the reason property and
the inferred property must be appropriately related, roughly such that
wherever the reason is present, so is the inferred property; (iii) the
example must be an uncontroversial place where both the reason
property and the inferred property are present.



Certain topics concerning this account are addressed in *The Manual
of Reason* and other Navya-Nyaya texts. Among them are: the
conditions under which inference can take place, and the conditions
under which the result is a knowledge-episode (TS 49, 54); the correct
account of the inference-warranting relation, between the inferential
sign and the property-to-be-inferred, called the
'pervasion' or '*vyapti*' relation
(TS 50); the distinction between inference and demonstration
(*svartha*- and *parartha*- inference) (TS 52,
53); the three-fold classification of inference types, those which are
'universally positive' (*kevalanvayin*), those
which are 'universally negative'
(*kevala-vyatirekin*), and those which are combined positive
and negative (*anvaya-vyatirekin*) (TS 55); the types of
inferential fallacy (*hetvabhasa*) (TS
57-64).



I will discuss mainly the definition of the 'pervasion'
relation. First, however, a brief note on how the causal model of
knowledge is applied to inference. The 'special'
instrumental cause (*karana*) of an inferential cognition
is said to be the inferrer's knowledge of the relevant pervasion
relation. The 'operative condition'
(*vyapara*) is said to be an awareness that the locus
of inference (*p*) possesses such an inferential sign
(*h*) as is pervaded by the property inferred (*s*).
This is, in effect, an awareness which combines the two premises of
the argument together immediately prior to the conclusion being
derived, and is called the '*paramarsa*'
or 'consideration'. The '*guna*'
or 'causal factor responsible for the truth' of the
inferential cognition is the condition that this
'consideration' be true, i.e. that the locus does in fact
possess such a sign as is pervaded by the inferred property. Another
auxiliary causal factor is that the inferrer must either not yet
already know the conclusion or else must have a particular desire to
infer (i.e. given, knowledge of the premises, the inference would
normally take place mechanically, but if the conclusion is already
known e.g. perceptually, then the inferrer has to have a special wish
to re-establish it inferentially). This condition is known as
'*paksata*', and should not to be
confused with '*paksadharmata*', which
is the name of condition (i) above.


### 8.2 Definitions of the Pervasion (*vyapti*) Relation



*Vyapti* or pervasion, is that relation between the
inferential sign (*hetu*) and the inferred property
(*sadhya*), which legitimises the inference. It would
typically be expressed by a sentence such as "wherever there is
smoke there is fire", or "whatever exists is
transitory". Knowledge of this relation, according to the
Nyaya, is the instrumental cause in the inferential
process--it is that relation knowledge of which, when combined
with observation of the inferential sign, will permit us to make a
sound or knowledge-yielding inference. Gangesa therefore
attaches great importance to the precise definition of this relation.
He notes as many as twenty-one definitions all of which he rejects for
some reason or other, and then he goes on to give seven further
formulations, each of which he considers acceptable. Of the
definitions he rejects, the first five came to be known as the
'*vyapti-pancaka*', and inspired a huge
literature both among the Sanskrit commentators and their modern
interpreters. These definitions are traceable to the earlier Buddhist
and Nyaya literature. Two more rejected definitions, known as the
'Lion and Tiger' definitions, are apparently due to
Gangesa's Navya-Nyaya predecessors (Wada 2007,
ch. 5). The definition Gangesa finally accepts is called
his '*siddhanta-laksana*'.


### 8.3 The 'No Counter-Example' Definition



The five definitions which make up Gangesa's
'*vyapti-pancaka*' are all varieties of
what we might dub the 'no counter-example' definition of
the pervasion relation. This states that the inferred property
*S* pervades the reason property *H* just in case there
is no place/entity where *H* is located but *S* is
absent. Formally:



V1
Pervades (*S*, *H*) iff
 !([?]*x*)(*Hx* &
 *S*'*x*).


where *S*' is used to denote the complement of
*S*. This definition is traceable both to the early Nyaya
notion of a 'deviating' pseudo-reason (i.e. one which
occurs somewhere where the inferable property *S* is absent),
and to Dinnaga's 'triple-condition'
theory of the inferential sign, his third condition being that H must
not be located in any "disagreeing case" (cf.
'*vipaksa*'), i.e. a place where *S*
is absent. In either case, the intuition is that a relation expressed
by "where there is smoke there is fire" obtains just in
case there is no place where fire is absent but smoke is present, i.e.
no counter-example. The first definition which Gangesa
considers is of just this form. It is that *S* pervades
*H* iff *H* has "non-occurrence in the loci of
absence of *S*"
(*sadhyabhavavad-avrttitvam*), i.e.
V1.



Why is this plausible-seeming interpretation of the notion of
pervasion rejected in Navya-Nyaya? There are two reasons:



*The Problem of Partially Locatable Properties*. The first
problem with the 'no counter-example' definition depends
on the Navya-nyaya notion of partial location
(*avyapya-vrtti*). A property is said to occur
wholly or completely in an object if it occurs in every part of that
object. For example, the property of being golden occurs completely in
a piece of (pure) gold; the object is 'saturated'
(*abhivyapya)* by the property, just as sesame oil
saturates a sesame seed. Some properties, however, occur in some parts
of the object but not others--these are called "partially
locatable". For example, the property of being molten occurs at
the centre of the Earth but not at the periphery. Note that the same
property can be wholly located in some loci and partially located in
others--e.g. redness occurs wholly in a ruby but partially in a
red snooker ball. The distinction concerns two modes of
property-possession, not two types of property. An important point is
that, if a property is partially located in an object, then so is its
negation. The Naiyayikas' standard example of a partially
locatable property, viz. "...is in contact with a
monkey" (*kapi-samyoga*), illustrates the point. If the
monkey is sitting on a branch of a tree, then the following statements
may be true:


1. The tree is in-contact-with-the-monkey at time *t*,
and
2. The tree is not-in-contact-with-the-monkey at time
*t*,



(2) being true because there are parts of the tree with which the
monkey is not in contact. Nyaya avoids the threatened violation
of the law of non-contradiction by relativising the notion of
occurrence. (1) is thus analysed as "the occurrence, of the
property being-in-contact-with-the-monkey in the tree, *is
delimited by (avacchinna)* the branch". Since a different
delimitor appears in (2), there is no inconsistency between the two
statements.



