by Hasok Chang
For even larger distances we use the unit of "light-year," but we cannot actually use the operation of sending off a light beam to a distant speck of light in the sky and waiting for years on end until hopefully a reflected signal comes back to us (or our descendants). Much more complex reasoning and operations are required for measuring any distances beyond the solar system: Thus at greater and greater distances not only does experimental accuracy become less, but the very nature of the operations by which length is to be determined becomes indefinite. … To say that a certain star is 105 light years distant is actually and conceptually an entire different kind of thing from saying that a certain goal post is 100 meters distant. (17-18; emphasis original)
Thus operational analysis reveals that the length is not one homogeneous concept that applies in the whole range in which we use it: In principle the operations by which length is measured should be uniquely specified. If we have more than one set of operations, we have more than one concept, and strictly there should be a separate name to correspond to each different set of operations. (10; emphases original)
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In practice, however, scientists do not recognize multiple concepts of length, and Bridgman was willing to concede that it is allowable to use the same name to represent a series of concepts, if the different measurement operations give mutually consistent numerical results in the areas of overlap: If we deal with phenomena outside the domain in which we originally defined our concepts, we may find physical hindrances to performing the operations of the original definition, so that the original operations have to be replaced by others. These new operations are, of course, to be so chosen that they give, within experimental error, the same numerical results in the domain in which the two sets of operations may be both applied. (23)
Such numerical convergence between the results of two different operations was regarded by Bridgman (16) as merely "the practical justification for retaining the same name" for what the two operations measure.
Even in such situations, we have to be wary of the danger of slipping into conceptual confusion through the use of the same word to refer to many operations. If our thoughts are not tempered by the operationalist conscience always referring us back to concrete measurement operations, we may get into the sloppy habit of using one word for all sorts of different situations without checking for the required convergence in the overlapping domains. Bridgman warned (1959, 75): "[O]ur verbal machinery has no built-in cutoff." In a similar way, we could be misled by the representation of a concept as a number, into thinking that there is naturally an infinitely extendable scale for that concept, the way the real-number line continues on to infinity in both directions. Similarly it would be easy to think that physical quantities must meaningfully exist down to infinite precision, just because the numerical scale we have pinned on them is infinitely divisible. Bridgman reminded us: Mathematics does not recognize that as the physical range increases, the fundamental concepts become hazy, and eventually cease entirely to have physical meaning, and therefore must be replaced by other concepts which are operationally quite different. For instance, the equations of motion make no distinction between the motion of a star into our galaxy from external space, and the motion of an electron about the nucleus, although physically the meaning in terms of operations of the quantities in the equations is entirely different in the two cases. The structure of our mathematics is such that we are almost forced, whether we want to or not, to talk about the inside of an electron, although physically we cannot assign any meaning to such statements. (Bridgman 1927, 63)
Bridgman thus emphasizes that our concepts do not automatically extend beyond the domain in which they were originally defined. He warns that concepts in far-out domains can easily become meaningless for lack of applicable measurement operations. The case of length in the very small scale makes that danger clear. Beyond the resolution of the eye, the ruler has to be given up in favor of various micrometers and microscopes. When we get to the realm of atoms and elementary particles, it is not clear what operations could be used to measure length, and not even clear what "length" means any more. Bridgman asked:
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What is the possible meaning of the statement that the diameter of an electron is 10−13 cm? Again the only answer is found by examining the operations by which the number 10−13 was obtained. This number came by solving certain equations derived from the field equations of electrodynamics, into which certain numerical data obtained by experiment had been substituted. The concept of length has therefore now been so modified as to include that theory of electricity embodied in the field equations, and, most important, assumes the correctness of extending these equations from the dimensions in which they may be verified experimentally into a region in which their correctness is one of the most important and problematical of present-day questions in physics. To find whether the field equations are correct on a small scale, we must verify the relations demanded by the equations between the electric and magnetic forces and the space coördinates, to determine which involves measurement of lengths. But if these space coördinates cannot be given an independent meaning apart from the equations, not only is the attempted verification of the equations impossible, but the question itself is meaningless. If we stick to the concept of length by itself, we are landed in a vicious circle. As a matter of fact, the concept of length disappears as an independent thing, and fuses in a complicated way with other concepts, all of which are themselves altered thereby, with the result that the total number of concepts used in describing nature at this level is reduced in number.54
Such a reduction in the number of concepts is almost bound to result in a corresponding reduction in the number of relations that can be tested empirically. A good scientist would fight against such impoverishment of empirical content in new domains.
