Aristotelian logic organised reasoning through identifiable terms, distinctions and disciplined inference. Arabic philosophers and medieval European scholars translated, developed and contested that inheritance; later, George Boole gave logical reasoning an algebraic form, and Claude Shannon connected Boolean operations to relay and switching circuits. This sequence, explored in Norman Wildberger’s Math Foundations lectures, reaches into electronic circuits and digital computation (Black, 1991; Wildberger, n.d.; Shannon, 1938). The argument now changes level, from representing operations to explaining how their material conditions are reproduced. A conventional logic gate operates through semiconductor materials and a power supply that its switching activity does not produce. A living cell, by contrast, continually produces components that participate in the network producing them. This recursive production is organisational closure, sustained through exchanges of matter and energy with the environment. Autopoiesis makes that mechanism explicit: the network produces the boundary that maintains conditions for the network’s continuation. A computer simulation models this production; the living system physically performs it (Varela, Maturana and Uribe, 1974).
“A is A” remains valid in formal reasoning. The error begins when its formal validity becomes a substitute for explaining how an identifiable A persists. Consider a cell’s membrane: metabolic activity repairs it, while the membrane maintains conditions supporting that activity. Repair supports metabolism; metabolism supports repair. The cell’s identity and its distinction from its surroundings are maintained together through this reciprocal dependence. Non-duality begins here: identity and distinction are inseparable aspects of organised difference. Their separation into independent foundations conceals the activity sustaining both. Institutional persistence involves a different mechanism: appointments, budgets and repeated decisions reproduce roles and procedures that enable subsequent decisions. Investigating either system means tracing these dependencies, measuring their rates and delays, and examining what happens when they are disturbed. “Field” names this interdependence, including the provisional distinctions used to describe it. Those distinctions remain tools of investigation, answerable to what the processes actually sustain. Understanding complexity requires explaining how identities and boundaries are constituted, maintained and transformed through activity.
References
Black, D.L. (1991) ‘Aristotle’s “Peri hermeneias” in medieval Latin and Arabic philosophy: Logic and the linguistic arts’, Canadian Journal of Philosophy Supplementary Volume, 17, pp. 25–83.
Shannon, C.E. (1938) ‘A symbolic analysis of relay and switching circuits’, Transactions of the American Institute of Electrical Engineers, 57, pp. 713–723.
Varela, F.G., Maturana, H.R. and Uribe, R. (1974) ‘Autopoiesis: The organization of living systems, its characterization and a model’, Biosystems, 5(4), pp. 187–196.
Wildberger, N.J. (n.d.) Math Foundations, lectures 251–261 [YouTube lecture sequence]. Insights into Mathematics. Available at: “https://www.youtube.com/user/njwildberger” (Accessed: 12 October 2026).
