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Shimon Malin writes in Nature Loves to Hide:

According to Whitehead, the ultimate blocks of reality are discrete items which he calls 'throbs of experience', 'occasions of experience', 'actual occasions' or just 'occasions' depending on context. He asserts: 'I hold that these unities of existence, these occasions of experience are the really real things, which in their collective unity compose the evolving universe ever plunging into the creative advance'.

Atoms, one imagines are solitary beings able to stand alone in the void.

Experience though seems to demand a tripartite division: the experiencer, the experienced and the moment of experience itself. It seems fundamentally relational.

  1. Does Whitehead himself characterise experience relationally?

Set theory, which in the usual account, founds mathematics, is atomistic. A set is ontologically composed of its elements and nothing else. This has a family resemblence to atomism.

Category Theory is fundamentally relational and also, on some accounts, is capable of founding mathematics.

  1. Given this, is there any mileage in contemplating Whiteheads process philosophy through Category Theory?
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Yes, Whitehead builds on Leibniz view of monads. The initial picture is that each monad reflects all others, so every thing is defined by its effects on everything else. Whitehead explicitly adopts this visual analogy in Science and the Modern World. He backs off from it moving forward with Process and Reality, because it is still too static. But it captures the idea.

As I see it Whitehead's notion of organic identity does not really fit the more simplified notion of category theory. A category has to have identity relations that carry each object back into itself.

This calls out what is and what is not a basic object in a way that would not be really possible in a process reality. Some collections of things have an identity, and others do not. So you would need some kind of model that derives identity from the other relations by minimizing in some lattice.

Category theory makes only half a step in the right direction.

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    Upvoted. You may have hit on an objection that seriously undermines W's view. He got as far as idealism but not as far as non-dualism so could not reduce intentional consciousness. The Upanishads deny the distinction between experience, experiencer and object of experience and this allows a complete reduction that avoids the problems you raise. Relations must be transcended for 'advaita' (not-two) Vedanta and the Perennial philosophy. if Whitehead proposes a fundamental dualistic consciousness then he denies the Unity of the Universe and creates problems of self-reference. . . . – PeterJ Jan 18 '18 at 11:55
  • @PeterJ: Just nitpicking, as this seems to be a pet issue of yours - idealistic reductionism is not the only thing that allows for non-dualism without losing the explicans for consciousness. Pragmatism, process ontologies of various sorts, and other more hermeneutical kinds of philosophies (of nature) do as well. – Philip Klöcking Jan 18 '18 at 13:38
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    @PeterJ When I am talking about Whitehead, answering a question about Whitehead, I really don't care what your religion has to say about it -- he was an Anglican. There is nothing in this question about consciousness,either. There is no reason for that comment at all. it is just not helpful, since you are basically conjecturing from ignorance about what someone might have said, who has actually bothered to write on the issue. – user9166 Jan 18 '18 at 17:08
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    Well pardon me. I thought it was a very good question and that one could learn a lot from examining it if one were to connect up all the issues. The question is clearly all about consciousness and the solution I mentioned specifically addresses it. Whitehead came close and I think we do well to take him seriously, but his ideas have flaws as stated in the OP. It is difficult not mention a workable solution for such philosophical problems when they come up but I'll try to be less helpful if it's causing trouble. – PeterJ Jan 19 '18 at 14:45
  • @PeterJ You reference problems that I raise. i didn't raise any. So this is not help, it is an intrusion where you can push what you want. There is a long tradition of Cardinal/Fixed/Mutable natures as a solution to this issue borrowed by Hegel, Lacan, Wittgenstein (ultimately in including meaning, usage and the game) and even to some degree going back to Aristotle. It occurs again here, not as a problem, but as a solution. Ignoring that completely and insisting only the opinion of removing all leverage is just bias – user9166 Jan 19 '18 at 17:33

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