Before closing this section, I would like to articulate more clearly a new interpretation of Bridgman's operationalism, which will also be helpful in framing further analysis of the problem of measuring extreme temperatures. Operationalism, as I think Bridgman conceived it, is a philosophy of extension. To the casual reader, much of Bridgman's writing will seem like a series of radical complaints about the meaninglessness of the concepts we use and statements we make routinely without much thinking. But we need to recognize that Bridgman was not interested in skepticism about established discourses fully backed up by well-defined operations. He started getting worried only when a concept was being extended to new situations where the familiar operations defining the concept ceased to be applicable.55 His arguments had the form of iconoclasm only because he was exceptionally
54. Bridgman 1927, 21-22. Similarly he asked (1927, 78): "What is the meaning, for example, in saying that an electron when colliding with a certain atom is brought to rest in 10−18 seconds? … [S]hort intervals of time acquire meaning only in connection with the equations of electrodynamics, whose validity is doubtful and which can be tested only in terms of the space and time coordinates which enter them. Here is the same vicious circle that we found before. Once again we find that concepts fuse together on the limit of the experimentally attainable."
55. This was not only a matter of scale, but all circumstances that specify the relevant measurement operations. For example, if we want to know the length of a moving object, such as a street car, how shall it be measured? An obvious solution would be to board the car with a meter stick and measure the length of the car from the inside just as we measure the length of any stationary everyday-size object. "But here there may be new questions of detail. How shall we jump on to the car with our stick in hand? Shall we run and jump on from behind, or shall we let it pick us up in front? Or perhaps does now the material of which the stick is composed make a difference, although previously it did not? All these questions must be answered by experiment" (Bridgman 1927, 11).
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good at recognizing where a concept had in fact been extended to new domains, especially when the
extension was made unthinkingly and most people were not even aware that it had been made. He felt that all physicists, including himself, had been guilty of such unthinking extension of concepts, especially on the theoretical side of physics. Einstein, through his special theory of relativity, taught everyone what dangerous traps we can fall into if we step into new domains with old concepts in an unreflective way. At the heart of the special theory of relativity was Einstein's recognition that judging the simultaneity of two events separated in space required a different operation from that required for judging the simultaneity of two events happening at the same place. Fixing the latter operation was not sufficient to determine the former operation, so a further convention was necessary. But anyone thinking operationally should have recognized from the start that the meaning of "distant simultaneity" was not fixed unless an operation for judging it was specified.56
In Bridgman's view, Einstein's revolution should never have been necessary, if classical physicists had paid operational attention to what they were doing. He thought that any future toppling of unsound structures would become unnecessary if the operational way of thinking could spread and quietly prevent such unsound structures in the first place. Operational awareness was required if physics was not to be caught off guard again as it was in 1905: "We must remain aware of these joints in our conceptual structure if we hope to render unnecessary the services of the unborn Einsteins" (Bridgman 1927, 24). As with Descartes, skepticism for Bridgman was not an end in itself, but a means for achieving a more positive end. Bridgman was interested in advancing science, not in carping against it. Operational analysis is an excellent diagnostic tool for revealing where our knowledge is weak, in order to guide our efforts in strengthening it. The Bridgmanian ideal is always to back up concepts with operational definitions, that is, to ensure that every concept is independently measurable in every circumstance under which it is used. The operationalist dictum could be phrased as follows: increase the empirical content of theories by the use of operationally well-defined concepts. In the operationalist ethic, extension is a duty of the scientist but unthinking extension is the worst possible sin.
56. See Bridgman 1927, 10-16. This lesson from Einstein was so dear to Bridgman that he did not shrink from attacking Einstein himself publicly when he seemed to betray his own principle in the general theory of relativity: "[H]e has carried into general relativity theory precisely that uncritical, pre-Einsteinian point of view which he has so convincingly shown us, in his special theory, conceals the possibility of disaster" (Bridgman 1955, 337). The article in which this argument occurs was initially published in the collection entitled Albert-Einstein: Philosopher-Scientist, edited by Paul A. Schilpp, in the Library of Living Philosophers series. Einstein replied briefly with bemused incomprehension, much the same way in which he responded to Heisenberg's claim that he was following Einstein in treating only observable quantities in his matrix mechanics (see Heisenberg 1971, 62-69).
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Beyond Bridgman: Meaning, Definition, and Validity
There is one stumbling block to clear away if we are to construe Bridgman's operationalism as a coherent philosophy of conceptual extension. That obstacle is an overly restrictive notion of meaning, which comes down to the reduction of meaning to measurement, which I will refer to as Bridgman's reductive doctrine of meaning. It is a common opinion that operationalism failed as a general theory of meaning, as did its European cousin, namely the verification theory of meaning often attributed to the logical positivists.57 I do not believe that Bridgman was trying to create a general philosophical theory of meaning, but he did make remarks that certainly revealed an impulse to do so. The following two statements are quite significant, and representative of many other remarks made by Bridgman: In general, we mean by any concept nothing more than a set of operations; the concept is synonymous with the corresponding set of operations. (Bridgman 1927, 5)
If a specific question has meaning, it must be possible to find operations by which an answer may be given to it. (28)
The reductive doctrine of meaning indicated by these remarks is not only untenable in itself but unhelpful for understanding the extension of concepts.
