by Hasok Chang
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Similar types of rough assumptions were also used in the study of lower temperatures, as can easily be gleaned from the narrative in "Can Mercury Tell Us Its Own Freezing Point?" and "Consolidating the Freezing Point of Mercury."
These cases illustrate that concepts can and do get extended to fresh new domains in which experiences are scant and observations imprecise, even if no definite measurement operations have been worked out. I will use the phrase semantic extension to indicate any situation in which a concept takes on any sort of meaning in a new domain. We start with a concept with a secure net of uses giving it stable meaning in a restricted domain of circumstances. The extension of such a concept consists in giving it a secure net of uses credibly linked to the earlier net, in an adjacent domain. Semantic extension can happen in various ways: operationally, metaphysically, theoretically, or most likely in some combination of all those ways in any given case. One point we must note clearly, which Bridgman did not tend to emphasize in his philosophical discourses, is that not all concrete physical operations are measurement operations (we may know how to make iron melt without thereby obtaining any precise idea of the temperature at which that happens). Therefore even operational meaning in its broader sense is not exhausted by operations that are designed to yield quantitative measurement results.58 What I would call metrological extension, in which the measurement method for a concept is extended into a new domain, is only one particular type of operational extension, which in itself is only one aspect of semantic extension. What I want to argue, with the help of these notions, is that the justification of a metrological extension arises as a meaningful question only if some other aspects of semantic extension (operational or not) are already present in the new domain in question.
Now, before I launch into any further discussion of semantic extension, I must give some indication of the conception of meaning that I am operating on, although I am no keener to advance a general theory of meaning than Bridgman was. One lesson we can take from Bridgman's troubles is that meaning is unruly and promiscuous. The kind of absolute control on the meaning of scientific concepts that Bridgman wished for is not possible. The most control that can be achieved is by the scientific community agreeing on an explicit definition and agreeing to respect it. But even firm definitions only regulate meaning; they do not exhaust it. The entire world can agree to define length by the standard meter in Paris (or by the wavelength of a certain atomic radiation), and that still does not come close to exhausting all that we mean by length. The best common philosophical theory of meaning for framing my discussion of conceptual extension is the notion of "meaning as use," which is often traced back to the later phase of Ludwig
58. Bridgman himself recognized this point, at least later in his career. In the preface to Reflections of a Physicist, we read (1955, vii): "This new attitude I characterized as 'operational'. The essence of the attitude is that the meanings of one's terms are to be found by an analysis of the operations which one performs in applying the term in concrete situations or in verifying the truth of statements or in finding the answers to questions." The last phrase is in fact much too broad, embodying the same kind of ambiguity as in Bridgman's notion of "paper and pencil operations," which threatened to take all the bite out of the operational attitude.
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Wittgenstein's work.59 If we take that view of meaning, it is easy to recognize the narrowness of Bridgman's initial ideas. Since measurement is only one specific context in which a concept is used, the method of measurement is only one particular aspect of the concept's meaning. That is why Bridgman's reductive doctrine of meaning is inadequate.
In fact, there are some indications that even Bridgman himself did not consistently subscribe to the reductive doctrine of meaning. Very near the beginning of The Logic of Modern Physics (1927, 5) as he was trying to motivate the discussion about the importance of measurement operations, Bridgman asserted: "We evidently know what we mean by length if we can tell what the length of any and every object is, and for the physicist nothing more is required." It would have been better if Bridgman had stuck to this weaker version of his ideas about meaning, in which possessing a measurement operation is a sufficient condition for meaningfulness, but not a necessary condition. Even more significant is Bridgman's little-known discussion of "mental constructs" in science (53-60), particularly those created in order "to enable us to deal with physical situations which we cannot directly experience through our senses, but with which we have contact indirectly and by inference." Not all constructs are the same: The essential point is that our constructs fall into two classes: those to which no physical operations correspond other than those which enter the definition of the construct, and those which admit of other operations, or which could be defined in several alternative ways in terms of physically distinct operations. This difference in the character of constructs may be expected to correspond to essential physical differences, and these physical differences are much too likely to be overlooked in the thinking of physicists.
They were very easily overlooked in the thinking of philosophers who debated his ideas, too. What Bridgman says here is entirely contrary to the common image of his doctrines. When it came to constructs, "of which physics is full," Bridgman not only admitted that one concept could correspond to many different operations but even suggested that such multiplicity of operational meaning was "what we mean by the reality of things not given directly by experience." In an illustration of these ideas, Bridgman argued that the concept of stress within a solid body had physical reality, but the concept of electric field did not, since the latter only ever manifested itself through force and electric charge, by which it was defined. To put it in my terms, Bridgman was saying that a mental construct could be assigned physical reality only if its operational meaning was broader than its definition.