The main effect of admitting partially located properties into the
system is that it is no longer the case that a property, *P*,
and its complement, *P*', are disjoint: they may now
intersect. If the inferred property is partially located, then the
class of "agreeing cases" (*sapaksas* -
places where the inferred property is present) and the class of
"disagreeing cases" (*vipaksas*--places
where the inferred property is absent) overlap rather than being
distinct classes. To put it another way, a property *P* should
be thought of as having both a "presence range"
(*P*+) and an "absence range" (*P*[?]),
and the two may overlap. Consider now the standard inference
"The mountain has fire, because it has smoke". Suppose we
find a place where smoke is present, and fire is both absent and also
present, e.g. the kitchen. Does this show the inference to be faulty?
According to definition V1, it does, because the kitchen
will be a counter-example, a place where smoke is present and fire
absent. But this is wrong: since fire is also present there, it is not
a real counter-example to the rule "where there is smoke there
is fire". The upshot is that we must examine the "presence
ranges" of the reason property and inferred properties, not
their "absence ranges". A real counter-example to rule is
a case which is in the presence-range of the reason property but not
in the presence range of the inferred property.



Gangesa's second definition is designed to solve this
problem: *H*'s "non-occurrence in the loci of
absence of *S* which are different from locus of
*S*". In other words, a locus of absence of *S*
which is also not a locus of *S* should not be a locus of
*H*:



V2
Pervades (*S*, *H*) iff
 !([?]*x*)(*Hx* &
 *S*'*x* & !*Sx*).


The effect of the new clause is precisely to rule out the problem of
partially locatable properties, by specifying more restrictively what
constitutes a counter-example.



*The Problem of Universally Positive Inference*. There are,
claim the Nyaya, patterns of legitimate inference in which the
property inferred has as its extension the entire domain. Such
inference are called '*kevalanvayin*' or
'universally positive' (cf. TS 55). The stock Nyaya
example is the inference "This is nameable, because it is
knowable", nameability being regarded as a property of
everything. Another example would be "This exists because it is
produced". If such an inference is sound, then its reason
property and inferred property must exemplify the pervasion relation.
According to the above definition, to say that nameability pervades
knowability is to say that any locus of the property
absence-of-nameability is not a locus of knowability. The problem is
that, since nameability is a universal property,
absence-of-nameability is an uninstantiated (*aprasiddha*)
property, and the Nyaya claim that such properties are
ontologically suspect. To put it another way, the statement "any
locus of the property absence-of-nameability is not a locus of
knowability" includes a non-referring expression,
"locus-of-absence-of-nameability" or "unnameable
thing", and hence is not truth-evaluable. The problem does not
arise for all uninstantiated properties, for some, e.g. being a
sky-lotus, or being a square circle, can be shown to be constructs
made out of simpler instantiated properties. Thus, the statement
"The square circle is circular" can be taken not as
containing a non-referring expression, but as meaning "The
circle is square and circular". However, 'unnameable
(thing)' is not decomposable into two distinct properties this
way.



None of the interpretations of the 'no counter-example'
definition considered by Gangesa can solve the problem of
universally positive inferences, and Gangesa accordingly
rejects them all. His own definition uses a trick to get round the
problem.


### 8.4 Gangesa's Definition: the '*siddhanta-laksana*'



*The Manual of Reason* reproduces with slight simplification
Gangesa's new definition. It says that *S* and
*H* are related by the pervasion relation just in case there is
collocation of *H* with *S* and *S* is not a
property the absence of which is collocated with *H*
(*hetusamanadhikaranatyantabhavapratiyogi-sadhyasamanadhikaranyam
vyaptih;* TS 50). Almost the same formulation is found
in other Navya-Nyaya texts, such as the
*Siddhanta-muktavali*. This definition is supposed to
be applicable even if the inferred property *S* is
'universally positive'. The idea, roughly, is that if
*S* pervades *H* then no property whose absence is
collocated with *H* can be identical to *S*. If we can
find an instance of a locus of smoke which is also a locus of the
absence of some property, coldness say, then coldness cannot be
identical with fieriness. That is:



Pervades (*S*, *H*) only if
([?]*x*)(*Hx* &
*P*'*x*) - (*P* [?] *S*).




(There is an implicit quantification over *P* here). What this
says is that there is no place where *H* is collocated with the
absence of *S*, but it does so without actually using the
potentially non-referring phrase "absence of S", and it
thereby avoids the problem of universally positive properties.
However, although this condition is necessary for pervasion, it is not
sufficient, for it is consistent with *H* (or *S*) being
uninstantiated. So Gangesa insists too that *H* and
*S* must be collocated:



 
Pervades (*S*, *H*) iff
 
i.
[?]*x* (*Hx* &
 *P*'*x*) - (*P* [?] *S*),
 and
ii.
[?]*x* (*Hx* & *Sx*).



Gangesa's trick implicitly trades on the theorem
"*A* - *B* [?] ! (*A* &
! *B*)". Thus clause (i) is virtually equivalent to
V1. This shows too that we do not yet have a definition
which can deal with the partially locatable properties, for which we
need something more like V2. Hence
Gangesa's final definition is:



V3
Pervades (S, H) iff
 
i.
[?]*x* (*Hx* &
 *P*'*x* & !*Px*) -
 (*P* [?] *S*), and
ii.
[?]*x* (*Hx* &
 *Sx*).



