Buddhist logic

This article presents the "formal background" to Buddhist logic which started at about 500 CE in ancient India and still has a living tradition in the Tibetan Gelug order. Like the logic of Aristotle, ancient Indian logic is a highly formal system although it has not been developed in a context of a symbolic language.

Origins

The Indian Syllogism

Vasubandhu: Avinābhāva

Doctrine of Trairūpya

Dignāga's Hetucakra

Dharmakirti's Theory of Inference

Dharmakīrti: Death of the Trairūpya doctrine

Later developments

Dharmakirti's Theory of Inference

Right Knowledge
A cognition (C) is Right-Knowledge (samyak-jnana (RK)) when
1) C is not contradicted by experience (avisamvadi) and
2) C’s object of cognition was unknown to the cognizer prior to having C.
From 1), it follows that C could be ascertained to be RK only a-posteriori.
From 2), it follows that only the first cognition of an object could count as RK.
Also, 2) could be ascertained only after 1) is ascertained to be true.
From 1) and 2), it follows that RK is essentially empirical.

Objects of Desire and Their Acquisition
An object-of-desire (purushartha (P)) is either an object-wanted (upadeya, an object of pro-desire), or an object-not-wanted (heya, an object of con-desire). An object-of-indifference (upekshaniya) is an object neither wanted nor not wanted. It is not a P.

RK (jnapaka, an information supplying cause of P) and/or non-empirical knowledge are necessary for P’s attainment. (RK and/or non-empirical knowledge) and karaka, an effectuating cause of P, are sufficient for P’s attainment.

Right Knowledge is desirable for its own sake too, that is, for its intrinsic value.

To attain a certain P; its RK is desired. RK itself can be viewed as an object-of-desire (P’). To attain P’; its (RK)’ is desired. (RK)’ is yet another object-of-desire (P’’), attainment of which it’s (RK)’’ is desired, so on ad infinitum. Thus P cannot be attained. But, for practical purposes, P’ need only be common sense knowledge of P, which one is already assumed to know. Thus the aforementioned infinite regress is avoided and P could be attained.

Perception and Inference
Perception (pratyaksha) is the only mode (pramana) of RK. Perception is not a means to RK. Rather, to perceive is to know. Perception of an object is a direct cognition of it, unmediated by, or independent of, any other cognition.
Definition of a perceivable object (DI): x is perceived at a place S (Px) iff
1) x exists at S (existential condition (Ex))
2) there must be a perceiver who is sufficiently motivated to perceive x, is properly located wrt to x to perceive it, has healthy eyes, has adequate time at his disposal, is provided with sufficient light in the place, etc.( other necessary conditions (Ox))

The other necessary conditions for the cognition of x and S are the same. S and x must be co-cognizable, ie. they must be cognizable in the same act/mode of cognition, or by the same sense organ.

DI assumes that x by its very nature is not unperceivable. For example, if x is an atom, Ex and Ox maybe be true yet Px would be false since an atom cannot be perceived by the naked eye. Thus an atom is not a valid x, given the above definition of DI.

DI also assumes that the existence of x at s in future cannot be determined by perception. Thus, perception at time t cannot determine the existence of any x after time t.

Anumana is a formally valid deductive inference with true premises. Anumana is a valid, indirect cognition of the object inferred(OI) since it is mediated by, or dependent on, another cognition, that is the cognition of another object called linga, hetu, sadhana (sign, logical reason, mark) with which the sadhya (OI) is invariably, unexceptionally, universally, related. Anumana’s conclusion is entailed by its premises, thus it says nothing which is not already known. Therefore, anumana is not a mode of RK. An inductive inference might say something which is not already known, but not with certainty. Thus it may be contradicted by experience. Therefore, inductive inference too isn’t a mode of RK.

Anumana could be for inference for oneself (svartha-anumana, SA) or inference for someone else (paratha-anumana, PA)

An object can neither be inferred subsequent to its perception, nor be perceived subsequent to its inference.

