Measurement without theory

Measurement without theory is possible, provided that the property to be mea­sured is actually measurable (there are properties, like beauty for instance, that are hardly measurable), that the person in charge of the measurement has a fair representation of the real-concrete thing and the property that is being measured, and that the measuring does not require sophisticated theory or instruments.

Men have performed measurements at least since they started allocating goods and labor, trading, building, and delimiting parcels of land. According to Struik (1954: 1), “our first conceptions of number and form date back to times as far removed as the Old Stone Age, the Paleolithicum”. Nevertheless, “numerical terms - expressing some of ‘the most abstract ideas which the human mind is capable of forming,’ as Adam Smith has said - came only slowly into use” (ibid.: 3) since the fifth millenium bc. Trade, in particular, required, on top of mere counting, to compare weights, lengths and volumes. The use of the balance in order to measure weights is very ancient, as Jammer (1964: 16-17) points out; it is mentioned in the Book of the Dead and in the biblical narrative of Genesis 23:16. As a matter of fact in Moses’ law (Leviticus 19:35-6) there is a demand to be fair in the measurement of weights, lengths, and volumes:

‘You shall do no injustice in judgment, in measurement of length, weight, or volume. ‘You shall have just balances, just weights, a just ephah, and a just hin.

Nevertheless, the first theory of equal-arms balance measurement appeared much later; it is due to Archimedes, specifically in Book I of On the Equilibrium of Planes? The point is that the practice of measurement, at least in some cases, did not have to wait for abstract theories in order to be carried on.

Econometrists are very prone to measure things without much appeal to theory. Famous vocal defenders of the practice of measurement without theory were Burns and Mitchell (1946). Koopmans (1947) described the approach of these authors as empirical, in the following sense:

The various choices as to what to “look for”, what economic phenomena to observe, and what measures to define and compute, are made with a minimum of assistance from theoretical conceptions or hypotheses regarding the nature of the economic processes by which the variables studied are gen­erated.

(Koopmans 1947: 161)

This agrees well with Suppes description of econometric work, where ‘models’ are “usually of a relatively simple character without substantial theoretical deduc­tions from the model itself” (Suppes 1976: 440).

Actually, an econometric ‘model’ is sometimes no more than a set of linear equations. Some econometrists distinguish an econometric model from an eco­nomic one in that the latter consists of mathematical equations describing diverse relationships used to test economic theories. Thus, the difference would be that the latter is obtained out of a theory as a sort of specification of its axioms, whereas the former is “not derived from any more fundamental assump­tions, nor is it the consequence of elementary qualitative assumptions or of some deeper running formulation of economic theory” (Suppes 1976: 441); that is to say, it is postulated without necessarily appealing to any economic theory. At any rate, if the econometric ‘model’ is not built as an application or testing of an economic theory, it is a model of probability theory, as we shall see in Chapter 12.

Koopmans criticized the pretension of performing econometric measurements “without theory”, on the ground that it is impossible to choose the relevant aspects of a phenomenon without some theoretical preconceptions:

even for the purpose of systematic and large scale observation of such a many­sided phenomenon [as business cycles], theoretical preconceptions about its nature cannot be dispensed with.

(Koopmans 1947: 163)

What I have claimed is that such preconceptions need not belong to a systema­tic abstract theory, but may proceed from a general concept of the phenomenon under interest. In Chapter 6 I will develop a map, a schema devised to generate Gedankenkonkreten, descriptions of what the econometricians call ‘data genera­tion processes’ (DGP), which are previous to the development of idealized models of the same.

Aris Spanos (1986: 11) has pointed out that the most important issue in econo­metric modelling is “the connection between estimated equations using observed data and the theoretical relationships postulated by economic theory”. Spanos himself has an interesting doctrine about such relationships that I will formalize with some detail below, in Chapter 12, from the point of view of SVT.

Summing up, measurement sometimes can or must be performed by means of a theory, making essential use of the theoretical systematizations, in particular nomological sentences, in order to find the value of a particular function. This is especially the case when the function is T-theoretical. Sometimes measurement is grounded in ancient traditions and common sense, and performed all of the time as a practical matter. Sometimes measurement is carried on by means of the application of the apparatus of probability theory and statistics, without much recourse to economic theory, and just based upon some understanding of the target system by means of a general concept of the same. And in all cases it can be proven that behind any measurement there must needs be a homomor­phism of some kind of structure. What seems far-fetched is the idea of a theory of measurement that takes into account all the messy details involved in every pos­sible measuring situation, since there is no science of the particular, as the Philos­opher pointed out.⁶

Notes

1 I will refer to this group of authors as klst from now on.

2 I shall make use of Holder’s methodology in Chapter 7, in order to prove the existence of differentiable utility functions.

3 For a proof see Varian (1983).

4 For a description of these see Garcia de la Sienra (2011).

5 The text is published in English in Heath (2010). The first edition of this work saw the light in 1897. Suppes (1971, 1980) reconstructs this theory by means ofhis concept of a conjoint structure in order to illustrate the use of fundamental measurement concepts in the history of science.

6 Aristotle, Prior Analytics, bk. II, chap. 21; also Posterior Analytics, bk. I, chapter 1. Cf. Barnes (1984, vol. 1: 39-166).

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