94
Q2. Are informational, and more specifically mathematical, constraints on the measured entities relevant for the definition of measurement, i.e., should the definition of measurement include reference to any mathematical conditions?
An affirmative response to this question means that only if the measurement process
is applied to entities fulfilling some set of mathematical conditions
20
is an evaluation to be considered a measurement; a negative response means that mathematical constraints are immaterial for characterizing measurement.
Given our preliminary condition that measurement is a property evaluation (see the
related discussion in Chap. 2),
• Q1 prompts an investigation into the conditions sufficient to identify measurement directly through the structure of the process: If it is not the case that every
evaluation is a measurement, how is measurement specified?
• Q2 prompts an investigation into the conditions sufficient to identify measurement indirectly through the structure of (i) measurable properties or (ii) measured values: If it is not the case that every property is measurable, how can we
specify which properties are measurable?
These questions do not in principle relate to the physical or nonphysical nature of
the property to be measured. Of course, further dimensions might be added to make
the framework more specific, but any standpoint on measurement has to account for
its position with respect to Q1 and Q2, which in principle may be treated as distinct
and independent criteria. Given that for simplicity Q1 and Q2 are phrased as yes–no
questions (thus bracketing out the possibility of intermediate positions) four general
positions can be identified, depending on whether one considers the conditions relevant for the definition of to be:
α: mathematical but not empirical, or
β: both empirical and mathematical, or
γ: neither empirical nor mathematical, or
δ: empirical but not mathematical.
As depicted in Fig. 4.2, this option space is a partially ordered set, where γ is the
least constraining position and β is the most demanding one. The perspectives on
measurement considered in previous sections of this chapter may be (partially)
understood by examining how they would address Q1 and Q2: let us explore this
option space.
4.4.1 Exploring perspectives on measurement
Euclid’s Elements (Euclid, 2008) set the stage by taking geometry to be the paradigm of measurement: “a magnitude is a part of a(nother) magnitude, the less of the
greater, when it measures the greater; the greater is a multiple of the less when it is
20 For example, a traditional condition might be the invariance of ratios of properties.
4 Philosophical perspectives on measurement
Q2. Are informational, and more specifically mathematical, constraints on the measured entities relevant for the definition of measurement, i.e., should the definition of measurement include reference to any mathematical conditions?
An affirmative response to this question means that only if the measurement process
is applied to entities fulfilling some set of mathematical conditions
20
is an evaluation to be considered a measurement; a negative response means that mathematical constraints are immaterial for characterizing measurement.
Given our preliminary condition that measurement is a property evaluation (see the
related discussion in Chap. 2),
• Q1 prompts an investigation into the conditions sufficient to identify measurement directly through the structure of the process: If it is not the case that every
evaluation is a measurement, how is measurement specified?
• Q2 prompts an investigation into the conditions sufficient to identify measurement indirectly through the structure of (i) measurable properties or (ii) measured values: If it is not the case that every property is measurable, how can we
specify which properties are measurable?
These questions do not in principle relate to the physical or nonphysical nature of
the property to be measured. Of course, further dimensions might be added to make
the framework more specific, but any standpoint on measurement has to account for
its position with respect to Q1 and Q2, which in principle may be treated as distinct
and independent criteria. Given that for simplicity Q1 and Q2 are phrased as yes–no
questions (thus bracketing out the possibility of intermediate positions) four general
positions can be identified, depending on whether one considers the conditions relevant for the definition of
α: mathematical but not empirical, or
β: both empirical and mathematical, or
γ: neither empirical nor mathematical, or
δ: empirical but not mathematical.
As depicted in Fig. 4.2, this option space is a partially ordered set, where γ is the
least constraining position and β is the most demanding one. The perspectives on
measurement considered in previous sections of this chapter may be (partially)
understood by examining how they would address Q1 and Q2: let us explore this
option space.
4.4.1 Exploring perspectives on measurement
Euclid’s Elements (Euclid, 2008) set the stage by taking geometry to be the paradigm of measurement: “a magnitude is a part of a(nother) magnitude, the less of the
greater, when it measures the greater; the greater is a multiple of the less when it is
20 For example, a traditional condition might be the invariance of ratios of properties.
4 Philosophical perspectives on measurement