>An observation and some thoughts emerging from it:
>
>Note how much discussion was generated by a
>simple unintentional error in coding/terminology
>- an instance of differences in what was meant
>and perceived by a proposition - in this case a
>type of instance not included in our recent
>previous discussion (simple unintentional error
>in expression). Had the proposer fully reviewed
>and revised the proposition, it would have
>sailed smoothly through the discussion (compared
>to the actual result).
>
>Note - I mean to cast no aspersions - I make
>plenty of such mistakes and am the first to hope
>for them to be excused or treated with no
>negative judgment, and furthermore for them to
>be corrected by myself or others before any
>negative effects occur due to them. My purpose
>here is to point out another kind of example
>that systems must take into account when dealing
>with categorizing or handling propositions -
>their meaning may vary or be uncertain for many
>reasons, including simple error in composition,
>as well as differences in perspectives,
>perceptions, experience, etc.
>
>In fact, one of the characteristics that could
>be considered to be in a well-functioning system
>is that it can accommodate and correct
>such errors through its functional processes,
>without causing "collateral damage" to the
>fallible human person involved and that person's
>ability to contribute constructively to the
>functioning of the system, and without
>negatively affecting other aspects of the
>functioning of the system -- as, I might point
>out, appears to have eventually happened here,
>as far as I can tell, to this discussion's
>credit.
>
>The stakes in such functionality depend on the
>functional purpose of the system - for example
>if it's a medical system in which lives or
>health are at stake, the importance of such
>robustness with respect to errors is obvious. In
>other kinds of systems, the nature and
>importance of how they deal with error may not
>be so obvious. In complex systems, small
>variations can have surprisingly great and
>hard-to-predict effects (sometimes represented
>by the "butterfly effect," in which a
>butterfly's wing-flapping theoretically could
>result in a hurricane elsewhere in the world).
>Stories abound about how small, understandable
>human errors have had disastrous results in
>systems that were not robust enough to
>accommodate and correct them or correct for
>their effects (including in high-stakes systems). (01)
All very true. And in fact the *reason* for this
small slip is revealing. The context, you will
recall, was a paper I wrote in which I showed
formally that a certain set of axioms were enough
to establish a result of some utility in 'context
reasoning'. Leaving aside details, the basic
mathematical structure being described there was
a partial ordering. Now, there are two 'styles'
one can adopt when describing such orderings
formally, which I can illustrate using the
integers and the less-than ordering. One can take
as basic the relation of being strictly
less-than; or, one can take as basic the relation
of less-than-or-equal. There is no absolute fact
of the matter about which is best: they both have
pros and cons, and the relations are of course
interdefinable. But the ordering axioms look
different depending on which one chooses, so it
is best to make a definite choice. (02)
If one chooses strict less-than, the axioms look like this: (03)
not x<x < is irreflexive
if x<y then not y<x < is asymmetric
if x<y and y<z then x<z < is transitive (04)
and if the latter, they look like this (05)
x<= x <= is reflexive
if x<=y and y<=x then x=y <= is antisymmetric
if x<=y and y<=z then x<=z <= is transitive (06)
I chose the latter, but thought of the former
terminology. So the moral is, when there are two
models which are very similar but need to be kept
distinct, always take extra care to not get them
muddled. My problem, of course, is mild dyslexia
(its wonderful how giving incompetence a
medical-sounding name makes it somehow
forgivable, has anyone else noticed this?) (07)
Pat
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