171
quantities, then), and nominal properties are properties that have no magnitude.
This concept system is depicted in Fig. 6.8.
The VIM does not define what a magnitude is, but a plausible hypothesis is that
“magnitude” can be generically interpreted there as “amount” or “size”, so that for
example the height of human beings is a quantity because it is a property that we
have in amounts. This stands in contrast with properties such as blood type, which
is only classificatory. Accordingly, the phrase “the magnitude of the height of a
given human being” refers to “the amount of height” of that human being: it is then,
plausibly, an individual length (for a more detailed analysis of the elusive concept
, see Giordani & Mari, 2012).
The simplicity of the VIM’s account is attractive, but the distinction between
quantitative and nonquantitative properties deserves some more analysis here, also
due to its traditional connection with the discussion about the conditions of measurability, as mentioned in Sect. 3.4.2.
30
As discussed in Chap. 4, several interpretations of measurement have been proposed, but a long tradition rooted on Euclid has connected the measurability of a
property with its being quantitative. The VIM keeps with this tradition in stating that
“measurement does not apply to nominal properties” (JCGM, 2012: 2.1 Note 1). As
also discussed in Sect. 1.1.1 and at more length in Sect. 4.2.3, tensions related to this
issue helped motivate the formation of a committee of physicists and psychologists
appointed by the British Association for the Advancement of Science and charged
with evaluating the possibility of providing quantitative estimates of sensory events
(see the discussion in Rossi, 2007; a more detailed analysis is in Michell, 1999: ch.
6). We might envision two distinct but complementary paths towards resolution of
these tensions:
• One is about the possibility of providing meaningful quantitative information for
properties which are not directly or indirectly evaluated (or evaluable) by means
of additive operations.
31
• The other is about the appropriateness of broadening the scope of measurement
so as to include the evaluation of nonquantitative properties.
From the beginning, both of these paths have been biased by the prestige of measurement, as witnessed by the key role attributed by some to Otto Hölder’s (1901)
paper, a mathematical work whose title has been translated in English as “The axioms of Quantity and the Theory of Measurement”, and about which Michell asserted
30 This subject has been widely debated at least since the seminal analysis by von Helmholtz
(1887), who opened his paper by claiming that “counting and measuring are the bases of the most
fruitful, most certain, and most exact of all known scientific methods”. Such prestige and epistemic
authority makes measurement a yearned-for target. From another perspective, “Measurement is
such an elegant concept that even with [properties] apparently lacking multiples, if the [property]
is capable of increase or decrease (like temperature is, for example), the temptation to think of it as
quantitative is strong” (Michell, 2005: p. 289). See Chap. 7 for more on this.
31 We already followed this path in the discussion about values of temperature and of reading comprehension ability in Sects. 6.3.6 and 6.3.7.
6.5 Generalizing the framework to nonquantitative properties
quantities, then), and nominal properties are properties that have no magnitude.
This concept system is depicted in Fig. 6.8.
The VIM does not define what a magnitude is, but a plausible hypothesis is that
“magnitude” can be generically interpreted there as “amount” or “size”, so that for
example the height of human beings is a quantity because it is a property that we
have in amounts. This stands in contrast with properties such as blood type, which
is only classificatory. Accordingly, the phrase “the magnitude of the height of a
given human being” refers to “the amount of height” of that human being: it is then,
plausibly, an individual length (for a more detailed analysis of the elusive concept
The simplicity of the VIM’s account is attractive, but the distinction between
quantitative and nonquantitative properties deserves some more analysis here, also
due to its traditional connection with the discussion about the conditions of measurability, as mentioned in Sect. 3.4.2.
30
As discussed in Chap. 4, several interpretations of measurement have been proposed, but a long tradition rooted on Euclid has connected the measurability of a
property with its being quantitative. The VIM keeps with this tradition in stating that
“measurement does not apply to nominal properties” (JCGM, 2012: 2.1 Note 1). As
also discussed in Sect. 1.1.1 and at more length in Sect. 4.2.3, tensions related to this
issue helped motivate the formation of a committee of physicists and psychologists
appointed by the British Association for the Advancement of Science and charged
with evaluating the possibility of providing quantitative estimates of sensory events
(see the discussion in Rossi, 2007; a more detailed analysis is in Michell, 1999: ch.
6). We might envision two distinct but complementary paths towards resolution of
these tensions:
• One is about the possibility of providing meaningful quantitative information for
properties which are not directly or indirectly evaluated (or evaluable) by means
of additive operations.
31
• The other is about the appropriateness of broadening the scope of measurement
so as to include the evaluation of nonquantitative properties.
From the beginning, both of these paths have been biased by the prestige of measurement, as witnessed by the key role attributed by some to Otto Hölder’s (1901)
paper, a mathematical work whose title has been translated in English as “The axioms of Quantity and the Theory of Measurement”, and about which Michell asserted
30 This subject has been widely debated at least since the seminal analysis by von Helmholtz
(1887), who opened his paper by claiming that “counting and measuring are the bases of the most
fruitful, most certain, and most exact of all known scientific methods”. Such prestige and epistemic
authority makes measurement a yearned-for target. From another perspective, “Measurement is
such an elegant concept that even with [properties] apparently lacking multiples, if the [property]
is capable of increase or decrease (like temperature is, for example), the temptation to think of it as
quantitative is strong” (Michell, 2005: p. 289). See Chap. 7 for more on this.
31 We already followed this path in the discussion about values of temperature and of reading comprehension ability in Sects. 6.3.6 and 6.3.7.
6.5 Generalizing the framework to nonquantitative properties