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According to Dvaita philosophy there are two selfs. One is Jeevatma and second is Paramatma. Paramatma is only a witness and has no influence whatsoever on the Jeevatma's karma. Parmatma is revered, respected and worshiped.
My question is: according to Dveta philosophy , why is Parmatma worshiped? In what ways does Parmatma express his control over Jivatma?
That what you said Paramatma is only a witness and has no influence whatsoever on the Jeevatma's karma is not correct.
Paramatma is not only the witness, he is also the one who gives out karma to all the living beings, jiva souls, jivatmas. Karma are activities or deeds that jivas have done, and the results of those deeds in the form of good and evil, namely happiness and suffering. All that is under control of paramatma.
This is confirmed by Lord Krishna in the Bhagavad gita 7.21-23:
Bg 7.21 — I am in everyone’s heart as the Supersoul. As soon as one desires to worship some demigod, I make his faith steady so that he can devote himself to that particular deity.
Bg 7.22 — Endowed with such a faith, he endeavors to worship a particular demigod and obtains his desires. But in actuality these benefits are bestowed by Me alone.
Bg 7.23 — Men of small intelligence worship the demigods, and their fruits are limited and temporary. Those who worship the demigods go to the planets of the demigods, but My devotees ultimately reach My supreme planet.
What is important to know about those verses is that Lord Krishna is that paramatma situated in all living beings, in their heart. We see that in verse 7.21 where Lord Krishna says "I am in everyone’s heart as the Supersoul (paramatma)".
In those verses Lord Krishna is telling Arjuna that there are people who worship gods in heaven, sometimes called demigods, such as Indra, Agni, etc, expecting good results of such karmic worship in the form of good things for enjoyment, wealth, cattle, good health, etc. And when people get those good results of their pious worship, ie pious or good karma, then they think that those gods in heaven gave them those good results in the form of things for enjoyment, wealth, etc. But Lord Krishna says that it is not actually quite true that those gods in heaven gave to the people those good karmic results, but it is he alone, Lord Krishna, who is giving all those karmic results to everyone. We see that from the verse 7.22 where Lord Krishna says "But in actuality these benefits are bestowed by Me alone". Of course, we can say that gods in heaven gave those karmic results, but they did that because Lord Krishna ordered them to do that. Thus in actuality those results are bestowed by Lord Krishna alone who is the Supreme controller. And because some people don't know this Vedic teaching about who is the controller of karma, in verse 7.23 the Lord says that less intelligent people think that they should worship gods in heaven and not paramatma, Lord Krishna, instead.
Thus we know that Lord Krishna is paramatma who is the controller of karma. And thus we know that paramatma, Lord Krishna, should be worshiped and not somebody else.
How is paramatma controlling the living beings (jivas)?
This is explained in the Bhagavad gita 18.61:
The Supreme Lord is situated in everyone’s heart, O Arjuna, and is directing the wanderings of all living entities, ...
Lord Krishna is paramatma situated in everyone’s heart, and from within the heart he is controlling the lives of everyone. Thus He is directing everyone’s life. What is this "directing"? This is explained in brief in verse 15.15:
I am seated in everyone’s heart, and from Me come remembrance, knowledge and forgetfulness.
In that verse the Lord says that our mental functions such as remembrance, knowledge and forgetfulness are under his control. Thus we can say that being situated in our heart He is making us to remember our past desires which we had in our previous lives, and thus He is impelling us and directing us to do something in this life according to our deeds and desires from our past, even past lives.
In this verse it is also said that knowledge or ability to know or comprehend something is under the Lord's control as well. We know that in this world some people are more capable to understand something and some people are not capable to understand much of what they want to learn about. The Lord will make some people more capable to learn something if they deserve that, and we deserve everything by our efforts, desires, and deeds in this and our previous lives. For example, some people naturally get inclination to strive for spiritual life because in their previous life they were yogis or pious people. Thus their ability to know or understand properly the Vedic wisdom and yoga in this life will be greater than the ability to understand those things of some other people who did not strive for spiritual life in the past lives. This ability is also under control of the Lord. See related: https://hinduism.stackexchange.com/a/7132/2790
By the way, not only Dvaita but all the other Vaishnava systems of Vedanta, such as Gaudiya Vaishnava (which is my favorite), Vishishtadvaita etc, teach the same thing that there is the difference between jivatma and paramatma, and that jivas and their karma are under control of paramatma.
