75
reality can be direct, in the sense of being unmediated by models or unfiltered by
forms of conceptual and linguistic schemes; such a view is sometimes referred to as
naïve realism.
In the case of measurement, such a perspective is sometimes associated with the
perspective that each property of each object has, inherently, a value—sometimes
called “true value”—and that measurement would simply aim at discovering such a
value.
3
This implies that measurement is a sort of transmission or communication
process, which, in the ideal case, perfectly transfers an entity from the object under
measurement to the measuring instrument and thus makes it in some sense observable. Hence this “true value” is “the value that would be obtained by a perfect measurement” (Bell, 1999), with the consequence that, formally, “measurement […] in
a deterministic ideal case results in an identity function” (Rossi, 2006: p. 40). This
fits well with an abstract understanding of the entities that constitute the domain of
the measurement processes, conceived in analogy with lengths of line segments in
an abstract mathematical space and therefore in continuity with the Euclidean
standpoint.
Such a view is sometimes traced back to Greek antiquity. Indeed, as described by
Aristotle in his Metaphysics (Book I, Part 5, 350 BC),
the so-called Pythagoreans […] who […] were the first to take up mathematics, not only
advanced this study, but also having been brought up in it they thought its principles were
the principles of all things. Since of these principles numbers are by nature the first […] all
other things seemed in their whole nature to be modeled on numbers, and numbers seemed
to be the first things in the whole of nature, [and] they supposed the elements of numbers to
be the elements of all things, and the whole heaven to be a musical scale and a number.
The formulation of this position later given in Galileo’s Assayer is well known (II
Saggiatore, 1632):
Philosophy [i.e. physics] is written in this grand book – I mean the Universe – which stands
continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the
language of mathematics […] without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.
According to this view, objects have an intrinsic mathematical structure, independent of human perception or cognition; once a reference for comparison has been
chosen, this position assumes then that measurement is a process aimed at discovering the values that properties of objects already and inherently have.
4
3 Under a Pythagorean conception that “numbers are in the world”, another position would be that
each property (or at least each quantitative property; see, e.g., Michell, 1999) of each object already
is a value prior to measurement.
4 If a property is specifically a quantity—which, again, is taken by this view (and consistently with
the Aristotelian tradition) to be an empirical feature of the property itself, independently of the way
in which it is modeled—the aforementioned reference for comparison would be a measurement
unit, and the aforementioned process of discovery of values specializes as a discovery of ratios of
quantities (see, e.g., Michell, 2004).
4.2 Characterizing measurement
reality can be direct, in the sense of being unmediated by models or unfiltered by
forms of conceptual and linguistic schemes; such a view is sometimes referred to as
naïve realism.
In the case of measurement, such a perspective is sometimes associated with the
perspective that each property of each object has, inherently, a value—sometimes
called “true value”—and that measurement would simply aim at discovering such a
value.
3
This implies that measurement is a sort of transmission or communication
process, which, in the ideal case, perfectly transfers an entity from the object under
measurement to the measuring instrument and thus makes it in some sense observable. Hence this “true value” is “the value that would be obtained by a perfect measurement” (Bell, 1999), with the consequence that, formally, “measurement […] in
a deterministic ideal case results in an identity function” (Rossi, 2006: p. 40). This
fits well with an abstract understanding of the entities that constitute the domain of
the measurement processes, conceived in analogy with lengths of line segments in
an abstract mathematical space and therefore in continuity with the Euclidean
standpoint.
Such a view is sometimes traced back to Greek antiquity. Indeed, as described by
Aristotle in his Metaphysics (Book I, Part 5, 350 BC),
the so-called Pythagoreans […] who […] were the first to take up mathematics, not only
advanced this study, but also having been brought up in it they thought its principles were
the principles of all things. Since of these principles numbers are by nature the first […] all
other things seemed in their whole nature to be modeled on numbers, and numbers seemed
to be the first things in the whole of nature, [and] they supposed the elements of numbers to
be the elements of all things, and the whole heaven to be a musical scale and a number.
The formulation of this position later given in Galileo’s Assayer is well known (II
Saggiatore, 1632):
Philosophy [i.e. physics] is written in this grand book – I mean the Universe – which stands
continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the
language of mathematics […] without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.
According to this view, objects have an intrinsic mathematical structure, independent of human perception or cognition; once a reference for comparison has been
chosen, this position assumes then that measurement is a process aimed at discovering the values that properties of objects already and inherently have.
4
3 Under a Pythagorean conception that “numbers are in the world”, another position would be that
each property (or at least each quantitative property; see, e.g., Michell, 1999) of each object already
is a value prior to measurement.
4 If a property is specifically a quantity—which, again, is taken by this view (and consistently with
the Aristotelian tradition) to be an empirical feature of the property itself, independently of the way
in which it is modeled—the aforementioned reference for comparison would be a measurement
unit, and the aforementioned process of discovery of values specializes as a discovery of ratios of
quantities (see, e.g., Michell, 2004).
4.2 Characterizing measurement