The surface of a Klein bottle is theoretically both internal and external.
Likewise, the branch of Metaphysics should be envisaged as being simultaneously internal and external to Epistemology and vice versa. Metaphysics is the bottle that contains Epistemology, yet in an equally legitimate purview, Epistemology incorporates Metaphysics.
Indeed, I'll argue that all five branches share this strangely looping topology: there’s a similar re-orientation of entire purview between Ethics, Politics and Aesthetics. They are each mutually defining parts of an integral whole — not mere static subsets — yet they ought also be seen holistically, part and parcel of the same thing.
The Klein bottle idea is just a small but vital step towards an improved visualisation of the five branches of philosophy, a property to bear in mind which is rather tricky to convey.
Next month I aim to show how five such forms might integrate…
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