flowchart LR
P[1. Pratijñā<br/>Claim] --> H[2. Hetu<br/>Reason]
H --> U[3. Udāharaṇa<br/>Example]
U --> A[4. Upanaya<br/>Application]
A --> N[5. Nigamana<br/>Conclusion]
classDef default fill:#003366,color:#ffffff,stroke:#ffcc00,stroke-width:3px,rx:10px,ry:10px;
28 Structure and kinds of Anumana (inference), Vyapti (invariable relation), Hetvabhasas (fallacies of inference)
28.1 What the Syllabus Covers
This sub-unit has three examined heads:
- Structure and kinds of Anumāna (inference) — the five-member syllogism (pañcāvayava) and the standard classifications.
- Vyāpti (invariable concomitance) — the foundation of inference; how it is established.
- Hetvābhāsas (fallacies of inference) — the five classical fallacies (with Sanskrit names) that vitiate an inference.
PYQs: (a) name and order the five members, (b) define vyāpti, (c) classify a given example as the correct hetvābhāsa, and (d) match the worked example to its Sanskrit fallacy name.
28.2 Anumāna — Quick Recap
Anumāna — inference — is the second pramāṇa, accepted by every Indian school except Cārvāka. Indian inference moves from known to unknown via a sign (liṅga) and the universal concomitance (vyāpti) between the sign and the thing inferred.
The classical example:
TipSmoke-on-the-Hill Inference
Pratijñā (claim): There is fire on the hill. Hetu (reason): Because there is smoke. Udāharaṇa (example): Wherever there is smoke, there is fire — as in the kitchen. Upanaya (application): The hill has smoke that is invariably accompanied by fire. Nigamana (conclusion): Therefore there is fire on the hill.
28.3 The Five Members — Pañcāvayava
Gautama’s Nyāya Sūtra (1.1.32–1.1.39) defines the five members of parārtha anumāna (inference for others):
TipThe Five Members in Order
| # | Sanskrit | Translation | Role |
|---|---|---|---|
| 1 | Pratijñā | Proposition / Statement of thesis | Asserts the conclusion to be proved |
| 2 | Hetu | Reason / Sign | States the liṅga |
| 3 | Udāharaṇa | Example | Gives a case where vyāpti is observed |
| 4 | Upanaya | Application | Applies vyāpti to present case |
| 5 | Nigamana | Conclusion | Re-asserts the proposition as established |
28.3.1 Comparison with Western Syllogism
TipIndian 5-Member vs Aristotelian 3-Member
| Indian (Nyāya) | Aristotelian | Role |
|---|---|---|
| Pratijñā | Conclusion (often stated as thesis) | The claim |
| Hetu | Minor premise | The reason / mark |
| Udāharaṇa | Major premise + example | Universal rule + concrete instance |
| Upanaya | Restated minor premise | Linkage |
| Nigamana | Restated conclusion | Sealed conclusion |
The Indian form doubles the proposition (Pratijñā + Nigamana) and doubles the universal rule (Udāharaṇa + Upanaya). The Buddhists (Dignāga, Dharmakīrti) shortened it to three members — Pratijñā, Hetu, Udāharaṇa — and the Buddhist three-member form is closer to Aristotle’s syllogism.
28.4 Kinds of Anumāna
28.4.1 Svārtha vs Parārtha (Direction)
TipTwo Directions
- Svārtha — inference for oneself; an internal cognitive process; need not be stated formally.
- Parārtha — inference for others; must be stated as the formal pañcāvayava.
28.4.2 Nyāya’s Three Kinds (Direction of Causal Link)
TipNyāya’s Three Kinds of Inference
| Sanskrit | Logic | Example |
|---|---|---|
| Pūrvavat | Cause → Effect | Seeing dense dark clouds → predicting rain |
| Śeṣavat | Effect → Cause | Seeing a flooded river → inferring rain upstream |
| Sāmānyatodṛṣṭa | Analogical / general | Seeing the moon move across the sky on different nights → inferring planetary motion |
28.4.3 Kevalānvayī, Kevalavyatirekī, Anvaya-vyatirekī
Based on how vyāpti is established:
TipThree Kinds by Vyāpti Establishment
- Kevalānvayī (only-positive) — vyāpti established by positive instances only; no negative instances. “All knowables are nameable; this is knowable; therefore nameable.”
