CORE Metadata, citation and similar papers at core.ac.uk Provided by Lirias Fundamenta/ measurement concepts Norms and facts in measurement J. van Brakel Foundations of Physics, Physics Laboratory, State University of Utrecht, PO Box 80.000, 3508 TA Utrecht, The Netherlands Publications concerned with the foundations of measurement often accept uncritically the theory/observation and the norm/fact distinction. However, measurement is measurement-in-a-context. This is analysed in the first part of the paper. Important aspects of this context are: the purpose of the particular measurement; everything we know; everything we can do; and the empirical world. Dichotomies, such as definition versus empirica//aw, are by themselves not very useful because the 'rules of measure- ment' are facts or norms depending on the context chosen or considered. In the second part of the paper, three methodological premises for a theory of measurement are advocated: reduce arbitrariness, against fundamentalism, and do not be afraid of realism. The problem of dichotomies • Extensive quantities are additive (mass, velocity, utility) • The empirical relation > (for mass, length, temperature, In the literature on the foundations of measurement, a ...) is transitive (Schleichert, 1966; Carnap, 1926; number of dichotomies are used in describing properties of Janich et al, 1974) statements about various aspects of measurement. One of • The existence of an absolute unit for velocity (a maxi- the most common distinctions is that between a convention mum velocity) (Wehl, 1949) and an empirical fact, or between an (a priori) definition • The existence of an absolute zero for temperature and an (a posterior/) empirical law. Some other dichotomies that roughly correspond to the two just mentioned are These are examples of statements for which it is not given in Table 1. The following are examples of statements self-evident whether they are true (or false) by agreement a to which these dichotomies have been applied: priori or true (or false) by virtue of inductive support obtained a posterior/. The references in brackets refer to • Electric conductivity is the inverse of electric resistance literature where we can find arguments supporting any of (Krantz et al, 1971) these sides. Some of the statements will be discussed in • Density is mass divided by volume (Krantz et al, 1971; more detail below. Grunstra, 1969; Osborne, 1976) A related set of dichotomies is used with respect to the • Force is mass times acceleration (Nagel, 1968; Palacios, status of quantities and the properties of their scales. Per- 1964; Gillies, 1973) haps the common denominator of this set of dichotomies is • Many cyclic processes in nature are isochronic (Christen- the distinction between what is basic (natural, necessary) sen, 1977; Roxburgh, 1977; Janich, 1969) and what are arbitrary (derived, inessential) additions. • All electrons have equal charge (Hanson, 1959) Some other related dichotomies are listed in Table 2. • A transported rod is of equal length everywhere What is there to be said about these dichotomies? What (Reichenbach, 1957; Jammer, 1959; Grtinbaum, 1968; is the meaning of the terms listed in the two tables in con- Balzer and Kamlah, 1980) nection with measurement? Along what lines should we • Physical quantities are continuous (Poincarr6, 1917; discuss the apparent disagreements about what is fact and Schleichert, 1966) what is norm, or about whether there is a need for basic, • Physical quantities are dimensionally homogeneous natural, absolute or fundamental quantities or units? What (Krantz et al, 1971; Palacios, 1964; Luce, 1976; is the relevance of worrying about this in the first place? It Roberts, 1980; Post, 1982) would be a terrible job to analyse all details of these dicho- • Coulomb's 'electrostatic density of charge' and Ohm's tomies. Moreover, it would be the wrong approach, I think, 'electroscopic force' refer to the same physical quantity because the primary question to ask is: what precisely is (Heidelberger, 1980) the subject of discourse in which these dichotomies appear? Superficial confusions can be cleared up by stating that TABLE 1: Dichotomies relating to the semantic or epistemological status of statements about (properties of) quantities measurement theory is a semantic theory. That is to say, measurement is considered as some sort of general/sat/on of a prior/ a posterior/ giving names. By distinguishing carefully between defining analytic synthetic normative, prescriptive descriptive, empirical TABLE 2: Dichotomies relating to quantities and rule, definition, principle empirical law special scale values (zero and unit) mathematical, logical, formal empirical coherence; form correspondence; content primary, basic fundamental