Anumāna
from 200 BCE Nyāya Sūtra; the five-member form is standard by the second century
Five steps, not three: thesis, reason, a general rule shown by example, application to this case, conclusion — and the example is doing real work.
- Active
- from 200 BCE
- Where
- North India
- Also
- anumāna
- Status
- In use
- Tradition
- Non-Western procedures
What it is
Anumāna is inference from a sign to what the sign indicates. The standard illustration is smoke and fire: seeing smoke on a hill, one infers fire, because wherever there is smoke there is fire.
Its distinctive feature is the five-membered form. Where the Greek syllogism has three statements, the Indian has five, and the two extra are not padding. One requires that the general rule be exhibited in a known case, and one requires that this case be explicitly brought under it. The tradition holds that an inference which cannot produce an example has not established its general rule.
How it works
State the thesis. Give the reason — the sign present in this case. State the pervasion, the invariable concomitance between sign and inferred thing, and produce a case where both are observed together. Apply it: the sign is present here in the same way. Conclude.
The pervasion is where everything happens. The tradition developed a detailed account of the ways it can fail — the reason being absent from the case, present where the conclusion is false, or contradicted by a stronger reason — and these fallacies are more finely classified than anything in the Greek tradition.
The form of the inference
- Thesis: the hill has fire
- Reason: because it has smoke
- Pervasion with example: wherever there is smoke there is fire, as in a kitchen
- Application: this hill has smoke of that kind
- Conclusion: therefore this hill has fire
The argument
Proposition There is a leak beneath the slab.
- Thesis: there is a leak in the pipework beneath the slab.
- Reason: because the meter registers flow with every fixture closed and the isolating valve to the house open.
- Pervasion with example: wherever the meter registers flow with all fixtures closed, water is escaping between the meter and the fixtures — as in the case of the burst garden line last spring, where the same reading was found and the break was later exposed.
- Application: this case shows that reading, with every fixture closed and checked twice, and no irrigation on the meter's side.
- The pervasion is tested for the standard failures: the reason is not absent from the case, and no case has been found where the reading occurs without an escape — a passing toilet valve would produce it, and all three were isolated at the cistern.
Therefore There is an escape between the meter and the fixtures, and since the only run in that stretch is beneath the slab, the leak is beneath the slab.
The example — the burst garden line — is not an illustration. On this account it is a required part of the argument, because a general rule nobody can produce an instance of has not been established.
What it is good for
Diagnostic reasoning where a sign has to carry a conclusion. The insistence on producing a case where the rule was observed is a genuinely useful discipline that the Greek form does not impose.
Where it fails
The pervasion has to be established, and establishing it requires induction, which brings the whole problem of induction with it. The tradition was acutely aware of this and Cārvāka pressed it hard: how do you know that wherever there is smoke there is fire, without having seen every case of smoke?
The example requirement also has limits. It works for repeatable relations and fails entirely for unique events, where no second case can be produced — which is why the method is strong in diagnosis and weak in history.
Common misconceptions
That the five-membered form is a clumsier version of the three-membered Greek one. The extra members are doing different work: the Greek syllogism has no requirement that a supporting instance be produced, and the Indian tradition regarded that as a defect rather than an economy.
Where it came from
The Nyāya Sūtra, with the five-membered form standard by the second century. Dignāga later argued that two of the five are redundant, and Buddhist logic often uses three.
What became of it
Refined continuously for fifteen hundred years, particularly by the Navya-Nyāya school from the thirteenth century, which developed a technical language of remarkable precision.
Lasting influence
The core of classical Indian debate. Its fallacy classification is more detailed than Aristotle's and has no equivalent in the West until the twentieth century.
Why it still matters
Alive in traditional scholarship and increasingly studied by logicians.
Put another way
Smoke on the ridge, and the memory of a kitchen.
Texts
Gautama, Nyāya Sūtra
Book I sets out the members; the fallacy classification is developed at length in the commentarial tradition.
Where to start
Ganeri's Indian Logic is the best entry for anyone who knows the Greek forms.
The surprising bit
The tradition requires an argument to produce a real instance of its own general rule, a demand no Western logic has ever made, and one that would eliminate a large share of bad reasoning if it were adopted.
In their own words
The hill has fire, because it has smoke, as in a kitchen
Who held it
the Navya-Nyāya school
Connections
- Relies on
- Pramāṇa theory, Induction
- Parallel to
- Categorical syllogism
The verdict
A more demanding inference form than the syllogism, resting on the same unsolved problem underneath.