Inference (anumana)
• All inferences are linguistic.
• An inference’s validity has nothing to do with the intention associated with the inference.
• PA does not yield RK to the demonstrator, but only to the demonstratee.
• There is no logical difference between SA and PA.
• Either the demonstrator demonstrating the truth of a proposition P has acquired knowledge of P’s truth by SA or it has been demonstrated to him/her by someone else by a PA. Thus, each PA has a SA as its basis.

PakshaVakya (PV): It is an existential proposition that asserts that the locus of logical reason (paksha) has a logical mark/sign (hetu). Hetu has three characteristics:
1) It is necessarily present in the paksha.
2) It is present only in things similar (wrt sadhya) to the paksha (sapaksha).
3) It is not present in things dissimilar (wrt sadhya) to the paksha (vipaksha)

All of 1), 2) & 3) are not necessary for all forms of inference.

Three Types of Hetu
1) Anupalabdhi hetu (AH): Px is not true.
2) Svabhava hetu (SH): Identity as logical reason
3) Karya hetu : Effect as logical reason

Vyapati (V): The universal proposition which states the invariable concomitance, both positive and negative, between a logical mark/sign (hetu) and the object inferred or to be inferred (anumeya or sadhya). Vyapati includes an example (udaharana or drstanta) which exemplifies the relation, both positive and negative, between hetu and sadhya, and also states that the subject of the universal proposition does not denote an empty class.
PV and V together are called as the HetuVakya (HV). HV is necessary and PV must be cognized in anumana.
Nigamana (N): It asserts that the locus of reason (paksha) has the sadhya.
Anuplabdhi Hetu inference (AHI) and its types
1) Sva-bhav-anuplabhdhi
HV: DI, Ox are true ie. x is uplabdhi-lakshana-prapta(ULP) and AH is true.
N: Ex is false.

Example:There is no jar there (Ex is false),
because
the jar is, by its very nature, perceivable and
other necessary conditions for its perception are satisfied (Ox is true),
yet the jar is not perceived there (Px is false).

2) Karya-anupalabhdhi
Non perception of the effect is the hetu for the non existence of its cause having unobstructed capability to produce it.

Example:
Non existence of a light source is inferred from no visual perception by a perceiver capable of visual perception.

3) Vyapak-anulabhdhi
Let a thing x (vyapya) be included in a thing y (vyapaka). The non existence of x is inferred from the non perception of y.

Example:
Watermelon seeds do not exist there
because
Watermelon was not perceived there.

4) Svabhava- virudhh-opalabhdhi
Non existence of x is inferred from the perception of y, when x and y cannot exist simultaneously.

Example:
There is no fire on the glacier
because
iced water are perceived to be present in the glacier
and
wherever there is iced water there can be no fire.
5) Viruddha-karya-opalabdhi
Non existence of z is inferred from the perception of x, where x is the effect of y and y is the effect of not-z. (Thus x implies y and y implies not-z.)

Example:
Non existence of depression is inferred from the perception of euphoria
Because
The perception of euphoria is an effect of increased serotonin levels in the brain
And
Increased serotonin levels in the brain causes the non existence of depression

6) Viruddha-vyapt-oplabhdhi
A is not-x is inferred from A’s dependence on y and y being pervaded by not-x.
Example:
A hurricane is non empty
Because
A hurricane depends on the earth’s atmosphere
And
The earth’s atmosphere is pervaded by non-emptiness

7) Karya-virudhha-oplabhdhi
Not-x is inferred from the perception of y, which is antagonistic of z, and z is an effect of x.

Example:
Non starving is inferred from the perception of satiety
because
perception of satiety is antagonistic of the perception of hunger
and
the perception of hunger is caused by starving.

8) Vyapaka-virudhha-opalabhdhi
Not-x is inferred from the perception of y, which is antagonistic of z, and z includes/subsumes x.

Example:
Non-attachment is inferred from the perception of indifference, which is antagonistic of desire, and desire subsumes attachment.

9) Karan-anuplabhdhi
Non-existence of x is inferred from the non perception of its cause y. It is assumed that the y invariably results in x and y alone results in x.
Example:
Non-existence of appeal is inferred from non perception of beauty.