This definition of pervasion is able to handle both universally
positive properties and partially located properties appearing as
inferred property.



One may wonder why it is that, since a pervasion relation is of the
form "all *H*s are *S*", the Naiyayikas
did not simply use the notion of universal quantification in their
definitions. The answer, perhaps, is that they were in fact trying to
define this notion, and to do so only in terms of certain other
notions which they took to be primitive, especially the notion of
co-location and absence. If this is correct, however, then we must
show how to reconstruct the definition without its implicit
quantification over a property *P* (cf. Goekoop 1967).


## 9. Meaning, Understanding and Testimony


### 9.1 The Language Processing Mechanism



Just as perception and inference are described, in the
*pramana* system, as knowledge-yielding faculties,
so too is language. This leads the Nyaya to formulate a
description of the mechanism by which a competent language-user is
able to decode noise-utterances and derive language-based knowledge.
The description *The Manual of Reason* gives of this
'language processing mechanism' is as follows (TS 67, 68).
The input to the process is the hearer's auditory perception of
a spoken utterance qua uninterpreted noise, and this is identified as
the 'special' instrument cause (*karana*).
For example, hearing the noise-string



[\*]
"The" "cat" "is"
 "on" "the" "mat".


The 'operative condition' (*vyapara*) is
the hearer's (tacit) knowledge of the meaning
(*sakti-jnana*) of each of the words in the
utterance. This is what marks off a person who understands the
language in question from one who does not (but who may, nevertheless
hear the words spoken, without having the capacity to interpret them).
For example, knowledge that



[M1]
"the cat" means the cat,
[M2]
"the mat" means the mat, and
[M3]
"is on" means the substratum-superstratum relation.


The output of the process, i.e. the effect of the combined causal
factors, is the hearer's forming a belief, for example belief
that



[P]
The cat is on the mat.


Just as, in the case of perception, a number of auxiliary causal
factors, such as there being adequate lighting, the perceiver's
sense-faculty being in good condition, the perceiver paying attention,
etc., so here too. Nyaya isolates four such factors for special
attention, namely: spatio-temporal 'contiguity'
(*sannidhi*) of the uttered words; the speaker's
intention (*tatparya*); 'syntactic expectancy'
(*akanksa*); and 'semantic
fitness' (*yogyata*) (cf. TS 67). The first is
self-explanatory: if the words in the utterance are uttered one at a
time over a long period of time, or mixed in with the words of a
distinct utterance, it will be impossible form a proper auditory
perception of the utterance. The second, 'speaker's
intention' is appealed to when the sentence contains an
ambiguous word--disambiguation proceeds via consideration of the
speaker's intended meaning. *The Manual of Reason*
defines 'syntactic expectancy' as 'the inability of
one word to produce, without another word, an awareness of the
relation between them', and it cites, as an example of an
utterance which fails to possess such expectancy, the sentence
"horse man elephant". Clearly the idea is at least that
the utterance must be grammatically correct. More than that, there is
a suggestion that it is in virtue of the syntactical rules that the
unarticulated semantic relations between the words are expressed. What
makes it the case that someone who understands the utterance
"the cat is on the mat" grasps a united proposition, and
not just a list of items [the cat, the on-relation, the mat]? The idea
here, perhaps, is that (knowledge of) the syntactical rules generates
an awareness of the connecting relations between each of these
items.



'Semantic fitness' (*yogyata*) is an
intriguing concept. *The Manual of Reason* defines it as
'the absence of incompatibility among what is signified by the
words', and illustrates its definition by contrasting the
sentence "He sprinkles the field with water" with
"He sprinkles the field with fire". The idea is that the
activity of sprinkling is 'compatible with' (i.e. can only
be done with) a liquid like water, and not with a substance like fire.
It would be like saying "Cathood is on the mat" or perhaps
Chomsky's "Colourless green ideas sleep furiously".
Such sentences, though grammatically correct, do not make sense. This
causal factor, then, is that an utterance is intelligible only if the
proposition expressed is ontologically possible, by the light of a
preconceived ontological system, such as the Vaisesika
system of categories. Some Naiyayikas, however, impose a more
demanding requirement, that to be 'semantically fit' the
utterance must be true, i.e. that 'fit' =
'true', not merely 'possible', and
consequently that an utterance is intelligible only if it is true! In
effect, they identify 'semantic fitness' with the
'*guna*' or 'causal factor leading to
truth', in the language-processing mechanism. We will return to
this dispute a little later.


### 9.2 Semantic Power and the Reduction of Semantic Properties



*The Manual of Reason*'s definition of a word is
celebrated and often quoted. It says (TS 66) that a word is that which
has semantic power (*saktam padam*). A sentence
(*vakya*) is defined as a collection of words. So *The
Manual of Reason*'s definition fits with the modern one,
according to which a word is a semantically significant sentential
constituent. Semantic power is that knowledge of which enables the
competent hearer to interpret the word, and this, for the
Naiyayikas, consists in the word's standing for an object.
Thus, someone who understands the word "cat" knows
something of the form <"cat" means cat>, where
"means" is a relation between words and objects of some
type. *The Manual of Reason* raises three questions about this
relation: (i) Is it a new and irreducible type or relation, not
reducible, that is, to any of the relations already admitted (TSD
66a)? (ii) What is the relatum, i.e. with what type of entity are
words semantically related (TSD 66b, k)? (iii) How do we learn the
meaning of a word (TSD 66c, d).



