31
example, both that length is a quantity and that length of a rod is a quantity (of the
rod). Whenever avoiding this ambiguity is appropriate, we call an entity such as
length or reading comprehension ability a general property, and an entity such as
the length of a given rod or the reading comprehension of a given person an individual property (and this would hold more specifically for quantities).
15
The notation we adopt for general and individual properties is presented in
Table 2.3.
15 This is what a reference text (the so-called Red Book) of the International Union of Pure and
Applied Physics (IUPAP) says about the distinction between general and individual properties in
the specific case of physical quantities: “There are two somewhat different meanings of the term
physical quantity. One refers to the abstract metrological concept (e.g., length, mass, temperature),
the other to a specific example of that concept (an attribute of a specific object or system: diameter
of a steel cylinder, mass of the proton, critical temperature of water). Sometimes it is important to
distinguish between the two and, ideally, it might be useful to be able to do so in all instances”
(IUPAP, 2010: 1.1). Note that the terms “general property” and “individual property” are not standard, and usually the same term “property”, and thus more specifically “quantity”, is used to designate both general and individual properties. Other corresponding pairs of terms are “properties
in the general sense” and “particular properties”, as in the second edition of the VIM in reference
to quantities (BIPM et al., 1993: 1.1), but also, e.g., “property” and “property manifestation”
(Benoit & Foulloy, 2013; Pfanzagl, 1971), “attribute” and “level of attribute” (Michell, 2002),
“quality” and “state of a quality” (Piotrowski, 1992), and—only applicable to quantities—
“quantity” and “magnitude” (Hölder, 1901, as translated by Michell and Ernst, and then adopted,
among others, by Kyburg, 1997). Given that in some definitions of the VIM the term “magnitude”
appears (e.g., “quantity” is defined as “property of a phenomenon, body, or substance, where the
property has a magnitude that can be expressed as a number and a reference”, JCGM, 2012: 1.1),
a few more words may be useful to justify why we do not use the term “magnitude” here. We have
three basic reasons to justify this position. First, the term “magnitude” is used today with different
and incompatible meanings—by claiming for example that magnitudes are quantities or that quantities have magnitudes (and in this second case the reference could be either to general quantities
(mass has a magnitude) or to individual quantities (the mass of this object has a magnitude))—so
that adopting it would require a more or less arbitrary selection. And while the term “magnitude”
is used to translate the Greek μεγεθος, a lexical reference to this tradition is now outdated, given
the Aristotelian contraposition of “magnitude” and “plurality” (πληθος, also translated as “multitude”): “a quantum is a plurality if it is numerable, a magnitude if it is a measurable” (Aristotle’s
Metaphysics, Book 5, Part 13). Second, the pair of terms “quantity” and “magnitude” seems to be
so semantically superposed that in languages other than English they are not distinguished (so that,
for example, the official French text of the VIM definition of “quantity” mentioned above is “grandeur”, “propriété d’un phénomène, d’un corps ou d’une substance, que l’on peut exprimer quantitativement sous forme d’un nombre et d’une référence”: the concept “magnitude” just disappeared
…). The third reason is related to our interest in providing a general presentation of properties, of
which quantities are a specific case. While the term “magnitude” could be intended as synonymous
with “amount”, so that for example one could say that mass is a quantity because objects have mass
in amounts, nonquantitative properties do not have magnitudes (as in the VIM3 definition of
, JCGM, 2012: 1.30), with the consequence that one or more terms corresponding to what magnitudes are for quantities should be adopted for nonquantitative properties.
Indeed, sometimes for ordinal properties the term “level” is used to this goal. In summary, we
believe that the pair “general property” and “individual property” provides a lexically simple and
semantically encompassing terminology.
2.2 The abstract structure of measurement
example, both that length is a quantity and that length of a rod is a quantity (of the
rod). Whenever avoiding this ambiguity is appropriate, we call an entity such as
length or reading comprehension ability a general property, and an entity such as
the length of a given rod or the reading comprehension of a given person an individual property (and this would hold more specifically for quantities).
15
The notation we adopt for general and individual properties is presented in
Table 2.3.
15 This is what a reference text (the so-called Red Book) of the International Union of Pure and
Applied Physics (IUPAP) says about the distinction between general and individual properties in
the specific case of physical quantities: “There are two somewhat different meanings of the term
physical quantity. One refers to the abstract metrological concept (e.g., length, mass, temperature),
the other to a specific example of that concept (an attribute of a specific object or system: diameter
of a steel cylinder, mass of the proton, critical temperature of water). Sometimes it is important to
distinguish between the two and, ideally, it might be useful to be able to do so in all instances”
(IUPAP, 2010: 1.1). Note that the terms “general property” and “individual property” are not standard, and usually the same term “property”, and thus more specifically “quantity”, is used to designate both general and individual properties. Other corresponding pairs of terms are “properties
in the general sense” and “particular properties”, as in the second edition of the VIM in reference
to quantities (BIPM et al., 1993: 1.1), but also, e.g., “property” and “property manifestation”
(Benoit & Foulloy, 2013; Pfanzagl, 1971), “attribute” and “level of attribute” (Michell, 2002),
“quality” and “state of a quality” (Piotrowski, 1992), and—only applicable to quantities—
“quantity” and “magnitude” (Hölder, 1901, as translated by Michell and Ernst, and then adopted,
among others, by Kyburg, 1997). Given that in some definitions of the VIM the term “magnitude”
appears (e.g., “quantity” is defined as “property of a phenomenon, body, or substance, where the
property has a magnitude that can be expressed as a number and a reference”, JCGM, 2012: 1.1),
a few more words may be useful to justify why we do not use the term “magnitude” here. We have
three basic reasons to justify this position. First, the term “magnitude” is used today with different
and incompatible meanings—by claiming for example that magnitudes are quantities or that quantities have magnitudes (and in this second case the reference could be either to general quantities
(mass has a magnitude) or to individual quantities (the mass of this object has a magnitude))—so
that adopting it would require a more or less arbitrary selection. And while the term “magnitude”
is used to translate the Greek μεγεθος, a lexical reference to this tradition is now outdated, given
the Aristotelian contraposition of “magnitude” and “plurality” (πληθος, also translated as “multitude”): “a quantum is a plurality if it is numerable, a magnitude if it is a measurable” (Aristotle’s
Metaphysics, Book 5, Part 13). Second, the pair of terms “quantity” and “magnitude” seems to be
so semantically superposed that in languages other than English they are not distinguished (so that,
for example, the official French text of the VIM definition of “quantity” mentioned above is “grandeur”, “propriété d’un phénomène, d’un corps ou d’une substance, que l’on peut exprimer quantitativement sous forme d’un nombre et d’une référence”: the concept “magnitude” just disappeared
…). The third reason is related to our interest in providing a general presentation of properties, of
which quantities are a specific case. While the term “magnitude” could be intended as synonymous
with “amount”, so that for example one could say that mass is a quantity because objects have mass
in amounts, nonquantitative properties do not have magnitudes (as in the VIM3 definition of
Indeed, sometimes for ordinal properties the term “level” is used to this goal. In summary, we
believe that the pair “general property” and “individual property” provides a lexically simple and
semantically encompassing terminology.
2.2 The abstract structure of measurement