The Five-Member Syllogism
Chapter Fifty-Six
Syllabus topic Module 2, "Five-member syllogism"
Pages 191 to 194 of 378
In one line
Nyāya requires an argument to be stated in five named parts, and an argument missing one of them has not been properly put.
In the wording you can write in an examination: the pañcāvayava or five-member syllogism is the form in which an inference must be stated for it to be assessed. Nyāya Sūtra 1.1.32 names the members as pratijñā, the proposition; hetu, the reason; udāharaṇa, the example; upanaya, the application; and nigamana, the conclusion. Each is defined in the sūtras immediately following, and each has a distinct job.
The provision
Nyāya Sūtra 1.1.32, in Vidyabhusana's translation:
The members (of a syllogism) are proposition, reason, example, application, and conclusion.
And the Sūtra's own illustration, printed with it:
1. Proposition. This hill is fiery.
2. Reason. Because it is smoky.
3. Example. Whatever is smoky is fiery, as a kitchen.
4. Application. So is this hill (smoky).
5. Conclusion. Therefore this hill is fiery.
The five members, each with its own sūtra
Pratijñā, the proposition. Nyāya Sūtra 1.1.33: "A proposition is the declaration of what is to be established." His illustration: sound is non-eternal.
Hetu, the reason. Nyāya Sūtra 1.1.34: "The reason is the means for establishing what is to be established through the homogeneous or affirmative character of the example." And 1.1.35 adds: "Likewise through heterogeneous or negative character."
Udāharaṇa, the example. Nyāya Sūtra 1.1.36 defines the homogeneous example as "a familiar instance which is known to possess the property to be established and which implies that this property is invariably contained in the reason given". Nyāya Sūtra 1.1.37 defines the heterogeneous example as "a familiar instance which is known to be devoid of the property to be established and which implies that the absence of this property is invariably rejected in the reason given".
Upanaya, the application. Nyāya Sūtra 1.1.38: "Application is a winding up, with reference to the example, of what is to be established as being so or not so." He records that it is of two kinds, affirmative, expressed by the word "so", and negative, expressed by "not so".
Nigamana, the conclusion. Nyāya Sūtra 1.1.39: "Conclusion is the re-stating of the proposition after the reason has been mentioned." He glosses it as the confirmation of the proposition after the reason and the example have been mentioned.
What each member is FOR
The definitions alone do not make the design visible. This table does.
| Member | Its job | What is missing without it |
|---|---|---|
| pratijñā | states the claim, so everyone knows what is at stake | the arguer can shift ground |
| hetu | states the evidence in the subject | the claim is an assertion |
| udāharaṇa | states the general connection AND anchors it in a case | the general claim is unstated and unattackable |
| upanaya | asserts that this subject falls under the connection | the general claim is left unapplied |
| nigamana | states the claim as now established | it is not on the record that anything has been proved |
The Five-Member Syllogism
The third member is the one that earns the form. It states the vyāpti explicitly, as its own step, where an ordinary argument leaves the general premise implicit. Making the general premise a required part of the statement is the single best idea in Nyāya logic.
Worked: the affirmative and the negative forms
The Sūtra gives both, and a question may ask for either.
Affirmative, from 1.1.38:
Proposition: sound is non-eternal. Reason: because it is produced. Example: whatever is produced is non-eternal, as a pot. Affirmative application: so is sound (produced). Conclusion: therefore sound is non-eternal.
Negative, from the same sūtra:
Proposition: sound is not eternal. Reason: because it is produced. Example: whatever is eternal is not produced, as the soul. Negative application: sound is not so, that is, sound is not produced ... Conclusion: therefore sound is not eternal.
Note what the negative form does with the example. It states the connection contrapositively, and anchors it in a case where the property is absent. That is the vipakṣa of [Anumāna: Vyāpti, and the Three Kinds of Inference], serving as the example member.