(i) The Mimamsakas and Grammarians were
'essentialists' about meaning, arguing that the Sanskrit
language is a natural entity, independent of human convention or
usage, whose words possess intrinsic semantic powers to signify
objects, just as fire has the intrinsic capacity to burn. The
Naiyayikas traditionally opposed this view, arguing instead that
language is a product of convention, and that it is possible to
account for a word's semantic power in terms of stipulations
governing its use. The claim is that we can define (and hence analyse)
the meaning-relation thus:



> 
> *x* means *y* iff there is a decree/stipulation
> (*sanketa*) of the form "Let utterances of
> *x* generate cognitions of *y*".
> 



Now a stipulation or decree is claimed to consist in the
decree-maker's having a certain mental state, viz. a
'desire' or 'will' (*iccha*) of
the form specified. Thus, the meaning relation is analysed in terms of
mental states and their contents, and not as a new type of relation.
Who is the decree-maker? *The Manual of Reason* states that it
is God, but most later Naiyayikas drew a distinction between
words which have belonged 'endlessly' in the language
(introduced by God) and words introduced by an explicit human
stipulation (e.g. the technical terms in Panini's
grammar).



(ii) What is the meaning-relatum of a word like "cow", a
generic nominal expression? Here again *The Manual of Reason*
contrasts the Nyaya view with that of the
Mimamsakas. One sub-school of
Mimamsakas (the Bhatta) claim that the meaning of
"cow" is the universal cowhood, since sentences like
"(The) cow is an animal", or injunctive laws like
"Never kick a cow", say something about the entire class
of cows, not about any one individual. Thus:



(Bh)
"cow" means cowhood.


In reply to the obvious objection, that in many other sentences, such
as "The cow is in the garden", a particular cow is
referred to, these Mimamsakas appeal to the idea that
a sentence can carry an 'implication'
(*aksepa*) other than its literal meaning. Thus the
sentence "The cow is in the garden" may mean literally
that cowhood is collocated with occurrence-in-the-garden (i.e. that
there exists a cow in the garden), but carries the implication that a
certain particular cow is in the garden. The principle here is that a
prior awareness of the qualifier (*visesana*)
leads to an implicated awareness of the thing qualified
(*visesya*) (TSD 66b). The Nyaya reply to this
argument proceeds by way of rejecting the principle cited, for, they
say, awareness of a qualifier or universal is possible only via an
awareness of the thing qualified.



*The Manual of Reason* states the modern Nyaya view: the
meaning of an utterance of the word "cow" is a particular
individual as qualified by cowhood
(*jati-visista-vyakti*):



(Ny)
"cow" means a-cow-as-qualified-by-cowhood.


The idea is this. Anyone who understands an utterance of the sentence
"(The) cow is in the garden" does so by (a) identifying a
certain object as the referent of the word "cow", and (b)
grasps that that individual is qualified by the property
occurrence-in-the-garden. However, one can only identify an object by
distinguishing it from others, and this involves the use of a
distinguishing feature. So the individual is grasped in awareness as
distinguished/qualified by the feature cowhood. Since the meaning of a
word is, by definition, its contribution to the final belief generated
by hearing the utterance containing the word, the meaning of
"cow" is an individual as qualified by cowhood. Note that,
on such a theory, token utterances of "cow" vary with
respect to the individual to which they refer, but every token
utterance nevertheless shares a common semantic property, viz. "
...--qualified-by-cowhood". The Naiyayikas in
this way draw a distinction between type- and token- meaning (or, as
some say, between meaning and reference).



The other Mimamaka sub-school (Prabhakara)
claim that, in order to explain the fact that, on hearing a sentence,
we grasp a unified proposition and not just a list of entities, the
meaning-relatum of a word like "cow" is 'an object
connected with another' (*itaranvita*). The
meaning-relatum is a cow along with a 'hook' to link it
with other meaning-relata. More precisely, the meaning of the word
would be something like



(Pr)
"cow" means a cow-individual, which is
 ......


So the sentence "The cow is in the garden" does not just
mean the list <cow, being in the garden>, as it would if each
word simply designated an object, but rather the connected proposition
<cow-which-is in-the-garden>. The idea, in effect, is that all
meaning-relata, are, in Frege's terminology,
'unsaturated'. To this ingenious suggestion, *The
Manual of Reason* replies (TSD 66k) that it is superfluous, for
"since it is possible for the relation [between meaning-relata]
to be apprehended as what is signified by the sentence [as a whole],
it is not necessary to postulate a semantic power with reference to
the relation". In other words, *The Manual of Reason*
claims that general (presumably syntactic) features of the sentence
are enough to connect the meaning-relata, without needing to claim
that those meaning-relata themselves do the connecting.



(iii) The Naiyayikas offer the following account (TSD 66c) of
language acquisition. The child makes a series of observations
concerning the linguistic behaviour of adults. She hears adult A utter
a certain noise "Bring the cow" say, and sees adult B
perform a certain action, bringing of the cow. Again, she hears A
utter the noise "Bring the horse", and sees B bring the
horse, and hears "Feed the cow" and sees the cow being
fed. Then, by a twin inductive process, of (a) "agreement in
presence" (*anvaya*) and "agreement in
absence" (*vyatireka*)--i.e. noticing the
correlation between A making or not making an utterance and B
performing or not performing an action, and (b)
'collection' (*avapa*) and
'rejection (*udvapa*)--i.e. noticing the
regularities between utterances of "cow" and events
concerning the cow, utterances of "bring" and bringing
events, etc., the child understands that the word "cow" is
linked with objects belonging the class of cows, etc.



This is an empiricist account of language learning reminiscent of the
account attributed by Wittgenstein to Augustine, and severely
criticised by him. Apart from the superhuman inferential powers
attributed to the child, the problem highlighted by Wittgenstein is
that no amount of observation can show, for example, that the relevant
correlation is between "cow" and cow-individuals, and not
between "cow" and B's cow-directed-actions, the
universal cowhood, heifers rather than cows, etc. (cf. TSD 66d).


