Reflections on methodology belonging to a serious of propaedeutics in the context of the research dissertation Principles of Liberty by Tabea Hirzel (2015). Reflections on methodology IV centers on Buddhis logic, especially Indian logic, especially the problem of the Catuṣkoṭi, inference in syllogism and 5 part syllogism.

1. Reflections on Methodology IV
Buddhist Logic
Doctoral Candidate: Tabea Hirzel
Program: Doctorate of Diplomacy/ Political Economy
University: SMC University, Zug, Switzerland
Date: 12.30.2011

2. Indian teaching
Veda
• The Rigveda, containing hymns to be recited by
the hotar, or presiding priest;
• The Yajurveda, containing formulas to be recited by
the adhvaryu or officiating priest;
• The Samaveda, containing formulas to be sung by
the udgatar or priest that chants;
• The Atharvaveda, a collection of spells and
incantations, apotropaic charms and speculative
hymns
Vedanga
• Shiksha (śikṣā): phonetics, phonology and
morphophonology (sandhi)
• Kalpa (kalpa): ritual
• Vyakarana (vyākaraṇa): grammar
• Nirukta (nirukta): etymology
• Chandas (chandas): meter
• Jyotisha (jyotiṣa): astronomy
© Tabea Hirzel 2

3. Indian logic (anviksiki )
• Vyākaraṇa: The Sanskrit grammar rules of Pāṇini (c. 5th century BCE)
• The Vaisheshika school's analysis of atomism (c. 2nd century BCE)
• the analysis of inference by Gotama (c. 2nd century)  Nyaya school
• The tetralemma of Nagarjuna (c. 2nd century CE)
TODAY: Navya-Nyāya school of logic
© Tabea Hirzel 3

4. Tetralemma
© Tabea Hirzel 4

5. The Nasadiya Sukta of the
Rigveda (RV 10.129)
• Ontological speculation
• the four circles of catuskoti:
"A",
"not A",
"A and 'not A'",
"not A and not not A"
© Tabea Hirzel 5

6. Shiva Sutras
IAST Devanāgarī
1. a i u ṇ
2. Ṛḷ k
3. e o ṅ
4. ai au c
5. ha ya va ra ṭ
6. la ṇ
7. ña ma ṅa ṇa na m
8. jha bha ñ
9. gha ḍha dha ṣ
10. ja ba ga ḍa da ś
11. kha pha cha ṭha tha ca
ṭa ta v
12. ka pa y
13. śa ṣa sa r
14. ha l
१. अ इ उ ण्।
२. ऋ ऌ क्।
३. ए ओ ङ्।
४. ऐ औ च्।
५. ह य व र ट्।
६. ल ण्।
७. ञ म ङ ण न म ्।
८. झ भ ञ्।
९. घ ढ ध ष्।
१०. ज ब ग ड द श ्।
११. ख फ छ ठ थ च ट त व्।
१२. क प य्।
१३. श ष स र्।
१४. ह ल ्।
Maheshwar/Shiva Sutra:
https://www.youtube.com
/watch?v=zYoLKHP7KO
8
https://www.youtube.com
/watch?v=3B6-u8c7Xp8
https://www.youtube.com
/watch?v=-r4YMMiUNA8
© Tabea Hirzel 6

7. Hetucakra (wheel of
justifications)
by Dignaga (c 480–540 CE)
1. It should be present in the case or object under consideration, the ‘subject-
locus’ (pakṣa)
2. It should be present in a ‘similar case’ or a homologue (sapakṣa)
3. It should not be present in any ‘dissimilar case’ or heterologue (vipakṣa)
Sign/Mark (linga)
Three possibilities: the sign may be present in____ of the sapakṣas
1. all
2. some
3. none
Modes (trairūpya)
The three modes of a valid cognition (pramana) of an inference (anumana):
necessary
sufficient
© Tabea Hirzel 7

8. 1: + sapakṣa, + vipakṣa 2: + sapakṣa, – vipakṣa 3: + sapakṣa, ± vipakṣa
4: – sapakṣa, + vipakṣa 5: – sapakṣa, – vipakṣa 6: – sapakṣa, ± vipakṣa
7: ± sapakṣa, + vipakṣa 8: ± sapakṣa, – vipakṣa 9: ± sapakṣa, ± vipakṣa
Key: + = all, ± = some, -- = none
2. & 8. meet all three conditions
5. Is a uniquely deviating pseudo-sign; it fails condition 2
4. & 6. are contradictory pseudo-sings (asādhāraṇa); they fail condition 2
1.; 3.; 7. & 9 are deviating pseudo-signs;
© Tabea Hirzel 8

