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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"?

Yechiam Weiss
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  • Maybe [McHenry's Axiomatic Matrix of Whitehead's Process and Reality](https://www.academia.edu/34427949/The_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 08 '21 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. – Yechiam Weiss Aug 09 '21 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 09 '21 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". – Yechiam Weiss Aug 21 '21 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. – Yechiam Weiss Aug 21 '21 at 12:17
  • That axioms can change is not a reason to not deduce from those at hand. But take Newton's *Principia*, for example. We have the three laws, some simple consequences. But not much of interest can be deduced from them without guesses about concrete forces involved (friction, gravity, etc.). Not even the conservation laws. Newton's axioms are merely guidelines/constraints for speculative models to be tested. That is roughly how I see Whitehead's axiomatic method for organizing his system too. And that is why he does not pretend to deduce much, thereby avoiding Spinoza's and Hegel's pitfalls. – Conifold Aug 21 '21 at 20:47
  • @Conifold that is reasonable. But contrary to the Newton example, here Whitehead provides a so-to-speak complete system (obviously not complete as per the mathematical notion of completeness, but he provides all the information you should need for comprehending the system). And furthermore - perhaps you understand it as him not pretending to deduce, but if so then why does he always refer back to his axioms? (now that I think about it perhaps I should include an example in the post) – Yechiam Weiss Aug 22 '21 at 07:24
  • Although I would say that statement like: "[i]t seems as though in practice, for human beings at least, only transmuted feelings acquire consciousness, never simple physical feelings" makes me doubt that any deduction was used here. Which I agree is one of the strong selling points of Whitehead, the fact that he always aims towards the practical and doesn't avoid using experiential facts as part of his system. – Yechiam Weiss Aug 22 '21 at 08:20
  • How else? Newton also constantly utilizes his laws when modeling applications, but not always deductively. He even abducts the laws themselves by citing experiments. If we speculate by inference to best explanations we are well advised to keep constraints on eligible explanations always in clear view, and even yes, deductively infer or rule out some features in them on occasion. Newton's *Principia*, it seems, is a better template for developing metaphysics than *Elements*, or the other *Principia*, philosophy is "*mystical*" and not to be "*misled by the example of mathematics*". – Conifold Aug 22 '21 at 08:57
  • Metaphysician, like Newton, must discern the general in the concrete. Surely, not by deduction. And Whitehead's axiomatic scheme is not really laid out from the outset, only sketched and evolved through applications, a telos."*Logic lies upon the universe as an iron necessity, the aesthetic harmony stands before it as a living ideal moulding the general flux*". As without so within. Btw, did you look at [Harrah's paper](https://www.jstor.org/stable/2708119) that McHenry cites? He discusses Whitehead's ambivalence towards deduction and "creative thinking" posited as its alternative on p. 421ff. – Conifold Aug 22 '21 at 09:03
  • @Conifold I haven't, I will make sure to do so. The problem I have with this sort of "creative thinking" (as I understand it) as opposed to deduction, is the difficulty of criticizing it. In deduction you can criticize the logical steps, what can you criticize in creative thinking? The real-world applications? Its completeness (even though we acknowledge that it needn't be complete)? Now that I think about it perhaps it should be asked in a different post. – Yechiam Weiss Aug 22 '21 at 09:43
  • Informal arguments get criticized and challenged, their steps can be implausible. Even better, we can criticize *conclusions* of a system, based on internal coherence, systematic interconnection, and foremost, matching, as a whole, the facts of experience. Like Peirce, Whitehead favors some approximation of science's speculate-and-correct routine over Cartesian deduction from first principles. And what better way to criticize the "best" explanation than to offer a better explanation. As we learned from Kuhn, even flawed paradigms persist until a credible alternative emerges to displace them. – Conifold Aug 23 '21 at 00:34

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