Define Vyapti.

Vyapti, in the context of Indian philosophy, particularly Nyaya (logic) and Vaisheshika (atomism), refers to the invariable concomitance or pervasion relationship between the hetu (reason) and the sadhya (probandum or predicate) in a logical or causal inference.

In logical inference, Vyapti denotes the universal and constant relation between the presence of the hetu and the presence of the sadhya. It establishes a connection wherein the occurrence of the reason invariably leads to the occurrence of the probandum. This relationship is crucial for establishing valid logical arguments and reasoning.

For example, if smoke (hetu) is present, there is an invariable concomitance that fire (sadhya) is present. The universal applicability of this relationship, where the presence of smoke always indicates the presence of fire, is Vyapti.

Vyapti is also significant in Vaisheshika philosophy, where it is associated with causation and the relationship between cause and effect. The idea is that there is a universal connection between a cause and its effect, and this pervasion is essential for understanding the principles of causation in the Vaisheshika system.

In essence, Vyapti is a foundational concept in Indian logic and philosophy, serving to establish the necessary connection between different elements in logical reasoning and causal relationships.