## 1. Reasoning and Logic



Humans reason: that is, taking some things to be true, they conclude
therefrom that other things are also true. If this is done in thought,
one performs an inference; and if this is done in speech, one makes an
argument. Indeed, inference and argument are but two sides of the same
coin: an argument can be thought, and hence become an inference; an
inference can be expressed, and hence become an argument.



Logic, at least as traditionally conceived, seeks to distinguish good
reasoning from bad. More particularly, it seeks to identify the
general conditions under which what one concludes is true, having
taken other things to be true. These conditions can be sought in the
nature of things. One asks, then, under what conditions do certain
facts require some other fact. This perspective on reasoning is an
ontic perspective. Next, insofar as facts are grasped in thought, one
can also ask under what conditions does knowledge of some facts permit
knowledge of another fact. Such conditions, once identified, would
distinguish good inferences from bad inferences. This perspective on
reasoning is an epistemic one. A third perspective is a dialectic one.
Here one asks under what conditions does the acceptance by someone of
some stated facts require him or her to accept some other stated fact.
Such conditions distinguish good arguments from bad arguments.
Finally, since an argument is an expression of an inference, and to
that extent, expressed in a language, it is natural to use the forms
of linguistic expressions to identify forms of inferences and
arguments, thereby distinguishing forms of good inferences and
arguments from forms of bad inferences and arguments. This perspective
is a linguistic one. The study of reasoning in India has been from the
ontic, epistemic and dialectic perspective, and not from the
linguistic perspective, the perspective best known to modern
thinkers.


## 2. Preclassical Period



The fact that humans reason is no guarantee that those who do reflect
on which reasoning is good and which is bad. Clearly, the activity of
reasoning, on the one hand, and the activity of reflecting on which
reasoning is good and which is not, on the other, are distinct, though
naturally they are intimately related. The exposition here, while
reporting primarily on what is explicit, will also report on what is
implicit. In looking at the origins of reasoning in India, it is
natural to begin with the practices in which reasoning played a role
and which, as a result, were likely candidates for reflection. The
obvious starting points for such practices are all forms of rational
inquiry.



Rational inquiry comprises the search for reasons for publicly
accepted facts, subject to public and rational scrutiny. This activity
involves people both severally and collectively. It involves people
severally insofar as people, individually, are the locus of inference.
It involves people collectively insofar as arguments, the public
manifestation of inferences, are sharpened by the scrutiny of
others.



Though the origins in India of public debate, one form of rational
inquiry, are not clear, we know that public verbal exchanges were
common in preclassical India, starting around the fifth century bce,
for they are occasionally alluded to in various
*Upanisads* and frequently described at some length in
the Buddhist canon. As pointed out by Todeschini (2011, 92), these
exchanges are not debates in the usual sense of the word, for they
include everything from verbal instruction in the ideas of the Buddha
to verbal sparring. The instruction may take the form of question and
answer, where the respondent is judged by how well he, or she,
expresses himself, or herself. An assessment depends on how persuasive
the answer is or how authoritative it sounds. Simile and analogy loom
large. Rare are what we would call arguments. More than half of the
suttas of the *Digha Nikaya* contain such
exchanges. These exchanges typically have the following features: a
central character, typically the Buddha, a statement of his or her
credentials, an adversary, a statement of his or her credentials, a
description of the location and audience, a greeting ceremony, a
challenge, a refutation of the adversary's position, the
establishment of the Buddhist position, a hypothetical case history, a
surrender and a reward (Manne, 1992, 117). These exchanges
contain much, sometimes nearly the only surviving, information on the
participants and the sects to which they belonged. (See Manne,
1992; von Hinuber, 1996, II.2.1; Solomon, 1976, 30-34;
Watanabe, 1983; Todeschini, 2011, 79-89 for details.)



Public verbal exchanges also include public assemblies
(*parisad* or *sabha*) of various sorts,
comprising relevant experts, convened to deliberate on a variety of
matters, including administrative, legal and religious matters. As
reported by Solomon (1976, ch. 3), much of the legal vocabulary for
such deliberations includes the well-known terms of debate and
argument found in the philosophical literature (see also Preisendanz
2009, 2010).



Also during this period, rational inquiry into a wide range of topics
was under way, including agriculture, architecture, astronomy,
grammar, law, logic, mathematics, medicine, phonology and statecraft.
Aside from the world's earliest extant grammar,
Panini's
*Astadhyayi*, however, no works
devoted to these topics actually date from this preclassical period.
Nonetheless, scholars agree that incipient versions of the first
extant texts on these topics were being formulated and early versions
of them were redacted by the beginning of the common era. They include
such texts as *Krsi-sastra* (*Treatise
on agriculture*), *Silpa-sastra*
(*Treatise on architecture*),
*Jyotisa-sastra* (*Treatise on
astronomy*), *Dharma-sastra* (*Treatise on
law*), *Caraka-samhita* (*Caraka's
collection*), a treatise on medicine, and
*Artha-sastra* (*Treatise on wealth*), a
treatise on politics.



Three late canonical Buddhist texts are especially noteworthy for the
study of the history of reasoning in India. They are
*Katha-vatthu* (Points of controversy), attributed to
Moggaliputta Tissa, *Yamaka* (*Couplets*) and
*Milinda-panha* (*Questions of King Milinda*).
While all three are from the Theravada (or Sthaviravada)
tradition, only the first two are canonical texts of the tradition,
both found in the Abhidhamma canon. The three date from around the
third century bce.


### 2.1 *Yamaka*



The *Yamaka* (*Couplets*) is the sixth of the seven
works comprising the Theravada Abhidhamma. Were it printed in its
entirety, it would be run to some 2,500 pages, according to von
Hinuber (1996, II.3.6). The printed editions are therefore highly
abridged.



The *Yamaka* comprises ten chapters, most with up to three
sections. Each chapter asks for various pairs, or *yamakas*, of
terms falling under the chapter's rubric whether or not the
corresponding universal categorical proposition holds. Here is chapter
2, section 1, in schematic form:




|  |  |
| --- | --- |
| 1.1 Are all M MA? | 5.1 Are all -M -MA? |
| 1.2 Are all MA M? | 5.2 Are all -MA -M? |
| 2.1 Are all M MA? | 6.1 Are all -M -MA? |
| 2.2 Are all A SA? | 6.2 Are all -SA -A? |
| 3.1 Are all M A? | 7.1 Are all -M -A? |
| 3.2 Are all A M? | 7.2 Are all -A -MA? |
| 4.1 Are all M A? | 8.1 Are all -M -A? |
| 4.2 Are all A SA? | 8.2 Are all -A -SA? |



where M is matter, A is aggregate, MA is matter-aggregate and SA
sensation aggregate. We note the repetition in 1.1 and 2.1, 3.1 and
4.1, 2.2 and 4.2, 5.1 and 6.2, 7.1 and 8.1 as well as in 6.2 and 8.2.
We also notice that 1.1 and 5.2 are contrapositives, as are 1.2 and
5.1. Though the text contains no arguments, the fact that the same
form of question is reinstantiated again and again reveals an
awareness of the importance of linguistic form, an essential aspect of
reasoning. However, while the systematicity of the text is evident,
its logical point definitely is not.


