No. It is "του κοριτσιού, του αρέσει η φιλοσοφία". It is not SOMEONE'S girl. It is THE GIRL who likes philosophy.
I know. I just put the comma to show the difference. The right sentence is "του κοριτσιού τού αρέσει η φιλοσοφία" (we emphasise on the verb), but "τού" is rarely written like this. The sentence which means "his girl likes philosophy" is "του κοριτσιού του τού αρέσει η φιλοσοφία".
As a kind of surrogate for the dative case, which Greek lost many centuries ago -- "to the girl is pleasing philosophy".