„You can't compare apples and pears“: true. Most ethical frameworks do it anyway, only less visibly. Utility comparisons between an ecosystem and an economic system assume both are measurable in the same currency. The debate then concerns the magnitude of the comparison value.
Path ethics asks differently: When is a comparison structurally permissible, and when does it fail at the categorial level?
One possible formalisation of this answer comes from category theory. Each A-A-P dimension (Autonomy, Connectivity, Persistence) maps systems to evaluations. As a working hypothesis, a category-theoretic formulation would say that a comparison is structurally supported when a suitable mapping preserves the evaluation across the domain shift. Evaluating first and translating afterward must then produce the same result as translating first and evaluating afterward.
The criterion is concrete: Mycelium and Bitcoin are comparable on Connectivity. Network propagation functions structurally similarly in both domains. The evaluation survives the domain shift. On Autonomy, the comparison fails: biochemical self-regulation and protocol consensus follow incompatible logics. The article maintains the stronger thesis here: the bridge breaks structurally; within this modelling, no viable translation exists. The category-theoretic formulation of that finding, however, is not yet fully worked out. A formal non-existence proof for natural transformations would have to specify source and target categories, bridge functors, and the naturality condition explicitly.
What follows? Incommensurability is no methodological failure. It is a statement about the systems. The diagnosis defended by the article is: „There can be no translation.“ The epistemic distinction remains decisive. A translation that has not been found marks a knowledge gap. A structurally impossible translation is a finding. As a category-theoretic non-existence theorem, this diagnosis has not been proved here; as the structural thesis of the example, it is the claim to be tested.
For governance, anyone comparing two paths to decide which to protect must specify, for each A-A-P dimension, whether the comparison holds. Where the comparison fails under this structural test, utility calculations must not simply presuppose a shared space of comparison. The decision framework shifts from quantification to political deliberation.
Apples and pears are incommensurable as total systems. Their suitability for jam can still be compared. Pectin, sugar, and cooking behavior run structurally in parallel. The evaluation survives the domain shift.
That is how precise ethics needs to become.