That last thought gives us a useful key to understanding how metrological validity can be judged: validity is worth debating only if the meanings involved are not exhausted by definitions. If we accept the most extreme kind of operationalism, there is no point in asking whether a measurement method is valid; if the measurement method defines the concept and there is nothing more to the meaning of the concept, the measurement method is automatically valid, as a matter of
59. See, for instance, Hallett 1967.
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convention or even tautology. In contrast, validity becomes an interesting question if the concept possesses a broader meaning than the specification of the method of its measurement. Then the measurement method can be said to be valid if it coheres with the other aspects of the concept's meaning. Let us see, in the next section, how this general view on validity can be applied to the more specific matter of metrological extension.
Strategies for Metrological Extension
I am now ready to consider what the validity of a metrological extension consists in and to apply that consideration to the case of extending temperature measurements to extreme domains. We start with a concept that has a well-established method of measurement in a certain domain of phenomena. A metrological extension is made when we make the concept measurable in a new domain. By definition, a metrological extension requires a new standard of measurement, and one that is connected to the old standard in some coherent way. In order for the extension to be valid, there are two different conditions to be satisfied:
Conformity. If the concept possesses any pre-existing meaning in the new domain, the new standard should conform to that meaning.
Overlap. If the original standard and the new standard have an overlapping domain of application, they should yield measurement results that are consistent with each other. (This is only a version of the comparability requirement specified in chapter 2, as the two standards are meant to measure the same quantity.)
As we have seen in the last section, the second condition is stated plainly by Bridgman, and the first is suggested in his discussion of constructs.60
With that framework for considering the validity of metrological extension, I would now like to return to the concrete problem of extending temperature measurement to the realms of the very cold and the very hot. In the rest of this section I will attempt to discern various strategies that were used in making the extension in either direction, each of which was useful under the right circumstances. As we have seen in chapter 2, by the latter part of the eighteenth century (when the main events in the narratives of the present chapter began), the widespread agreement was that the mercury-in-glass thermometer was the best standard of temperature measurement. From around 1800 allegiances distinctly started to switch to the air thermometer. Therefore the extensions of temperature measurement that we have been considering were made from either the mercury or the air thermometer as the original standard.
60. The target of Bridgman's critique of constructs was what we might call theoretical constructs, generally defined by mathematical relations from other concepts that have direct operational meaning. But concepts like pyrometric temperature are also constructs. The only direct experience we can have of objects possessing such temperatures would be to be burned by them, and nothing in our experience corresponds to various magnitudes of such temperatures.
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Disconnected Extension
It is a somewhat surprising consequence of the viewpoint I have taken, that the original Wedgwood pyrometric scale, without the conversion to the Fahrenheit scale, constituted a valid extension of the mercury standard. What Wedgwood did was to create an entirely new measurement standard that was not connected directly to the original standard. As there was no direct area of overlap between the mercury thermometer and the Wedgwood pyrometer, the overlap condition was irrelevant. The conformity condition was met in quite a satisfactory way. The connections between Wedgwood temperatures and various aspects of ceramic chemistry and physics were amply testified by Wedgwood's increased success in the art of pottery achieved with the help of the pyrometer, and the stated satisfaction of numerous others who put the Wedgwood pyrometer to use. It is true, as noted earlier, that Daniell made a compelling critique of Wedgwood's melting point of silver on the basis of pre-existing meanings, but that only amounted to a correction of an isolated data point, rather than the discrediting of the Wedgwood pyrometric standard on the whole.
The Wedgwood Patch
The only obvious shortcoming of the original Wedgwood extension was that it left a considerable stretch of the scale without a measurement standard, as the starting point of the pyrometric scale was already quite a bit higher than the endpoint of the mercury scale. Although that gap does not make the Wedgwood pyrometer invalid in itself, it is easy enough to understand the desire for a continuous extended temperature scale, particularly for anyone doing practical work in the range between the boiling point of mercury and red heat. As we have seen in "It Is Temperature, but Not As We Know It," Wedgwood's solution to this problem was to connect up the new standard and the original standard by means of a third standard bridging the two. The intermediate silver scale connected with the Wedgwood scale at the high end, and the mercury scale at the low end. In principle, this strategy had the potential to satisfy both the conformity and the overlap conditions.
