Some Thoughts About “Reality Is Scalar”

[Galilée] déclare que dans tous ces phénomènes il faut mesurer tout ce qui est mesurable, et tâcher de rendre mesurable tout ce qui ne l’est pas directement.
[“[Galileo] declares that in all these phenomena we must measure all that is measurable, and try to make measurable all that is not directly so.”]
-Thomas-Henri Martin, Galilée: Les Droits de la Science et la Méthode des Sciences Physiques (1868)

When we describe the world, we often use categories to do so. We say that there are red objects and blue objects, poor people and rich people, lions and tigers, etc ad inf. These categories are useful to us, because they provide useful rules of thumb for understanding the world and predicting what the effects of our and others' actions will be. We can predict that a lion will behave differently to a tiger, or a red object will match some othe object better than a blue one.

Where we go wrong is to think that those categories that we apply to the world for our convenience are “real” and absolute. Taking the colour example, really these are just ranges on a scale, and fuzzy ranges at that. English is developed enough that we have basic colour names to a fairly high degree of specificity, but there are many languages with far fewer basic colour names, and even in English the crossover points between different colours are fuzzy, ill-defined.

The word “real” is itself ambiguous, and our categories are useful precisely because (or insofar as) they correspond to real differences between scalar ranges. In particular there are often threshold effects: tipping points at which a major change in some property of the object occurs, even when there is little change in that property outside of those ranges. Temperature and states of matter are a good example of this. For many basic substances there are two temperature thresholds where the substance undergoes a rapid and significant—and real—change in its properties: the melting / freezing point; and the boiling condensing point. Water at 90°C behaves differently to water at 10°C, but in some important ways they are still more similar to each other than either is to water at 110°C. The temperature is scalar in a linear way; the state of matter depending (largely) on the temperature is scalar in a stepped way. Around the thresholds, the scale moves faster and is observable as a scale.

These differences in properties between ranges are real, but that does not make the categories real in themselves. Reality itself can be seen as scalar.¹ Some of our concepts or models are entirely abstract and divorced from reality, while some are only very minor abstractions. The binary treatment of entities as either “real” or “not real”, like “perfect” or “not perfect”, is a product of our concepts, of what we find useful. It is useful to draw a line in the sand and say that this is real and this is not, and the same applies to any property based in that scalar reality. At some point we do need to make decisions, and because those decisions are categorical, we must crystallise the spectrum into categories corresponding to the decisions we need to take. But just because we have to treat reality as categorical does not mean that it is categorical.

The problematic effects of treating reality as categorical (sometimes called “binary thinking”, the most extreme version of the error) appear in many places. Most of all, they stem from our treating our decisions as iron laws rather than pragmatic guidelines. Because reality is scalar, even when there are extreme threshold effects, there will always be edge cases that cannot be appropriately covered by iron laws. It may sometimes even be more appropriate to treat the edge cases as a category in themselves, but either this is precluded by categorical thinking rigidly insisting on its categories, or the edge cases are treated so rigidly as their own category that their similarities to their adjacent categories on the continuous scale are themselves ignored.

This is especially true in the social sciences and moral philosophy, because they themselves exist in the central portions of the reality scale between hard material reality, where it is usually obvious to think in a scalar fashion, and pure concept, where it is unimportant or even appropriate to think in categorical terms. The social and moral domains are precisely about how our concepts map to underlying behaviours that are impossible to measure precisely, and where our decisions are of profound personal importance. But just because it is difficult for us to measure socio-moral properties does not mean that those properties are not reflections of the real world, that they are purely conceptual, and therefore categorical rather than scalar. (It is not a coincidence that I am especially interested in this issue given that “social sciences and moral philosophy” covers a large part of my intellectual interests!)

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