Bridgman reminded us so forcefully that measurement operations did not have unlimited domains of application and that our conceptual structures consequently had "joints" at which the same words might continue to be used but the actual operations for measuring them must change. But there can be no "joints" if there is no continuous tissue around them at all. Less metaphorically: if we reduce meaning entirely to measurement operations, there are no possible grounds for assuming or demanding any continuity of meaning where there is clear discontinuity in measurement operations. Bridgman recognized that problem, but his solution was weak. He only proposed that there should be a continuity of numerical results in the overlapping range of two different measurement operations intended for the same concept. Such numerical convergence is perhaps a necessary condition if the concept is to have continuity at all, but it is not a positive indication of continuity, as Bridgman recognized clearly. If we are to talk about a genuine extension of the concept in question, it must be meaningful to say whether what we have is an entirely accidental convergence of the measured values of two unrelated quantities, or a convergence of values of a unified concept measured by two different methods. In sum: a successful extension of a concept requires some continuity of meaning, but reducing meaning entirely to measurement operations makes such continuity impossible, given that measurement operations have limited domains of application.
Moreover, if we accept Bridgman's reductive doctrine of meaning, it becomes unclear why we should seek extensions of concepts at all. That point can be illustrated very well through the case of Wedgwood pyrometry. It would seem that Wedgwood had initially done exactly what would be dictated by operationalist
57. For this and other various important points of criticism directed against operationalism, see Frank 1954.
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conscience. He created a standard of temperature measurement that applied successfully to pyrometric phenomena. As the new instrument did not operate at all in the range of any trustworthy previous thermometers, he attached a fresh numerical scale to his own thermometer. Why was that not the honest thing to do, and quite sufficient, too? Why did everyone, including Wedgwood himself, feel compelled to interpret the Wedgwood clay scale in terms of the mercury scale? Why was a continuous extension desired so strongly, when a disjointed set of operations seemed to serve all necessary practical purposes? It is difficult to find adequate answers to these questions, if we adhere to Bridgman's reductive doctrine of meaning.
The key to understanding the urge for conceptual extension, in the Wedgwood case, lies in seeing that there was a real and widespread sense that a property existed in the pyrometric range that was continuous in its meaning with temperature in the everyday range. Where did that feeling come from? If we look closely at the situation in pyrometry, numerous connections that are subtle and often unspoken do emerge between pyrometric temperature and everyday temperature. In the first place, we can bring objects to pyrometric domains by prolonged heating—that is to say, by the continuation of ordinary processes that cause the rise of temperature within the everyday domain. Likewise, the same causes of cooling that operate in the everyday domain, if applied for longer durations or with greater intensity, bring objects from pyrometric temperatures down to everyday temperatures; that is precisely what happens in calorimetric pyrometry (or when we simply leave very hot things out in cold air for a while). These are actually concrete physical operations that provide a continuity of meaning, even operational meaning, between the two domains that are not connected by a common measurement standard.
The connections listed earlier rest on very basic qualitative causal assumptions about temperature: fire raises the temperature of any ordinary objects on which it acts directly; if two objects at different temperatures are put in contact with each othe
r, their temperatures tend to approach each other. There are semi-quantitative links as well. It is taken for granted that the consumption of more fuel should result in the generation of more heat, and that is based on a primitive notion of energy conservation. It is assumed that the amount of heat communicated to an object is positively correlated with the amount of change in its temperature (barring changes of state and interfering influences), and that assumption is based on the rough but robust understanding of temperature as the "degree of heat." So, for example, when a crucible is put on a steady fire, one assumes that the temperature of the contents in the crucible continues to rise, up to a certain maximum. That is exactly the kind of reasoning that Daniell used effectively to criticize some of Wedgwood's results: Now, any body almost knows, how very soon silver melts after it has attained a bright red heat, and every practical chemist has observed it to his cost, when working with silver crucibles. Neither the consumption of fuel, nor the increase of the air-draught, necessary to produce this effect, can warrant us in supposing that the fusing point of silver is 4 1/2 times higher than a red heat, fully visible in day-light. Neither on the same grounds, is it possible to admit that a full red-heat being 1077°[F], and the welding heat of iron 12,777°, that the fusing point of cast iron can be more than 5000° higher. The welding of iron must surely be considered as incipient fusion. (Daniell 1821, 319)