9. Jainism
Doctrines of relativity used for logic and
reasoning:
Anekāntavāda – the theory of relative pluralism or manifoldness;
Syādvāda – the theory of conditioned predication and;
Nayavāda – The theory of partial standpoints.
© Tabea Hirzel 9

10. Pramana
Pramāṇa forms one part of a tripuţi (trio) concerning pramā (the correct
knowledge of any object arrived at by thorough reasoning, Sanskrit), namely,
• Pramātā (< pramātŗ), the subject, the knower
• Pramāņa, the means of obtaining the knowledge
• Prameya, the object, the knowable
Modern Buddhist schools do not use these three distinct terms particularly, but
instead employ the 'three spheres' (Sanskrit: trimaṇḍala; Tibetan: 'khor gsum):
• subject
• object, and
• action.[3]
© Tabea Hirzel 10

11. Accepted categories of
pramana
School Vaisheshika Sankhya,
Vishishtadvaita
Vedanta, Dvaita
Vedanta
Nyaya Advaita Vedanta,
Mimamsa
Perception pratyakṣa Pratyakşa Pratyakṣa;
a) Ordinary (Laukika or Sādhārana)
Pratyakşa
b) Extraordinary (Alaukika or Asādhārana)
Inference anumāna Anumāna Anumāna:
a) For one self (Svārthānumāna; informal)
Anumāna
b) For others (Parāthānumāna; 5 formal
steps)
Verbal testimony/
Word
Śabda Śabda :
a) Vedic (Vaidika)
Śabda
b) Laukika (Testimony)
Comparison Upamāna (relationship, analogy)
Postulation Arthāpatti
Non-cognition Anupalabdi
© Tabea Hirzel 11

12. Inference (Nyaya)
• 3 types: Pūrvavat (inferring an
unperceived effect from a perceived
cause), Śeṣavat (inferring an unperceived
cause from a perceived effect)
and Sāmānyatodṛṣṭa (when inference is
not based on causation but on uniformity
of co-existence). A detailed analysis of
error is also given, explaining when
anumāna could be false
© Tabea Hirzel 12

13. Nyaya Sutras
sixteen categories (padārtha)
1. means of valid knowledge (pramāṇa);
2. objects of valid knowledge (prameya);
3. doubt (saṃśaya);
4. purpose (prayojana);
5. example (dṛṣṭānta);
6. conclusion (siddhānta);
7. the constituents of a syllogism (avayava);
8. argumentation (tarka);
9. ascertainment (nirṇaya);
10. debate (vāda);
11. disputations (jalpa);
12. destructive criticism (vitaṇḍa);
13. fallacy (hetvābhāsa);
14. quibble (chala);
15. refutations (jāti);
16. points of the opponent's defeat (nigrahasthāna).
© Tabea Hirzel 13

14. 5 part Syllogism
The Nyaya Sutra supports a five-part syllogism, widely followed in the Indian tradition:
1. This hill is fiery (pratijñā: a statement of that which is to be proved).
2. Because it is smoky (hētu: statement of reason).
3. Whatever is smoky is fiery, as is a kitchen (udāharaṇa: statement of a general rule supported by
an example).
4. So is this hill (upanaya: application of the rule of this case).
5. Therefore this hill is fiery (nigamana: drawing the conclusion).
The characteristic feature of the Nyaya syllogism is its insistence on the example, which suggests that
the Nyaya logician wanted to be assured not only of formal validity but also of material truth.
© Tabea Hirzel 14

15. 5 types of logical error
Five kinds of fallacious "middle" (hetu) are distinguished:
1. the inconclusive (savyabhicara), which leads to more conclusions than one;
2. the contradictory (viruddha), which opposes that which is to be established;
3. the controversial (prakaranasama), which provokes the very question that it is meant to settle;
4. the counterquestioned (sadhyasama), which itself is unproved; and
5. the mistimed (kalatita), which is adduced "when the time in which it might hold good does not
apply".
© Tabea Hirzel 15

16. Buddhism
the Vedas are apauruṣeya "not of human
agency,"[15] are supposed to have been
directly revealed, and thus are called śruti
("what is heard").[16][17] Vedic injunctions
required sacrifices, Śrauta (an etymon of the
English 'slaughter'), particularly 'animal
sacrifices' (Pashu-Yajna,[18][19]
Ashvamedha) and which the compassionate
Shakyamuni Buddha countered.
© Tabea Hirzel 16