- Kevalavyatirekī (only-negative) — vyāpti established by negative instances only; no positive examples available. “Earth is different from other elements because it has smell — and only earth has smell among elements.”
- Anvaya-vyatirekī (positive-negative) — vyāpti established by both positive and negative instances. The smoke-fire inference (positive: kitchen; negative: lake).
28.4.4 Buddhist Three-Member Inference
Dharmakīrti shortens the Indian five-member form to three: Pakṣa-dharma · Vyāpti · Conclusion.
28.5 Vyāpti — The Heart of Inference
Vyāpti is the invariable concomitance between hetu and sādhya — “wherever there is the hetu, there is the sādhya”.
28.5.1 Definition
TipVyāpti Defined
- Niyata-sāhacarya — invariable togetherness of two things.
- Hetu is vyāpya (pervaded); sādhya is vyāpaka (pervader).
- “Wherever smoke (vyāpya), there fire (vyāpaka)” — vyāpti.
28.5.2 How Vyāpti Is Established (Nyāya)
TipThree Methods of Establishing Vyāpti
- Anvaya — agreement: in all observed positive instances, A and B occur together.
- Vyatireka — difference: in all observed negative instances, both A and B are absent.
- Sāmānya-lakṣaṇa pratyakṣa — extraordinary perception of universals (Nyāya); a single perception of “smokeness-fireness” sets up the vyāpti universally.
- Tarka (counterfactual) — by considering “if A then not-B were possible, what would follow?” — strengthens belief.
- Repeated observation (bhūyodarśana) — many positive cases without exception.
28.5.3 Sapakṣa and Vipakṣa
TipThe Three Loci
- Pakṣa — the subject under inquiry (the hill in question).
- Sapakṣa — similar instances where sādhya is known to be present (the kitchen).
- Vipakṣa — dissimilar instances where sādhya is known to be absent (the lake).
A valid hetu must be present in the pakṣa, present in some sapakṣa, and absent from every vipakṣa.
28.6 The Five Hetvābhāsas — Fallacies of Inference
A hetvābhāsa is a pseudo-reason — a hetu that appears valid but is actually defective. Gautama’s Nyāya Sūtra (1.2.4) names five classical fallacies of the hetu.
TipThe Five Hetvābhāsas
| # | Sanskrit | Translation | What it does |
|---|---|---|---|
| 1 | Savyabhicāra (Anaikāntika) | Inconclusive / irregular | Hetu is too broad — found in vipakṣa too |
| 2 | Viruddha | Contradictory | Hetu proves the opposite of the sādhya |
| 3 | Prakaraṇasama (Satpratipakṣa) | Counterbalanced | Equally strong counter-reason exists |
| 4 | Sādhyasama (Asiddha) | Unproved | Hetu itself needs proof; not established in the pakṣa |
| 5 | Kālātīta (Bādhita) | Mistimed / contradicted | Conclusion contradicted by another pramāṇa (e.g., perception) |
(Different Nyāya commentators give slight variations of these names. The standard modern names appear in the table.)
28.6.1 Savyabhicāra / Anaikāntika (Inconclusive)
The hetu appears with the sādhya in some cases but also without it. So the hetu does not always lead to the sādhya.
TipSavyabhicāra Example
“All knowable things are eternal, because they are knowable. (Like the ātman.)” Problem: Knowable-ness is found in non-eternal things too (a pot is knowable but not eternal). The hetu is too broad.
Three sub-types are sometimes given: Sādhāraṇa (common — hetu in sapakṣa and vipakṣa); Asādhāraṇa (uncommon — hetu found only in pakṣa, nowhere else); Anupasaṃhārī (non-conclusive when no example available).
28.6.2 Viruddha (Contradictory)
The hetu, instead of supporting the sādhya, actually proves its opposite.
TipViruddha Example
“Sound is eternal, because it is produced.” Problem: “Being produced” is the hetu for non-eternality, not eternality. So the hetu contradicts the sādhya.