### 2.2 *Katha-vatthu*



The *Katha-vatthu* (*Points of controversy*) is the
fifth of the seven canonical Abhidhamma works in the Theravada
tradition. Unlike the *Yamaka*, the *Katha-vatthu*
consists of arguments. The arguments are designed to show the
inconsistency of some two hundred propositions which are at odds with
the views of the Theravadins. The kind of arguments found in the
text is well exemplified in the following often cited passage, where
the Theravadin questions his opponent, here a Pudgalavadin,
about whether or not the soul is known truly and ultimately.




|  |  |
| --- | --- |
| Sthaviravadin: | Is the soul known truly and ultimately? |
| Pudgalavadin: | Yes. |
| Sthaviravadin: | Is the soul known truly and ultimately just like any ultimate
fact? |
| Pudgalavadin: | No. |
| Sthaviravadin: | Acknowledge your refutation, |
|  | If the soul is known truly and ultimately, then indeed, good
sir, you should also say that the soul is known truly and ultimately
just like any ultimate fact. |
|  | What you say here is wrong: namely, that we ought to say (a)
that the soul is known truly and ultimately; but we ought not to say
(b) that the soul is known truly and ultimately just like any ultimate
fact. |
|  | If the latter statement (b) cannot be admitted, then indeed the
former statement (a) should not be admitted. |
|  | It is wrong to affirm the former statement (a) and to deny the
latter (b). |



One easily abstracts from this the following form,




|  |  |
| --- | --- |
| Sthaviravadin: | Is A B? |
| Pudgalavadin: | Yes. |
| Sthaviravadin: | Is C D? |
| Pudgalavadin: | No. |
| Sthaviravadin: | Acknowledge your refutation, |
|  | If A is B, then C is D. |
|  | What you say here is wrong: namely, that |
|  | A is B but that C is not D. |
|  | If C is not D, then A is not B. |
|  | It is wrong that A is B and C is not D. |



Indeed, this form is repeatedly instantiated throughout Book 1,
Chapter 1.



Three features of this text are important to note from the point of
view of the history of logic. First, as the schema above shows,
arguments are put into a canonical form. While we have no record that
semantic ascent had taken place, there is no doubt from the arguments
are intended to satisfy a certain form. Second, the sentences of the
argument are logically related. The author takes for granted that the
sentences assented to are inconsistent, corresponding to an instance
of the following inconsistent propositional schemata of \(\alpha\),
\(\neg \beta\), \(\alpha \rightarrow \beta\). He also takes it for
granted that it is wrong to hold inconsistent propositions. And he
finally presupposes that, if a sentence corresponding to propositional
schema \(\alpha \rightarrow \beta\) is true, then the sentence
corresponding to the propositional schema \(\neg \beta \rightarrow
\neg \alpha\) is also true; that is, he presupposes the natural
language counterpart to one direction of the equivalence of a
conditional and its contrapositive. (See Ganeri 2001 for the most
recent attempt to explicate the dialectic implicit in the text.)


### 2.3 *Milinda-panha*



*Milinda-panha* (*Questions of King Milinda*),
unlike the *Katha-vatthu* which comprises an argumentative
exchange adhering to identifiable patterns, comprises a dialogue
between the Greek Bactrian king, Menander (Pali: Milinda), and an
otherwise unknown Buddhist monk, Nagasena (von Hinuber,
1996, III.4). The text is an exposition of Buddhist doctrine and
practice, cast in terms of questions put by King Milinda to the monk
Nagasena and the latter's answers. Though there is some
argumentation, for the most part, the text is expository, where the
exposition is done almost entirely through analogy, sometimes very
elaborate ones. For example, Book 5, entitled 'the problem of
inference', which has almost nothing to do with inference, sets
out an elaborate analogy between a great city and its various parts,
on the one hand, and the Buddha's teaching and its various
parts, on the other. The pretext for this expository analogy is an
argument put to Nagasena by King Milinda. King Milinda asks
whether Nagasena or his teachers has seen the Buddha.
Nagasena replies that neither he nor his teachers has. King
Milinda concludes, then, that the Buddha did not exist. Nagasena
replies by making a similar argument whose premiss King Milinda
accepts but whose conclusion he rejects. King Milinda admits that
neither he nor those who have taught him has seen the founders of his
kingly lineage, yet he believes that the founder of his lineage
existed. (Bk. 5, sec. 2) Then King Milinda replies that he has
evidence for belief in the existence of a founder, the existence of
the royal insignia. Nagasena then counters that he too has
evidence for the existence of the Buddha, namely, his various
doctrines, metaphorically the royal insignia of the Buddha. (Bk. 5,
sec. 3) In short, just as one infers the existence of a founder of a
lineage from the legacy of his royal insignia, so one infers the
existence of the Buddha from the legacy of his teachings.
Nagasena then turns to a similar argument which serves as a
pretext to elaborate various aspects of the Buddha's teaching:
just as one can infer from a well planned city the fact that it had a
designer, so one can infer from the well ordered doctrines of the
Buddha that the Buddha existed. Over the ensuing 20 sections,
Nagasena first enumerates various features of the city and then
elaborates on aspects of Buddhist doctrines put in correspondence with
them. The final section ends with eight arguments, each paired through
analogy with an argument pertaining to features of Buddhist thought
and the existence or features of the Buddha. (1) From the greatness of
the city one infers the greatness of the architect. (2) From the
greatness of the waves, one infers the greatness of the ocean; (3)
From seeing the peaks of mountains from afar, one infers the height of
the mountains; (4) From the greatness of an elephant's
footprint, one infers the size of the elephant; (5) From seeing
creatures crouching in fear, one infers that a lion has roared; (6)
From the luxuriance of the vegetation, one infers the ampleness of
rainfall; (7) From the marshiness of the earth, one infers the excess
of rainfall; (8) From the scent in the air, one infers that flowers
are in bloom. Each of these arguments has the form of what is dubbed
to be the *pramana*, the means of epistemic
cognition, known as *anuman*a, or inference.



One important principle of logic is presupposed in the dialogue: the
principle of non-contradiction. It is presupposed in a variety of
places throughout the text, but it is particularly in evidence in Book
4, which is entitled 'Solving the dilemmas'. The book
consists of dilemmas put to Nagasena by King Milinda. Many of
them are pairs of apparently inconsistent statements or practices
inconsistent with doctrine. They correspond to the following schema in
propositional logic: \(p \land q,\) \(p \to \neg q,\) \(q \to \neg
p.\) One particularly clear instance occurs in section 6 of Chapter 2.
There King Milinda says:



> 
> 
> If the Blessed one, Nagasena, really said that all men tremble at
> punishment and all are afraid of death, then the statement that the
> Arhat has passed beyond fear must be false. But if that last statement
> is really by him, then the other must be false. (T. W. Rhys Davids
> 1980.)
> 
> 
> 



Nagasena's response is to point out, in effect, that the
intended meaning is different from the literal meaning. He gives
several examples of sentences in which the word all occurs but where
all in not intended to include everyone in what we today call the
domain of discourse. He points out (in section 8) that a king might
tell his four ministers that all must pay taxes, but the king does not
intend that the ministers are included by all, ministers being free
from the burden of taxation. In another example (section 9), he points
out that a village headman may tell the village crier to bring
together all the villagers, but in fact, what he intends is that only
all the heads of households gather.


## 3. Classical Period



The first five hundred years of the common era also saw the redaction
of philosophical treatises in which proponents of diverse
philosophical and religious traditions put forth systematic versions
of their world views. These latter works bear witness, in a number of
different ways, to the intense interest in argumentation during this
period. Among the diverse forms of argument from this period, one
emerges as a canonical one. In this section, we first review the texts
relevant to the development of logic from the end this preclassical
period. We then turn our attention to surveying the emergence of a
canonical argument form. Finally, we conclude with a very brief
overview of the treatment of fallacies in arguments and of missteps in
debate.


### 3.1 Texts of the early classical period



The texts relevant to the study of the development of logic during
this period may be divided into three kinds: those which have
arguments but which do not mention or discuss either argument or
inference as such, those which mention or discuss inference as such
but do not mention or discuss arguments as such, and those which
mention or discuss arguments and possibly also mention or discuss
inference, and may even provide illustrations of either.


