According to Yin Shun’s The Formation of Early Buddhist Texts, the connection between SN/SA and the other three Nikayas/Agamas in historical context are:
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SN/SA has three-anga structure (sutra, geya, vyakarana angas), whose structure had its origin in the first council.
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These three angas formed in sequence. The sutra-anga was the earliest of the three.
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MN/MA was expanded mainly from vyakarana (弟子所說) of SN/SA.
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DN/DA was expanded mainly from geya (祇夜) of SN/SA.
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AN/EA was edited mainly for the promotion of Buddhist teachings for the general public.
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Saṃyukta-āgama/Saṃyutta-nikāya was not at first being termed as nikāya or āgama, but generally named the ‘Connected Discourses’ 相應教 Saṃyukta-kathā.
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Calling the Saṃyukta/Saṃyutta as āgama/nikāya ‘collection’ was until when the other three nikāyas/āgamas (MN/MA, DN/DA, AN/EA) were gradually developed and expanded from it (相應教 Saṃyukta-kathā)
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MN/MA, DN/DA, and AN/EA originated at the second council.
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However, the extant four principal Nikayas/Agamas are sectarian texts. One can seek an understanding of early Budhist teachings by studying them comparatively.
The following is a quotation, in Chapter 10, Section 4, from the book The Formation of Early Buddhist Texts by Yin Shun:
第四節 結說
經上來的比對研究,「四阿含」(「四部」)的成立,可得到幾點明確的認識。1.佛法的結集,起初是「修多羅」,次為「祇夜」、「記說」——「弟子所說」、「如來所說」。這三部分,為組成「雜阿含」(起初應泛稱「相應教」)的組成部分。「弟子所說」與「如來所說」,是附編於「蘊」、「處」、「因緣」、「菩提分法」——四類以下的。這是第一結集階段。
在「雜阿含」三部分的集成過程中,集成以後,都可能因經文的傳出而編入,文句也逐漸長起來了。佛教界稟承佛法的宗本——「修多羅」,經 「弟子所說」的學風,而展開法義的分別、抉擇、闡發、論定,形成了好多經典。結集者結集起來,就是 「中阿含」;這是以僧伽、比丘為重的,對內的。
將分別抉擇的成果,對外道、婆羅門,而表揚佛是正等覺者,法是善說者,適應天、魔、梵——世俗的宗教意識,與「祇夜」精神相呼應的,集為「長阿含」。
「雜」、「中」、「長」,依文句的長短而得名。
以(弟子所說)「如來所說」為主,以增一法而進行類集,《如是語》與《本事經》的形成,成為「九分教」之一,還在「中」、「長」——二部成立以前。但為了便於誦持,著重於一般信眾的教化,廢去「傳說」及「重頌」的形式,而進行擴大的「增壹阿含」的編集,應該比「長阿含」更遲一些。
以「雜阿含」為本而次第形成四部阿含,《瑜伽師地論》的傳說,不失為正確的說明!近代的研究者,過分重視巴利文(Pāli);依巴利文聖典,不能發見四部阿含集成的真相。
即使以「雜阿含」的原形為最古,而不能理解為三部分(「修多羅」、「祇夜」、「記說」)的合成;不知三部分的特性,與三部阿含形成的關係,也就不能理解依「雜阿含」而次第形成四部的過程。
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Cf. pp. 7-11 in Choong Mun-keat’s The Fundamental Teachings of Early Buddhism.
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See also “Ācāriya Buddhaghosa and Master Yinshun 印順 on the Three-aṅga Structure of Early Buddhist Texts”, pp. 883-932.