Crisis? What Crisis? The Case For Neo-Intuitionism in Formal Science, Natural Science, and Philosophy, #3–Putting Neo-Intuitionism To Work, & Conclusion.

By Robert Hanna

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I. Introduction

II. What is Neo-Intuitionism?

III. Putting Neo-Intuitionism To Work

IV. Conclusion

REFERENCES

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This, the third and final installment of this essay, contains sections III and IV.

You can also download and read or share a .pdf of the complete text of this essay–including the REFERENCES–HERE.

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III. Putting Neo-Intuitionism To Work

In this section, I’ll provide some indications of how neo-intuitionism can be put to work for the purpose of fully facing up to and adequately resolving the mega-crisis in contemporary formal and natural sciences and post-classical Analytic philosophy. Obviously, each of these claims, on its own, would require an essay or even a book to demonstrate. So, all I’ll do here is provide references to other texts in which I’ve provided detailed arguments for the claims. In any case, the synoptic overview of neo-intuitionism in section II above should be sufficient for providing the attentive and charitable reader with a fairly good general sense of how the various arguments and details would go.

First, if neo-intuitionism is true, then Cantor’s paradox and Russell’s paradox are fully faced up to and adequately resolved, because there’s no gap whatsoever between the universe V of set theory and the set of actual or possible objects of human sensibility, hence there’s also no gap whatsoever between the scope of sensibility-restricted Zermelo-Fraenkel set theory plus the axiom of choice (ZFC) and the set of all actual or possible objects of human sensibility (Hanna, 2022a: appendices 2 and 4).

Second, if neo-intuitionism is true, then The Continuum Hypothesis is provable in sensibility-restricted ZFC (Hanna, 2015: pp. 391–392; 2022a: appendices 2 and 4).

Third, if neo-intuitionism is true, then the Löwenheim-Skolem Theorem (LS), whether downward LS or upward LS, is logically supervenient on Cantorian set theory, precisely insofar as Cantorian set theory is interpreted essentially within the bounds of sensible set theory (Hanna, 2022a: appendices 2 and 4).

Fourth, if neo-intuitionism is true, then the inexhaustible source of truth and consistency-proofs for mathematics is rational human mathematical intuition (Hanna, 2015: chs. 6–8).

Fifth, if neo-intuitionism is true, then The Liar sentence is logically complementary to and mutually entangled with The Lector sentence (Hanna, 2022e).

Sixth, if neo-intuitionism is true, then the logocentric predicament is adequately resolved by the thesis of logical cognitivism:

logic is nothing more and nothing less than a strictly a priori, universal, and non-instrumentally practical, innately-specified structure of the human capacity for theoretical and practical rationality, in the Ur-format of a proto-logic that’s presupposed and used in the construction of every other other logic whatsoever, every scientific or non-scientific theory whatsoever, every justification whatsoever, and every explanation whatsoever. (Hanna, 2022b; see also Hanna, 2006, 2015: esp. ch. 5; )

Seventh, if neo-intuitionism is true, then strong AI is false, weak AI is trivially true, and the Turing Test is cognitively empty, because all the Test shows is that computing machines can be built which effectively deceive some rational human animals into falsely believing that there are other rational minded beings mysteriously and indeed noumenally present, as Rylean “ghosts in the machine” (Ryle, 1949). See, for a contemporary example, the Google employee fired during July 2022 for publicly asserting that the company’s current computational language model is sentient (NYT, 2022).