#### 3.1.1 Texts with arguments



During this period polemical texts, which consist almost entirely of
arguments, start to appear. The earliest among these are texts
attributed to Nagarjuna (2nd century ce),
among which are the
*Mula-madhyama-kakarika* (*Basic verses on
the middle way*), the *Vigrahavyavartani*
(*Exclusion of disputes*) and the
*Vaidalya-prakarana* (*Tract on pulverization*).
Shortly thereafter came a text by Aryadeva (c. 3rd century ce),
said to be a student of Nagarjuna,
entitled *Sataka-sastra* (*Treatise in one
hundred verses*), now extant only in its Chinese translation,
*Bai lun* (Bai Lun ). Of these texts, only
the *Vaidalya-prakarana* is a prose text. While the
others are in verse, the *Vigraha-vyavartani*
and the *Sataka-sastra*, unlike the
*Mula-madhyama-kakarika,* are accompanied by the
author's own commentary. Of the latter two, only the
*Vigraha-yavartani* survives in its Sanskrit
original. That the text has a commentary by its author and that both
the text and the commentary have survived in the original Sanskrit
original make it the text which best reveals the reasoning of the
period.



The text comprises seventy verses, each supplemented with the
author's own commentary. The central question addressed is the
claim that nothing has a nature. The first twenty verses present four
arguments supporting the claim followed by six arguments against it.
The following fifty verses elaborate on the arguments and objections
in the first twenty. The argumentation in the text is complex, using a
number of different forms of argument and invoking or presupposing
several principles of reasoning. To appreciate the kind of reasoning
found in this and the other texts mentioned above, we shall consider
briefly some of the arguments found in verses 31-50 and in their
accompanying commentary.



Nagarjuna's aim in the verses 31-50 is to show
that any argument to establish that there are
*pramana*s, means of epistemic cognition, ultimately
leads to contradiction. He considers two cases: the case where it is
maintained that *pramana*s are established by other
*pramana*s and the case where each
*pramana* establishes itself. The first case is
addressed in verse 31 and its accompanying commentary, where
Nagarjuna argues that, if to establish a
*pramana* other *pramana*s are
required, then there results an endless (*an-avastha* :
literally, foundationless) chain of such pramanas, in other
words, an infinite regress, which is taken to be an impossibility. The
second case spans the remaining verses (33-50) and has two
parts. In the first part (vv. 33-39), the proponent of the
existence of *pramana*s is challenged to justify
why, of all the things whose existence is established by
*pramana*s, *pramana*s alone have
the peculiarity of not being established by (other)
*pramana*s. The opponent's answer is to
maintain that *pramana*s are not alone; light too,
the opponent claims, has the property of revealing the existence both
of other things and itself. Nagarjuna then puts forth four
arguments to show either that light does not reveal itself or that it
does not reveal anything. In the second part (vv. 40-48),
Nagarjuna maintains that a *pramana* and
its *prameya*, the object revealed by the
*pramana*, are indistinguishable, which he seems to
think is absurd. He goes on to bolster this argument with what he
takes to be, and what he says is, another argument of the very same
form, and which concludes father and his son, by dint of their
relation, are indistinguishable (vv. 49-50).



With the argumentative structure of the passage in mind, let us
consider three arguments in it which can be understood without
elaboration. In verse 34, Nagarjuna says:



> 
> 
> For fire does not illuminate itself. Just as a pot in the dark, not
> yet illuminated by fire, is not apprehended, and then at the very next
> moment, illuminated by fire, is apprehended as existent, in the very
> same way, if a fire were in the dark, not yet illuminated [and] at a
> later time there were be [its] illumination by fire, then it would
> illuminate its existence. Yet that is not so.
> 
> 
> 



The point is that, while the opponent holds that a
*pramana* is self revealing, fire is not. When fire
illuminates something, the thing the fire illuminates already exists
in the dark before the fire's light reveals it; but a fire does
not exist in the dark before the fire's light reveals it. In
this way, Nagarjuna has shown that the opponent has failed
to show that there is anything other than *pramana*s
which are self revealing and that therefore the
*pramana*s remain exceptional.



This argument has, even to modern eyes, *prima facie* merit.
However, the next two arguments do not. The argument in verse 35 is
restated in the
  

commentary as follows:



> 
> 
> And if, according to what you say, a fire illuminates its own
> existence in the very same way as it illuminates the existence of
> other things too, will it not burn itself in the very same way as it
> burns other things too?
> 
> 
> 



The argument is this: Fire illuminates other things and itself. Fire
burns other things. Therefore fire burns itself. But fire does not
burn itself. Therefore fire does not illuminate itself. The argument
is framed as an argument by *reductio ad impossibile* with an
argument by analogy within. As it happens, this argument by analogy is
easily recast in the form of an analogical argument through
similarity, one of two forms of argument treated as canonical in other
texts and to be discussed below. We can see that the argument here has
no deductive cogency, if we render the argument as deductive by
supplying the following premiss: if fire bears one relationship to
other things and to itself, then any other relationship it bears to
other things it bears to itself.



An equally unconvincing argument is given in the next verse (36).



> 
> 
> And if, according to your thinking, fire illuminates its existence and
> that of other things, would not darkness, being the opposite of fire,
> also hide its existence and that of other things? Yet that is not
> observed. In that case, your statement that fire illuminates its own
> existence and that of other things is not true.
> 
> 
> 



The argument here is also framed as an argument by *reductio ad
impossibile* with an argument by analogy within. As it happens,
this argument by analogy is easily recast in the form of an analogical
argument through dissimilarity, the other of two forms of argument
treated as canonical in other texts and to be discussed below.


**3.1.2 Texts discussing inference**

We know of four texts from this period which identify inference
(*anumana*), as distinguished from argument
(*sadhan*a), as a means of epistemic cognition
(*pramana*). They are the
*Vaisesika-sutra* (*Aphorisms on
individuation*), a treatise of speculative ontology attributed to
Kanada (c. 1st century ce), the
Spitzer manuscript, a collection of fragments of a Sanskrit text (c.
3rd century ce) of unknown authorship (Franco,
2004, v. 1, 32-33), *Samdhi-nirmocana-sutra*
(*Aphorisms on release from bondage*), an early Mahayana
text (between the 3rd and 5th centuries ce),
also of unknown authorship, and the
*Sasti-tantra* (*Sixty doctrine*s), a
Samkhya text attributed Varsaganya (4th
century ce).



The *Vaisesika-sutra* has passages which allude
to inferences whereby one unobserved thing is inferred on the basis of
something observed which bears one of five relations to the thing
inferred (VS 9.18; Jambuvijaya (ed), 1961, 69; cp. VS 3.1.8). However,
no examples are given. In contrast, six examples of inference are
found in the Spitzer manuscript among the surviving fragments
referring to the four means of epistemic cognition
(*pramana*s) of perception
(*pratyaksa*), inference (*anumana*), analogy
(*aupamya*) and tradition (*aitihya*) (Franco, 2003,
126), though these inferences require piecing together (Franco, 2003,
126-136). A passage which also refers to the same
*pramana*s but with different words
  

is found in the tenth and last chapter of the
*Samdhi-nirmocana-sutra*, an early Mahayana
Buddhist text, of unknown authorship, which survives only in a Tibetan
and Chinese translation. The passage in question has also been
translated into English and critically discussed by Yoshimizu (2010,
142-148). (See also Powers (trans.), 1991, 321ff.)



