In order for an “ideal” to make relevance, it is not mandatory, certainly, to be able to reach it. It is enough that it is possible to approach it, and even only to a certain extent. To be able to approach the ideal arbitrarily closely is not needed, even “theoretically.” To make sense of the “improvement” we can get in approaching an ideal, the measure of how close the ideal needs to be must be determined. In the thermometer's case, the measure was determined by the bias in the error distribution at different points on the scale. An essentially internal measure was given, a measure related closely to the pertinent kind of measurement.
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