1. St. Thomas Aquinas identified 3 virtues which serve as criteria for determining whether a contract qualified as morally good. In a previous note, we detailed the first virtue called Promise-keeping. In this note, we investigate the second virtue, Commutative Justice. And in a future note, the third, liberality.
2. Commutative Justice is the most conceptually mathematical of the three virtues. Commutative simply means that which relates to exchange, substitution or interchangeability. In mathematics, to say something commutes means that we can change the order of operations and obtain the same result. This idea is central to how we think of operations in the abstract, and generally speaking, when we say we can be sure something is the same as another, it is probably because we would also hold that there is a commutative relation to our beliefs. We'll speak a lot more about commutativity when we investigate Category Theory. But for now, we examine St Thomas' not so primitive bifurcated concept of commutative justice. First, the Arithmetic and then, the Geometric.
3. Arithmetic Commutative Justice. The Arithmetic arises in a bilateral exchange formation. When two parties exchange goods for value, the Arithmetic justice is simply that the value between the parties should be relatively equivalent or balanced. The notion of balancing equivalence probably comes from the act of using scales to measure a point of equivalence by approximating the point of equivalence by adding (or subtracting) lesser weights In this way, fairness can be found by the operation of addition. For about 8 centuries, this concept of fairness in bilateral exchange comes back frequently in the law, despite attempts to relegate it into meaninglessness under 19th century morally de-linked interpretations of contracts. See, for example, the doctrine of "nominal consideration" where mere legal recital of a valued for exchange is sufficient to overcome the bar of unfairness. Note also that in more recent consumer contract legislation from the mid-1960's, there are explicit attempts to bring back this sense of fairness where there is very unequal bargaining power between the corporate monopolistic price-setter and debt-addicted consumer slave. In a high powered radical reconceptualisation of Arithmetic Commutative Justice (ACJ, please forgive the acronym because life is too short to spell everything out explicitly), we see its reflection in a Risk Symmetries Framework where the x-axis is Perceived Risk and the y-axis is Definition (i.e. Increments of information) where horizontal line segments divided into equivalent length left and right segments relative to a middle vertical line represent a fair trade of perceived risk. Under a Risk Symmetries Framework, we have the theorem: Equivalent bilateralisation of perceived risk between two parties at the same level of Definition results in a commutative risk trade. This will become clearer much later on--hopefully, I can explain what this means clearly enough so we can use it in a natural way to understand risk in our daily lives. Some of my students know that I have an 80 page unpublished paper on the Risk Symmetries Framework which explains modern finance theory and behavioural finance theory locked up in my drawer which is based on answering the question, "What is the fundamental unit of psychological space that preserves risk?" When I wrote it, I thought it could be based on group theory. Now, I realise that that was much too narrow a view. Anyway, this is a digression. Let us return to commutative justice of the Geometric kind.
3. Geometric Commutative Justice (GCJ). If ACJ involves two parties, then GCJ involves groups of three or more. Just as we are concerned with distribution in ACJ so are we with GCJ. The question is naturally how to distribute equally among many. Aristotle and St Thomas appear to be socially or social structurally conservative on this point. Note when Aristotle uses the term "individual," he means the class of individuals. So distribution to various groups means distribution in proportion to those classes or groups of individuals. Compare the normativity of say Rawls' second formulation of his principle of justice wherein we are asked to imagine the most socio-economically deprived class of individuals in society, and to not implement any law that would do harm to such a group. The Aristotelian-Aquinian position by contrast would say that so long as the distribution to the various groups in society replicated the hierarchical structure of society, that would be considered just. For Aristotle and St Thomas, we have a ready reckoning tool where geometric justice simply means to replicate the interests of those in the existing social hierarchy while for Rawls, everyone is tasked to become a Socratic philosopher questioning every law for the sake of protecting those most vulnerable to its effects. What may be interesting is to determine which groups various presidential candidates intend to replicate. For example, Obama appears to exaggerate the differences between groups in the socio-economic hierarchy (classic class war rhetoric) and for this reason, he appears geometrically commutatively unjust to all groups in society. Strange place to be in? Obviously, back room deals with Wall St and war mongering without Congressional approval just don't add up for all Americans.