Finally, there is the *Sasti-tantra*, which
also survives only in fragments, first collected by Frauwallner
(1958), later expanded by Steinkellner (2017, Appendix 1). It defines
inference (*anumana*) as follows: To infer is to establish
something in the remainder, on the basis of a relation and something
perceptible. One of the text's fragments lists six relations as
ones which underpin an acceptable inference. They are: the master
servant relation (*sva-svami-bhava-sambandha*),
the matter alteration relation
(*prakrti-vikara-sambandha*), the part whole
relation (*karya-karana-sambandha*), the
cause effect relation (*nimitta-naimittika-sambandha*),
the source product relation
(*matra-matrika-sambandha*), the
association relation (*sahacari-sambandha*) and the
incompatibility relation
(*vadhya-ghataka-sambandha*). Though each of the
relations is illustrated, no example of an inference using them is
found among the known fragments.



What emerges from the passages of the
*Vaisesika-sutra* and the
*Sasti-tantra* and what is consistent with
those in the Spitzer manuscript and
*Samdhi-nirmocana-sutra* is that inferences have the
following form:



inferential syllogism


|  |  |
| --- | --- |
| proposition: | p has S |
| reason: | because p has H. |
| relation: | A relation which possessors of H bear to possessors of S. |



#### 3.1.3 Texts discussing argument



Interest in the nature of argument itself appears also at this time.
The best known text from this period is the Brahmanical treatise
*Nyaya-sutra* (*Aphorisms on logic*) by
Gautama, also known as Aksapada (c. 2nd ce),
the actual redaction of which is thought by
some to date to the third century ce. This
concerns topics primarily pertaining to epistemology and debate.
Though a few aphorisms found in the first chapter of the first and
second books speak of inference, much more attention is devoted to
debate, essentially all of both chapters of Book 5, the entirety of
the second chapter of Book 1, and several aphorisms in the first
chapter of Book 1. Unfortunately, the text's aphorisms
(*sutra*s) are often not much more than lists of terms.
With little discussion and few examples, it is hard to get a clear
idea of what the key terms mean.



Some light is shed on this work by a contemporaneous Buddhist work,
Nagarjuna's *Vaidalya-prakarana,* mentioned
above. It is organized around the key terms listed in the first
aphorism of the *Nyaya-sutra* (NS 1.1.1). However, it
does not explain the terms nor does it illustrate them. Instead, it
sets out for each term arguments intended to show its incoherence. It
is therefore rich in arguments, most of which are analogical. The
author also judges a number of counter arguments as fallacious,
pointing out either that they are circular or that they lead to an
infinite regress.



Less laconic passages pertaining to some of the same topics are found
in the *Caraka-samhita*, Classical India's
earliest medical text, conjectured by some to have been redacted in
its current form at the beginning of first century ce.
The text has three relevant passages: a short
one concerned with inference (CS 1.11.21-22), a longer one
concerned with *pramana*s (CS 3.4.1-14 ) and a
still longer one concerned with argument (CS 3.8.16-67).



Not all Buddhist texts from this period are hostile to argumentation.
Two works contain short passages with lists and classificatory
definitions of terms pertaining to debate. One is the
*Samdhi-nirmocana-sutra* (*Aphorisms on release
from bondage*), mentioned above. Another is the
*Abhidharma-samuccaya* (*Compendium of the higher
teachings*), a text usually attributed to the Buddhist thinker,
Asanga (5th century ce), whose fifth
chapter has a section, its seventh, often referred to as
*Vada-viniscaya* (*Settling on what debate
is*), also devoted to debate.



In contrast to the passages in the two texts just mentioned, which
list, and even sometimes gloss, terms ive other texts from this period
not only mention and sometimes discuss, terms pertinent to inference
and debate the *Yogacara-bhumi-sastra*
(*Treatise on the stages of the practice of yoga*), a work
traditionally attributed to Asanga, but now generally thought to
be by a number of authors, has a passage, usually referred to as
*Hetu-vidya* (*Science of reasons*), which provides
some fifty examples of simple common sense inferences, all of which
are easily recast in the form of the inferential syllogism given
above. The inferences are divided into five categories. While relation
words are used for each category, the logical force of these relations
is not made clear. The inferences provided include ones such as the
inference of fire from smoke, of the presence of a lion from its roar,
of being sick from unusual eating practices, as well as inferences
more closely connected with Buddhist doctrine.



There are two other works which have passages pertinent to the study
of the history of reasoning in India, both works attributed to
Asanga. The first is the *Xian yang sheng
jiao lun*
(Xian Yang Sheng Jiao Lun ), or *Treatise which
reveals and disseminates the wise teachings*, which is a condensed
version of the
*Yogacara-bhumi-sastra*, and the
*Shun zhong lun* (Shun Zhong Lun ),
or *Treatise on following the middle way*, which seems to be a
commentary on the introductory verse of Nagarjuna's
*Mula-madhyamaka-karika* (Katsura 1985 p.
166).



The first work devoted entirely to argument and inference is the
*Fang bian xin lun*
(Fang Bian Xin Lun ), or *Treatise on the heart of
means*, translated into Chinese in 472 ce
without attribution, though it later came to be attributed to
Nagarjuna. This text, translated into Sanskrit by G. Tucci
(1929), is commonly known by scholars by the translation of its title
by Tucci as *Upaya-hrdaya*.



Finally, shortly after Asanga, Vasubandhu (c. 5th century ce),
another Buddhist idealist, thought to be the
younger brother of the Asanga, wrote at least three works on
debate: *Vada-hrdaya* (*Heart of debate*),
*Vada-vidhana* (*Precepts of debate*) and
*Vada-vidhi* (*Rules of debate*). These texts have
been lost, though fragments of the latter two, some in Sanskrit, many
in Tibetan, have been collected (Frauwallner 1933, 1957; Ono 2020).
Another work, ascribed to Vasubandhu, which survives only in Chinese,
is the *Rushi lun*
(Ru Shi Lun ), *Treatise on truth*. G. Tucci
(1929), translating it back into Sanskrit, gave it the Sanskrit title
*Tarka-sastra*, by which it is now generally known.
However, as has been shown recently by Ono Motoi (Ono 2020 SS1),
this rendition is not correct.



Having surveyed the texts from the late preclassical period pertinent
to the study of the development of logic, we now turn to the emergence
of a canonical Indian syllogism.


### 3.2 The emergence of a canonical syllogism



The earliest known example of the canonical Indian syllogism is found
in the *Caraka-samhita*. The argument is clearly an
analogical one. The earliest known deductive version of the syllogism
is found in the *Fang bian xin lun*, or
*Upaya-hrdaya*; and the earliest known discussion of
a deductive version of the syllogism is found in the
*Rushi lun*, usually referred to as the
*Tarka-sastra*. A concise version of the deductive
version is found in Vasubandhu's *Vada-vidhi*.



The *Caraka-samhita* (CS 3.8.31), like the
*Nyaya-sutra* (NS 1.1.32), takes the syllogism to
have five parts, the names for four of them being identical; however,
unlike the *Nyaya-sutra*, the
*Caraka-samhita* provides an illustration of the
syllogism.



canonical syllogism (analogical)


|  |  |
| --- | --- |
| proposition: | The soul is eternal |
| reason: | because of being un-produced. |
| example: | Space is unproduced and it is eternal. |
| application: | And just as space is unproduced, so is the soul. |
| conclusion: | Therefore, the soul is eternal. |




Observe that the first three statements in the syllogism have the form
of the analogical syllogism using similarity as discussed above: p,
the soul, has S, the property of being eternal, because p, the soul,
has H, the property of being unproduced; as d, or space, has H, the
property of being unproduced, and d, space, has S, the property of
being eternal. However, the argument here adds two more statements:
the first spells out the analogy between the subject of the
proposition and the example, using the correlative expression
*as* (*yatha*) ... *so*
(*tatha*) ...; the second restates the
argument's proposition.