### 9.3 Testimony



*The Manual of Reason* says that statements are either Vedic or
secular. It adds that (hearing a) Vedic statement is a
*pramana*, a means of knowing that which is stated,
because Vedic statements are originally uttered by God. (The
Mimamsakas dispute this. Not believing in God, they
say instead that a Vedic statement is a means of knowing precisely
because it has no personal origin, and error in testimony is always a
result of human error in the source!) Hearing a secular statement is a
means of knowing only if the speaker is an 'authoritative
person' (*apta*). An authoritative person is defined
as one who speaks the truth (*yatharthavakta*). There
is an ambiguity here: is an authoritative person one who is speaking
the truth with respect to the particular utterance in question, or one
who is generally truthful? Another question here is: must the
testifiee know that the testifier is an authority in this sense or
not?



To confuse matters further, *The Manual of Reason* says that
the '*guna*', causal factor responsible for
the truth of the testifiee's belief, is
'*yathartha-yogyata-jnana*',
which can mean either (i) veridical cognition of semantic fitness, or
(ii) cognition of veridical semantic fitness. In either case, the
'*guna*' has nothing to do with the
speaker's credentials, it seems. Option (ii), however, must be
wrong, for it cannot be a condition upon testimony that the hearer
already knows that what was said is true. Option (i), however, would
not guarantee that the final hearer's belief is true, unless by
'fitness' *The Manual of Reason* now intends a
rather stronger notion, according to which the meaning-relata
'fit' together iff they are in fact connected, i.e. if the
utterance expresses a truth. This is, indeed, how some other
Naiyayikas understand the notion of *yogyata*, but
does not accord with *The Manual of Reason*'s own
definition.



I propose the following resolution. The language processing mechanism
was described above as one which issues in the testifiee believing
that which the testifier says. The truth of the testifiee's
belief will therefore depend upon whether or not the testifier is
speaking truly, and so this should be called the
'*guna*' here. However, we do not always
believe what we hear, especially if we have reasons to suppose that
the speaker is not likely to be speaking the truth. It is possible,
then, that the output of the language processing mechanism is not
simply belief in *what* was said, but rather belief simply
*that* it has been said. There are, roughly, two sorts of case
when this can happen: (1) if the testifiee judges that the testifier
is deceitful or unreliable or simply uninformed about the topic, and
(2) if the testifiee knows on independent grounds that what the
testifier is saying is false (which is consistent with the testifier
believing it and testifying sincerely), perhaps on *a priori*
grounds concerning the plausibility of the assertion. With a little
interpretative licence, we might think that these two conditions
correspond to the two conditions imposed by *The Manual of
Reason* on testimony: that the testifier must be an
'authority' (*apta*), and that the sentence
must be 'semantically fit' (*yogya*).


## 10. The Vaisesika Concepts of Universal, Inherence, and Basic Differentium


### 10.1 Universals



*The Manual of Reason* reports the standard
Nyaya-Vaisesika definition of a universal
(*samanya, jati*):



> 
> A universal is something which is (i) eternal, (ii) unitary, and (iii)
> located in a plurality of things (substances, qualities or motions).
> (TS 82)
> 



Universals are thus conceived of as unstructured, objective properties
which necessarily reside in individuals. The postulation of such
entities in the Vaisesika schema has explanatory force,
accounting for the distinction between 'natural' and
'conventional' classifications. Intuitively, this is the
distinction between groupings such as the class of cows or horses,
which reflect natural divisions ("cut nature at the
joints"), and those such as the class of Cabinet Ministers or
the class of endangered species, which reflect anthropocentric
concerns. The Naiyayikas mark this distinction by calling natural
properties "universals" (*jati*) and
anthropocentric properties "imposed" or
"nominal" properties (*upadhi*).
Correlatively, a semantic distinction is drawn between "natural
kind terms" (*naimittiki*), i.e. terms the basis for
whose application is a universal, and "imposed kind
terms", terms whose basis for application is an anthropocentric
property. Udayana tried to make this distinction more precise by
giving a list of criteria for a property to count as natural.
Examination of his list (which are called the
"*jati-badhakas*"--impediments
distinguishing natural properties) will reveal something further about
the nature of the natural properties according to Nyaya.



The six impediments are (1) 'non-plurality'--a
genuine universal must be plurally instantiated; (2)
'equipollence' (*tulyatva*)--two co-extensive
properties cannot both be genuine universals; (3)
'cross-connection' (*samkara*)--two
genuine universals must not partially overlap; (4)
'regress'--a property like universality cannot itself
be a universal, on pain of infinite regress (universality-hood, etc.
etc.); (5) a property like differentia-hood cannot be a genuine
universal, for by definition the basic differentia share no common
universal property; (6) a property like inherence-hood cannot be a
universal, since it does not inhere in its loci. Of these six, the
last three are there basically to maintain the internal consistency of
the Vaisesika system, and the first is a straightforward
consequence of the definition of a universal. It debars a
singly-instanced properties such as space-hood from the status of
genuine natural kind, perhaps motivated by the thought that the very
nature of a universal consists in its grounding judgements of the form
"*x* is of the same kind as *y*", which
presuppose that there are at least two entities.



