Ayutasiddhi is a term used to express an internal relationship in Hindu logic. Ayutasiddhi is the inherent relationship existing between an object/substratum and a quality/content, part and whole, universal and individual, action and agent, and between an external object and its special characteristic termed vishesha.
Hindu logic accepts that the two components are indivisible.
The 9th century philosopher Vacaspati Mishra reasons out by describing
them as always experienced as mutually joined. A part cannot be conceived as
independent and the whole is unthinkable without its components; they are ayutasiddha.
This relationship is more popularly known as samavaya.
External objects comprise every atom of the five physical
objects, namely, earth, water, fire, air and ether (askasha) and the four ternal
objects, namely, time, space, soul and mind. Some have subsumed samavaya under
the later concept of svarupa sambandha, that is individual nature; but
Vaiseshika School rejects this idea.
Samavaya being one, objections have been raised leading to
several discrepancies, but these also have been explained away. One of the
ayutasiddha relata is subordinate to or dependent on the other and both occupy
the same space. The relata are always mutually heterogeneous. A quality cannot
exist part from the substance in which it inheres, whereas the substance can
exist independently. The relation is external in that dependence is not mutual.
The word ayuta comes from the root ya meaning to join, or to
separate two mutually opposite concepts. Ayutasiddha in the present context
means accomplishment or proof of complete union. The concept was postulated by
logicians to uphold the realistic pluralism. Later, however, Ramanuja (1017 –
1137 CE), who established the Visishtadvaita school of Vedanta, named this relationship
as a-prithak-sambandha, identity-and-difference, as an internal relationship.