One reading note. The text this book quotes prints the conclusion of the affirmative form, at 1.1.39, as "therefore sound is produced" where the proposition was "sound is non-eternal". That is a slip, in the scan or in the printing: the conclusion is defined in the same sūtra as the re-stating of the proposition, so it must restate the proposition. The book says so rather than reproducing it silently.
The five extra members
Vidyabhusana records, immediately after 1.1.32, that "some lay down five more members", and gives them. They are worth having because each names something the five do not do.
| Extra member | What it adds | His illustration |
|---|---|---|
| jijñāsā, inquiry as to the proposition | fixes the scope of the claim | is this hill fiery in all its parts, or in a particular part? |
| saṃśaya, questioning the reason | challenges the observation | what you call smoke may be nothing but vapour |
| śakyaprāpti, capacity of the example | challenges the vyāpti | is smoke always a concomitant of fire? in a red-hot iron ball there is no smoke |
| prayojana, purpose | states why the conclusion is wanted | to determine whether the hill may be approached, avoided, or ignored |
| saṃśayavyudāsa, dispelling all questions | records that the challenges are answered | it is beyond question that the hill is smoky and that smoke invariably accompanies fire |
Read them as a whole and the point is clear. The five extra members are the OPPONENT's moves, promoted into the form. Three of them are challenges, one fixes scope and one records resolution. The five-member form is a statement; the ten-member form is a dialogue.
The Five-Member Syllogism
And the third extra member is the best of them. "Is smoke always a concomitant of fire? In a red-hot iron ball there is no smoke." That is a counterexample offered against the vyāpti, and it is the exact move [Anumāna: Vyāpti, and the Three Kinds of Inference] says destroys a connection.
What the five members are NOT
They are not five premises. The conclusion and the application restate what is already there. Logically the argument has two premises and a conclusion; the five members are a presentation.
They are not a proof procedure. Nothing in the form checks that the vyāpti is true. The form makes it visible so that it can be checked, which is a different and more modest claim.
They are not optional. Vidyabhusana records, in his note on the mistimed fallacy, that placing the members in the wrong order is itself an occasion for rebuke, called inopportune. So the order is part of the requirement.
Quick revision
- Nyāya Sūtra 1.1.32: proposition, reason, example, application, conclusion.
- Their sūtras: 1.1.33 to 1.1.39, with the example having an affirmative form at 1.1.36 and a negative form at 1.1.37.
- The example member states the vyāpti explicitly and anchors it in a case, which is what an ordinary argument leaves implicit.
- The affirmative form uses "so"; the negative form states the connection contrapositively and uses "not so".
- Five extra members are recorded by some: inquiry, questioning the reason, capacity of the example, purpose, dispelling questions. They are the opponent's moves, promoted into the form.
- The form is a presentation, not a proof procedure: it makes the general premise attackable, it does not verify it.
Test yourself
1. Name the five members with the Sūtra's own illustration.
Proposition, this hill is fiery. Reason, because it is smoky. Example, whatever is smoky is fiery, as a kitchen. Application, so is this hill, smoky. Conclusion, therefore this hill is fiery.
2. Which member does the real work, and why?
The example. It states the invariable connection as an explicit step and anchors it in a familiar instance, where an ordinary argument leaves the general premise unstated and therefore unexamined.
3. Give the negative form of the argument about sound, and say what the example member does in it.
Proposition, sound is not eternal. Reason, because it is produced. Example, whatever is eternal is not produced, as the soul. Negative application, sound is not so. Conclusion, therefore sound is not eternal. The example states the connection contrapositively and anchors it in a case where the property is absent.
The Five-Member Syllogism
4. What do the five extra members add, taken as a group?
They add the opponent's part: a question about the scope of the claim, a challenge to the observation, a counterexample against the invariable connection, a statement of purpose, and a record that the challenges have been met. They turn a statement into a dialogue.
The rest of this subject
These notes are cut from the University's printed syllabus. Open the syllabus itself for the same subject.