Eighth, if neo-intuitionism is true, then the paths of particles under quantum indeterminacy are uncomputable functions that are nevertheless effectively performed by experimenters, so that the particle being measured by the experimenter ends up with a determinate set of physical values satisfying the Schroedinger equation, aka “the collapse of the wave function,” aka “superposition,” yet this is neither the anti-realist/Copenhagen interpretation, nor the realist/many-worlds interpretation, nor the realist/ superdeterminist interpretation, but instead a new version of the realist/Bohmian interpretation, since we appeal to Bohmian mechanics and its commitment to non-local hidden variables together with the neo-organicist, non-deterministic interpretation of non-equilibrium thermodynamics, so that

(i) these non-local hidden variables are uncomputable, negentropic, processual, purposive, and self-organizing wavicles that inherently embody the wave/particle duality, and

(ii) the experimenter imaginatively anticipates “what it’s like to be a Bohmian beable” — that is, the experimenter imaginatively anticipates the unfolding of the Bohmian “pilot wavicle” — precisely insofar as they’re actually performing the experimental measurements in The Two-Slit Experiment and other similar dual-path experiments, thereby providing an egocentric centering that determines and fixes not only the “handedness” of the orientable local space through which the wavicle moves, but also the asymmetric temporal directionality of the local time in which the wavicle evolves, of the actual experimental situation, aka “contextuality” (Hanna, 2022a: section 4.3).

More generally, the Standard Models of cosmology and particle physics are revised and revolutionized by adopting a neo-organicist, non-equilibrium thermodynamic model of motion and the fabric of spacetime, the rubber-sheet cosmos, that fully incorporates our essentially non-conceptual intuition of essentially embodied rational human agency into the revised-&-revolutionized foundations of general relativity and quantum mechanics (Hanna, 2022a: ch. 4, and appendices 3 and 5; Hanna and Maiese, 2009: esp. chs. 3–8). Or in other and fewer words, this is manifest-realist physics with a human face (Hanna, 2022g).

Ninth, if neo-intuitionism is true, then microbiology and evolutionary biology nomologically supervene on the fundamental uncomputable, negentropic, processual, purposive, and self-organizing non-equilibrium thermodynamics of macroscopic living organisms (Varela, Maturana, and Uribe, 1974; Varela, 1979; Prigogine, 1997), thereby fully incorporating into the natural science of biology what Evelyn Fox Keller — referring to the life and work of Nobel Prize-winning cytogeneticist Barbara McClintock — aptly called “a feeling for the organism” (Keller, 1983), now understood as an essentially non-conceptual mode of human rational intuition specifically and veridically targetting organismic living systems.

Tenth and finally, if neo-intuitionism is true, then not only is there a fully intelligible and defensible analytic-synthetic distinction, but also and above all, philosophy itself is ultimately grounded on synthetic a priori truth and knowledge, via our innately-specified cognitive capacities for essentially non-conceptual content and human rational intuition (Hanna, 2015: esp. chs. 2 and 4–8; 2017).

IV. Conclusion

If what I’ve argued in this essay is sound, then, first, the contemporary formal and natural sciences and post-classical Analytic philosophy, alike, are in mega-crisis — no matter what the practitioners of “normal science” in those sciences and in post-classical Analytic philosophy might actually individually self-consciously think or dare to admit publicly, owing to the lamentable pervasive intellectual pathology of crisis-denial — precisely because a set of basic and indeed framework-testing open problems in each of these sciences and in post-classical Analytic philosophy still continue to defy any adequate resolution, and second, the only way out of this mega-crisis, by fully facing up to and adequately resolving all these open problems, is neo-intuitionism. To be sure, given all the crisis-denial that’s happening out there in professional-academy-land, I’m far-from-confident and even fairly doubtful — to put it mildly — that they’ll actually take this way out. But I remain rationally hopeful, nevertheless. For if I’m right, then not only the theoretical, moral-practical, social-institutional, and political fates of the formal sciences, the natural sciences, and post-classical Analytic philosophy, alike — and indeed, the fate of real philosophy itself, independently and outside of post-classical Analytic philosophy in particular and of professional academic philosophy in general (Hanna, 2021, 2022c, 2022d) — but also, in view of Frankenscience, the existential fate of humankind (Hanna and Paans, 2022), all essentially depend on their actually taking it.