from those concerned about the subjective character of ordinary experience and the desire for scientific objectivity. If, so they thought, we could compare properties of different objects (taken in a wide sense) with a standardized measuring instrument as opposed to using our unaided observation, certain errors could be minimized. For example, trying to gauge the temperature of a pot with a very warm hand might lead to questionable results. Better to use a thermometer. However, there are some interesting philosophical issues that are raised by the employment of measurement, and a couple of those issues rise to the status of serious problems and puzzles, such as the matter of measurement in quantum mechanics. But we start with its less problematic features.
2.3.1 Measurement Scales
In general, a measuring instrument sets up a correspondence between numbers and physical properties. However, not all features of the number system (the natural numbers in most cases) are relevant to all measuring devices. What is relevant depends on the sort of scale one uses. We can distinguish between at least
Ordinal Scales (e.g., hardness)
Interval Scales (e.g., temperature)
Ratio Scales (e.g., length)
First, ordinal scales. For minerals, the so-called Mohs Scale is the standard way for comparing their hardness. It consists of numbers 1 to 10 with which various minerals are associated. For example, in a standard Mohs laboratory hardness kit, we find 1 = talc, 2 = gypsum, 3 = calcite … 9 = corundum, and (if you have enough research money, you include) 10 = diamond. We measure the hardness of some mineral M by a scratch test. If M can be scratched by calcite but not by gypsum, and if M cannot scratch gypsum, we assign 2 as the number of its hardness. If, however, gypsum cannot scratch M, but M can scratch gypsum (but not calcite), we assign 2.5. In this way, each mineral specimen can be located on the Mohs scale.
Notice what the scale does not provide. First, it does not provide a unique number to each mineral. The scratch test cannot deliver verdicts for minerals that do not scratch each other except that they are of the same hardness. Second, and more importantly, it only delivers ordinal information, i.e., information about the location of the mineral on the scale. It does not, however, let you infer that if one mineral has hardness 2 and the other hardness 4, that the latter is twice as hard as the former. Diamonds are not, in any meaningful way, ten times as hard as talc. Finally, it does not even tell you that if M is 4, another sample N is 6, and still another one P, is 8, that P is harder than N by the same amount that N is harder than M. The Mohs scale does not provide this information, and it would be a mistake to believe that it does.
This latter sort of information can be gleaned from interval scales, however. Those are used, for example, for measuring temperature. The difference between 90 and 100 degrees F is the same as the difference between 80 and 90 degrees. With an interval scale, we not only rank temperatures on an ordinal scale, we can also measure temperature differences. What we still can’t do, however, is make magnitude comparisons between temperatures. For example, something with a temperature of 60 degrees F is not twice as hot as something with a temperature of 30 degrees F. This is so because the Fahrenheit scale has no natural zero point. 0 degrees F does not mean the absence of temperature altogether (as it does with the Kelvin scale).
Contrast this with ratio scales, such as the centimeter scale. A measurement of 0 centimeters means the absence of extension (in the direction measured; never mind how this could be done). Thus, if you measure something to be 200 centimeters long, you can infer that it is twice as long as the thing which I measure to be 100 centimeters long. Therefore, the use of ratio scales provides more information than that of interval scales, and much more than we can get from ordinal scales: you can rank different objects by length ordinally, and you can measure differences in length. In addition, you can measure length ratios (thus the name). The interesting point here is that what information you can glean from the world is not only dependent on the physical characteristics of the measuring instruments, but also on the scale you choose to implement. Such choices are often determined by practical concerns.
Given that ratio scales deliver much more information than, say, ordinal scales, the question arises why we don’t use ratio scales for measuring any property. The example of the property of hardness makes this implausible. What would it mean to measure hardness on a ratio scale? First, we would need an absolute zero point – but what material would exhibit the property of the absence of hardness? Second, even interval scales seem to be inapplicable to hardness. In what exact sense could differences in hardness be exactly same for different pairs of materials? What the implausibility of developing ratio (and interval) scales for some properties tells us about these properties is unclear. One possibility is that being hard is simply not a fundamental property of the universe, and that only fundamental properties are amenable to being measured on a ratio scale. However, it would be quite surprising if it turned out that the notion of a fundamental property corresponds to what scales are appropriate for its measurement.
2.3.2 Operationalism
An entirely different answer to the puzzle about hardness (and related ones) is that the measurement procedure actually defines our scientific terms in the first place. This view is called operationalism. According to it, measurement procedures give meaning to otherwise ill-defined predicates (those are the terms used to refer to properties). A famous example is the predicate “intelligent.” An operationalist would claim that the term “intelligent,” as ordinarily used, is unsuited for scientific purposes. We simply don’t know whether or not it applies to the behavior of a person, because we don’t have sufficient agreement between researchers as to what property is singled out by the term. Thus, we define “intelligent” more precisely as standing for a property which is causally responsible for the performance of a person in a standardized intelligence test. Such tests deliver numbers on a scale. The view is that those numbers may or may not measure any property we were interested in before we started to theorize, but rather single out a property as corresponding to a precise predicate that is scientifically useful. On this view, hardness may be a pretheoretical property, corresponding to different human experiences of resistance to pressure, but the “scientific hardness” of a sample of material is its location on the Mohs scale. End of story.
A form of operationalism was influential for Swiss physicist Alfred Einstein’s development of the special theory of relativity; he also insisted that legitimate scientific concepts have to be defined by appropriate measurement operations. Thus, the meaning of “space” is given by the operations we apply for measuring length, and that of “time” by the operations for measuring duration. We will revisit this issue in Chapter 11. However, as a general theory of the meaning of scientific terms, operationalism is inadequate, as can be shown by the following consideration.
First, if methods of measurement indeed fix the meaning of a predicate, then there can be no such thing as an incorrect method of measurement, because there is simply no room for a mismatch between a property and how it is being measured – the former is defined in terms of the latter! For example, if intelligence is defined in terms of the standardized test with which we measure it, the test cannot fail to measure intelligence correctly. The measurement methods are correct as a matter of convention. But, second, it seems that it is possible to develop methods for measuring some quantity that are wildly inadequate. For example, measuring hardness by shining lights of various colors onto minerals seems clearly wrong, even if we supply a “scale” (looking prettiest under color 1 (red) = hardness 1). Seeing that this “measurement” of hardness is just crazy clearly shows that there is a well-(enough)-understood notion of hardness even before we try to measure it.
This seems to support a sort of realism about the properties we try to measure, in the sense that measurement is the estimation of the magnitude of an independently existing
