@The Pentacle Queen,
At the risk of oversimplification:
1.Paradoxes indicate the limits of classical logic (as already suggested by other posts)
2. These limits are a direct consequence of the calculus of logic being isomorphic to
static set theory in which set membership is considered axiomatic i.e. "given" or outside the actions of observers.
3. Paradoxes arise because "observer states" dynamically re-classify set membership in the course of inter-action with "the observed".
4. Paradoxes therefore (
) indicate the significance of the interactive relationship between observer and observed.
5. "Profundity" describes the difficulty of attaining a vantage point from which to describe the interaction of observer and observed.
6. Post-modernism is in essence an attack on "the given" and is therefore iconoclastic with respect to foundationalist analytic philosophy. Since such the quest for foundationalism underpins the concept of philosophy as an "academic" discipline, this accounts for the animosity of so-called "professional philosophers" to Derrida (et al).