This began as a diary entry written in London around 2008, while reading Jan Yoors during a period of immersion in Gypsy and Balkan music and dance. Revisited and developing since.

In “Offense at the Paradox: An acoustical illusion” (Appendix to Ch. III in Philosophical Fragments – “The Absolute Paradox – A Metaphysical Caprice”), Kierkegaard quotes Goethe to illustrate “the understanding surrendered itself and the Paradox gave itself” – “Halb zog sie, ihn, halb sank er hin” (“She half dragged him, he half sank down”). It describes Faust being drawn toward Gretchen – a movement that is neither purely active nor purely passive. He is both pulled and yielding. Kierkegaard uses it to characterise the relation between the understanding and the Paradox: The understanding surrenders – and yet the Paradox gives itself. Half it draws him, half it sinks. It becomes a model of epistemic eros (the philosophical concept of love/longing as a driving force for inquiry).

This piece circles an intuition I was working with in my undergraduate thesis around 2003. It remains unresolved.

What immortal hand or eye / Could frame thy fearful symmetry?

- William Blake, "The Tyger" (1794)

Russell’s paradox arises because set theory treats membership as a static inclusion relation within a fixed totality. Russell resolves paradox by stratifying types and forbidding certain forms of self – reference. He arranges objects into types. A function or class of objects of type N belongs to a higher type (N+1). No entity can be a member of itself because it would require crossing type level boundaries.

Russell’s paradox arises because set theory treats membership as a static inclusion relation within a fixed totality. Russell resolves paradox by stratifying types and forbidding certain forms of self – reference. He arranges objects into types. A function or class of objects of type N belongs to a higher type (N+1). No entity can be a member of itself because it would require crossing type level boundaries.

What has always unsettled me is the static relation between a set and its members (the symmetry that makes totality dangerous). The role of asymmetry in grounding hierarchical relations appears in Kit Fine’s paper Essence and Modality and more broadly in the concept of Greek “aitia” – the “that because of which” – the direction of the relation of causation in an explanation for something.