Literally, Anvaya (Sanskrit: अन्वय) means - positive; affirmative or nexus;[1] but in grammar and logic this word refers to - 'concordance' or 'agreement', such as the agreement which exists between two things that are present, as between 'smoke' and 'fire', it is universally known that - "where there is smoke, there is fire".
[2] Anvaya-vyatireka, is the term used by the Buddhists and Hindu logicians as a dual procedure - to signify 'separation' and 'connection', and to indicate a type of inference in which hetu (reason) is co-present or is co-absent with sādhya (major term), as the pair of positive and negative instantiations which represent the inductive and the deductive reasoning, both.
Shankara holds that immediately after the hearing of a sacred scripture (shravana) from his Guru the disciple can rely in his own ascent on the four values that prepare the ground for the arousal of the 'desire to know Brahman'.
Therefore, Vidyaranya in his Panchadasi (I.37) explains that by differentiating the Atman from the causal body or the five sheaths through the method of distinguishing between the variable presence of the Self (when the Self persisting in all states but the subtle body is not perceived in deep sleep), and the invariable presence (anvaya) of the Self (pure consciousness persisting in both the waking and dream states), one can draw out one's own Atman from the five sheaths and attain the supreme Brahman, and that:- In this context Swami Swahananda drawing attention to Katha Upanishad VI.17 and Shvetashvatara Upanishad III.13 reminds us that (quote) - "though the flowers in a garland are different, the thread passing through them is one and unchanging.
[8] The analogy presented by the Bhagavata Purana (II.ix.35) indicates that when the atman is in the body in the waking states etc., means that the cause is inside the effects as the invariable factor (anvaya).