  Recent engineering developments in specialised computational hardware,
data-acquisition and storage technology have seen the emergence of Machine
Learning (ML) as a powerful form of data analysis with widespread applicability
beyond its historical roots in the design of autonomous agents. However --
possibly because of its origins in the development of agents capable of
self-discovery -- relatively little attention has been paid to the interaction
between people and ML. In this paper we are concerned with the use of ML in
automated or semi-automated tools that assist one or more human decision
makers. We argue that requirements on both human and machine in this context
are significantly different to the use of ML either as part of autonomous
agents for self-discovery or as part statistical data analysis. Our principal
position is that the design of such human-machine systems should be driven by
repeated, two-way intelligibility of information rather than one-way
explainability of the ML-system's recommendations. Iterated rounds of
intelligible information exchange, we think, will characterise the kinds of
collaboration that will be needed to understand complex phenomena for which
neither man or machine have complete answers. We propose operational principles
-- we call them Intelligibility Axioms -- to guide the design of a
collaborative decision-support system. The principles are concerned with: (a)
what it means for information provided by the human to be intelligible to the
ML system; and (b) what it means for an explanation provided by an ML system to
be intelligible to a human. Using examples from the literature on the use of ML
for drug-design and in medicine, we demonstrate cases where the conditions of
the axioms are met. We describe some additional requirements needed for the
design of a truly collaborative decision-support system.