28.6.3 Prakaraṇasama / Satpratipakṣa (Counterbalanced)
The hetu is balanced by an equally strong opposing hetu, so neither side wins.
TipPrakaraṇasama Example
“Sound is eternal because it is audible. Sound is non-eternal because it is produced.” Problem: Both reasons seem to have force; the inference is stalemate.
28.6.4 Sādhyasama / Asiddha (Unproved)
The hetu itself is not established — either not present in the pakṣa, or not known to exist, or to be proved by the very inference at hand.
TipAsiddha Example
“The sky-lotus is fragrant, because it is a lotus.” Problem: The “sky-lotus” doesn’t exist. The hetu’s locus (sky-lotus being a lotus) is not established.
Three sub-types of asiddha: Āśrayāsiddha (locus not established); Svarūpāsiddha (the hetu’s own existence not established); Vyāpyatvāsiddha (vyāpti not established).
28.6.5 Kālātīta / Bādhita (Contradicted)
The conclusion is directly contradicted by another pramāṇa — typically perception.
TipBādhita Example
“Fire is cold, because it is a substance.” Problem: Perception directly shows that fire is hot. So the conclusion is bādhita — contradicted by another, stronger pramāṇa.
28.7 Conditions for a Valid Hetu — Trairūpya
Dignāga’s trairūpya (three characteristics) gives the formal conditions for a valid hetu:
TipDignāga’s Three Conditions for Valid Hetu
- Pakṣa-dharmatā — the hetu must be present in the pakṣa.
- Sapakṣe sattva — the hetu must be present in at least one sapakṣa (positive example).
- Vipakṣe asattva — the hetu must be absent from every vipakṣa (negative example).
Dharmakīrti added two more, giving pañca-rūpa (five characteristics): + niścitatva (certainty) + abādhita-viṣayatva (subject not contradicted).
When one or more of these conditions fail, a hetvābhāsa results.
28.8 Hetvābhāsa Mapping
TipMapping Hetvābhāsas to Trairūpya Failures
| Condition Failed | Hetvābhāsa |
|---|---|
| Hetu absent from pakṣa | Asiddha (unproved) |
| Hetu present in vipakṣa too | Savyabhicāra (inconclusive) |
| Hetu proves opposite of sādhya | Viruddha (contradictory) |
| Equally strong counter-reason | Prakaraṇasama (counterbalanced) |
| Conclusion contradicted by another pramāṇa | Bādhita (contradicted) |
28.10 Indian Inference vs Western Syllogism — A Compact Summary
TipCompact Comparison
| Feature | Indian (Nyāya) | Western (Aristotle) |
|---|---|---|
| Members | 5 (Buddhist 3) | 3 (categorical syllogism) |
| Heart of inference | Vyāpti + sign | Validity of form |
| Example required | Yes (udāharaṇa) | Not required |
| Universal premise role | Doubled (Udāharaṇa + Upanaya) | Major premise |
| Fallacies | 5 hetvābhāsas (+ sub-types) | Formal + informal |
| Founder | Gautama (~2nd c. CE) | Aristotle (4th c. BCE) |
| Foundational text | Nyāya Sūtra | Organon |
28.11 Theory Anchors
TipPersons, Texts, and Concepts
| Person | Period | Contribution |
|---|---|---|
| Gautama (Akṣapāda) | ~2nd c. CE | Nyāya Sūtras; 5-member syllogism; 5 hetvābhāsas |
| Vātsyāyana | ~5th c. CE | Nyāya Bhāṣya |
| Dignāga | 5–6th c. CE | Trairūpya (3 conditions for hetu); 3-member Buddhist syllogism |
| Dharmakīrti | 7th c. CE | Pramāṇa-vārttika; pañca-rūpa (5 conditions); 3 hetus |
| Uddyotakara | 6th c. CE | Defends Nyāya against Buddhist critique |
| Vācaspati Miśra | 9-10th c. CE | Nyāya-vārttika-tātparya-ṭīkā |
| Udayana | 10–11th c. | Nyāya-kusumāñjali; proofs of God |
| Gaṅgeśa | 12-13th c. | Founder of Navya-Nyāya; Tattva-cintāmaṇi |
| Raghunātha Śiromaṇi | 16th c. | Navya-Nyāya systematiser |
| Annaṃbhaṭṭa | 17th c. | Tarka-saṅgraha — standard manual |
28.12 Practice Questions
Q 01
Members
Easy
The Nyāya syllogism has how many members?
