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iplicitly establishes
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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