Neo-Platonism (NP)

Prelude to Mathematical Neo-Platonism

"Is not being, then, unified number,
and beings number unfolded,
and Intellect number moving in itself,
and the living creature number
embracing everything?"
  -Plotinus

Is there any substance to MNP? Or is it no more than a pretentious sounding but ultimately empty combination of words, a mere flatus vocis? Very interesting in this regard is the remarkable role played by axiomatic set theory in contemporary mathematics. As most mathematicians nowadays recognize, axiomatic set theory functions as the foundation for virtually all of mathematics – and some mathematicians would go even further than this, e.g. John Mayberry: "set theory is not really, or not just, a foundation for mathematics. It simply is modern mathematics." (1988: 353) This privileged role played by axiomatic set theory holds in particular for ZFC, which is standardly used in mathematics and mathematical logic. As I will show in the following, ZFC reproduces surprisingly many of the conceptual structures characteristic of NP, notably its hierarchical universe deriving from a single and indeterminate source. Now, suppose that this analogy between ZFC and NP holds up under closer analysis. Wouldn't we then be justified in concluding that ZFC = MNP, since ZFC reproduces NP in the context of mathematics? Let's see how far this analogy goes.

Plotinus's Metaphysics of Creative (Self-)Contemplation

In my previous post I introduced the idea of Mathematical Neo-Platonism (MNP), where a transcendent source -- analogous to the One/Good in historical Neo-Platonism -- is seen as generating the Platonic reality of mathematics which in turn generates the physical universe in which we find ourselves. This MNP is a long-term project I am working on, and I hope to write more about it in the future. But since MNP obviously harks back to historical Neo-Platonism, especially the system of Plotinus, I want to say more about the latter in this post, where I give some historical background to my proposal for MNP. I also want to discuss Plotinus because his system is highly interesting in itself and deserves much wider recognition as being the true birthplace of Absolute Idealism in Western philosophy.