Abhidharma had its origin in certain systematizing, analytical, and exegetical features found in the Sūtra, particularly, mātṛikā (summary list), abhidharma-kathā (discussion about the doctrine), vibhaṅga (“analytical exposition”), and upadeśa (exegetical elaboration). Buddhist philosophies may have been primarily initiated and vigorously elevated in the Abhidharma tradition. However, while the Abhidharma treatises undoubtedly exhibit highly developed scholastic and hermeneutical components, Abhidharma is essentially a soteriology. The Sarvāstivāda Ābhidhārmikas consistently claim that Abhidharma is truly “Buddha-word,” being the sine quo non for ascertaining the true intents of the sutras—it constitutes the ultimate authority for discerning the definite and explicit discourses (nītārtha-sūtra) of the Buddha.
Sarvāstivāda, the “All-exist School,” was undoubtedly one of the most important Buddhist schools in the period of Abhidharma Buddhism. Since its establishment around the 2nd century bce, it exerted tremendous impact, directly or indirectly, on the subsequent development of Indian Buddhism. This school possesses a complete set of seven canonical Abhidharma texts, nearly all of which are now preserved in Chinese translation, and one, the Prajñapti-śāstra, is preserved in a complete Tibetan translation. A huge compendia, The Great Abhidharma Commentary (Abhidharma-mahāvibhāṣā), whose gradual compilation must have spanned over more than half a century and was fully completed around 150 ce, is now extant only in Chinese. This compendia, encyclopedic in scope, defines the doctrinal positions of the orthodox Sarvāstivādins based in Kaśmīra, who subsequently came to be known as the Vaibhāṣikas.
The central thesis of the school is sarvāstivāda or sarvāstitā (/sarvāstitva), which claims that all “dharmas”—fundamental realities or real entities of existence—sustain their unique intrinsic natures throughout the three periods of time. That is, whether future, past, or present, a dharma’s intrinsic nature remains the same, even though its mode of existence (bhāva) varies. This thesis was vehemently challenged by the Vibhajyavādins (Distinctionists) who denied the reality of the past and future dharmas. The reverberation of this “Sarvāstivāda-versus-Vibhajyavāda” controversy can be observed to have generated decisively significant doctrinal implications throughout the history of Buddhist thoughts.
The Savāstivāda school was also known as Hetuvāda, a “school which expounds on causality.” Kātyāyanīputra (c. 150 bce), often regarded as the effective “founder” of the Sarvāstivāda school, was credited with the innovation of a theory of sixfold causes, of which the coexistent or simultaneous causality was the most important legacy. For the first time in human history, he systematically articulated a form of causality in which the cause and its effect coexist simultaneously. This theory contributed importantly to Buddhist doctrinal development, particularly its epistemology. Mahāyāna Yogācāra had embraced it from their very inception, finding it indispensable for the establishment of many of their fundamental doctrines, including “store consciousness” (ālaya-vijñāna) and “cognition-only” (vijñaptimātratā).
Dualwavelet frames in Sobolev spaces on local fields of positive characteristic
