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In the 1970s, the Chilean biologists Francisco Varela and Humberto Maturana developed a systems theory of life as self-creating, or autopoietic, on the formal basis of the mathematician George Spencer-Brown’s 1969 book Laws of Form and its calculus of indications. While Spencer-Brown’s calculus has had an important effect on the fields of cybernetics and systems theory, autopoietic theory has had a broad influence on disciplines such as biology, ecology, neuroscience, sociology, and others. Although Varela recognized the power and simplicity of Spencer-Brown’s calculus, he modified it by adding a potentially redundant third law to the original two titular laws of form, calling the result the calculus interpreted for self-reference and the extended calculus of indications (ECI). This third law makes self-reference explicit, but I argue that it is unnecessary, as self-reference is already implied by the nature of the two laws governing the inner workings of form in Spencer-Brown’s calculus. The addition of this redundancy has the effect of separating the primordial dynamics of the transcendental realm—epistemically and ontically constitutive operations disclosed by phenomenological investigations—from the natural realm of cause and effect among finished forms. Anna-Teresa Tymieniecka’s phenomenology of life as ontopoiesis, by contrast, succeeds in developing an ontological theory of life on the formal ontological basis prepared by Husserl’s phenomenology, transcendental logic, and the living tradition of a mathesis universalis rooted in ancient Greek philosophy. Tymieniecka’s phenomenological theory of life uncovers a breakthrough into life’s inner workings and rests on an ontologically robust foundation. By drawing attention to the calculus behind the calculus, I aim to initiate an interpretation of Spencer-Brown’s calculus of indications as an important manifestation of the mathesis universalis, and to apply this interpretation to the place prepared by Tymieniecka’s phenomenology of ontopoiesis. Finally, I will provide an interpretive guide to the key elements of Laws of Form, including Spencer-Brown’s calculus of indications.

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Ontopoiesis, Autopoiesis, and a Calculus Intended for Self-Reference

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  • 发表日期：

    2025年

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  • Randolph Dible

摘要

In the 1970s, the Chilean biologists Francisco Varela and Humberto Maturana developed a systems theory of life as self-creating, or autopoietic, on the formal basis of the mathematician George Spencer-Brown’s 1969 book Laws of Form and its calculus of indications. While Spencer-Brown’s calculus has had an important effect on the fields of cybernetics and systems theory, autopoietic theory has had a broad influence on disciplines such as biology, ecology, neuroscience, sociology, and others. Although Varela recognized the power and simplicity of Spencer-Brown’s calculus, he modified it by adding a potentially redundant third law to the original two titular laws of form, calling the result the calculus interpreted for self-reference and the extended calculus of indications (ECI). This third law makes self-reference explicit, but I argue that it is unnecessary, as self-reference is already implied by the nature of the two laws governing the inner workings of form in Spencer-Brown’s calculus. The addition of this redundancy has the effect of separating the primordial dynamics of the transcendental realm—epistemically and ontically constitutive operations disclosed by phenomenological investigations—from the natural realm of cause and effect among finished forms. Anna-Teresa Tymieniecka’s phenomenology of life as ontopoiesis, by contrast, succeeds in developing an ontological theory of life on the formal ontological basis prepared by Husserl’s phenomenology, transcendental logic, and the living tradition of a mathesis universalis rooted in ancient Greek philosophy. Tymieniecka’s phenomenological theory of life uncovers a breakthrough into life’s inner workings and rests on an ontologically robust foundation. By drawing attention to the calculus behind the calculus, I aim to initiate an interpretation of Spencer-Brown’s calculus of indications as an important manifestation of the mathesis universalis, and to apply this interpretation to the place prepared by Tymieniecka’s phenomenology of ontopoiesis. Finally, I will provide an interpretive guide to the key elements of Laws of Form, including Spencer-Brown’s calculus of indications.