Considering The Science of Logic and Modern Counter-Enlightenment alongside Alex Ebert and Layman Pascal
Modern counter-enlightenment is an interesting term. This paper is just a massive exposition of thought, very thorough work here! Reaching to organize many different thinkers across a broad landscape of ideas, into a coherent and concise framework. I very much appreciate this headway into sense making.
I take it that A / A here refers to analysis, while A / B refers to synthesis. This is an old division of schools in geometry, that goes back to Apollonius of Perga and Euclid. Cartesian geometry is analytic geometry that uses an algebraic method (using the coordinate plane). And thus the invention of the differential calculus by Leibniz and Newtown is also analytic (A / A), and is the basis of neo-classical economics and introductory classical physics. Euclid actually wrote another book called *Data* that had the same proofs as the first five books of the *Elements* but in analytic form, rather than the synthetic geometry method of the Elements.
I think a question for the presumptions of material science is whether Cartesian analytic geometry needs to be algebraic/quantitative, or whether there can be a *purely analytic geometry* that is qualitative primarily and also quantitative, that describes the common sense view of the world, and uses similarity (analogy) and congruence relations instead of equality relations. This is what Leibniz attempts to prove in his work On Analysis Situs, and succeeds in my view.
Immanuel Kant made famous the prominent the priority of the *synthetic* approach over the analytic, asking the question, how are the synthetic a priori statements possible? Meaning how is it that we *derive* that 5 + 7 is equivalent to 12, when it is not obvious beforehand through normal experience (analytically) that 7 + 5 is equivalent to 12. He thought that the 12 appears as an insight or an intuition in the mind or intellect, almost like a revelation, when we work out 5 + 7. Note that the modern analytic school (logical positivism), rejects that mathematical statements such as 5 + 7 = 12 are synthetic. And the anti-modern take on the priority of the synthetic would be that it curtails the importance of eternal truths and Aristotle's embodied hylomorphism, wherein experience and intellect are completely integrated, holistically. The Aristotelian notion of the forms is as perfectly embodied, not disconnected rational constructs. And I very much appreciate your approach in this paper, as to try to form a bridge between that ancient view and the modern Hegelian view. I take this to be the vision of the perennial philosophy.
Kant's insights into the synthetic regard gave rise to the entire movement of German idealism -- many consider it to have been the most fertile movement in philosophy since Ancient Greece -- many immense thinkers like Goethe, Fichte, Schelling, Schiller, von Humboldt, and of course Hegel, and many others. The foundations of the modern research university.
I have written a paper recently, regarding the difference/relation between A / A and A / B. https://dionysiosareopagite.substack.com/p/being-and-analogy , FWIW I consider A / A as necessity or eternity while A / B is contingency or temporality, and try to show how the latter is derived from the former. I think it makes sense to emphasize that we cannot reach eternity within time, and the attempt to do so through modern material science methods is futile, thus the emphasis in your paper on A / B as 99% over A / A as 100%. Eternity ought to be approached and approximated without ever presuming to have been attained, which is the conceit and the pride of materialistic science models like the standard model or the periodic table or the theory of evolution.