Inference (anumana), according to Vedanta, is made by our notion of concomitance (vyaptijnana) between two things, acting through specific past impressions (sa@mskara).  Thus when I see smoke on a hill, my previous notion of the concomitance of smoke with fire becomes roused as a subconscious impression, and I infer that there is fire on the hill.  My knowledge of the hill and the smoke is by direct perception.  The notion of concomitance revived in the subconscious only establishes the connection between the smoke and the fire.  The notion of concomitance is generated by the perception of two things together, when no case of the failure of concomitance is known (vyabhicarajnana) regarding the subject.  The notion of concomitance being altogether subjective, the Vedantist does not emphasize the necessity of perceiving the concomitance in a large number of cases (bhuyodars’anam sak@rddars’anam veti vis’e@so nadara@niya@h).  Vedanta is not anxious to establish any material validity for the inference, but only subjective and formal validity.  A single perception of concomitance may in certain cases generate the notion of the concomitance of one thing with another when no contradictory instance is known.  It is immaterial with the Vedanta whether this concomitance is experienced in one case or in hundreds of cases.  The method of agreement in presence is the only form of concomitance (anvayavyapti) that the Vedanta allows.  So the Vedanta discards all the other kinds of inference that Nyaya supported, viz. anvayavyatireki (by joining agreement in presence with agreement in absence), kevalanvayi (by universal agreement where no test could be applied of agreement in absence) and

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kevalavyatireki (by universal agreement in absence).  Vedanta advocates three premisses, viz. (1) pratijna (the hill is fiery); (2) hetu (because it has smoke) and (3) d@rs@tanta (as in the kitchen) instead of the five propositions that Nyaya maintained [Footnote ref 1].  Since one case of concomitance is regarded by Vedanta as being sufficient for making an inference it holds that seeing the one case of appearance (silver in the conch-shell) to be false, we can infer that all things (except Brahman) are false (Brahmabhinnam sarvam mithya Brahmabhinnatvat yedevam tadevam yatha s’uktirupyam).  First premiss (pratijna) all else excepting Brahman is false; second premiss (hetu) since all is different from Brahman; third premiss (dr@s@tanta) whatever is so is so as the silver in the conch [Footnote ref 2].

Atman, Jiva, Is’vara, Ekajivavada and D@r@s@tis@r@s@tivada.