A formal theory of the measurement system

Measurement aims at obtaining a numerical description of objects/events/persons in the real world by means of a measuring system. Measurement is widely used as a key way for obtaining high quality information from the real world, across disciplines. In the present day, there is growing consensus in holding that measurement is characterized by the use of something that qualifies as a “measuring system”. Therefore, we discuss sufficient conditions for an empirical system to qualify as a measuring system and we present a formal model of the measuring system, in terms of empirical relations among objects to be measured and the measuring device. The theory applies to all the main structures of metrological interest - order, difference, intensive and extensive, and we hope that this may help to fill a gap in these studies. We also briefly address practical applications of the theory, including calibration, modelling of measuring devices and performance statement.