Pancha Avayavas (पञ्चावयवाः)

Avayavas (Samskrit : अवयवाः) are one of the sixteen Padarthas enumerated by Gautama Maharshi in the Nyaya sutras. Knowledge and understanding of these sixteen Padarthas bring about a way to Nihshreyas according to the Nyaya Darshana. Avayavas are Statements or Premises required to prove a concept. Since five such statements are collectively required they are termed as "Factors" on which an an assumption or inference can be proved.

It is noteworthy to mention that Pramanas or the means of valid cognition are found to be significant concepts among these factors.

Pratijna (प्रतिज्ञा) : Statement of Proposition

Statement of Proposition (first enunciation) to be proved is called Pratijna and is based on Shabda pramana.

साध्यनिर्देशः प्रतिज्ञा॥३३॥ {प्रतिज्ञालक्षणम्} (Nyay. Sutr. 1.1.33)

Meaning : Pratijna, the statement of proposition consists in the assertion of what is to be proved (Sadhya). Vatsyayana Bhasya elaborates as follows

प्रज्ञापनीयेन धर्मेण धर्मिणो विशिष्टस्य परिग्रहवचनं प्रतिज्ञा। प्रतिज्ञा साध्यनिर्देशः । अनित्यः शब्दः इति॥

Pratijna is that assertive statement which mentions the Subject which is intended to be proved by reasoning. Pratijna consists of the mention of that property (of the Subject) to be proved. (As an example of this, we have the statement) "sound is non-eternal". (Page No 63 of )

It is of two kinds described in the bhashyam for Udaharana.

Hetu (हेतुः) : Statement of Reasoning

Statement of Reasoning which establishes the conclusion on the strength of the similarity of the case in hand with known similar or opposite examples or illustrations. It is based on Anumana pramana.

उदाहरणसाधर्म्यात्साध्यसाधनं हेतुः॥३४॥ {हेतुलक्षणम्} तथा वैधर्म्यात्॥३५॥ {हेतुलक्षणम्} (Nyay. Sutr. 1.1.34 and 35)

Hetu is that (statement or sentences) which demonstrates, proves the thing to be known (Sadhya), through its similarity and through dissimilarity to the Udaharana (an example, a Corroborative Instance).

उदाहरणेन सामान्यात्साध्यस्य धर्मस्य साधनं प्रज्ञापनं हेतुः । साध्ये प्रतिसंधाय धर्ममुदाहरणे च प्रतिसंधाय तस्य साधनतावचनं हेतुः उत्पत्तिधर्मकत्वादिति । उत्पत्तिधर्मकमनित्यं दृष्टमिति । उदाहरणवैधर्म्याच्च साध्यसाधनं हेतुः । कथम् अनित्यः शब्दः उत्पत्तिधर्मकं नित्यं यथा आत्मादिद्रव्यनिति ॥ (Vats. Bhas. Nyay. Sutr. 1.1.34 and 35) (PDF Pages 88 and 89 of )

That (sentences, statements) which demonstrates the property to be proved (as belonging to the Subject) through a property common to the Udahara or example is called the Hetu. When one notices a certain property in the subject (pertinent to the conclusion to be proved) and notices the same property also in the example, and then puts forward that property as a proof statement to assert the Sadhya - this is called the Hetu. As for the example : Sound is non-eternal, we have the statement "because sound has the characteristic of being a 'product' (उत्पत्तिधर्मकत्वम्); it has been known that everything that is a product is not eternal."

Hetu also comprises of the statement of dissimilarity of the object of comparison with the Subject. As for the example : Sound is non-eternal, because it has the characteristic of being ''produced'. That which does not have the characteristic of being produced is always 'eternal', e.g., substances such as the Atman and the like. (Book Page No 64 and 65 of )

Udaharana (उदाहरणम्) : Statement of Instance

Statement of Instance (similar or opposite examples or illustrations) is based on Pratyaksha pramana.

साध्यसाधर्म्यात्तद्धर्मभावी दृष्टान्तः उदाहरणम् ॥३६॥ {उदाहरणलक्षणम्} तद्विपर्ययात्वा विपरीतम्॥३७॥{उदाहरणलक्षणम्} (Nyay. Sutr. 1.1.36 and 37)

Udaharana is that illustration (दृष्टान्तः) about a property of a familiar instance which is common or concomitant (साधर्म्याम्) with what has to be proved in Sadhya (साध्यः).

साध्येन साधर्म्य समानधर्मता साध्यसाधर्म्य त्कारणात्तद्धर्मभावी दृष्टान्त इति

Similarity to what is proved consists in the presence of the same property in both (Page No 65 to 68 ).

Anitya shabda till end of sentence and next sentence till page no 43 first line.

Upanaya (उपनयः)

उदाहरणापेक्षः तथा इति उपसंहारः न तथा इति वा साध्यस्य उपनयः ॥३८॥ {उपनयलक्षणम्}

Statement of Minor premise (a minor summary) made with support of the Udaharana is thus based on Upamana pramana. Sadhya... till end of sentence.

Nigamana (निगमनम्)

हेत्वपदेशात्प्रतिज्ञायाः पुनर्वचनं निगमनम्॥३९॥{निगमनलक्षणम्}

Statement of the Final Conclusion. It is the indication of the capability of the aforesaid statements to arrive at a single conclusion pertaining to the same object or purpose. First line of Bhashya and complete english translation.

It is this five-fold declaration that constitutes the highest form of reasoning because only when thus stated that the Reasoning succeeds in convincing the nonbeliever.