Standardization in Measurement

Philosophical, Historical and Sociological Issues

Oliver Schlaudt, Lara Huber, Oliver Schlaudt, Lara Huber

• Publisher: Routledge
• Year: 2015
• ISBN:
  9781317316688
• Edition: 1
• Topic: History
• Subtopic: World History
• Index: History

The application of standard measurement is a cornerstone of modern science. In this collection of essays, standardization of procedure, units of measurement and the epistemology of standardization are addressed by specialists from sociology, history and the philosophy of science.

1
‘A Branch of Human Natural History’: Wittgenstein’s Reflections on Metrology

Martin Kusch

Introduction

In this paper I want to defend two theses. According to the first, Ludwig Wittgenstein’s occasional remarks on metrology give content and support to the idea of a ‘sociology of metrological knowledge’. According to the second thesis, Wittgenstein’s remarks on metrology, relativism and rule following give support to Bas van Fraassen’s ‘constructive-empiricist form of structuralism’.¹

My paper has four sections. I shall begin by showing that metaphors of measuring are a pervasive feature of Wittgenstein’s work, and that they allow us to identify key elements of his thinking about metrology. Subsequently I shall argue that the way in which Wittgenstein leans on Einstein’s clock coordination as a metaphor for rule following supports: (i) a ‘communitarian’ and ‘finitist’ reading of rule following; and (ii) an analysis of measuring in sociological rule following terms. It is these two ideas that first and foremost bring Wittgenstein into the proximity of a ‘sociology of metrological knowledge’. I strengthen this link by proposing that Wittgenstein’s thinking about metrology is best summed up as a form of ‘metrological relativism’. Finally I shall turn to van Fraassen. I shall propose that he is right to lean on Wittgenstein in defending a subject- or agent-centred philosophy of measurement.

Analogy and Beyond

In this section I shall briefly review the central metrological analogies in Wittgenstein’s work from the 1930s to the 1950s. I leave aside the interesting metrological ideas in the Tractatus since explaining the latter would take too much stage setting. I begin with the area of grammar and language. Here the most important analogy is that between unit of measurement and rule of grammar on the one hand, and result of measurement and empirical proposition on the other hand:

The rules of grammar are arbitrary in the same sense as the choice of a unit of measurement.²

The relation between grammar and language is similar to that between deciding upon the metre as the unit of length and carrying out a measurement…³

One idea Wittgenstein seeks to make plausible with this comparison is that rules of grammar are arbitrary – or at least: as arbitrary as, and not more arbitrary than, choices of units of measurement. Later in this paper we shall see that this condition limits the arbitrariness of rules of grammar considerably.

Another metrological analogy important in Wittgenstein’s reflections on grammar is that between language and ruler: ‘To express something in the same language’ means to use the same ruler’.⁴ In order to compare different measurements of length we need to know the ruler or scale upon which the measurements are based. Analogously, in order to understand individual sentences we need to be able to situate them in the context of a language to which they belong. This thought gestures towards a form of ‘meaning holism’.

Turning from grammar to mathematics, two key passages are the following:

Rules of deduction are analogous to the fixing of a unit of length … [Wittgenstein] thought … that the comparison … would … make you see that [rules of deduction] are really neither true nor false.⁵

Geometry and arithmetic … [are] comparable to the rule which lays down the unit of length. Their relation to reality is that certain facts make certain geometries and arithmetics practical.⁶

One implication of the analogy is that, like units of measurement, mathematical propositions or rules cannot be evaluated as true or false in any correspondence sense. Instead they must be thought of as being more or less useful within the institution of mathematics. A related point is put forward in terms of an intriguing analogy between logical or mathematical proofs and the role of the standard metre in Paris:

If I were to see the standard metre in Paris, but were not acquainted with the institution of measuring and its connexion with the standard metre – could I say, that I was acquainted with the concept of the standard metre? Is a proof not also part of an institution in this way?⁷

In other words, to understand the standard metre is to understand its (former) role in our metrological institutions. Likewise, to understand a proof is to understand its function in an area of mathematical practice.

Sometimes Wittgenstein uses ‘archive’ (i.e., the location of the standard metre) to refer metaphorically to a ‘social location’ or a ‘social status’. This is the social status of being in the common ground of mathematicians: ‘A calculation could always be laid down in the archive of measurements. It can be regarded as a picture of an experiment … It is now the paradigm with which we compare…’.⁸ That is to say, a calculation ceases to be an experiment and becomes a paradigm when it is given the social status of being indisputable.

The status that accrues to calculations when they are ‘deposited’ in the common ground of mathematics also influences what we take these calculations to be about. In depositing them in the archive we stop treating them as being about worldly objects and start thinking of them as being about nothing but numbers. Decisions about the reference of mathematical terms thus follows decisions about their social status:

‘20 apples + 30 apples = 50 apples’ may not be a proposition about apples. … It may be a proposition of arithmetic – and in this case we could call it a proposition about numbers. … When it is put in the archives in Paris, it is about numbers.⁹

As far as Wittgenstein’s account of ‘certainties’ (‘hinges’ or ‘hinge propositions’) is concerned, I have argued elsewhere that the general distinction ‘unit vs. result of measurement’ is central here, too.¹⁰ Certainties are like units of measurement, and empirical propositions are like results of measurements – accordingly certainties cannot be true or false in a straightforward correspondence-theoretical sense.

