Definition - Prof. V. Krishnamurthy
These two words anvaya and vyatireka occur often in Vedanta. Anvaya is concordance or agreement and Vyatireka is discordance or difference. In vedAnta, the example of the beads strung to form a necklace is used to explain these two words. The fact that without the string which holds together the beads, there is no necklace of beads is anvaya. The fact that, however, the string is separate from the beads is vyatireka. The all-pervasiveness of the Absolute is anvaya. The distinctness of the Absolute is the vyatireka.
The last of the four verses called the Four-Verse-Bhagavat-am where the Impersonal Absolute `teaches' the very first born, namely Creator BrahmA: ( Bhagavatam: II– 9 – 35) says:
etAvadeva jij~nAsyam tattva-jij~nAsunAtma-naH |
anvaya-vyatirekAbhy-Am yat syAt sarvatra sarvadA ||
(Translation adapted from Swami Tapasyananda'-s.): What the seeker after Truth has to grasp is that Substance which persists -- this is anvaya -- always through all its transformations into its various effects or forms, but suffers no diminution in the process – this is vyatireka -- as also when all these effects or forms are eliminated in the causal condition. The Supreme Spirit is the ultimate Substance.
Vidyaranya's Panchadashi IV – 32 says: By anvaya and vyatireka one comes to the conclusion that it is the `mental' creation which causes bondage to the jIva, for when these mental constructs are there, pleasure and pain are also there and when they are not there, there is neither pleasure nor pain.
The words occur almost in the same context, in the boy Prahlada's teaching to his contemporaries. He says: By these two exercises in logic (anvaya and vyatireka) one should be able to realize the Self within. (Bhagavatam: VII – 7 – 21).
Definition - Dennis Waite
When the pot exists, so too does the clay. But when the pot is broken, the clay still exists. Therefore, we conclude that the clay is real while the pot is only mithyA. Similarly, when the world and thoughts are present, we exist and when these are absent, as in deep sleep, we still exist. Consequently, we must conclude that who we really are - the Atman - is real, while the world, including body and mind etc. is mithyA. This logical process is called anvaya vyatireka (anvaya means "connection, association"-; vyatireka means "distinction, separateness, exclusion").
Dhyanasaraswati gave the following reference from "The Philosophy of Life" by Swami
Krishnananda for a detailed account of "anvaya - vyatireka ".
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