169
• As a result of the evaluation, a number x is found such that the hypothesis is supported that the individual quantity q and the individual quantity q x , that were
known according to different criteria, are in fact one and the same, i.e., Q[a] and
x q ref are identifiers of the same individual quantity.
As a consequence, Basic Evaluation Equations are ontologically irrelevant: if they
are true, they simply instantiate the tautology that an individual quantity is equal to
itself.
28
But, of course, their widespread use is justified by their epistemic significance: if they are true, they inform us that two individual quantities that were known
according to different criteria are in fact one and the same.
This gives us the tool to interpret a common way of presenting measurement:
“the input to the measurement system is the true value of the variable [and] the system output is the measured value of the variable [, so that] in an ideal measurement
system, the measured value would be equal to the true value” (Bentley, 2005: p. 3),
with the consequence that “in a deterministic ideal case [it] results in an identity
function” (Rossi, 2006: p. 40). Let us concede that in the deterministic ideal case the
Basic Evaluation Equation is not just an indistinguishability but an equality, Q[a] = x
q ref . Nevertheless, the position exemplified in these quotes confuses the ontological
and epistemic layers: for those who already know that Q[a] and x q ref are the same
quantity, the relation is an ontological identity, as is the Evening Star = the Morning
Star for current astronomers (see Sect. 5.3.2). And in fact those who already know
that Q[a] and x q ref are the same quantity would have no reasons for measuring Q[a].
But measurement is aimed at acquiring information on a measurand, not at identically transferring values of quantities through measuring chains as is the implicit
supposition behind the quotations above.
Indeed, the idea of deterministic ideal measurement as an identity function
becomes understandable if it is applied not to measurement, but to transmission
systems, as mentioned in Sect. 4.2.1. It is correct indeed to model a transmission
system in such a way that the input to the transmission system is the value of the
variable and the system output is the transmitted value of the variable, so that “in an
ideal transmission system, the transmitted value would be equal to the input value”
(by paraphrasing Rossi’s quote above). If in fact values were empirical features of
phenomena, measuring instruments could be interpreted as special transmission
channels, aimed at transferring values in such a way that the transmission is performed without errors and therefore as an identity function. But a basic difference
between transmission and measurement is manifest: the input to a transmission system is a value, explicitly provided by an agent who or which operates on purpose by
encoding the value into the quantity of an object and sending the quantity through a
channel, the purpose of which is to faithfully transfer this input. In this case, the
28 This contrasts with any position which attributes a special ontic role to values. For example,
Hasok Chang, as an illustration of “ontological principles … that are regarded as essential features
of reality in the relevant epistemic community” and in defense of what he calls “the pursuit of
ontological plausibility”, mentions the “Principle of single value (or, single-valuedness): a real
physical property can have no more than one definite value in a given situation” (Chang, 2001:
p. 11, also presented in Chang, 2004: p. 90).
6.4 The epistemic role of Basic Evaluation Equations
• As a result of the evaluation, a number x is found such that the hypothesis is supported that the individual quantity q and the individual quantity q x , that were
known according to different criteria, are in fact one and the same, i.e., Q[a] and
x q ref are identifiers of the same individual quantity.
As a consequence, Basic Evaluation Equations are ontologically irrelevant: if they
are true, they simply instantiate the tautology that an individual quantity is equal to
itself.
28
But, of course, their widespread use is justified by their epistemic significance: if they are true, they inform us that two individual quantities that were known
according to different criteria are in fact one and the same.
This gives us the tool to interpret a common way of presenting measurement:
“the input to the measurement system is the true value of the variable [and] the system output is the measured value of the variable [, so that] in an ideal measurement
system, the measured value would be equal to the true value” (Bentley, 2005: p. 3),
with the consequence that “in a deterministic ideal case [it] results in an identity
function” (Rossi, 2006: p. 40). Let us concede that in the deterministic ideal case the
Basic Evaluation Equation is not just an indistinguishability but an equality, Q[a] = x
q ref . Nevertheless, the position exemplified in these quotes confuses the ontological
and epistemic layers: for those who already know that Q[a] and x q ref are the same
quantity, the relation is an ontological identity, as is the Evening Star = the Morning
Star for current astronomers (see Sect. 5.3.2). And in fact those who already know
that Q[a] and x q ref are the same quantity would have no reasons for measuring Q[a].
But measurement is aimed at acquiring information on a measurand, not at identically transferring values of quantities through measuring chains as is the implicit
supposition behind the quotations above.
Indeed, the idea of deterministic ideal measurement as an identity function
becomes understandable if it is applied not to measurement, but to transmission
systems, as mentioned in Sect. 4.2.1. It is correct indeed to model a transmission
system in such a way that the input to the transmission system is the value of the
variable and the system output is the transmitted value of the variable, so that “in an
ideal transmission system, the transmitted value would be equal to the input value”
(by paraphrasing Rossi’s quote above). If in fact values were empirical features of
phenomena, measuring instruments could be interpreted as special transmission
channels, aimed at transferring values in such a way that the transmission is performed without errors and therefore as an identity function. But a basic difference
between transmission and measurement is manifest: the input to a transmission system is a value, explicitly provided by an agent who or which operates on purpose by
encoding the value into the quantity of an object and sending the quantity through a
channel, the purpose of which is to faithfully transfer this input. In this case, the
28 This contrasts with any position which attributes a special ontic role to values. For example,
Hasok Chang, as an illustration of “ontological principles … that are regarded as essential features
of reality in the relevant epistemic community” and in defense of what he calls “the pursuit of
ontological plausibility”, mentions the “Principle of single value (or, single-valuedness): a real
physical property can have no more than one definite value in a given situation” (Chang, 2001:
p. 11, also presented in Chang, 2004: p. 90).
6.4 The epistemic role of Basic Evaluation Equations