While *Caraka-samhita* provides only one
illustration of its canonical syllogism, the earliest extant
commentary on the *Nyaya-sutra*, called the
*Nyaya-bhasya* (*Commentary on logic*),
has passages in its commentary on NS 1.1.33-39, which permit the
reconstruction of two analogical syllogisms, corresponding to those
using similarity and using dissimilarity discussed above. The
commentary, attributed to Vatsyayana (fifth ce),
also known as Paksilasvamin,
explicitly distinguishes the syllogisms as one based on similarity
(*sadharmya*) and the other based on dissimilarity
(*vaidharmya*) discussed earlier. (For details, see Gillon
2020.) The analogical syllogism based on similarity differs but
slightly from the syllogism found in the
*Caraka-samhita*.



The *Fang bian xin lun*, or
*Upaya-hrdaya*, purports to be a primer on argument
and reasoning, listing and defining many terms. It also contains many
arguments, several of which are analogical arguments both through
similarity and through dissimilarity. The author of the text neither
states what an argument is nor what its parts are. Yet, in the first
chapter, he speaks of excessive and deficient statements and says that
there are three kinds: deficiency of reason, deficiency of proposition
and deficiency of example. (T1632 24.3.14-18; Gillon and Katsura
2017 p. 215). Arguments which are not deficient in any of these ways
is said to be complete. From the illustrations, it is clear that a
nondeficient argument has the form: p has S, because of having H, like
d, where d is assumed to have both H and S. In other words, a complete
argument could be spelled out in the form whose explicit counterpart
would be that of an analogical syllogism using similarity of the kind
found in the polemical texts discussed earlier.



The only argument to appear in a form with five parts is given in the
fourth, or last, chapter (T1632 28.1.4-6). Here is the argument
as it occurs with the labels for the parts supplied for ease
comparison. Though the Chinese equivalent of *proposition*,
*reason* and *example* appear in the text, the
equivalents of *application* and *conclusion* do
not.



canonical syllogism (deductively valid)


|  |  |
| --- | --- |
| proposition: | The self is eternal |
| reason: | because it is not perceptible by the senses. |
| example: | Space, because of not being perceptible by senses, is
eternal. |
|  | **Everything** which is not perceptible by senses
is eternal. |
| application: | And the self is not perceptible by senses. |
| conclusion: | Could the self possibly be non-eternal? |




Note that example statement comprises two sentences: the first
restates what is expressed in the proposition and reason statements,
the second affirms a universal proposition, *everything which is
not perceptible by senses is eternal*. The example statement
comprises a deductively valid argument, as does the second sentence
together with the reason and proposition statements. Surprisingly, the
author rejects the syllogism as a bad one. The rejection is justified
by an argument by analogy through dissimilarity.



When we turn to the *Rushi lun*,
customarily referred to as the *Tarka-sastra*, we
find the logical situation has changed. A deductive syllogism similar
to the one just set out is endorsed. Moreover, analogical syllogisms
are explicitly rejected. For example, the text rejects the following
analogical syllogism (T1633 30.3.2-4).



canonical syllogism (analogical)


|  |  |
| --- | --- |
| proposition: | Sound is not eternal |
| reason: | because, arising due to an effort, it arises immediately. |
| example: | **As** a clay vessel, arising due to an effort, and
having arisen, perishes, |
| application: | sound too is that way. |
| conclusion: | Therefore, sound is not eternal. |




That the syllogism is analogical is made clear by the formulation of
the example and application statements.



What the text's author advocates instead are syllogisms which
are in fact deductively valid, similar to the syllogism cited and
rejected in the *Fang bian xin lun*.
Here is one example (T1633 30.3.7-10).



canonical syllogism (deductively valid)


|  |  |
| --- | --- |
| proposition: | Sound is not eternal |
| reason: | because, arising due to an effort, it arises immediately. |
| example: | If a thing is eternal, (then) it does not arise due to an
effort. For example, space is eternal and does not arise due to an
effort. |
| application: | Sound too is not that way. |
| conclusion: | Therefore, sound is not eternal. |




This argument, like the one rejected in *Fang bian
xin lun*, is deductively valid. The example statement
also comprises two sentences: the first, however, affirms a universal
proposition, *If a thing is eternal, (then) it does not arise due
to an effort*, and the second states an instance of the universal
proposition, which is distinct from the subject of the argument. The
proposition and reason statements, together with the first sentence of
the example statement, comprise a deductively valid argument.



Moreover, we know that the author is fully aware of the
syllogism's logical force, for he states the three conditions,
or three forms (*tri-rupa*), which a reason must satisfy
for the argument in which it occurs to be sound.



> 
> 
> three forms (T1633 30.3.18-26):
>   
> 
> The reason you set forth is not definite because eternality and
> non-eternality appear throughout it. The reason I set forth has the
> three marks. (1) The (reason) is a property of the subject, (2) it is
> included in things similar and (3) it is excluded from things
> dissimilar. Therefore, the reason I set forth succeeds in not
> deviating, your reason does not. Therefore, your objection is
> confused. If the reason you set forth were like my reason (in this
> respect), your objection would succeed in being a proper
> objection.
> 
> 
> 



As noted by H. Ui 1929 (reported in Katsura 1985 p. 166), the earliest
mention of the three forms appears in a brief passage in a non-logical
text, *Shun zhong lun* (T1565 42a12,22ff).
However, the author of this text, said to be Asanga, rejects the
criterion, a criterion thought to be of a non-Buddhist origin.



Finally we come to Vasubandhu's *Vada-vidhi*. Here
the endorsed argument retains the proposition and the reason, abandons
the application and the conclusion and simplifies the example, so that
the resulting syllogism has this form:



canonical syllogism (deductively valid):
Vasubandhu


|  |  |
| --- | --- |
| proposition: | p has S |
| reason: | because p has H. |
| example: | That which has H has S, like d. |
|  | (where d, distinct from p, has properties H and S). |




It harks back to the form of the inferential syllogism mentioned
earlier in our discussion of the
*Sasti-tantra* and the
*Vaisesika-sutra*. However, there is one
crucial difference: Vasubandhu is absolutely clear that the example
statement expresses an indispensability relation
(*a-vina-bhava*: lit. *not existing without*,
or *sine qua non*). As is clear, instances of this schema are
deductively valid arguments.


### 3.3 Fallacies in arguments and missteps in debates



The obverse side of identifying a proper argument is identifying
fallacious arguments. Fallacious arguments include, on the one hand,
syllogisms whose reasons have been identified as specious and, on the
other hand, counter arguments, or rejoinders, identified as
defective.



The *Caraka-samhita* (CS 3.8.57) identifies and
illustrates three kinds of arguments as defective. The first chapter
of the fifth book of the *Nyaya-sutra* (NS 5.1) lists
and briefly describes 24 arguments, which it designates as fallacious
rejoinders (*jati*). The fourth chapter of the
*Fang bian xin lun* lists and describes
twenty such arguments, which are either the same as, or similar to,
the arguments identified as fallacious rejoinders in the chapter of
the *Nyaya-sutra* just mentioned. Surprisingly, the
*Fang bian xin lun* treats these
arguments as good rejoinders, as noted by Kajiyama (1989 p. 108). The
most interesting treatments of fallacious rejoinders are those found
in the *Rushi lun* and in the
*Vada-vidhi*, where many of fallacious rejoinders have
names which are the same as those exemplified in the
*Nyaya-sutra* (Ono 2020 SS3.2 and SS3.5).
(See also Randle 1930 ch. 6.2 and Solomon 1976 ch. 5.)



