How Robust Can Inconsistency Get?

In 2011 Carl Hewitt introduced the concept of inconsistency-robustness (IR). IR is a property of information systems when the following conditions are met. The system is inconsistent, large, practical, inferentially self-aware, and the inconsistency is impossible to expel. Its inconsistency is also empirically discernible and a drag on the system’s performance. Yet distinctively it is also the motivation occasion for performance improvement, albeit with no possibility of inconsistency-free successors. In this attenuated sense, inconsistency is also a desirable feature of IR systems. The technical details of IR are laid out in Hewitt’s logic in progress IRL, itself an extension of his Direct Logic. It is possible that the idea of inconsistency-robustness is exhausted by the formal provisions of IRL. But I want to consider here a more latitudinarian possibility, according to which the idea of inconsistency-robustness admits of intellectually fruitful application well beyond the arcana of IRL. As we proceed, there will be occasion to close in on an interesting idea. It is that inconsistency has a more robust presence in human cognition than in Hewitt’s large systems. More particularly, it is a presence unattended by cognitive dissonance. Concerning which, we conjecture that there is a plenitude of propositions unambiguously both true and false which cause no affront to the law of contradiction. Rightly enough, some will see this as a dialethic conclusion. But it is not to be found in the present-day logics of dialethic logic.

Authors

• John Woods

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