Comments on the use of propositional logic to examine sustainability concepts

Patten [1998. Ecological Modelling, 108(1–3):97–105] uses propositional logic to explore three properties of sustainability: stability, continuation and longevity. Here, I discuss some of the inconsistencies between the statements in the text and those expressed in propositional logic. In addition, I examine some of the conclusions reached by Patten in the context of dynamic systems theory. A model of a zero-sum system demonstrates that part stability does not necessarily imply system sustainability as conferred by stability, and that part continuation does not necessarily imply system sustainability as conferred by continuation. The statements of propositional logic are about models of the real world, and herein lies its utility. Propositional logic in principle can help us to identify the formal relationships between sustainability concepts in our models, and to begin to tie together results from both ecology and systems theory by pointing out incongruities between intuition and theory. A formal implementation of sustainability is challenging for two reasons. First, sustainability comprises many properties, not all of which can be applied to every ecosystem at all times and over all scales. Second, the nature of any formal system representation has inherent biases derived from the identification and aggregation of its measures and their organizational structure.