View solution
Correct Option: C
Five-member (*pañcāvayava*) syllogism — Pratijñā, Hetu, Udāharaṇa, Upanaya, Nigamana.
Q 02
Order
Medium
The correct order of the five members of the Nyāya syllogism is:
View solution
Correct Option: B
Pratijñā → Hetu → Udāharaṇa → Upanaya → Nigamana.
Q 03
Identify
Medium
"Wherever there is smoke, there is fire — as in the kitchen" is which member of the Nyāya syllogism?
View solution
Correct Option: C
Udāharaṇa states the universal rule with a positive example (kitchen).
Q 04
Buddhist
Hard
The Buddhist logicians (Dignāga, Dharmakīrti) shortened the Nyāya five-member syllogism to:
View solution
Correct Option: B
Three members — Pakṣa-dharma, Vyāpti, Conclusion.
Q 05
Vyāpti
Medium
"Vyāpti" in Indian logic means:
View solution
Correct Option: B
Invariable concomitance (niyata-sāhacarya) between hetu and sādhya.
Q 06
Pakṣa
Medium
In "There is fire on the hill, because there is smoke", the HILL is called:
View solution
Correct Option: A
Pakṣa = subject under inquiry. Sapakṣa = positive example (kitchen). Vipakṣa = negative example (lake).
Q 07
Trairūpya
Hard
Dignāga's "trairūpya" — three characteristics of a valid hetu — was extended by Dharmakīrti to:
View solution
Correct Option: C
Dignāga's 3 (Pakṣa-dharmatā, Sapakṣe sattva, Vipakṣe asattva) → Dharmakīrti adds 2 → pañca-rūpa (5).
Q 08
Hetvābhāsa Count
Easy
The number of classical Nyāya hetvābhāsas (fallacies of inference) is:
View solution
Correct Option: C
Five: Savyabhicāra, Viruddha, Prakaraṇasama, Asiddha, Bādhita.
Q 09
Fallacy Identify
Medium
"Sound is eternal because it is produced." This commits which hetvābhāsa?
View solution
Correct Option: B
Viruddha — the hetu "being produced" proves the opposite (non-eternal), not the claim (eternal).
Q 10
Fallacy Identify
Medium
"The sky-lotus is fragrant because it is a lotus." This commits which hetvābhāsa?
View solution
Correct Option: C
Asiddha — the locus (sky-lotus) is not established (āśrayāsiddha sub-type).
Q 11
Fallacy Identify
Hard
"Fire is cold because it is a substance." This commits which hetvābhāsa?
View solution
Correct Option: A
Bādhita / Kālātīta — the conclusion is contradicted by perception (we directly perceive fire as hot).
Q 12
Inconclusive
Medium
A hetu that is "too broad" — appearing in both sapakṣa and vipakṣa — is the fallacy of:
View solution
Correct Option: A
Savyabhicāra = inconclusive / irregular. Hetu does not reliably lead to sādhya.
Q 13
Counterbalance
Hard
When an equally strong opposing reason can be put forward, the fallacy is:
View solution
Correct Option: C
Prakaraṇasama / Satpratipakṣa — stalemate produced by equally strong counter-reason.
Q 14
Kinds
Medium
In Nyāya's three kinds of inference, "Pūrvavat" moves from:
View solution
Correct Option: B
Pūrvavat = Cause → Effect (dark clouds → rain). Śeṣavat = Effect → Cause. Sāmānyatodṛṣṭa = analogical.
Q 15
Direction
Medium
Inference stated formally with all five members is:
View solution
Correct Option: B
Parārtha = inference for others; must be stated formally with all five members.
Q 16
Vyāpti
Hard
In "wherever smoke, there fire", smoke is called:
View solution
Correct Option: B
Smoke is vyāpya (pervaded); fire is vyāpaka (pervader, the bigger class).