The second and third criteria are the most important, and can be
stated more formally as follows. If *P* and *Q* are
distinct properties, then (equipollence, *tulyatva*):



> 
> [*P*] = [*Q*] - either *P* or *Q* (or
> both) is not a universal,
> 



where '[*P*]' denotes the extension of *P*.
The contraposed form is:



> 
> *P* and *Q* are universals - [*P*] [?]
> [*Q*].
> 



Note that this does not entail that universal properties are
extensionally individuated or equivalent to classes, as some have
maintained. It shows only that corresponding to each class, there is
at most one universal. Although, within the domain of universals, a
universal is uniquely determined by its extension, the distinction
between a universal and a co-extensive imposed property (e.g. pothood
and conch-shell-like-neck-hood) is an intensional distinction.



As for the third impediment (*samkarya*), if
*P* and *Q* are distinct properties, then



> 
> [*P*] partially overlaps [*Q*] - either *P*
> or *Q* (or both) is not a universal.
> 



The contraposed form is:



> 
> *P* and *Q* are universals - [*P*] [?]
> [*Q*] or [*P*] [?] [*Q*] or [*P*] [?]
> [*Q*] = [?].
> 



(The inclusion is strict because of the 'equipollence'
constraint.) In other words, genuine universals are arranged in a
hierarchy: given two universals, either they are related as genus and
species, all instances of one being instances of the other, or else
they are completely disjoint, having no instance in common (e.g.
cowhood-animalhood, cowhood-treehood). The Nyaya say that, if one
universal is thus subsumed by another, the former is
'lower' (*apara*) and the latter is
'higher' (*para*) (cf. TS 6). The
'highest' universal of all is 'existentness'
(*satta*), into whose extension falls every substance,
quality and motion. The demand that universals be organised
hierarchically shows that the Nyaya took as their paradigm the
biological species, which tend to exhibit this structure. Bearing in
mind that the term for "universal", i.e.
"*jati*" is also the word for caste, Matilal
(1971: 76) speculates that



> 
> [O]ne might discover in the Nyaya doctrine of generic property a
> remote influence of the socio-religious ideas of the Brahmins.
> Translated into biological terms, the ... principle of
> 'non-overlapping' becomes a principle which opposes
> cross-breeding. There is thus some evidence that the Nyaya bias
> for real generic properties was partly influenced by the Brahmanical
> concept of an ideal social order where intermixture of classes is not
> to be permitted.
> 



Some Naiyayikas, especially Bhasarvajna and
Raghunatha, reject the 'cross-connection' impediment,
pointing out the problems encountered trying to apply it to
non-biological natural kinds (e.g. redness and greenness overlap, as
do pothood and goldhood). Raghunatha suggests that consistent
application of this principle would eliminate virtually all universals
from the ontology. Udayana's criterion of a property to be
'natural' is thus not a necessary one, and neither is it
sufficient: none of his impediments shows why the pair
'blue-green' is more natural than Goodman's pair
'grue-bleen' (where x is grue iff x is green and examined
before time t, and is blue otherwise, and vice versa for bleen.)



The idea that universals are, in some sense, 'located' in
particulars generated two distinctive objections to the theory.
Dinnaga trades on the spatial metaphor to argue that the
Nyaya conception of universals is incoherent. For, if a universal
is 'unitary', it can be located in at most one place, and
thus not 'plurally instanced'. If, conversely, if is
located simultaneously at many places, that can only be because it has
parts, each located at a different place, and hence is not
'unitary'. This argument plays on the ambiguity of the
notion of 'being located', and pretends that a universal
like cowhood is located in individual cows in just the same sense that
a cow is located in a field. Nevertheless, it forces the Nyaya to
be more careful in its account of the universal-particular relation.
As *The Manual of Reason* notes (TS 84), a universal is said to
reside in its instances by the relation of 'inherence'
(*samavaya*), defined as an "inseparability"
(*ayutasiddhi*) relation. Of two entities, *x* and
*y*,



> 
> *x* is inseparable from *y* iff *x* cannot exist
> unless *y* exists.
> 



The idea is that a cow cannot exist unless the universal cowhood
exists, and that it is in this sense that cowhood is located in the
cow. (The same relation is claimed to occur between non-repeatable
'qualities' (*guna*) and substances, a whole
and its parts, and the basic differentia and the atoms.) Spatial
location, on the other hand, involves a quite different relation,
namely contact (*samyoga*). In this way, the term
'location' is disambiguated.



The other problem is the classic one: what happens to a universal if
all its instances are destroyed? Can universals exist without being
instantiated? The definition of the inherence relation permits this,
for the requirement is that cows cannot exist without cowhood, not
vice versa. We might say that the cow's existence supervenes on
that of the universal cowhood. However, it is not so clear that we can
say in the same way that the parts (of a car, say) cannot exist unless
the whole (car) exists.


### 10.2 The Basic Differentia (*visesa*)



The Vaisesika traditionally and uniquely accept into their
ontology a category of item called 'basic differentia'
(*visesa*), from which, some claim, they derive
their name. *The Manual of Reason* defines these items as
follows (TS 83): "those entities which reside in the eternal
substances [i.e. the atoms] and function as their differentiators are
called *visesa*". The idea is that, just as a
cow and a horse are distinct entities, as they have distinct
properties, so too even two atoms of the same substance, e.g. earth,
must differ with respect to at least one property. Each atom,
therefore, possesses a 'differentium' unique to itself,
which serves to distinguish it from any other atom of the same type.
The assumption, then, is that any two non-identical items are
distinguished by virtue of possessing distinct properties. This is the
contraposed version of Leibniz' Law that Indiscernibles are
Identical, that ([?]*P*)(*Px* [?]
*Py*) - (*x* = *y*), where
"*P*" ranges over properties. The principle faces
triviality unless certain constraints are placed on the range of
properties quantified over. For example, if the property
"... = *y*" is permitted, the principle states
vacuously that identicals are identical. The Vaisesikas
implicitly restrict the principle to intrinsic, non-relational
properties of the objects concerned, ruling out, for example,
'being at a certain spatial or temporal location' as being
a property capable of discriminating two otherwise identical objects.
Thus, the claim seems to be that no two objects, including atoms, can
be intrinsically identical. This is how Leibniz himself appears to
have understood his Law, saying that "It is always necessary
that beside the difference of time and place there be internal
principles of distinction....thus although time and place serve
in distinguishing things, we do not easily distinguish them by
themselves," and that "There is no such thing as two
individuals indiscernible from each other. Two drops of water, or
milk, viewed with a microscope, will appear distinguishable from each
other".