The *Vaisesika-sutra* (VS 3.1.10-11) and
the *Nyaya-sutra* (NS 1.2.4-9) name kinds of
specious reasons (*hetvabhasa*), but give neither
examples nor explanations of what they are. Three kinds are listed,
and even briefly discussed, in the *Caraka-samhita*
(CS 3.8.57). The *Fang bian xin lun*
merely lists eight kinds. Three kinds are exemplified and briefly
discussed both in the *Vada-vidhi* and in the
*Rushi lun*. (See Randle 1930 ch. 3.5 and
Solomon 1976 ch. 7.)



Besides identifying fallacious syllogisms and rejoinders, some of
these texts also have either extended passages or entire chapters
devoted to the identification of behavior in debates which, when
displayed by someone, warrants his being deemed to have lost. These
missteps, known as *grounds for defeat*
(*nigraha-sthana*), range from making fallacious arguments
to infringing the rules of debate procedure. The second chapter of the
fifth book *Nyaya-sutra* (NS 5.2) sets out 22 cases,
as does the third chapter of the *Rushi
lun*. An extended passage of the
*Caraka-samhita* (CS 3.8.50-65) lists 14
cases. Asanga's *Hetu-vidya* has an extended
passage which classifies them into three kinds and provides cases of
each. (See Randle 1930 ch. 6.3 and Solomon 1976 ch. 6.)


## 4. Culmination of the Classical Period



The Buddhist thinker, Dignaga (c. 5th - 6th century ce),
consolidates the insights into the canonical
deductively valid syllogism of his predecessors, and in particular
those of his teacher, Vasubandhu, as well as deepens them. He is, in
fact, a pivotal figure in the history of Indian logic. This section is
divided into two parts: the first devoted to Dignaga's
contributions to Indian logic, especially the canonical syllogism, the
second part summarizing other contributions from his contemporaries
and successors, both Buddhist and non-Buddhist.


### 4.1 Dignaga



Dignaga wrote three works pertaining to reasoning and argument.
Unfortunately, in each case, the original Sanskrit text is not
available. One, the *Nyaya-mukha* (*Introduction to
logic*), is extant in Chinese translation. However, a
Sanskrit manuscript is now known to exist in Tibet. It has yet to be
edited and published. The remaining two are extant only in Tibetan
translation: *Hetu-cakra-damaru* (*The drum wheel of
reason*) and his *magnum opus*,
*Pramana-samuccaya* (*Compendium on epistemic
means of cognition*), four of whose six chapters are devoted to
inference or argument.



One idea which is particularly clear in Dignaga's work is
his explicit recognition that arguments which are expressed as
syllogisms are expressions of inferences. This is reflected in his
terms *inference for oneself*
(*svartha-anumana*), which refers to the cognitive
process expressible as a syllogism, and *inference for another*
(*parartha-anumana*), which refers to the verbal
expression of the syllogistic inference. These terms are also the
titles of the second and third chapters of his
*Pramana-samuccaya*.



Dignaga apparently enlarges the form of Vasubandhu's
canonical syllogism. Even though the texts just mentioned are not
extant in Sanskrit, some of their commentaries are and some of these
texts' passages are found cited in existing Sanskrit works.
Availing himself of these works, S. Katsura (2004a p. 143) has
identified the following as an argument instantiating what
Dignaga considers the canonical form of a good syllogism.



canonical syllogism (deductively valid):
Dignaga


|  |  |
| --- | --- |
| thesis: | Sound is non-eternal |
| reason: | because it is immediately connected with an effort. |
| similarity example: | That which is immediately connected with an effort is observed
to be non-eternal, like a pot. |
| dissimilarity example: | That which is eternal is observed not to be immediately
connected with an effort, like space. |




Before discussing the syllogism, we must take notice of the word
*paksa* (*thesis*), which Dignaga uses
instead of *pratijna* (*proposition*). The
word is used both for the statement, previously called a proposition
and now called a thesis, as well as for the factual situation it
expresses. It is also used to refer to the grammatical subject of the
thesis statement as well as to the thing denoted by the grammatical
subject. (See Staal 1973 for a lucid exposition of this and other
ambiguities in the technical terms of classical Indian logic.)



Dignaga's canonical syllogism, like that of Vasubandhu, has
neither an application statement nor a conclusion statement. However,
unlike that of Vasubandhu, it has two example statements. Each example
statement comprises a universal statement and a phrase naming
something. In the case of the statement of similarity example, the
universal statement asserts that whatever has the property adduced as
a reason (*hetu*) has the property to be established
(*sadhya-dharma*), which is mentioned in the
syllogism's thesis, while the phrase names something, distinct
from the subject (*paksa*), yet similar to it with
respect to the property to be established
(*sadhya-dharma*), and has the property adduced as the
reason. The example named is said to be subject-like
(*sa-paksa*). In the case of the statement of
dissimilarity example, the universal statement asserts that whatever
does not have the property to be established
(*sadhya-dharma*) does not have the property adduced as a
reason (*hetu*) and the phrase names something dissimilar to
subject with respect to the property to be established and not having
the property adduced as the reason. The example named here is said to
be subject-unlike (*vi-paksa*). Finally, Dignaga
seems to have added a word to the formulation of the universal
statement, namely, the word *observed*
(*drsta*), the past passive participle of the
verb *to see* (*drs*), which means not only
to see but also to observe, to notice and even to know. Hereafter, we
shall refer to a syllogism's reason statement as its minor
premiss and the universal statement in its example statement as its
major premiss.



Perhaps most original in Dignaga's work on argument and
inference is what he called the *wheel of reasons*
(*hetu-cakra*), an equivalent alternative to the three forms of
reason (*tri-rupa-hetu*). It comprises a three by three
matrix, which distinguishes a proper from an improper reason. It
specifies, on the one hand, the three cases of the reason
(*hetu*) occurring in some, none, or all of subject-like things
(*sa-paksa*), and, on the other, the three cases of the
reason (*hetu*) occurring in some, none, or all of
subject-unlike things (*vi-paksa*). Letting H be the
reason, S the subject-like things and \(\bar{\mbox{S}}\) the
subject-unlike things, we obtain the following table.





|  |  |  |  |
| --- | --- | --- | --- |
| H occurs in: | all S | all S | all S |
|  | all \(\bar{\mbox{S}}\) | no \(\bar{\mbox{S}}\) | some \(\bar{\mbox{S}}\) |
| H occurs in: | no S | no S | no S |
|  | all \(\bar{\mbox{S}}\) | no \(\bar{\mbox{S}}\) | some \(\bar{\mbox{S}}\) |
| H occurs in: | some S | some S | some S |
|  | all \(\bar{\mbox{S}}\) | no \(\bar{\mbox{S}}\) | some \(\bar{\mbox{S}}\) |




Dignaga identified the syllogisms corresponding to the top and
bottom cases of the middle column as good syllogisms and those
corresponding to the other cases as bad.



These developments have led to a rather lively debate among scholars
of the development of logic in early classical India. A very succinct,
but somewhat misleading, way to put the question at the center of the
debate is whether or not Dignaga's canonical syllogism is
inductive or deductive. A more cumbersome, but more precise, way to
put the question is this: Is there a choice of a subject, of a
property adduced as a reason, and of a property to be established
which Dignaga would accept as constituting a good syllogism but
which fails to satisfy the form corresponding to the canonical
syllogism given above?



