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The Sublimity of Measurement

My recent interest is in the aesthetics of measurement, that is, in the criteria we use to chose a scale, or metric, when we make measurements of any kind, scientific or as part of everyday life. This choice of metric is the most important factor in measurement since mistakes in choosing an inappropriate metric are far more significant than any subsequent errors in using a metric. Mistakes in the choice of metric are also far more difficult to detect because they involve judgmental not technical lapses. Judgments about these criteria of importance and value tend to become ‘self-sealing� by eliminating rival criteria as a matter of course.

Immanuel Kant wrote a great deal about aesthetics but almost all of what he wrote concerns the limited area of beauty in art. This is a subject treated with special depth in The Critique of Judgment. So, although there is unlikely to be much explicit about the broader considerations of aesthetics, I’m hopeful of some inspiration that can be useful in my own theory.

As far as I am aware Kant unfortunately says nothing systematic about measurement. Nevertheless there are hints and suggestions about his views scattered in The Critique of Judgment. My intention is to investigate a few of these clues to his thinking, and to steal them if I can for my own purposes.

As part of his analysis, Kant assesses what he calls ‘teleological judgment�, that is the choices we make about ends, purposes and goals, rather than about the means to achieve these. This is where I shall focus my investigation since it most closely touches on the pivotal question in any measurement: Why? This is a question of value that is typically neglected in the discussion of measurement simply because measurement can appear to be purely instrumental. That it never is places it squarely in the realm of teleological judgment.

For Kant, judgment is a human ‘faculty�, a capability which has certain powers and limits. Judgment is “the capacity to subsume under rules, that is, to distinguish whether something falls under a given rule.� In my terminology this ‘rule� is the practical name for an aesthetic. In choosing such a rule, we are taking a definite ‘stance� regarding the world. The rule is both a filter and an ordering principle. The act of judgment presumes, I believe, that the rule is more or less articulate and therefore subject to conscious revision. In other words, we can learn about the rule.

Judgment has two functions therefore: determining and reflecting. Determining involves finding the right ‘universal�, that is concept or word for the situation at hand. Thus this function covers the choice of rule or aesthetic, that is, the metric of measurement. Reflective judgment is particularly relevant to the related activities of aesthetic choice and purposeful behaviour. It is the source of what Kant calls ‘empirical concepts�, that is, for my purposes, the range of aesthetic rules or metrics that one has at one’s disposal.

An aesthetic judgment, Kant says, is based on a ‘feeling�, that is a sensory perception of satisfying ‘rightness�. Unlike subsequent 19th century philosophers and 20th century neo-liberals, Kant does not consider such a feeling fixed or isolated from social effects, so I have no objection to using feeling as the basis for aesthetic judgments in measurement. Once again, since this feeling is the emotional equivalent to a rule, it can be, indeed must be, made more or less explicit in language.

Kant’s ideas about beauty, although stimulating for my purposes, are not directly relevant to the issues of measurement. But his concept of the Sublime is. “The experience of the sublime consists in a feeling of the superiority of our own power of reason, as a supersensible faculty, over nature.� The specific category of the ‘mathematically sublime� appears especially important for empirical measurement.

The feeling of the mathematically sublime is not one of human arrogance but of a recognition that we can reason beyond that which we can imagine. For example, we can’t imagine what infinity is or looks like, but we can use the idea of infinity in our reasoning with little difficulty. The mathematically sublime, therefore, appears to me as a sort of power of transcendent imagination, what the 19th century American philosopher, C S Peirce would call ‘abduction�. Briefly, this power manifests itself as the ability to create, invent, discover novel hypotheses about the world. Such hypotheses can be neither inductively nor deductively derived. They appear more as intuitive but plausible guesses about what might fit best with our intentions.

My suggestion is that the mathematically sublime is the source of metrics, as both a range of alternatives and as a particular choice from among these. Metrics are not found in nature; they are imposed upon it. As far as we know, only human beings have this power of imposition. Things like numbers and metrics can’t be considered as anything other than ‘real�, but their reality is the consequence of human reasoning not natural evolution. Sublimity strictly speaking “is not contained in anything in nature, but only in our mind�

Thus the mathematically sublime, or abduction, or any other description of this ability is a “faculty of the mind which surpasses every standard of sense.� In other words, the mathematically sublime goes beyond ‘mere� feeling. It may have its roots in feeling but according to Kant, it then transcends feeling completely. This, I believe, is the pivotal link between aesthetics and measurement in his philosophy. Measurement imposes our purpose on whatever is being measured. This is a crucial recognition. The properties measured are not part of the object, they are the product of our intention.

This recognition also raises the possibility of a ‘morality of measurement�. If we inevitably impose our purposes on things measured, we have at least two moral responsibilities: to consider those purposes explicitly and to recognise that measurement is not a morally neutral or objective activity of inquiry. The aesthetic judgments involved in measurement are arguably the most significant and profound of any in science.

Thank you, Immanuel, for your inspiring thought.