10) Karana-viruddh-oplabhdhi
Assume that y causes x, then the non-existence of x is inferred from the perception of not-y. It is assumed y invariably causes x and y alone causes x.
Example:
Non existence of vibration, in a medium capable of vibration, is inferred from the perception of no sound, in a perceiver capable of aural perception.
11) karan-virruddha-karyoplabhdhi
Assume that y causes x, then the non-existence of x is inferred from the perception of z, which is the effect of not-y.

Example:
Absence of the perception of danger is inferred from the perception of security.
Absence of fear is inferred from the absence of the perception of danger.
Thus,
Absence of fear is inferred from the perception of security.

Svabhava Hetu Inference (SHI)
A has/is s is inferred from A has/is h, where being h, in a way, is identical to being s. The vyapati in SHI is obvious and is often unstated.

Example:
A is a musical instrument
because
A is a sarod

Karya Hetu Inference (KHI)
The existence of a cause is inferred from the cognition of its effect.
Example:
PV: There is smoke (hetu) on the hill (paksha).
V: Wherever there is smoke, there is fire (sadhya) as in a kitchen (sapaksha), and wherever there is no smoke, there is no fire, as in a pond (vipaksha).
N: Therefore there is fire on the hill.

In the above example the existence of fire (cause) is inferred from the perception of smoke (effect)

AHI, SHI and KHI do not form an exhaustive set of inferences. Thus Dharmakirti’s Theory of Inference is incomplete.

References
Rajendra Prasad(2002)"Dharmakirti's Theory of Inference : Revaluation and Reconstruction" New Delhi, India: Oxford university press.

Doctrine of Anyapoha

"Apoha" is negative "abhavatmaka" in nature. Apohas are different due to the diversity in apohyas (things to be excluded). The word "apoha" which is the abridged form of anyapoha means the 'exclusion of negation of others (ataddvyavrtti)'. The word 'cow' gives its own meaning only by the exclusion of all those things which are other than cow. Dingnaga declares : word can express its own meaning only by repudiating opposite meanings, just as the words like 'krtaka'(i.e. that which has origin) designate their meanings only through the exclusion of their opposite like 'akraka'(i.e. that which does not have origin).Dingnaga admits apoha can also possess some characteristics of the realists' universals such as oneness, enternity, complete subsistence in each individual etc. Dingnaga apprehends concept of universal through the negation of its non-self. He explains that if the non-self of a universal is absent in a locus, its presence in that locus can be inferred. For example, a cow is qualified by the deniability of the non-cow. This concept of Dingnaga similar to that Hegel,he also believes that universality of a concept is posited through its negativity."Apoha" is not the object of sense perception ("pratyaksa")Itis apprehensible only through word or inference.In essence, Dingnaga uses "anyyapoha"as a substitute for universal.The concept of "apoha" depends upon the law of contradiction. The words blue and non-blue negate each other just because they are opposite to each other. According to Dingnaga,similar exclusion of others is due to the non-apprehension of the meaning of a particular word in other words. A particular word excludes the other particular words because its own meaning is not apprehends in the other ones.For example, the word "simsapa"-tree excludes the word "palasa"-treebecause its own meaning is not available in the latter one.

References : 1. 'Pramanasamuccaya' of Dingnaga : 5/14,1,

2. 'Six Buddhist Nyaya Tracts', p.3, line7 edited by M.M. Har Prasad Shastri, Bibliotheca Indica,Calcutta,1910 ,3. 'Apohasiddhi', ( p.3) RatnakÏrti, Bib..Indica. See also Buddhist Doctrine of Universal Flux (p. 132-133) by Satkari Mukerjee.4. "...Hegel was quite right when he said that Negativity is the soul of the world. Buddhist logic: part -I (1930) page no.498 : F. Th. Stcherbatsky. [Insert footnote text here] 21. arthasya bahudharmasca sarve lingannakalpitam. yo'nubandho'nyasmat vyatireka'dhigamyate.: 'Pramanasamuccaya' : 2:1322. bhedo bhedantarartham tu virodhitvad apohate, samanyantara bhedartha svasamanya virodhinah . : 'Pramanasamuccaya' 5:28