Let us now consider those aspects of Dignaga's treatment of
the syllogism which are at the center of this debate. One reason to
think that Dignaga would accept as a good syllogism one failing
to be deductively valid might be his inclusion of the word
*observed* (*drsta*) in the example
statement. In other words, one might think that Dignaga would
accept as a good syllogism one in which, even though it is not the
case that whatever has H has S, it is the case that whatever is
observed to have H has S: that is to say, the major premiss pertains
only to observed cases of H, and not for every case of H. However, no
such syllogisms are accepted by Dignaga. Indeed, the addition of
the word *observed* (*drsta*) does not
permit attributing such an idea to Dignaga, for the word is
added, not to the major premiss's subordinate, relative clause,
but to its main clause. Thus, what the major premiss says is not that
every observed instance of the reason (H) is an instance of the
property to be established (S), but rather that every instance of the
reason (H) is observed to be an instance of the property to be
established (S). Moreover, if the word *observed*
(*drsta*) has a factive sense, that is, a
sense which presupposes the truth of the clause into which the word is
inserted, as do several of its English translations, for example,
*noticed*, *known*, then the word in the statement
leaves the truth conditions of major premiss unaffected.



A further reason which has prompted scholars to think that included
among the syllogisms Dignaga would accept as good ones are ones
which might not be deductively valid is the fact that he has retained
an example phrase in example statements, for such phrases have no
bearing on the deductive validity of Dignaga's canonical
syllogism. This doubt is re-enforced by the fact that example
statements, stripped of their example phrases, are contrapositives of
one another. Thus, one being logically equivalent to the other is also
logically superfluous with respect to it. Yet, Dignaga seems to
be aware of the equivalence, for he acknowledges in his commentarial
discussion of the three forms (PS 2.5) that the second and third forms
are equivalent (Katsura 2000 p. 245; Katsura 2004b pp. 121-124),
from which it follows that any two statements, one of which satisfies
the second form and the other of which satisfies the third form are
equivalent.



That said, it is nonetheless perfectly reasonable to exclude some
deductively valid syllogisms as good syllogisms. Consider, for
example, a syllogism whose conclusion is identical with one of its
premisses. It is a deductively valid syllogism, though it is utterly
unpersuasive. Dignaga, like any rational thinker, would not, and
did not, accept as a good syllogism any syllogism in which the reason
(H) and the property to be established (S) are the same property, even
if such syllogisms have the same form as the canonical syllogism
above. Excluding such circular syllogisms is fully consistent with the
view that the syllogisms accepted by Dignaga are only deductively
valid ones. (For extensive scholarly discussion of the role of
examples in Buddhist arguments, see the collection of articles in
Katsura and Steinkellner (eds.) 2004.)



A good reason for Dignaga to retain an example phrase in the
example statements of his canonical syllogism would be to exclude
syllogisms which are patently unpersuasive, even though, like circular
syllogisms, they are deductively valid. Consider the following
argument:




|  |  |
| --- | --- |
| thesis: | Sound is eternal |
| reason: | because it is audible. |
| similarity example: | Whatever is audible is eternal. |



This syllogism, rejected as a bad syllogism by Dignaga, was put
forth by a school of Brahmanical thinkers who held, for doctrinal
reasons, that sound is eternal. To maintain this claim in the face of
observation to the contrary, these thinkers maintained instead that
what is transitory is the revelation of sound, not sound itself.
According to them, in other words, sound is constantly present, but we
hear it only when its presence is revealed.



Their syllogism as stated above, though deductively valid, is utterly
unpersuasive. The reason is that the instances of audibility (H), are
coextensive with sound (p). Thus, there is no independent empirical
evidence to support the universal statement that whatever is audible
is eternal. Requiring that there be at least some thing different from
sound which is both audible and eternal is an obvious and plausible
way to eliminate such patently unpersuasive syllogisms. Dignaga,
therefore, rules out the syllogism as a bad syllogism, rather than, as
we would, accept it as a valid syllogism with an unpersuasive premiss.
(See also Tillemans 1990.)



But this cannot be the entire explanation of why Dignaga appears
to insist on example phrases in example statements, for nowhere does
he rule out as a good syllogism one which, though valid, is
unpersuasive for want of some subject-unlike thing.



Because of the doubts just discussed, some scholars think that
Dignaga was not striving to work out a deductive form of
reasoning and argument. Rather, according to some, such as Hayes
(1980; 1988 ch. 4.2), Dignaga was seeking to develop an inductive
form of reasoning and argument. According to others, such as Oetke
(1994; 1996), Dignaga and some of his predecessors and
contemporaries were striving to spell out a defeasible form of
reasoning and argument. (See Taber 2004 for a critical assessment of
Oetke's view.)



A final contribution by Dignaga is found in the sixth and final
chapter of his *Pramana-samuccaya*, where he
addresses fourteen fallacious rejoinders (*jati*), each
bearing the same name as one of the fourteen treated in
Vasubandhu's *Vada-vidhi*, though sometimes the
argument associated with a particular name in the
*Pramana-samuccaya* is different from the one
associated with the name in the *Vada-vidhi*. His
treatment is often different from, and critical of, the treatment
found in this earlier work.


### 4.2 Dignaga's contemporaries and immediate successors



However much scholars may disagree about Dignaga's aim in
the formulation of the canonical syllogism, all agree that his works
set the framework within which subsequent Buddhist thinkers addressed
philosophical issues pertaining to inference and debate. Thus,
Sankarasvamin (c. 6th century ce),
a pupil of Dignaga (Frauwallner 1961,
140), wrote a brief manual of inference for Buddhists, called the
*Nyaya-pravesa* (*Beginning logic*), based
directly on Dignaga's work. Not long thereafter,
Dharmakirti (c. 7th century ce), the
great Buddhist metaphysician, also elaborated his views on inference
and debate within the framework found in Dignaga.



The canonical syllogism, treated as an inference, is that whereby one
who knows the truth of its premisses may also come to know the truth
of its conclusion. While the truth of a particular statement is
thought to be known either through perception or through inference,
how is the truth of a universal statement, such as the major premiss
of a canonical syllogism, known? To know its truth would seem to
require that one know of each thing which has H, whether or not it
also has S. Yet if one knew that, one would already know by perception
the canonical syllogism's conclusion. As a result, inference
would be a superfluous means of knowledge.



The earliest classical Indian philosopher thought to have recognized
the problem of how one comes to know the truth of a universal
statement seems to have been Isvarasena (Steinkellner 1997
p. 638). He appears to have thought that knowledge of the major
premiss is grounded in non-perception (*anupalabdhi*). That is,
according to Isvarasena, knowledge that whatever has H has S
comes from the simple failure to perceive something which has H but
which does not have S. (See Steinkellner 1993, where he draws on
Steinkellner 1966.)



However, this suggestion does not solve the problem, for reasons laid
out in detail by Dharmakirti (c. 7th century ce).
His extensive writing on epistemology in
general and on reason and argument in particular formed a watershed in
classical India philosophy. Besides his *magnum opus*,
*Pramana-varttika* (*Gloss on the means of
epistemic cognition*), one of whose four chapters is devoted to
inference (*svartha-anumana*), comprising 340 verses
and a commentary by him to it, and another devoted to argument
(*parartha-anumana*), which comprises 285 verses, he
wrote several smaller works, including
*Pramana-viniscaya* (*Settling on what the
epistemic means of cognition are*), *Nyaya-bindu*
(*Drop of logic*), *Hetu-bindu* (*Drop of
reason*) and *Vada-nyaya* (*Logic of
debate*). As he makes abundantly clear in verses 13-25 and
his commentary thereto of the chapter on inference
(*svartha-anumana*) of his
*Pramana-varttika*, the simple failure to
perceive something which has H but which does not have S is no
guarantee that whatever has H has S; after all, while one has never
encountered something which has H and does not have S, what guarantee
is there that something which has H and does not have S is not among
the things which one has yet to encounter? Dharmakirti's
answer was that the truth of the first premiss is guaranteed by either
of two relations obtaining between properties: the causation relation
(*tadutpatti*) and the identity relation
(*tadatmya*). Unfortunately, as one might suspect,
Dharmakirti's solution does not work. (See Gillon 1991; see
Steinkellner 2015 for a dissenting view.)



