What are the competing philosophies throughout the play King Lear?

In assessing the primary relationship between Lear and his
daughters, I think that one can see the competing philosophies that collide and leave
all of them as victims in the end.  Lear is a believer in the old ways of tradition.  In
such a setting, the word of the father is taken above all, the role of the parent is
beyond reproach, and there is a natural "pecking order" that sees him at the top and all
else underneath.  This collides with the vision of modernity, where individuals freedom
defies hierarchy and where self interest reigns over all else.  It is in this philosophy
that Regan and Goneril operate.  These two worlds come into direct conflict with one
another when Lear recognizes that his value system is obsolete, that tradition has been
usurped by modernity, and the result is his abandonment.  In this light, I think that
one can see the powerful nature of ideas and philosophies and how they underscore the
action in the drama.