78
have a (true) position, and therefore the idea that an observed position can be at least
conceptually decomposed into a true position and error seemed straightforward:
6
observation truth error
However, this reference to truth became murkier as the theory of errors was imported
into the human sciences, in particular demography, psychology, and economics. As
discussed by, for example, Stigler (1999) and Ian Hacking (1990), when in the
1830s the Belgian astronomer Adolphe Quetelet applied the theory of errors to measurements of the chest sizes of a sample of 5000 Scottish soldiers, he referred to the
average (39.75″) as an estimate of the “true” girth of a Scottish soldier’s chest, a sort
of Platonic ideal, and at times even appeared to have ascribed to it a moral mandate.
Shortly thereafter, Francis Galton (1869) found that the theory of errors could just
as easily be applied to test scores as to chest sizes, now adding the idea that the average of a collection of observations (e.g., test scores, or individual item responses)
about an individual person could be used to estimate something “true” of that person, an idea that was central to his studies of the inheritance of intelligence. But
other scholars, like the philosopher and economist Francis Ysidro Edgeworth
(1885), were less immediately convinced that such averages could be considered an
estimate of something “true”: as he put it,
measurements by the reduction of which we ascertain a real time, number, [and] distance
[are] cause[s], as [they] were the source from which diverging errors emanate. […] Returns
of prices, exports and imports, legitimate and illegitimate marriages or births and so forth,
the averages of which constitute the premises of practical reasoning, are […] descriptions.
[…] In short [the former] are different copies of one original; [the latter] are different originals affording one ‘generic portrait’.
Indeed, as already discussed in Sect. 3.2.2, the concept of true value can be well
defined mathematically; it is just a fact that, under well-defined conditions, sample
means converge to the expected value of the underlying probability distribution.
What is critical is the empirical interpretation of this convergence process and its
limit point. A strongly realist perspective might suppose that the limit point reflects
some kind of lawful feature of the world, and that, under the hypothesis of repeatability and the absence of biasing factors, the sampling process is required only to
reveal it beyond experimental errors. But while such a perspective might have
seemed relatively straightforward in the case of averaging estimates of the locations
of planets, it is considerably less obvious what “feature of the world” is estimated
by the average of a set of scores on test items, or in Edgeworth’s other examples
from the human sciences and social demography. As the theory of errors was
6 Of course, the problem remains whether the number in the value of position is a real number with
infinitely many significant digits, as a geometric model might imply. Were such a hypothesis to be
maintained, and given that planets are not geometric points, the measurand should be changed to,
e.g., the position of the center of mass of the planet. This would create the new problem that, for
the center of mass of a body to be uniquely defined, what is part of the body itself needs to be
uniquely established, a condition that is hardly fulfilled by planets. Hence the unavoidability of a
non-null definitional uncertainty—as introduced in Sect. 3.2.4—soon emerges also in these cases.
4 Philosophical perspectives on measurement
have a (true) position, and therefore the idea that an observed position can be at least
conceptually decomposed into a true position and error seemed straightforward:
6
observation truth error
However, this reference to truth became murkier as the theory of errors was imported
into the human sciences, in particular demography, psychology, and economics. As
discussed by, for example, Stigler (1999) and Ian Hacking (1990), when in the
1830s the Belgian astronomer Adolphe Quetelet applied the theory of errors to measurements of the chest sizes of a sample of 5000 Scottish soldiers, he referred to the
average (39.75″) as an estimate of the “true” girth of a Scottish soldier’s chest, a sort
of Platonic ideal, and at times even appeared to have ascribed to it a moral mandate.
Shortly thereafter, Francis Galton (1869) found that the theory of errors could just
as easily be applied to test scores as to chest sizes, now adding the idea that the average of a collection of observations (e.g., test scores, or individual item responses)
about an individual person could be used to estimate something “true” of that person, an idea that was central to his studies of the inheritance of intelligence. But
other scholars, like the philosopher and economist Francis Ysidro Edgeworth
(1885), were less immediately convinced that such averages could be considered an
estimate of something “true”: as he put it,
measurements by the reduction of which we ascertain a real time, number, [and] distance
[are] cause[s], as [they] were the source from which diverging errors emanate. […] Returns
of prices, exports and imports, legitimate and illegitimate marriages or births and so forth,
the averages of which constitute the premises of practical reasoning, are […] descriptions.
[…] In short [the former] are different copies of one original; [the latter] are different originals affording one ‘generic portrait’.
Indeed, as already discussed in Sect. 3.2.2, the concept of true value can be well
defined mathematically; it is just a fact that, under well-defined conditions, sample
means converge to the expected value of the underlying probability distribution.
What is critical is the empirical interpretation of this convergence process and its
limit point. A strongly realist perspective might suppose that the limit point reflects
some kind of lawful feature of the world, and that, under the hypothesis of repeatability and the absence of biasing factors, the sampling process is required only to
reveal it beyond experimental errors. But while such a perspective might have
seemed relatively straightforward in the case of averaging estimates of the locations
of planets, it is considerably less obvious what “feature of the world” is estimated
by the average of a set of scores on test items, or in Edgeworth’s other examples
from the human sciences and social demography. As the theory of errors was
6 Of course, the problem remains whether the number in the value of position is a real number with
infinitely many significant digits, as a geometric model might imply. Were such a hypothesis to be
maintained, and given that planets are not geometric points, the measurand should be changed to,
e.g., the position of the center of mass of the planet. This would create the new problem that, for
the center of mass of a body to be uniquely defined, what is part of the body itself needs to be
uniquely established, a condition that is hardly fulfilled by planets. Hence the unavoidability of a
non-null definitional uncertainty—as introduced in Sect. 3.2.4—soon emerges also in these cases.
4 Philosophical perspectives on measurement