Wedgwood's implementation of the patching strategy, however, left much to be desired. He did not check whether the pattern of expansion of silver was the same as the pattern of expansion of mercury in the range up to mercury's boiling point, or whether the expansion of silver at higher temperatures followed a congruent pattern with the contraction of his clay pieces. Instead, Wedgwood simply picked two points and calculated the silver-clay conversion factor assuming linearity. In the case of the silver-mercury comparison he did make two different determinations of the conversion factor and saw that they agreed well with each other, but that was still not nearly enough. Therefore Wedgwood's patched-up scale was only as good as a bridge made of three twisted planks held together with a few nails here and there. This bridge was not good enough to pass the Bridgman test (that is, to satisfy the overlap condition). However, Wedgwood's failure should not be taken as a repudiation of the general strategy of patching.
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Whole-Range Standards
Instead of patching up disconnected standards, one could seek a single standard to cover the entire range being considered. This was a popular strategy in the history that we have examined, but its success depended entirely on whether a suitable physical material could be found. For extension into the pyrometric range, measurement methods based on ice calorimetry, water calorimetry, cooling rates, and metallic expansion were all candidates for providing a whole-range standard. For extension into the very cold domain, the alcohol thermometer was a clear candidate but there was a problem with satisfying the overlap condition: it was well known that the alcohol thermometer disagreed significantly with the mercury thermometer and the air thermometer in the everyday temperature range, which is their area of overlap. In the end the best solution was found in Pouillet's air-in-platinum thermometer, which in fact covered the entire range from the lowest known temperatures at the time up to near the melting point of platinum (see the last parts of "Consolidating the Freezing Point of Mercury" and "Ganging Up on Wedgwood").61
But there is ultimate futility in this strategy. No matter how broadly a standard is applicable, it will have its limits. Even platinum melts eventually; air liquefies at the cold end and dissociates at the hot end. There are also more mundane limits, for example, in how hot an object one can drop into a bucket of ice or water, as that operation is really only plausible as long as the hot object remains in a solid form, or at least a liquid form. Generally, if one aspires to give a measurement standard to the entire range of values that a quantity can take on, then one will have to fall back on patching. The best agreed-upon modern solution to the problem of thermometric extension is in fact a form of patching, represented in the International Practical Scale of Temperature. But there are more secure ways of patching than the Wedgwood patch.
Leapfrogging
The least ambitious and most cautious of all the strategies discussed so far, which I will call "leapfrogging," is exemplified very well in the development of metallic pyrometers. Initially the pattern of thermal expansion of a metallic substance was studied empirically in the lower temperature ranges, by means of the mercury thermometer. Then the phenomenological law established there was extrapolated into the domain of temperatures higher than the boiling point of mercury. Another exemplary case of leapfrogging was Cavendish's use of the alcohol thermometer for temperatures below the freezing point of mercury (see "Consolidating the Freezing Point of Mercury"). Extension by leapfrogging satisfies the overlap condition by design, since the initial establishment of the phenomenological law indicates exactly
61. The search for a whole-range temperature standard continues to this day. A team at Yale University led by Lafe Spietz is currently working on creating a thermometer using an aluminum-based tunnel junction, which would be able to operate from very near absolute zero to room temperature. See Cho 2003.
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how to ensure quantitative agreement in the overlapping domain. The conformity condition may or may not be satisfied depending on the particular case, but it seems to have been quite well satisfied in the cases we have discussed. The leapfrogging process could be continued indefinitely in principle. Once the new standard is established, a further extension can be made if a new phenomenological law can be established in the new domain by reference to the new standard, and that law is extrapolated into a further new domain.
Theoretical Unification
Instead of trying to find one material standard or a directly linked chain of material standards to cover the entirety of the desired domain, one could also try to establish an all-encompassing theoretical scheme that can provide justification for each proposed measurement standard. Using a common theory to validate various disparate standards would be a method of forging co
nnections between them. If various new standards are linked to the original standard in this way, they could all be regarded as extensions of it. This is certainly a valid strategy in principle, but in the historical period I am presently discussing, there was no theory capable of unifying thermometric standards in such a way. Distinct progress using the strategy of theoretical unification was only made much later, on the basis of Kelvin's theoretical definition of absolute temperature, which I will discuss in detail in chapter 4.
Mutual Grounding as a Growth Strategy
The discussion in the last section makes it clear that we are faced with a problem of underdetermination, if that was not already clear in the narrative part. There are many possible strategies for the extension of a measurement standard, and each given strategy also allows many different possible extensions. So we are left with the task of choosing the best extension out of all the possible ones, or at least the best one among all the actual ones that have been tried. In each valid extension the original standard is respected, but the original standard cannot determine the manner of its own extension completely. And it can easily happen that in the new domains the existing meanings will not be precise enough to effect an unambiguous determination of the correct measurement standard. That is why the conformity condition, demanding coherence with pre-existing meanings, was often very easily satisfied.