ONT Re: Prospects for Inquiry Driven Systems

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PRO.  Note 50

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2.2.1.3.  Relevant Measures

Differences between problem states are not always defined.
And even when they are, relevant differences are not always
defined in the manner that would form the most obvious choice.
Relevant differences are "differences that make a difference",
in the well-known pragmatist tag, bearing on the problem and the
purpose at hand.  The qualification of relevance adds information
to the abstractly considered problem space.  This extra information
has import for the selection of a relevant metric, but nothing says
it will ever determine a unique metric suited to a given situation.

Relevant metrics are generally defined on semantic features of the
problem domain, involving pragmatic equivalence classes of objects.
Measures of distinction defined on syntactic features, in effect,
on the language that is used to discuss the problem domain, are
subject to all of the immaterial differences and the accidental
collisions of expression that act to compound the computational
confusion and distraction.

When the problem of finding a fitting metric develops the intensity
to cross a critical threshold, a strange situation is constellated.
The new level of problemhood is noticed as an afterthought but may
have a primeval reality about it in its own right, its true nature.
The new circle of problem states may circumscribe and underlie the
initial focus of attention.  Can the problem of finding a suitable
metric for the original problem space be tackled by the same means
of problem solving that worked on the assumption of a given metric?
A reduction of that sort is possible but is hardly ever guaranteed.
The problem of picking the best metric for the initial problem space
may be as difficult as the problem first encountered.  And ultimately
there is always the risk of reaching a level of circumspection where
the problem space of last resort has no metric at all to be defined.

Jon Awbrey

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http://www.cs.bsu.edu/homepages/mighty/history.html
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