Starting with Dignaga, those interested in logic started to add
the particle *eva* to the various clauses of the three forms of
reason (*tri-rupa-hetu*) (Katsura 1986).
Dignaga's formulation of the three forms came in for
criticism at the hands of the Nyaya thinker, Uddyotakara (c. late
6th century ce), which was, in turn, addressed
by Dharmakirti, who uses the particle to express each of the
three conditions (NB 2.5).



three forms of reason (tri-rupa-hetu)


|  |  |
| --- | --- |
| first form: | the reason's definite (*eva*) existence in the
subject; |
| second form: | the reason's existence in subject-like things only
(*eva*); |
| third form: | the reason's utter (*eva*) non-existence in
subject-unlike things. |




Unfortunately, the precision hoped for is undermined by the ambiguity
in the meaning of the particle *eva*. The particle *eva*
has two principal uses: one emphatic, the other restrictive. What it
emphasizes or restricts depends on the word after which it is placed.
The particle in the statement of the first form applies to the
abstract noun *existence* and, in its emphatic use, is well
translated by *definite* or *actual*. The particle in
the statement of the third form applies to the negative abstract noun
*non-existence* and, in its emphatic use with negation, is best
translated by *utter* or *at all*. (Some scholars
translate the particle in these statements as *necessary*.
There is, however, no philological justification for such a
translation.) The particle in the second form applies to a concrete
noun. Though here the particle could have either an emphatic or a
restrictive use, only the restrictive use fits the context. A problem
arises from the word *subject-like* (*sa-paksa*).
It can be construed in two ways: either as including or as excluding
the subject. If *subject-like* is construed as inclusive and
the particle *eva* is taken as restrictive, then the second and
third forms are logically equivalent; but the statement of the three
forms has the rhetorical blemish of containing a logically superfluous
form. If *subject-like* is taken as exclusive and the particle
is taken as restrictive, then the three forms are inconsistent, for in
that case the second form entails the contradictory of the first form.
(For details, see Gillon 1999.)



Ideas on the nature of reasoning and argumentation very similar to
those of Dignaga's are found in the
*Padartha-dharma-samgraha* (*Summary of
categories and properties*), a work better known as
*Prasastapada-bhasya*
(*Prasastapada's commentary*, customarily
regarded as a commentary on the
*Vaisesika-sutra*). Its author,
Prasastapada (c. 6th century ce), is
a near contemporary of Dignaga. Like Dignaga,
Prasastapada uses the expression *inference for
another* (*parartha-anumana*) to refer to
arguments cast in a syllogistic form, thereby making clear his
recognition that inferences, or cognitive processes, and arguments, or
verbal expressions, are two sides of the same coin. Also like
Dignaga, Prasastapada adopts as a canonical syllogism
an argument whose core is the same deductively valid argument as
Dignaga's. However, unlike Dignaga, he retains the
five members for the syllogism, in keeping with the five members of
the analogical syllogism set out by Vatsyayana, though some
of the names for the members are different. The following syllogism is
reassembled from Prasastapada's treatment of
inference. (See Randle 1930 p. 176.)



canonical syllogism (deductively valid):
Prasastapada


|  |  |
| --- | --- |
| proposition: | Wind is a substance [266] |
| reason: | because it possesses action. [268] |
| example: | That which possesses movement is observed to be a substance,
like an arrow. [278] |
| application: | And in the same way wind possesses action. [281] |
| conclusion: | Therefore, it is indeed a substance. [282] |




(The numbers above in square brackets refer to the paragraph numbers
of the passages containing the relevant sentences in Bronkhorst and
Ramseier (eds.) 1994.) Again, like Dignaga,
Prasastapada appeals to the same three conditions to define
a proper reason as those used in the three forms of a reason. And
finally, he identifies and classifies specious reasons in terms of the
failure of a reason to satisfy one or other of the three forms.



The question of whether the deductively valid canonical syllogism
spread from Dignaga to Prasastapada, or from
Prasastapada to Dignaga, or from some other person to
the two of them both has yet to be decided. Whatever the answer is to
this question, it is clear that a deductively valid version of the
canonical syllogism came to be adopted virtually by every classical
Indian thinker and that it made its way to China, Korea and Japan
through the spread of Buddhism.



It was not long before the ideas pertaining to the canonical syllogism
became generally accepted not only by other non-Brahmanical thinkers,
such as the Jains, but also by Brahmanical thinkers. For example, the
Jain thinker, Jinabhadra (6th ce), a junior
contemporary of Dignaga, wrote a commentary on the Jain thinker
Bhadrabahu where he took claims in the latter's work and
recast them in the form of the canonical argument as found in
Dignaga's work (Uno 2009). In addition, one finds that the
Mimamsa thinker Kumarila Bhatta
(c. early 7th century ce) adopted, without
special comment, a deductively valid version of the canonical
syllogism. His thoughts on the matter are developed at length in the
one hundred eighty-eight verses of his
*Sloka-varttika*'s (*Gloss in verses*)
*Anumana-pariccheda* (*Section on inference*). At
the same time, though the Nyaya thinker Uddyotakara argued
vigorously against many of Dignaga's views, he nonetheless
advocated a version of the canonical syllogism which is deductively
valid.



In spite of the metaphysical differences which distinguished the
various schools of thought, both Buddhist and Brahmanical, all
thinkers came to use a naive realist's ontology to specify the
states of affairs in connection with the canonical syllogism.
According to this view, the world consists of individual substances,
or things (*dravya*), universals (*samanya*)
and relations between them. The fundamental relation is the one of
occurrence (*vrtti*). The relata of this relation are
known as substratum (*dharmin*) and superstratum
(*dharma*) respectively. The relation has two forms: contact
(*samyoga*) and inherence (*samavaya*). So,
for example, one individual substance, a pot, may occur on another,
say the reason, by the relation of contact. In this case, the pot is
the superstratum and the reason is the substratum. Or, a universal,
say treeness, may occur in an individual substance, say an individual
tree, by the relation of inherence. Here, treeness, the superstratum,
inheres in the individual tree, the substratum. The converse of the
relation of occurrence is the relation of possession. In addition, the
relation of pervasion (*vyapti*), or what had also been
referred to as the relation of indispensability
(*a-vina-bhava*), can also be defined in terms of the
occurrence relation: one superstratum pervades another just in case
wherever the second occurs the first occurs. The converse of the
pervasion relation is the concomitance relation (*anvaya*) and
its contrapositive is exclusion (*vyatireka*). As a result of
these relations, the world embodies a structure: if one superstratum,
designated as H, is concomitant with another superstratum, designated
as S, and if a particular substratum, say p, possesses the former
superstratum, then it possesses the second. This structure is the one
which underlies the classical Indian canonical syllogism.



Though the canonical syllogism is central to the development of
reflection on argument and reasoning in preclassical and classical
India, other forms of argument were also recognized as good. One form,
as mentioned above, is *reductio ad absurdum*
(*prasanga*). Others include suppositional reasoning
(*tarka*) (Bagchi 1953) and a form of reasoning akin to what
contemporaries would call disjunctive syllogism
(*arthapatti*) (Keating (ed.) 2020). At the same time,
there are forms of argument, different from the fallacious rejoinders
and specious reasons, which were also regarded as bad. They include
arguments which lead to an infinite regress (*anavastha*),
mentioned above, as well as various forms of circularity. Finally,
there are two important forms of argument: one peculiar to Buddhists,
known as the tetralemma (*catuskoti*), and the
other peculiar to the Jains (*syadvada*).