On the consistent reasoning paradox of intelligence and optimal trust in AI: The power of 'I don't know'

TL;DR

The paper introduces the Consistent Reasoning Paradox, showing that trustworthy AI must admit ignorance ('I don't know') to handle fallibility and maintain consistency, revealing fundamental limits of AI reasoning and explainability.

Contribution

It formalizes the Consistent Reasoning Paradox, demonstrating that AI must incorporate 'I don't know' to be trustworthy and consistent, highlighting a new concept called the 'I don't know' function.

Findings

Consistent reasoning implies AI will hallucinate on some problems.

Detecting hallucinations is harder than solving the problems.

Trustworthy AI must be able to say 'I don't know' to handle fallibility.

Abstract

We introduce the Consistent Reasoning Paradox (CRP). Consistent reasoning, which lies at the core of human intelligence, is the ability to handle tasks that are equivalent, yet described by different sentences ('Tell me the time!' and 'What is the time?'). The CRP asserts that consistent reasoning implies fallibility -- in particular, human-like intelligence in AI necessarily comes with human-like fallibility. Specifically, it states that there are problems, e.g. in basic arithmetic, where any AI that always answers and strives to mimic human intelligence by reasoning consistently will hallucinate (produce wrong, yet plausible answers) infinitely often. The paradox is that there exists a non-consistently reasoning AI (which therefore cannot be on the level of human intelligence) that will be correct on the same set of problems. The CRP also shows that detecting these hallucinations, even in a probabilistic sense, is strictly harder than solving the original problems, and that there are problems that an AI may answer correctly, but it cannot provide a correct logical explanation for how it arrived at the answer. Therefore, the CRP implies that any trustworthy AI (i.e., an AI that never answers incorrectly) that also reasons consistently must be able to say 'I don't know'. Moreover, this can only be done by implicitly computing a new concept that we introduce, termed the 'I don't know' function -- something currently lacking in modern AI. In view of these insights, the CRP also provides a glimpse into the behaviour of Artificial General Intelligence (AGI). An AGI cannot be 'almost sure', nor can it always explain itself, and therefore to be trustworthy it must be able to say 'I don't know'.