The principle is, admittedly, as strong one. Wittgenstein
(*Tractatus* 5.5302) points out that it entails the logical
impossibility of a universe containing two identical spheres; Wiggins
notes that it implies the logical impossibility of even a single
sphere (or any other symmetrical object), since it entails the
identity of the two hemispheres (and so on until one reaches a
geometrical point). More to the point, as the Vaisesikas
implicitly realised, it implies the logical impossibility of more than
one atom of a given substance (having a certain velocity, spin, etc.).
Rather than reject the principle, however, they instead introduced new
intrinsic properties, the basic differentia, thereby avoiding the
unpalatable consequence.


## 11. The Ontology of Nonexistence (*abhava*) and the Semantics of Negative Statements


### 11.1 Motivations



The later Naiyayikas develop a remarkable theory of nonexistence.
According to them, the *absence* of an object or feature at a
particular spatial or temporal location is a state of affairs just as
objective as the *presence* of the object or feature there. To
Kanada's original list of six categories
(*padartha*) or types of existent, they therefore add a
seventh, 'absence' (*abhava*). This
ontological doctrine is underpinned by (i) phenomenological and (ii)
semantic considerations.



(i) The phenomenological point was that a negative awareness, say that
a certain person is not in the room, is a kind of awareness
phenomenally distinct from any awareness about what is in the room.
Cognition of what is not has an autonomous phenomenology (this idea is
notably articulated by Sartre). The principle appealed to is thus:



P1
Experiences of nonexistence are phenomenally distinct from, and
 irreducible to, experiences of existents.


The idea emerges in the Nyaya epistemology with their claim that
absence is perceived, and that this perception is a *sui
generis* type of perceptual experience, not reducible to a
combination of ordinary perception and inference (cf. the sixth type
of sensory connection in Uddyotakara's list).



(ii) The semantic point is that the Nyaya espouse a version of
the correspondence theory of truth, according to which true sentences
correspond to facts. It is alleged that true negative sentences (e.g.
"The pot is not on the ground") correspond to
'negative facts'. Facts, however, are all, for the
Nyaya, of the same basic relational form, 'bRa' (they
are said to have a qualificand-relation-qualifier structure; i.e. they
are complexes of existing entities). This restriction on what
constitutes a fact is expressible via the following semantical
principle:



P2
Sentences correspond to facts constructed out of simple or
complex entities (i.e. entities like 'a', 'absence
of a', 'a-&-b', 'a-or-b').


The principle entails that one cannot use the truth-functional
connectives to construct facts, except where they are equivalent to
term-logical connectives. (For example, the sentence "Rama and
Sita are righteous" is equivalent to "Rama is righteous
and Sita is righteous", but the term-connective in "Rama
and Sita are married" is not similarly eliminable in favour of
the truth-functional conjunction "Rama is married and Sita is
married".) The point is that a sentence like "The pot is
not on the ground" cannot correspond to a fact of the form
'!bRa' (as there are no such facts according to
P2), but must rather correspond to a fact of the form
'bRa'. Hence the introduction into one's
ontology of negative entities.


### 11.2 Temporally and Spatially Located Absence



*The Manual of Reason* (TS 85-88) reports the usual
Nyaya view that there are four types of absence: prior
nonexistence (*pragabhava*); posterior nonexistence
or 'destruction' (*dhvamsa*);
'constant' or 'absolute' absence
(*atyantabhava*); and difference
(*anyonyabhava*). Of these, the first two refer to
possible temporal states of a transient object. Suppose we represent
the temporal duration of a person *A* by the following line
(assuming that he lived between 1650 and 1750):




|  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- |
| *t*1 | 1650 | *t*2 | 1750 | *t*3 |  |
|  |  |  |  |  |  |



At any time *t*1 prior to 1650, *A* does not
yet exist, and at any time *t*3 later than 1750,
*A* no longer exists. In accordance with the above principles,
Nyaya reformulates these negative existential claims as positive
existential statements about negative entities, namely, the
'prior absence of *A*',
'<*A*' say, and the 'posterior absence of
*A*', '*A*>' say. Thus, the first
reads:



<*A* exists at *t*1,




or, since, in the Nyaya idiom, objects are said to be located in
time as well as in space,


1. <*A* is located at *t*1.



Similarly,


2. *A*> is located at *t*3.



What happens at times such as *t*2? These are times
at which *A* exists or is present (is located). Note,
furthermore, that, at *t*2, there is a posterior
absence of <*A* (for the prior absence of *A* is
destroyed when *A* comes into existence), which we designate by
'(<*A*)>'. There is also a prior absence of
*A*> (for the posterior absence of *A* does not yet
exist), i.e. '<(*A*>)'. *The Manual of
Reason* (TSD 89E) records the older Naiyayikas' claim
that these double absences must be identical with the original entity,
on pain of an infinite regress. Thus:



(<*A*)> = <(*A*>) = *A*.




Later Naiyayikas apparently disputed this natural identity (which
corresponds to the Law of Double Negation in classical logic), on the
ground that double negative constructions contain the concept of
negation, and hence are logically more complex.



