Tarka means deliberation on an unknown thing to discern its real nature; it thus consists of seeking reasons in favour of some supposition to the exclusion of other suppositions; it is not inference, but merely an oscillation of the mind to come to a right conclusion.  When there is doubt (sa@ms’aya) about the specific nature of anything we have to take to tarka.  Nir@naya means the conclusion to which we arrive as a result of tarka.  When two opposite parties dispute over their respective theses, such as the doctrines that there is or is not an atman, in which each of them tries to prove his own thesis with reasons, each of the theses is called a vada.  Jalpa means a dispute in which the disputants give wrangling rejoinders in order to defeat their respective opponents.  A jalpa is called a vita@n@da when it is only a destructive criticism which seeks to refute the opponent’s doctrine without seeking to establish or formulate any new doctrine.  Hetvabhasas are those which appear as hetus but are really not so. Nyaya sutras enumerate five fallacies (hetvabhasas) of the middle (hetu):  savyabhicara (erratic), viruddha (contradictory), prakara@nasama (tautology), saddhyasama (unproved reason) and kalatita (inopportune).  Savyabhicara is that where the same reason may prove opposite conclusions (e.g. sound is eternal because it is intangible like the atoms which are eternal, and sound is non-eternal because it is intangible like cognitions which are non-eternal); viruddha is that where the reason opposes the premiss to be proved (e.g. a jug is eternal, because it is produced); prakara@nasama is that

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[Footnote 1:  The doctrine of negation, its function and value with reference to diverse logical problems, have many diverse aspects, and it is impossible to do them justice in a small section like this.]

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where the reason repeats the thesis to be proved in another form (e.g. sound is non-eternal because it has not the quality of eternality); sadhyasama is that where the reason itself requires to be proved (e.g. shadow is a substance because it has motion, but it remains to be proved whether shadows have motion or not); kalatita is a false analogy where the reason fails because it does not tally with the example in point of time.  Thus one may argue that sound is eternal because it is the result of contact (stick and the drum) like colour which is also a result of contact of light and the object and is eternal.  Here the fallacy lies in this, that colour is simultaneous with the contact of light which shows what was already there and only manifested by the light, whereas in the case of sound it is produced immediately after the contact of the stick and drum and is hence a product and hence non-eternal.  The later Nyaya works divide savyabhicara into three classes, (1) sadhara@na