Strangely, Silas is stubbornly insistent that he should be the one to care for the girl, as the girl was brought to him and not to anyone else. He repeatedly states this in response to a number of people. In Chapter 13, for example, Godfrey seems to be assessing what will happen to his daughter when he asks what plans Silas has for her. He responds very abruptly but also in a way that shows his own amazement at what has transpired:
"The mother's dead, and I reckon it's got no father: it's a lone thing--and I'm a lone thing. My money's gone, I don't know where--and this is come from I don't know where. I know nothing--I'm partly mazed."
Interestingly, Silas himself recognises a kind of balance between the loss of his money and the gain of the girl, a balance we have seen when he first lays eyes on her and confuses her with his gold, indicating the way that Eppie comes to symbolise his wealth for him. However, in response to your question, Silas shows that he is "determined" to keep the girl, until the girl's father can be identified and comes to claim her.