Читать книгу This is Philosophy of Science - Franz-Peter Griesmaier - Страница 29

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.