Books like Science of Logic

Nothing So Practical As a Good TheoryI read Hegel’s Phenomenology of Spirit almost a half-century ago. I can recall its poetic beauty but none of its content. I have never read The Science of Logic, a definite gap in my education but one I will have to live with, at least in part. My purpose in consulting The Science of Logic at this late date is only to understand Hegel’s conception of measurement. Since everything in Hegel’s work is intimately connected to everything else, I will undoubtedly make substantive interpretive errors. Nonetheless I hope my reading is adequate to establish if my own theory of measurement (see below) is compatible with his, and if not where it differs.Like the Phenomenology, I take the Logic as a treatise about language and language-using more than about reasoning or science as it is or should be conducted. Hegel’s concern is inquiry in general not specific issues in any scientific discipline. Language, unavoidably, mediates all inquiry. So Hegel developed a somewhat complex language about language. And language about language always seems somewhat dense if not cramped and arbitrary. But since I am not attempting to re-establish Hegel’s language system, I feel entitled to ‘translate’ the terms relevant to my inquiry into terms which are in more or less everyday use. Hegel begins his discussion of measurement with the statement: “Abstractly expressed in measure, quality and quantity are united.” Quality and quantity do have technical categorical meaning in the Logic. But they seem to me to near enough in denotation to be used colloquially. I consider this statement therefore to be in my Propositions (1) & (2). That is, measurement requires the qualitative choice of a metric or scale, which is itself quantitative. Thus quality and quantity are indeed united in the establishment of a metric.Hegel’s definitional argument then brings in his category of ‘mode’, a term to which there is no convenient colloquial term. Modes are forms of ‘productive expression’, in other words, of meaning. There are two modes, relative and absolute. A relative mode has an indeterminate meaning since there is no established link between possibility and necessity. In absolute mode there is no contingency, or more precisely, contingency and necessity are congruent because of what he calls the “initial conditions of productive expression.” “Mode,” he says, “has the specific meaning of measure.”The modal character of a metric, I believe, corresponds to my Proposition (3). Metrics are defined, that is, their initial conditions are established, so that they are absolute in Hegel’s sense. There is no question, for example, that the choice of a linear numerical metric means that the number 1 is always less than the number 2, which is twice 1. This is not contingent but necessary as part of the metric.After a digression into Spinoza’s (faulty) consideration of mode, he returns to his own theory, and says, “everything depends on the kind and manner of the mode; such an admission means that the mode itself is declared to belong essentially to the substantial nature of a thing.” Despite its degree of abstraction, which is absolute, a metric nevertheless exists. Metrics are, in other words, real objects even though their tires cannot be kicked nor their attributes described except in terms of a definition. This is implicit in my Propositions (2), (3), & (4), but probably should be made explicit.Hegel then gets to the heart of his theory when he says, “Measure... is an external kind and manner of determinateness, a more or less, but at the same time it is equally reflected into itself, a determinateness which is not indifferent and external but intrinsic; it is thus the concrete truth of being. That is why mankind has revered measure as something inviolable and sacred.” Unpacking this a bit: measure, in my terms a metric, is ‘external’, that is to say it is not an attribute or a property of an object other than the metric itself. It is, in a sense, sovereign because of its existence as absolute mode.This externality of the metric is explicit in my first two Propositions. Measurements are not properties of objects other than the metric. Rather objects become properties of the metric. They are assigned a specific place or space on a metric in the act of measurement. On the other hand, metrics are also intrinsic to themselves, that is, any part of the metric is representative of the whole, and is fundamentally unchanged by the assignment of extrinsic properties of the objects that are measured. To summarise: measured objects do not have the properties measured; measurements are properties only of the metric employed. This is why the metric is “reflected into itself... and has a determinateness which is intrinsic.” A measurement may be made at various degrees of precision, but at whatever degree it is made, it is determinate. This too is implicit in Proposition (3) but also needs to be made explicit. Among other things this determinateness of measurement solves a number of quasi-problems such as those of Chaos Theory in which very small measurement errors involve large systems changes. This will be discussed further in subsequent reviews.Another way of speaking about the definiteness or modal character of a metric is to say that a metric is its own verification. Once a metric has been established it cannot be corrected or gainsaid by any other metric. It becomes its own standard of correctness. One can speak of error ‘on’ a metric but not error ‘of’ a metric in any meaningful quantitative way. As Hegel says, a metric is “the concrete truth of being.” There certainly may be other truths, but not within the truth of a metric which has been chosen for measuring. This is covered in my Proposition (5)Hegel’s reference to the quasi-divine nature of measurement I interpret in two ways. In the first instance, numbers, from at least Ancient Greece onwards, have had a mystical connotation. In fact in several mystical traditions, Stoicism and Kabbalah for example, numbers themselves are considered divine. Since metrics are composed of numbers, they share in their transcendental character. Platonist philosophy considered