A third type of absence, called 'constant' or
'absolute' absence (*atyantabhava*) is
illustrated by constructions of the form "The pot is not on the
ground". *The Manual of Reason* states (TS 87) that what
distinguishes this type of absence is that it is located in the three
times--past, present and future. This seems odd, as it might be
that the pot is on the ground at some times but not others. Perhaps
the point is that the locus of the absence here is a spatial entity
rather than a temporal one. For example, the construction "Heat
is not in ice" illustrates this kind of absence. Perhaps,
furthermore, the force of this negation is that the pot is
*never* located on the ground--hence we cannot speak of
the prior or posterior absence of the pot (for these concepts are
defined in terms of times when the pot is present). (E.g.
Udayana's definition of a substance as that which does not have
a constant absence of qualities.)



The fourth type of absence, 'difference'
(*anyonyabhava*), is illustrated by the sentence
"The pot is not (the) cloth". This is to be read as a
non-identity statement.



The Naiyayikas thus say that every negative sentence is the
negation of a sentence of the form
"*aRb*", and they distinguish
between cases where the relation *R* is the identity relation
and cases where it is a relation other than identity. The object
*a* is called the locus of the absence, and the object
*b* is called the 'counterpositive' or
'negatum' (*pratiyogin*) of the absence, i.e. it is
the object whose presence in the locus is being denied. This
highlights the fact that absences are thought of as a kind of property
or 'locatable', rather than as a kind of
'location' (at least when the relation is not identity).
For example, the absence of *A* is located in many places at
once. It is not said that there is a distinct absence-of-*A* at
each and every place where *A* is absent. We can now see how
the Nyaya parse negative sentences without using a sentential
negation. Take the sentence "The pot is not blue". The
first-order paraphrase of this would be: It is not the case that the
pot is blue (!*Fa*). The Nyaya strategy is
first to say that every property, such as blueness, has both an
extension *F* (places where it is located) and a
counter-extension *F*' (places where its absence is
located), and then to paraphrase the sentence as: The pot has
absence-of-blue. Note that a partially locatable property is one for
which the extension and counter-extension overlap--it is possible
for a feature to be collocated with its absence.


### 11.3 The Logic of Negation



*The Manual of Reason* (TS 89) makes some very interesting
observations about the logical properties of absence or negation.



**Reference versus description**. It is claimed that
there is a distinction between a qualified absence
(*visistabhava*) and a mere absence
(*kevalabhava*). Consider the following pair of
sentences:


3. Annambhatta is not in the room, and
4. The author of *The Manual of Reason* is not in the
room.



The idea is that in (3) the 'mere' absence of
Annambhatta is located in the room, whereas in (4) a
qualified absence (of Annambhatta as qualified by
authorhood) is located in the room. Do (3) and (4) really have
distinct logical forms? Perhaps we find here a realisation that
nominal expressions such as "The author of *The Manual of
Reason*" have two distinct logical functions, namely those
of *referring* to an individual and *describing* an
individual *via* his properties. (4) can thus be read either as
asserting the same as (3), that Annambhatta is not in the
room, or as saying that the author of *The Manual of Reason*,
whoever it or she is, is not in the room, i.e. that the properties
"being the author of *The Manual of Reason*" and
"being in the room" are not collocated. If that is the
sense in which (4) involves a qualified absence, then (3) and (4) do
have different logical forms.



**Universal Quantification**. *The Manual of
Reason* draws another very important distinction, between a
specific absence (*visesabhava*) and a
generic absence (*samanyabhava*). These are
illustrated by the following sentences:


5. (This) pot is not in the room, and
6. (Any) pot is not in the room



(N.B. they would be expressed by the same sentence in Sanskrit; hence
the brackets). To say that there is a specific absence of pot in the
room is to say that some particular pot is not in the room, but to say
that generic absence of pot in the room is to say that any pot is not
in the room (i.e. no pot is in the room). The distinction is thus
linked to the formulation of universally quantified constructions.
Indeed, in Nyaya logical theory, generic absences are used to
formulate the pervasion (*vyapti*) relation: "where
there is smoke there is fire" is contraposed to give
"where there is no fire there is no smoke", and this is
expressed by saying that there is a generic absence of smoke in places
where there is a generic absence of fire (cf. Ingalls 1951:
54-5). It is clear that (5) and (6) do have distinct logical
forms. In the Nyaya technical language, the distinction is made
out by saying that the property which delimits the counterpositiveness
of the absence (i.e. the *pratiyogitavacchedaka*) is
this-pot-hood in (5), but pothood in (6).



**Logical Connectives and De Morgan's Laws**.
*The Manual of Reason* touches on the meaning of conjunctive
and disjunctive absence, i.e. absence of (both *A* and
*B*) (*ubhayabhava*) and absence of (either
*A* or *B*) (*anyatarabhava*). It
observes that an awareness that two pots are absent is consistent with
an awareness that one pot is present (and the other absent). In fact,
as Ingalls shows (1951: 63-67) the Nyaya recognised the
validity of two general equations:



> 
> 
> absence of (both *A* and *B*) = (absence of *A*)
> or (absence of *B*), and
> 
> 
> 
> absence of (either *A* or *B*) = (absence of *A*)
> and (absence of *B*).
> 
> 
> 



These are recognisably versions of De Morgan's Laws, that
!(*A* & *B*) [?] !*A* [?]
!*B*, and that 
! (*A*[?]*B*) [?] !*A* & !*B*. 
As an example of the second of
these laws, consider Mathuranatha's remark (1951: 66) that
a 'heap' of (specific) absences
(*abhava-kuta*) is equivalent to a generic
absence. A place which is the locus of generic absence of fire is a
place at which every particular fire is absent, and conversely, if
every specific fire is absent, then fire is generically absent. Thus
the 'heap' (conjunction) of specific absences of fire, is
equivalent to the absence of any fire at all (the disjunction of
specific fires).