17. Karma (Buddhist agency)
• Karma (Sanskrit: कमम; IPA: [ˈkarmə] ( listen); Pali: kamma) means action, work or deed
• Is the principal of causality
• Saṃsāra or Sangsāra (Sanskrit: संसार) (in Tibetan called 'khor ba (pronounced /kɔrwɔ/ in many
Tibetan dialects), meaning "continuous flow"), is the repeating cycle of birth, life and death
(reincarnation) as well as one's actions and consequences in the past, present, and future in
Hinduism, Buddhism, Bön, Jainism, Taoism[1] and Sikhism.
• Moksha/ NIrvana: means emancipation, liberation or release. Soteriologically: Freedom of
Karma. In the Buddhist context nirvana refers to the imperturbable stillness of mind after the
fires of desire, aversion, and delusion have been finally extinguished.[2] In Hindu philosophy, it is
the union with the divine ground of existence Brahman (Supreme Being) and the experience
of blissful egolessness.
© Tabea Hirzel 17

18. Doctrine of Anyapoha, Identity
and Hegel
• 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)'. For example, the word 'cow' gives its own
meaning only by the exclusion of all those things which are other than cow. Dingnaga declares
that a word can express its own meaning only by repudiating opposite meanings, just as 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).
© Tabea Hirzel 18

19. Lexikon
1. Apoha:
2. Argument: vada, rtsod pa
3. Characteristic: laksana, mtshan nid
4. Condition: pratyaya, rkyen
5. Demonstrandum: sadhya, bsgrub par bya ba
6. Demonstrator: sadhaka, grub byed
7. Dialectician: tartika, rtog ge ba
8. Dialectics: tarka, rtog ge
9. Direct perception: pratyaksa, mnon sum
10. Event: dharma, chos
11. Event-associate: dharmin, chos can
12. Exemplification: drstanta, dpe
13. Inference: anumana, rjes su dpag pa
14. Interference: vyavakirana, hdres pa
15. Invariable concomitance: avinabhava, med na mi hbyun ba
16. Judgment: prajnanana, shes-rab
17. Justification: hetu, gtan-tshigs
18. Means of cognition: pramana, tshad pa
19. Means of evidence: linga, rtags
20. Pervading/pervasion/logical pervasion: vyapti, khyab pa
© Tabea Hirzel 19

20. Dharmic vs. Western logic
(Enlightenment or Emancipation?)
Indian Logic includes general questions
regarding the ‘nature of the derivation of
knowledge’, epistemology, from information
supplied by evidence, evidence which in turn
may be another item of knowledge.
Robinson (1957: p. 295) holds that, building upon the methodology of Schayer [1933],[11] Nakamura (1954)[12]
...presents the case for the superiority of modern scientific, notational logic as an instrument for investigating
Indian logic. Notational statement avoids the pitfalls and awkwardness of linguistic statement and rhetorical
logic. It does not necessitate conversion of Indian forms into the standard forms of traditional Western logic,
but clarifies the traditional Indian structure without requiring reformulation. To Nakamura's points I may add that
modern logic asks a greater range of questions and hence sharpens the observation of the investigator.[13][14]
© Tabea Hirzel 20

21. Islamic logic & Kalam
• Kalām cosmological argument
• the possibility of the existence of actual
infinities
© Tabea Hirzel 21

22. Kalam’s simplified syllogism
Craig states the Kalām cosmological argument as a brief syllogism, most commonly rendered as
follows:[2]
Everything that begins to exist has a cause;
The universe began to exist;
Therefore:
The universe has a cause.
From the conclusion of the initial syllogism, he appends a further premise and conclusion based upon
ontological analysis of the properties of the cause:[3]
The universe has a cause;
If the universe has a cause, then an uncaused, personal Creator of the universe exists, who sans the
universe is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful;
Therefore:
An uncaused, personal Creator of the universe exists, who sans the universe is beginningless,
changeless, immaterial, timeless, spaceless and enormously powerful.
Referring to the implications of Classical Theism that follow from this argument, Craig writes:
"This, as Thomas Aquinas was wont to remark, is what everybody means by 'God".
Why must the
universe have a
beginning?
© Tabea Hirzel 22

23. Aristotle
• Actual infinity: describes a complete
totality (e.g. set theory)  closed system
• Potential infinity: a non-terminating
process  open system
Actuality = definite, completed, extended or existential,
but NOT physical existence (Aristotelian)= there is (∃),uniqueness (∃!)
Inifity = potential, becoming, constructive (Intuitionists like Stephen Kleene)= for all (∀),
everywhere (:⇔), implies ⇒, ∞
according to Aristotle, a completed infinity cannot exist even as an idea in the mind
of a human.
© Tabea Hirzel 23