There also seem to be other respects in which Wittgenstein’s thinking about metrological units and standards informs his reflections about certainties. Indeed, there seems to be a parallel between his famous claim that the standard metre cannot properly be said to be, or not to be, one metre long, and his proposal that certainties are best not regarded as things we can know or doubt. Certainties function as standards of reasonableness, and such standards are not self-predicating.¹¹

A further central theme of On Certainty is that agreement in certainties is essential for shared knowledge. Wittgenstein often illuminates this theme by referring to the importance of clock coordination for the determination of simultaneity across locations. The destruction of certainties ‘would amount to the annihilation of all … yardsticks’;¹² and: ‘Here once more there is needed a step like the one taken in the theory of relativity’.¹³

The analogy between clock coordination and agreement in responses is not an altogether new theme in On Certainty. It played a significant role in Wittgenstein’s comments on colour classification and calculation already in the early 1940s:

The certainty with which I call this colour ‘red’ is the rigidity of my ruler. … My investigation is similar to the theory of relativity since it is, as it were, a reflection on the clocks with which we compare events.¹⁴

The clocks have to agree: only then can we use them for the activity that we call ‘measuring time’. … One could call calculations ‘clocks without time’.¹⁵

Up to this point I have focused on metrological phenomena as analogues or models of, or metaphors for, other phenomena. It remains for me to document the further idea that the relationship between metrological and other phenomena is more than just an analogy. Two respects stand out. First, the fixing of units of measurement usually happens through grammatical rules. As we shall see, this link allows us to throw new light on measurement from the perspective of the rule following considerations:

A rule fixes the unit of measurement; an empirical proposition tells us the length of an object (And here you can see how logical analogies work: the fixing of a unit of measurement really is a grammatical rule, and reporting a length in this unit of measurement is a proposition that uses the rule.).¹⁶

The second and related way in which the relationship between metrological and other phenomena is more than an analogy for Wittgenstein is that samples – standards, prototypes – are thought of by him as parts of language. They are grammatical items and thus part and parcel of what makes a shared language possible: ‘It is most natural, and causes least confusion, to reckon the samples among the instruments of the language’.¹⁷

To sum up, for the later Wittgenstein (proven) mathematical propositions, rules of grammar and certainties can be understood on the model of units or standards of measurement. Accordingly, they are not true or false in a correspondence-sense, and best thought of as more or less practical. Wittgenstein uses the metrological analysis to sketch a sociological account of mathematical, linguistic and epistemic phenomena: to be a unit or standard of measurement is to have a social status within an institution. In the next two sections I shall follow this sociological theme more closely.

Einstein and the Rule Following Considerations

Einstein was important for Wittgenstein in more than one way. In this section I am interested primarily in Wittgenstein’s use of Einstein in the context of the rule following considerations. The following lines are central:

… Someone asks me: What is the colour of this flower? I answer: ‘red’. – Are you absolutely sure? … The certainty with which I call this colour ‘red’ is the rigidity of my ruler… When I give descriptions, that is not to be brought into doubt…

Following according to the rule is fundamental to our language-game. It characterizes what we call description.

My investigation is similar to the theory of relativity since it is, as it were, a reflection on the clocks with which we compare events.¹⁸

In an important paper Carlo Penco interprets this passage in the following way. Einstein’s coordinate systems stand to invariant laws as Wittgenstein’s cultural systems stand to rule following: ‘as we use physical invariants and systems of transformation for comparing different coordinate systems, we may find in the human ability of rule following the universal medium through which we may compare different cultural systems’.¹⁹ While I have benefitted from Penco’s analysis, I am inclined to put the emphasis differently. I submit that in the quote given Wittgenstein stresses the general and silent agreement that makes rule following possible. This aspect is of course central to Saul Kripke’s well-known interpretation of the rule following considerations: ‘If there was no general agreement in the community responses, the game of attributing concepts to individuals … could not exist’.²⁰ The importance Wittgenstein gives to ‘the common behaviour of humankind’ when analysing the possibility of rule following shows that Kripke is on the right track.²¹ These commonalities are the backdrop against which different language games can be ‘tabulated’ – or ‘measured’ – in Wittgenstein’s ‘übersichtlichen Darstellungen’ (‘well-ordered synopses’).²²

Moreover, the analogy between clock coordination and the agreement underlying rule following points towards a more substantive idea in the philosophy of metrology, to wit, that measuring can, and perhaps should, be analysed as an instance of rule following. Wittgenstein conceptualizes the role of standards in rule following terms. This much seems obvious given the following exchange in a 1939 seminar with Alan Turing:

Wittgenstein: Making this picture of so-and-so’s experiment and depositing it in the archives – you might call it doing it an honour. …

Turing: … and when I do a multiplication … not in your archives …?

Wittgenstein: … We have the metre rod in the archives. Do we also have an account of how the metre rod is to be compared …? Couldn’t there be in the archives rules for using these rules one used? Could this go on forever? … we might put into the archives just one … paradigm …²³

The general point – that measuring is a rule-guided practice – is hardly worth stating. But these questions are not trivial: which account of rule following is the correct one? Which interpretation of Wittgenstein on rule following should be adopted? And what difference does the correct account of rule ...

Table of contents

• Cover Page
• Half Title Page
• Title Page
• Copyright Page
• Contents
• List of Contributors
• List Of Figures And Tables
• Introduction
• Part I: Making the Field
• Part II: Standardizing and Representing
• Part III: Calibration – Accessing Precision from Within
• Part IV: The Apparatus of Commensurability
• Part V: Standards and Power – The Question of Authority
• Index