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In Process and Reality Whitehead starts off the investigation by giving his categoreal scheme - different types of categories and their derivatives, as well as some axioms. If I understand correctly, and by the references Whitehead sometimes makes for different categories, he presumably derived all of his metaphysical scheme from those categories.

Now that might be an exaggeration and he might have stepped out of his own boundaries, but I'm curious to know if anyone has ever tried to provide a formal deduction of Whitehead's philosophy based on that a "categoreal scheme"?

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  • Maybe McHenry's Axiomatic Matrix of Whitehead's Process and Reality is in a vicinity of what you are looking for. It is probably a blessing that Whitehead did not follow Spinoza's template very far. Considering the abductive and provisional character of metaphysical arguments the "deriving" needs to be taken loosely, and Whitehead acknowledged it.
    – Conifold
    Aug 8, 2021 at 21:53
  • @Conifold I personally think that if you provide a structured scheme, you should follow it through, which is one of Spinoza's greatest achievements. I support providing a "readable" version, but I would've expected Whitehead, especially with his mathematical background, to provide an alternative version that is more deductively-structured. Anyway, McHenry's is a nice start, but it's more of a preliminary work than the actual deduction. Aug 9, 2021 at 12:02
  • Well, Hegel provided a "derivation" in Science of Logic, which Peirce characterized as reaching "each category from the last preceding by virtually calling 'next'!" I think a scheme provides only constraints, and one proceeds by guessing something that meets them, not by deriving it from them. Pretending otherwise, as was often the case in older systems, only leaves an impression of pulling rabbits out of a hat. According to McHenry, Whitehead was instead treating his axioms as guiding hypotheses for creative metaphysics to be tested by experience.
    – Conifold
    Aug 9, 2021 at 18:55
  • @Conifold Sorry, at the time I wrote my last comment I only skimmed through the article and now have thoroughly read it. From McHenry's footnotes: "although it is clear the Whitehead is not proceeding deductively, his setting out a definite statement of his first principles at the outset of his system indicates that he held the exiomatic method to be an ideal form in which one should strive to organize thought into a system". Aug 21, 2021 at 12:16
  • Also there is a difference between not having an axiomatic, derivable system (but rather, for example, guidelines), and simply acknowledging that the axioms are liable to change (but are still exactly that, axioms in a derivative system). The latter, as I understand McHenry, is what Whitehead push forwards in his writings. Aug 21, 2021 at 12:17

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