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the objectivity of this standpoint upon such an 
embarrassing layer of idealism. 
In other terms, this standpoint does not recognize, or 
minimize, the role of language, assumed as a plain means 
to express the empirically acquired knowledge. Mother 
Nature speaks mathematics, that is therefore the elective 
language for anyone interested in understanding her. The 
only problem would be that she is somehow shy and 
diffident. But measurement experts are skilled in let her 
speak! 
4.... AND LANGUAGE 
It is a well-known fact that physics is, or at least has been, 
considered the methodological paradigm of any science. 
An essential part of this assumption derives from its ability 
to express the available information in quantitative form. 
In the first decades of the XIX century numbers kept to 
pervade any science (for example, in 1832 C.Babbage 
suggested to list “the constants of nature and arts” in a 
book aimed at «gathering all the facts that can be 
expressed by numbers in the sciences and the arts». His 
list included nineteen “kinds of constants”, ranging from 
the constants of the solar system and the atomic weights 
to number of the books in the libraries and of the students 
in the universities. In commenting the contents of this list, 
I.Hacking has noted that «the most universal among the 
constants of the XX century, the speed of light, was 
included in the same section with the speed of several 
species of birds» (Hacking, 1990)). 
Surely numbers can be obtained by means of subjective 
criteria, by “estimation”, “guess”, “experience”, ... But 
when their objectivity is a goal, physicists had taught: 
apply measurement! It is no amazing that, since then, also 
“behavioral and social” scientists tried to measure and, as 
a consequence, started to call “measurement results” their 
numbers. But what marks the distinction between, for 
example, “estimation” and “measurement”? Surely the 
reason cannot be so extrinsic as the fact that numbers are 
used to represent the available information. 
It is plausible that physicists would have been answering: 
the adoption, within the measuring system, of sensors 
whose functionality is independent of the human operator. 
On the other hand, with this kind of answer, only very 
specific quantities would be “measurable” in the context of 
behavioral and social sciences. 
From the tentative of finding a sound position for this 
issue the so-called “measurement theory” arose. Such a 
theory, usually designated as “representational approach" 
(Krantz et al., 1971), has been explicitly the outcome of 
the work of behavioral and social scientists (Roberts, 
1979). Physicists and engineers simply did not need a 
theory for that operation that the neo-positivistic 
philosophy was identifying as the “protocol of truth”, i.e. 
able to produce true results “by definition” (and 
accordingly physical measurement has originated 
foundational issues only in quantum theories, in which 
such a truth is challenged by the Heisenberg principle). 
The best, and most extreme, synthesis of the 
representational approach comes perhaps from one of its 
original proposers (who also introduced the formal 
concept of scale type), S.Stevens: «measurement is the 
assignment of numbers to objects or events according to 
rule, any rule» (Stevens, 1959). 
An example, taken in its essence from (Roberts, 1979). A 
human subject prefers Mozart to Bach, and Mahler to 
Mozart. If he assigns the labels 3, 2, and 1 to Mahler, 
Mozart, and Bach respectively, then this assignment is a 
measurement, since it has been performed according to 
the rule of ordering preservation, a condition that is 
formally characterized in terms of homomorphisms. On 
the other hand, it is manifest that the empirical component 
of such a condition is immaterial: it defines a guideline to 
produce linguistic evaluations that are consistent with an 
information body that in principle could be wholly 
subjective. 
Would the Lord Kelvin famous assertion, «when you can 
measure what you are speaking about, and express it in 
numbers, you know something about it; otherwise your 
knowledge is of a meager and unsatisfactory kind», be 
relevant even in such cases? 
5. A PROBLEM IN EPISTEMOLOGICAL 
FOUNDATIONS OF MEASUREMENT 
Formal theories are particularly attractive. Lacking an 
alternative theory of measurement, also physicists kept to 
support the representational approach. The price that has 
been paid is that they are now supporting a theory that 
substantially neglects the role of the measuring systems 
and the related issues of calibration, standard reference 
identification, traceability. Therefore this support remains 
extrinsic, often for presentational and didactic purposes 
only. 
As an indicator of this situation, one of the main issues in 
measurement (according to the “physical viewpoint”, of 
course ...) such as uncertainty is only marginally 
considered in representational texts, and inversely the 
literature about uncertainty rarely deals it in 
representational terms (for example the ISO Guide to the 
expression of uncertainty in measurement (ISO, 1993b) 
completely ignores it). 
The situation is somehow schizophrenic. While everyone 
recognizes to measurement the role of bridge between 
the empirical and the linguistic worlds, natural scientists 
and engineers are focused almost exclusively on the 
empirical component, and behavioral and social scientists 
almost exclusively on the linguistic component. 
Does this mean that in reality two (or more ...) distinct 
concepts of measurement exist? In either case, I see this 
as the most fundamental issue which theoretical 
metrology is now facing. If a suggestion can be made 
here, I believe that a synthesis will be found at the 
semiotic level, in the comprehensive context of 
information sciences. Signals in this sense come from the 
wide attention currently paid to topics such as the 
semantic information conveyed by the measurement and 
the so-called intelligent measuring systems (the author is 
presented in Mari, 1999). 
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