115
lows applies to all properties, we often refer more specifically to quantities, due to
their widespread use in the tradition of measurement science and their richer algebraic structure, which makes examples easier to present and understand (Box 5.1).
completely clear, as it does not maintain the distinction between general quantities and individual
quantities. By writing the left-hand-side entity as Q[a] we make explicit the reference to the quantity Q of the object a. This also highlights that, while the unit is a feature of the general quantity Q,
and therefore writing it as [Q] is correct (recalling that brackets in “Q[a]” and “[Q]” have different
meanings: “Q[a]” stands for the Q of a, e.g., the length of a given rod; “[Q]” stands for the unit of
Q), the numerical value depends on both the quantity of the object and the chosen unit. A more
complete form of the expression is then {Q[a]} [Q] , to be read “the numerical value of Q[a] in the
unit [Q]” (see also ISO, 2009b: 6.1).
Box 5.1: A very short introduction to ontology
Given our statement that this chapter is mainly devoted to exploring a measurement-oriented ontology of properties, a few preliminary words might be
useful about what we consider to be an ontology. As Willard V.O. Quine
wrote, “A curious thing about the ontological problem is its simplicity. It can
be put in three Anglo-Saxon monosyllables: ‘What is there?’ It can be
answered, moreover, in a word – ‘Everything’ – and everyone will accept this
answer as true. However, this is merely to say that there is what there is. There
remains room for disagreement over cases; and so the issue has stayed alive
down the centuries” (1948: p. 21).
Cases about which there can be or has been disagreement include the
sphere of fixed stars, phlogiston, and continuous flows of electricity, not to
mention nearly every proposed property in the human sciences, perhaps most
famously general intelligence: it was not at all trivial to arrive at the conclusion that, for example, phlogiston does not exist, and in fact required a radical
revision of several related bodies of knowledge. But of course even today we
can talk in a meaningful way about the sphere of fixed stars, phlogiston, and
continuous flows of electricity; otherwise a sentence such as “all visible stars
are fixed to a celestial sphere” would be meaningless rather than false (on par
with a phrase like “all qwerty uiop are fixed to a celestial sphere”).
Hence the fact that x appears in meaningful sentences is not sufficient to
conclude that x exists. It should be acknowledged that there are indeed different modes of existence: for example, both paper books and prime numbers
greater than 1 million exist, but their modes of existence differ. The “disagreement over cases” to which Quine refers is related to the existence in a given
mode, not to the generic situation of any possible mode of existence. As
another well-known example, unicorns do not exist as physical entities, but do
exist as literary entities. Thus, our ability to talk in a grammatically correct
5.1 Introduction
lows applies to all properties, we often refer more specifically to quantities, due to
their widespread use in the tradition of measurement science and their richer algebraic structure, which makes examples easier to present and understand (Box 5.1).
completely clear, as it does not maintain the distinction between general quantities and individual
quantities. By writing the left-hand-side entity as Q[a] we make explicit the reference to the quantity Q of the object a. This also highlights that, while the unit is a feature of the general quantity Q,
and therefore writing it as [Q] is correct (recalling that brackets in “Q[a]” and “[Q]” have different
meanings: “Q[a]” stands for the Q of a, e.g., the length of a given rod; “[Q]” stands for the unit of
Q), the numerical value depends on both the quantity of the object and the chosen unit. A more
complete form of the expression is then {Q[a]} [Q] , to be read “the numerical value of Q[a] in the
unit [Q]” (see also ISO, 2009b: 6.1).
Box 5.1: A very short introduction to ontology
Given our statement that this chapter is mainly devoted to exploring a measurement-oriented ontology of properties, a few preliminary words might be
useful about what we consider to be an ontology. As Willard V.O. Quine
wrote, “A curious thing about the ontological problem is its simplicity. It can
be put in three Anglo-Saxon monosyllables: ‘What is there?’ It can be
answered, moreover, in a word – ‘Everything’ – and everyone will accept this
answer as true. However, this is merely to say that there is what there is. There
remains room for disagreement over cases; and so the issue has stayed alive
down the centuries” (1948: p. 21).
Cases about which there can be or has been disagreement include the
sphere of fixed stars, phlogiston, and continuous flows of electricity, not to
mention nearly every proposed property in the human sciences, perhaps most
famously general intelligence: it was not at all trivial to arrive at the conclusion that, for example, phlogiston does not exist, and in fact required a radical
revision of several related bodies of knowledge. But of course even today we
can talk in a meaningful way about the sphere of fixed stars, phlogiston, and
continuous flows of electricity; otherwise a sentence such as “all visible stars
are fixed to a celestial sphere” would be meaningless rather than false (on par
with a phrase like “all qwerty uiop are fixed to a celestial sphere”).
Hence the fact that x appears in meaningful sentences is not sufficient to
conclude that x exists. It should be acknowledged that there are indeed different modes of existence: for example, both paper books and prime numbers
greater than 1 million exist, but their modes of existence differ. The “disagreement over cases” to which Quine refers is related to the existence in a given
mode, not to the generic situation of any possible mode of existence. As
another well-known example, unicorns do not exist as physical entities, but do
exist as literary entities. Thus, our ability to talk in a grammatically correct
5.1 Introduction