them as Eternal Forms. But whatever terminology is employed, numbers and metrics have a distinctive ontology or mode of being.Secondly, in philosophical terms “The absolute, God, is the measure of all things.” I take him to mean by this that God includes all possible metrics. In fact God is the reconciliation of all metrics, each of which is a sort of ‘spark’ of the divine. Within God alternative metrics are not contraries but ‘track’, as it were, consistently with one another. I think this is parallel to my Propositions (7) & (8) in which I attempt to articulate the possibility for ‘larger’ metrics. God is the largest, most encompassing metric of all. There is, I believe, a political implication, or at least a possibility, which arises from this, namely what I term below the Ethical And Political Principles of Propositions (7) & (8).There is obviously much more to be said about metrics, numbers, aesthetic choice, and the politics of measurement from others parts of the Phenomenology and the Logic. But I think that I have made a sufficient argument that my outline theory can at least be interpreted as consistent with the Hegelian concept. Onward and upward.An Outline Aesthetic Theory of Measurement 1. Measurement is not the quantification of the properties of an object, event or phenomenon. Nothing has the property of being, say, 1 yard square. Such a designation runs into all sorts of philosophical problems having to do with human sensory perceptions and the epistemological difficulties of determining the inherent properties of what Kant called “the thing in itself.”2. Rather measurement is the establishment of the position of a thing, event or phenomenon, on a scale. The thing is a property of the scale, not vice versa. When we measure we are ordering things on a scale not determining the properties of a thing. This is the primary Ontological Principle of measurement3. The scale used in measurement is called a metric, and can have a variety of properties. Metrics, unlike other things, can have properties because they are mathematically defined to have them. Metrics, like all numbers, have a unique mode of existence. We do not ‘find’ metrics in the natural world, we create them. They are both imaginary and incontrovertibly real at the same time. GDP is a metric, economic utility can be a metric if it is specified mathematically, price and costs are metrics. 4. Metrics are expressed in terms of a numeraire, that is a unit of measurement like feet, dollars, utiles, but these should no be confused with the nature of the metric itself which is purely mathematical. For example, the metric of price is one of constant proportions: $2 is exactly twice $1 and half of $4. But $4 of income may not be twice as many utiles as $2. The metric of utility recognizes what economists call declining marginal utility.5. A metric is what economists call an aesthetic, the more general term used for a criterion for judging value, worth, importance etc. GDP, for example, is an aesthetic that treats increases as beneficial. Unlike utility, benefit is directly proportionate to the ‘place’ an economy is placed on that metric. Such a metric is not required by any scientific or moral method, but it is an aesthetic choice, the most fundamental choice that all economists make. The choice of metric is a work of art.6. The error in choosing an aesthetic is always greater than the error of measurement on or within an aesthetic. The aesthetic of GDP for example is not necessarily correlated with a metric of ‘National Happiness.’ As GDP increases, National Happiness could conceivably decrease due to pollution, and other environmental degradation. A 1% error in the measurement of GDP (that is enough to make it useless for policy-making purposes) would be far less significant than the error of choosing GDP over the National Happiness measure, for example.7. An aesthetic itself has a value, that is, is better or worse, depending on how effective it is in expressing the experience of a population. To the degree that an aesthetic is accepted politically as such an expression, it is more or less verified for that population for the purposes of the issues at hand. This can be called the Ethical Principle of the aesthetic. The art of the economic aesthetic is, like all aesthetics, social. In a sense the aesthetic is ‘true’ to the degree it represents the sentiment of a population.8. The Ethical Principle of the aesthetic implies that its choice can neither be objective nor subjective, only communal. Any attempt to restrict the politics of a community in its choice of aesthetic is the primary source of aesthetic error. The only way in which contrary aesthetics can be reconciled within any community is the the discovery of a synthetic or ‘larger’ aesthetic that recognises the conditions in which these ‘lesser’ aesthetics are relevant. Thus, for example, measurement with a everyday yardstick is perfectly sensible so long as what is measured is not too small or too fast, in which case quantum measures are necessary. This is the Political Principle of measurement. Illustration of the relative importance of the choice of metricBelow is a simple graph showing a strait forward linear metric on the x axis and the natural logarithm of the values of this metric on the y axis [y = f(x) = ln(x)]. Each is a very distinct metric despite the fact that both are expressed in the same numerical scale of 1,2,3 etc. Measurements taken on one will be dramatically different from measurements taken on the other. Any error in measurement on either metric will likely be insignificant in comparison with the difference in measurements between the two metrics. Students of economics will recognise this graph as indicating the declining marginal utility of money, an established principle of micro-economics. Yet the declining marginal utility is rarely used in analysis because it is difficult to estimate and to use in calculations. Therefore it is presumed in all of financial and risk analysis that there is constant marginal utility of wealth and income - an example of the many times that economics and other social sciences look for their keys under a lamp post simply because there is light there.