secondary, derived convention, norm, value* fact independent, direct dependent, indirect convenient or rational choice inductive or empirical support absolute, natural arbitrary necessary convenient *Also: arbitraryL convention, pragmatic (convenient) convention, essential inessential ethical convention (or principle). Measurement Vol 2 No 1, Jan--Mar 1984 45 van Brake/ Fundamental measurement concepts the concept of measurement and carrying out measure- nature, suggest at once theoretical modifications (ad hoc or ments, some order can be created. However, this approach otherwise). It is therefore a myth that numerical data are only clears up some structural (if you want, 'logical') very likely to produce new generalisations. It is already aspects of measurement. What is still left out is that, in the clear from this very short analysis of the purpose of end, measurement is a social act. Measurement is carried measurement that an isolated measurement result has no out in a context and a measurer is just like any other deci- meaning: it is like an isolated 'fact' in history (Kushner, sion maker: he ought to select what best serves his 1972). purposes. Apart from the formal aspects of the metric used, measurement includes operational and teleological aspects (Churchman, 1949 ; Adams, 1979; Gonella, 1983). (b) The theoretical context of measurement We will find reason to refer to this dependence all through this paper: but only a few remarks at the outset. The context Although measurements produce 'statements of the first level', that is, 'here-thus-relations', which may suggest at Hence the crucial point is to start with the perspective once that what physics calls an object is nothing ultimately that measurement is a rational activity in a context. A num- but an aggregate of characteristic numbers, this is only one ber of aspects of this context are of prime importance: side of the coin. At this lower level, the higher theoretical (a) What is the purpose of the measurement (teleological levels are already implied or presupposed. As Cassirer aspect)? (1956) formulated it: all physical judgements, whether (b) What theoretical assumptions are given (theoretical empirical or theoretical, mutually condition and support aspect)? one another. Perhaps two categories of theoretical assump- (c) What are the limitations of human capabilities (opera- tions made in carrying out measurement can be distin- tional aspect)? guished: (d) What are the properties of the world around us (empiri- (i) Firstly, the normal situation is that a quantity is 'in- cal aspect?) vented' theoretically and described qualitatively This whole context is, of course, dependent on the (usually in terms of a set of ordering relationships) general historical and cultural context - but space does not before it is or can be measured. We could here make a permit a discussion of these aspects here. Aspects of (a)- distinction between quantitating, which is an armchair (d) together determine the rules of the game in the context occupation, and measuring, which is an empirical concerned. Let us see how the perspective of measurement- operation (Bunge, 1973). This might imply that the in-a-context elucidates some aspects of measurement. discovery and identification of quantities is logically independent of the discovery of a means of measure- ment, as is argued, for example, by Ellis (1966). (a) The purpose of measurement (ii) Secondly, very general assumptions are presupposed about the structure of the world. This may refer to a The purpose of measurement can be quite varied, particular case, as when we assume that melting ice although (without going into much detail) the following always represents the same, constant temperature. distinctions can be made (Kuhn, 1961): Also, they can be assumptions which bear on all (i) to gather factual information to be inserted in scienti- measurement: for example, the assumption of a parti- fic theories such as wavelengths and boiling points, but cular space-time structure. whose numerical outcome these theories to not predict; These two categories of assumptions together structure (ii) to develop possibilities of quantitative comparison of the idealised context in which measurement is carried out. observation by developing apparatus, reducing per- turbing effects, and so on; more generally: to improve the measure of 'reasonable agreement' and to establish (c) Limitations of our operational capabilities new measures of 'reasonable agreement' between theory and observation; We can roughly divide these limitations into three cate- (iii) to establish the exact quantitative relation between a gories: number of variables (of which it is already known or (i) Our capabilities of making and doing things. The logic hypothesised that