The Guillotine

Note 1. Hume, David, A Treatise of Human Nature (1739–1740), Book III, Part I, Section I. Hume’s observation that moral reasoning smuggles in an unannounced transition from “is” to “ought” became known as “Hume’s guillotine” and remains the central challenge for any naturalistic ethics.

Note 2. Moore, G.E., Principia Ethica (Cambridge University Press, 1903). Moore’s “naturalistic fallacy” generalized Hume’s insight: any attempt to define “good” in terms of natural properties (pleasure, survival, evolutionary fitness) commits an error, because one can always meaningfully ask “but is that good?”

Note 3. Mill, J.S., Utilitarianism (1863). Mill’s formulation—“actions are right in proportion as they tend to promote happiness”—explicitly grounds normativity in a felt state, which Mill himself acknowledged could not be proven but only shown to be desirable.

Note 4. Kant, Immanuel, Groundwork of the Metaphysics of Morals (1785). Kant’s categorical imperative—“act only according to that maxim whereby you can at the same time will that it should become a universal law”—attempts to ground ethics in pure rational consistency rather than empirical fact.

Note 5. Aristotle, Nicomachean Ethics, Book II. Aristotle’s virtue ethics centers on eudaimonia (flourishing or well-being) as the highest good, achieved through the cultivation of virtuous character traits as a mean between extremes.

Note 6. Sharma, A., Czégel, D., Lachmann, M., Kempes, C.P., Walker, S.I., and Cronin, L., “Assembly theory explains and quantifies selection and evolution,” Nature 622 (2023): 321–328. The exponential growth of combinatorial space with assembly depth is formalized in the assembly equation. See also Marshall, S.M., et al., “Identifying molecules as biosignatures with assembly theory and mass spectrometry,” Nature Communications 12 (2021): 3033, for experimental validation of the complexity threshold. The argument that coercion collapses combinatorial spaces is ours, extending assembly theory into normative territory.

Note 7. Bohr, Niels, “The Quantum Postulate and the Recent Development of Atomic Theory,” Nature 121 (1928): 580–590. Bohr’s complementarity principle, presented at the 1927 Como conference, holds that quantum objects possess complementary properties (wave/particle, position/momentum) that are mutually exclusive in observation but jointly necessary for a complete description. The principle has been extended beyond its original quantum-mechanical domain: Bohr himself explored its application to biology (an organism can be studied as alive or analyzed as a mechanism, but not both in the same experiment) and epistemology. The application to the is-ought distinction proposed here is new: the descriptive and the normative are complementary observations of one underlying reality (thermodynamic selection inhabited by persisting beings), visible only in alternation. This framing does not resolve the gap (complementarity principles clarify trade-offs rather than eliminating them) but it recharacterizes the gap as perspectival rather than ontological.

Note 8. Hofstadter, Douglas R., Gödel, Escher, Bach: An Eternal Golden Braid (Basic Books, 1979). Hofstadter’s central claim about levels is that the brain is a multi-level system that can be described at any of its levels, and that the higher-level descriptions are just as real as the lower-level ones. The argument that higher levels are causally real, that “beliefs interacting” does work that “neurons firing” cannot capture, is developed throughout the book and refined in I Am a Strange Loop (2007), especially Chapters 2, 12, and 22. The application to the is-ought gap (that normative properties emerge at the coordination level the way mental properties emerge at the neural level) is novel synthesis. The key disanalogy (synchronic vs diachronic levels) is acknowledged in the text. See also Jaegwon Kim, “Multiple Realization and the Metaphysics of Reduction,” Philosophy and Phenomenological Research 52 (1992): 1–26, for the standard philosophical treatment of how higher-level properties relate to lower-level substrates.

Note 9. Rovelli, Carlo, “Why bad philosophy is stopping progress in physics,” Nature 641 (2025): 585–587. Rovelli argues that real advances in fundamental physics come from taking established knowledge seriously and resolving its internal tensions, not from speculating beyond it. This book takes that approach. The claim that ethics can be constrained by physics follows the same method that produced special relativity (trusting Maxwell’s equations and Galilean relativity, discarding absolute simultaneity) and general relativity (trusting special relativity and Newtonian gravity in tested regimes, discarding instantaneous action at a distance).

Note 10. Gödel, Kurt, “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I,” Monatshefte für Mathematik und Physik 38 (1931): 173–198. The first incompleteness theorem proves that any consistent formal system powerful enough to express arithmetic contains true statements it cannot prove from within its own axioms. The application to the is/ought partition is ours and remains a structural analogy: whether moral underdetermination is formally a Gödelian property, or merely rhymes with one, is unsettled. The later interlude “The Incompleteness” develops the same point at length.