The Vedanta sutras discuss in connection with the kartritva (doer ship) of jiva ,whether jiva acts independently or its activity is dependent on paramatma and is handled in a separate adhikarana called “Paraayattaadhikarana” in Vedanta sutras.
This is an important issue related to the theory of free will and determinism.
The prima facie view is that jiva is totally free without depending on paramatma.
To answer this, Badarayana (Vyasa) the author of Vedanta sutras introduces a sutra called “Paraat tu tat sruteh” (Vedanta sutra 2-3-41)
Badarayana refutes the above prima facie view and affirms that the activity of jiva is prompted by Isvara because, it is declared so by the scripture. The “tu” in the sutra distinguishes the view of Badarayana from that of the prima facie view. “Parat means from the paramatma or the highest self.
Now, coming to the Principle Bhasyakaras (Shankara, Ramanuja and Madhva) commentaries on Vedanta Sutra:
As per Shankara, it implies that Supreme being impels to act – “Isvara tad anujnayaa siddhih” The bondage of jiva as well as its liberation is caused by Paramatma.
According to Ramanuja, the word “parat” means that the activity of jiva takes place on account of Paramatma – “Kartritvam asya jivasya Paramatmanaa eva heto bhavati”
Antaryami Brahmana says that ‘Paramatma abides in jivatma and controls it from within.
Taittriya Aranyaka -3-11-10, indicates Paramatma enter into all beings and controls them .
Bhagavad Gita (Chapter 9- verse 29) also clearly says that the paramatma resides in the heart of all being and their by controls them . Also, the Bhagavad Gita (Chapter 15 – Verse 15), Lord Krishna says that “I am seated in the hearts of all. From me, memory, knowledge and their loss arise”
According to Madhva , the word “parat” means that the god has implanted this power to act in jiva, and it is in that sense power is intrinsic to it.
Though there is a slight variation in the meaning of word “parat”, Badarayana clearly says that the kartritva of Jiva is prompted by paramatma.
Swami Vedanta Desika, great philosopher, belonging to Srivaishnava sampradaya ( 13-14th century) in his work Adhikara Saaravali, indicates that Jiva is dependent for all its activities on several factors such as karma in form of punya and papa accruing from deeds of the past, indriyas (sense organs), Kala (time), nature, unseen potency. But, none of these affect the kartritva (doer ship) of the Jiva. Similarly, if Isvara being the controller of all, prompts jiva to act, the doer ship of jiva is not affected.
There are two types of kartritva,
Prayojaka kartritva : Paramatma impels the Jiva to act
Prayojya Kartritva : Jiva acts being impelled by paramatma
Though divine influence is accepted in respect of kartritva, Badarayana further clarifies that god’s will operate in accordance with the effort made by an individual in accordance with his former actions (krita prayatnaapeksastu), so that the injunctions and prohibitions of sastras are not rendered futile. This also absolves the god of criticism of cruelty and partiality.
In short, according to Badarayana, Jiva as a karta (agent of action), is prompted to act by god, who is the inner controller, in accordance with the past karma of the Jiva.
(The details provided here are gleaned from the following works of Dr.S.M.Srinivasachari, (1) The philosophy of Vedanta Sutras and (2)Philosophy of Visistadvaita)