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Although Utpaladeva mentioned his father's name as Udayakara1, Abhinavagupta, in his Tantraloka, referred to him as the son and disciple of Somananda2. It is clear from this that Udayakara must have been another name for Somananda. Lakshmanagupta, the son and disciple of Acarya Utpala, who was a contemporary of Bhatta Induraja, was the Pratyabhijna teacher of the great Mahesvara Acarya Abhinavagupta. Abhinava also received education in poetics from Bhatta Induraja3.
In the Kashmiri Shaiva tradition, it is accepted that the Siddha Vasugupta received the Pratyabhijna knowledge directly from Srikantha, that is, Lord Shiva. From Vasugupta, this knowledge was passed to Bhatta Kallata. In his Shivasutra-vimarshini, Acarya Kshemaraja himself reveals this fact—
The Guru named Vasugupta, having fully grasped these (Shivasutras), revealed them to his good disciples such as the blessed Bhatta Kallata.
In this way, the tradition of the Pratyabhijna philosophy began with Shiva (Srikantha) himself and developed through Bhatta Kallata and Somananda. Utpaladeva, Lakshmanagupta (the son), Rajanaka Ramakantha (disciple of Utpala), Abhinavagupta, and Kshemaraja made exceptional contributions to the development of this tradition. Vibhramakara (the second son of Utpala), Padmananda (a fellow student), and Manorathagupta are also the next links in the same tradition. Since the time of Bhatta Kallata and Abhinava is confirmed by the authority of the Rajatarangini and Kshemendra, it can be said that the period of the influence of the Pratyabhijna-Shaiva philosophy must have been between 825 and 1025 CE4.
In Vallabha-Vedanta, devotion to Krishna is established as the Pushti-tattva principle of grace/nourishment. From this perspective, the Pratyabhijna-Shaiva philosophy seems to be a sibling of Shuddhadvaita Pure Non-dualism; because in this philosophy, too, 'Devotion-Lakshmi' the goddess of devotion is given supreme status for the attainment of the ultimate reality or liberation. There is no one as wealthy as a person possessed of the grace of devotion, and no one as destitute as one without it.
1. To enable the easy understanding of the people, this Ishvarapratyabhijna was provided by Utpala, the son of Udayakara. (I.Pr.Ka. 4.18)
2. Utpala, the son of Somananda, who rested in the ocean of the Triyambaka tradition, and the master Lakshmanagupta. (Tantra. 37.61)
3. I, known by the name Abhinavagupta, who heard charming [teachings] having resided at the lotus feet of Bhatta Induraja. (Dhvanyalokalocana). The words of the Guru, the blessed Lakshmanagupta, who teaches Pratyabhijna which cuts through the cycle of births, are victorious. (Malinivijaya-vartika, Mangala 2)
4. For the grace of the people, the blessed Bhatta Kallata and others descended to the earth during the time of Avantivarman. (Raj. 5.66). Having heard literature from the ocean of wisdom named Abhinavagupta. (Kshemendra)