Randolph Dible

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.

In 1912, Husserl’s foremost student at the University of Göttingen, Hedwig Conrad-Martius, made world headlines for her award-winning ontological critique of positivism. In time, her ontological phenomenology was eclipsed by that of Martin Heidegger. Lately, however, her work is being rediscovered. In her final period of philosophical development, Conrad-Martius advanced an ultimate systematic philosophy of nature and cosmos, built upon her earlier ontology of reality (realontologie), that is both empirically scientific and deeply metaphysical in character. Her theoretical physics is a critical evolution of philosophical cosmology in the tradition of early German critical realism (kritischer realismus), and the following account of its development to a fully mature hypothesis of a trans-natural foundation and corresponding trans-natural hyperspace model will help to make her contribution to the phenomenological scientific philosophy of nature clear.

This chapter explores foundational issues in the philosophy of time and space by comparing the phenomenological contributions of Anna-Teresa Tymieniecka and Peter Byrne Manchester. Each of these two philosophers have revived an ancient paradigm for thinking about problems of continuity in the philosophy of space and time. Peter Byrne Manchester’s 2005 book, The Syntax of Time: The Phenomenology of Time in Greek Physics and Speculative Logic from Iamblichus to Anaximander—the second in the Brill series Studies in Platonism, Neoplatonism, and the Platonic Tradition—traces Husserl’s phenomenology of inner time-consciousness back through Plotinus to Aristotle’s philosophy of time, and thereby reconnects its problematic to the most archaic origins of philosophy in the Presocratics. Through the philosophical reconstruction of an ancient worldview on the basis of an insight about the ordering principle of time as a logical syntax, Peter Manchester uncovers a neglected ancient doctrine called spherics (sphairikē, or sphairikon logon), which has deep implications not only for time but for all the dimensions of experience. He names his guiding figure the Sphere of the All, a formulation belonging to his ancient sources. Anna-Teresa Tymieniecka’s phenomenology of life also recognizes a previously unnoticed syntax. For her, it is the intrinsic functioning of life, which she elaborates in her phenomenology of life as ontopoietic process. Her extensive account of life’s inner-workings yields a phenomenological cosmology of multiple spheres of being grounded in a “great vision of the All” (Tymieniecka 2000, 643), much like Manchester’s spherics. The convergence to similar frameworks arrived at independently by these two philosophers is a philosophical synchronicity due to the teleology at play in their phenomenological thought, common to multiple philosophical cosmologies, but what is more remarkable is the convergence of their specific functional systems and metrological terms. This convergence arises from the pursuit of an ancient and perennial cosmology rooted in a deep synthesis of order and measure. The ancient intuition that the language of God is the language of mathematics plays a special role in classical phenomenology, and the recovery of the doctrine of the spheres represents a new contribution to the synthetic and geometrical side of this intuition. By arriving at a synthesis of the most fundamental ontological units in these two systems, a new paradigm of speculative cosmology and transcendental logic emerges from the paradigm of the sphere.