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A Note on the Role of Precision in Definitions

The term "precision" seems to have changed its meaning over the centuries, which may cause confusion to anyone dealing with the literature of definitions.  It signifies more than one concept, which muddles things up.  Unfortunately, I may be adding to the muddle, as some of my points in this post are from memory, and I will have to rediscover the references for them.  However, I wanted to capture what I now have about precision. 

The etymology of "precision", according to Peirce, means "to cut off at the end" (from "Issues in Pragmatism", The Monist, Vol 15, Oct 1905 pp481-499).  Apparently, it is connected with "curt denials and refusals" - cutting someone off.  Oddly, this seems to have tradionally meant that the more cutting off you did, the greater precision you achieved.  As such, it runs counter to our idea of numerical precision, where the greater the number of decimal places, the greater the precision.  On the traditional view, the fewer the number of decimal places (the more chopping off we have done) would seen to mean the greater the precision (though I cannot find an example to confirm this numerical aspect of precision in traditional literature).

Peirce also had something to say about precision in definitions.  According to him, removal of superflous words achieves greater precision in a definition (again from my memory, so needs to be checked).  I think that this rule applies more to summary than to definition, and Peirce may have been thinking about definition work he was doing for dictionaries, where printing costs are a factor.  Too much text may be repetitous or confusing.  However, repetition may be valuable to drive a point home.  Confusion is not always produced by additional text, but can be a danger.

Perhaps a more important point involves using the word "prescind" (the act of precision) which today seems to be replaced by the overloaded term "abstraction".  When we prescind we cut away from concrete instances.  E.g. the concept "animal" can apply to individual instances, but "animality" cannot (from Sullivan, An Introduction to Traditional Logic ISBN 1-4196-1671-4, pp 23-24).  The greater the precision of a concept, the greater its "abstraction".  Traditionally, "concrete concepts" are abstractions "without precision" (since they apply to individuals), while "abstract concepts" are concepts "with precision" since they cannot apply to individuals (Sullivan, footnote on p24).  So, perhaps counter-intuitively, the more abstract a concept is, the more precise it is.

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