Q 17
Navya-Nyāya
Hard
The school of "Navya-Nyāya" (New Logic) was founded by:
View solution
Correct Option: B
Gaṅgeśa (~12–13th c.), *Tattva-cintāmaṇi*. Foundational figure of Navya-Nyāya.
Q 18
Sub-type
Hard
"Sādhāraṇa", "Asādhāraṇa", and "Anupasaṃhārī" are sub-types of which hetvābhāsa?
View solution
Correct Option: A
Three sub-types of Savyabhicāra: common (in both sapakṣa and vipakṣa), uncommon (only in pakṣa), and non-conclusive.
Q 19
Establish Vyāpti
Medium
Vyāpti established by both positive AND negative instances is called:
View solution
Correct Option: C
Anvaya-vyatirekī = vyāpti established by agreement AND difference. Smoke-fire is the classic case.
Q 20
Match
Hard
Match each hetvābhāsa with its description:
| (i) | Savyabhicāra | (a) | Hetu proves the opposite |
| (ii) | Viruddha | (b) | Conclusion contradicted by perception |
| (iii) | Asiddha | (c) | Hetu inconclusive (too broad) |
| (iv) | Bādhita | (d) | Hetu itself unestablished |
View solution
Correct Option: A
Savyabhicāra → too broad; Viruddha → proves opposite; Asiddha → unestablished; Bādhita → contradicted by perception.
28.13 Quick Recall
ImportantQuick recall
- Anumāna = inference. Accepted by every Indian school except Cārvāka.
- Five members of Nyāya syllogism (Pañcāvayava): Pratijñā → Hetu → Udāharaṇa → Upanaya → Nigamana.
- Buddhist (Dignāga, Dharmakīrti): 3 members — Pakṣa-dharma, Vyāpti, Conclusion.
- Smoke-on-the-hill example: Pakṣa = hill; Sādhya = fire; Hetu/Liṅga = smoke; Vyāpti = “wherever smoke, fire”; Dṛṣṭānta = kitchen.
- Three Loci: Pakṣa (subject) · Sapakṣa (positive example) · Vipakṣa (negative example).
- Vyāpti = invariable concomitance (niyata-sāhacarya). Vyāpya = pervaded (smoke); Vyāpaka = pervader (fire).
-
Kinds of anumāna:
- Svārtha vs Parārtha (for self vs for others).
- Pūrvavat (cause→effect) · Śeṣavat (effect→cause) · Sāmānyatodṛṣṭa (analogical).
- Kevalānvayī (only-positive) · Kevalavyatirekī (only-negative) · Anvaya-vyatirekī (both).
- Establishing vyāpti: Anvaya (agreement) · Vyatireka (difference) · Sāmānya-lakṣaṇa pratyakṣa · Tarka · Bhūyodarśana.
-
Dignāga’s Trairūpya — 3 conditions for valid hetu:
- Pakṣa-dharmatā (in pakṣa).
- Sapakṣe sattva (in positive example).
- Vipakṣe asattva (absent from negative example).
- Dharmakīrti’s Pañca-rūpa = 3 above + niścitatva (certainty) + abādhita-viṣayatva (not contradicted).
-
5 Hetvābhāsas (classical Nyāya fallacies of inference):
- Savyabhicāra / Anaikāntika — inconclusive, hetu too broad (3 sub-types: Sādhāraṇa, Asādhāraṇa, Anupasaṃhārī).
- Viruddha — contradictory, hetu proves opposite (“Sound is eternal because produced”).
- Prakaraṇasama / Satpratipakṣa — counterbalanced by equally strong reason.
- Asiddha / Sādhyasama — unproved hetu (3 sub-types: Āśrayāsiddha, Svarūpāsiddha, Vyāpyatvāsiddha). Sky-lotus example.
- Bādhita / Kālātīta — contradicted by another pramāṇa (“Fire is cold because substance”).
- Navya-Nyāya = Gaṅgeśa (~12-13th c.) Tattva-cintāmaṇi. Precise technical vocabulary; Raghunātha Śiromaṇi, Annaṃbhaṭṭa (Tarka-saṅgraha).
- Indian vs Western: 5 vs 3 members; vyāpti-and-sign vs validity-of-form; example required vs not; hetvābhāsa vs formal/informal fallacies.