Tuesday, 27 October 2020



The “laws” of economics invoked by equilibrium analysts serve to indicate the necessity that the scarcity of available resources (the Walrasian rarete’, rarity) determines as the inexorable constraint on the insatiability of human needs and wants. For bourgeois economic science, then, the social relations of production are not conditioned by the political choices of social agents determining the coercion imposed by some of them on others, but rather by the scientifically objective fact of the limitless claim of human beings to the same resources – a conflict over the distribution of resources that relegates economics to the epistemological status of a “dismal science”, but a science nevertheless – one based on “scientific laws” as inexorable as those of physics and indeed of mathematics. As we have demonstrated, the laws of mathematics are absolutely conventional in the extreme sense that not only do they enjoy universal agreement (con-vention), but the convention itself is absolutely irresistible for the sheer fact that mathematical laws are tautologous (!), they are mere id-entities, they are utterly neutral to the point that, left in their pure form, as mere formality, they tell us absolutely nothing about the world – they are inform (shapeless) because left to themselves, in their formal purity, they do not in-form us about anything at all!

But the absolute conventionality of logico-mathematical tools is precisely what leaves them open to their application as practical effectual hypotheses on the state of the objective world. By assigning objective values to real variables, logico-mathematics allows us to measure our social reality in ways that either preserve it or trans-form it in ways, manners and directions implicit in the hypothesis that we are advancing – that is, implicit in the selection of variables to which we apply logico-mathematical tools so as to measure and test the validity of the hypothesis we are advancing. The hypothesis, then, is “pure supposition” (Ernst Cassirer on Hobbes in History of Philosophy), sheer “conjecture” (Cusanus to Karl Popper [Conjectures and Refutations]).

What we have is a combination of convention and hypothesis that is the very essence of bourgeois economic analysis. Here are Arrow and Hahn:


The great virtue of mathematical reasoning in economics is that by its precise account of assumptions it becomes crystal clear that applications to the “real” world could at best be provisional. When a mathematical economist assumes that there is a three good economy lasting two periods, or that agents are infinitely lived (perhaps because they value the utility of their descendants which they know!), everyone can see that we are not dealing with any actual economy. The assumptions are there to enable certain results to emerge and not because they are to be taken descriptively. (Hahn, 1994, p. 246)” (434)


The immediate "common sense" answer to the question "What will an economy motivated by individual greed and controlled by a very large number of different agents look like?" is probably: There will be chaos. That quite a different answer has long been claimed true and has indeed permeated the economic thinking of a large number of people who are in no way economists is itself sufficient grounds for investigating it seriously. The proposition having been put forward and very seriously entertained, it is important to know not only whether it is true, but also whether it could [hypothetically be made to] be true. (Historical Introduction to General Competitive Analysis)

The “assumptions” used in bourgeois economic equilibrium analysis – the variables attached to the conventional mathematical tools applied in the measurement of reality – “are there to enable certain results to emerge”! The hypothesis is not to describe reality as it is – which in any case is just a mythical entity -, but rather to measure certain variables in the perceived existing reality that can lead to its manipulation or transformation in a desired direction! The hypothesis advanced by bourgeois analysis is advance to establish “not only whether it is true, but also whether it could [hypothetically be made to] be true”!




A closed system is not a description of reality because it zeroes in, focuses on, select items of reality, on hypothetical variables which are then measured in relation to other constant variables – “all things being equal”, caeteris paribus! In other words, a closed system is a hypothetical experiment or an experimental hypothesis! It is not a description but rather it is a prescription because it tells us to intervene when the schematic equations or equivalences are not satisfied. It is also not a description because it tells us nothing about the historical evolution of the variables (they are timeless). A closed system is a “frame” [a procedure] into which “facts” are fitted so as to form a “picture” of reality – a “vision” (Anschauung) or snapshot (Blick): but it is not a prediction, because it is inexorable – and it is inexorable because its variables are logically interdependent so that they “close” the system.

A closed system does not predict because it is inexorable. It allows logically of no changing outcomes because its components are defined interdependently. A closed system does not theorize an economy: it formulates a destiny! It was Hayek’s cousin, Ludwig Wittgenstein, who penetrated the profound and dramatic Kafkaesque implications of this realization. In paragraph 118 of the Remarks on the Philosophy of Mathematics, Wittgenstein examines a statement of the type, “The law always catches [or punishes] the criminal”. This is a classic closed system because “the law” and “the criminal” are inexorably linked (“always”, without exception) by “being caught” (detection, arrest) and “the punishment”, in such a way that “the law” means inexorably “punishment of the criminal”. What we notice in this closed system is that the “logical closure” of the relation between “the law” and “punishment of the criminal” by the adverb “always” – without fail or exception, inexorably – turns the conceptual meaning of “the law” from an institutional reality (legal rules) that may be successfully evaded by the criminal (he does not get caught) or avoided (he is absolved or pardoned by a judge) into a destiny – because now “the law” is no longer a real institutional body that can make mistakes or make an exception, but instead has turned into an inexorable, unavoidable fate or destiny! The criminal will be punished because he is a criminal – by definition!

This is the real meaning, the purpose, of a closed system. As a destiny – as pure convention – a closed system is a tautology: it is meaningless. But as a purpose – equating the law with punishment of a criminal as an imperative, as a prescription, as a hypothesis - a closed system acquires practical meaning! And the purpose of the closed system as a combination of convention and hypothesis is to measure reality in a manner – by keeping all other variables immutable (caeteris paribus) - that assumes that it is inescapable and inexorable – a destiny. In this case, “the Law” has turned into a curse. Guilt need not be proved. Guilt exists as an inexorable attribute of “punishment” and necessarily (“always”) of “the criminal”. Here “the Law” is pure formality, pure procedural application, implacably merciless bureaucratic destiny. “The law always catches and punishes the criminal”! As Cacciari ominously put it (in Krisis, p.67), no-one will ever understand anything about Kafka’s “The Trial” or “The Castle” if they do not first understand paragraph 118 in Wittgenstein’s Remarks!

118. It looked at first as if these considerations were meant to shew that 'what seems to be a logical compulsion is in reality only a psychological one'--only here the question arose: am I acquainted with both kinds of compulsion, then?! Imagine that people used the expression: "The law §... punishes a murderer with death". Now this could only mean: this law runs so and so. That form of expression, however, might force itself on us, because the law is an instrument when the guilty man is brought to punishment. Now we talk of 'inexorability' in connexion with people who punish. And here it might occur to us to say: "The law is inexorable--men can let the guilty go, the law executes him". (And even: "the law always executes him".)--What is the use of such a form of expression?--In the first instance, this proposition only says that such-and-such is to be found in the law, and human beings sometimes do not go by the law. Then, however, it does give us a picture of a single inexorable judge, and many lax judges. That is why it serves to express respect for the law. Finally, the expression can also be so used that a law is called inexorable when it makes no provision for a possible act of grace, and in the opposite case it is perhaps called 'discriminating'. 60 Now we talk of the 'inexorability' of logic; and think of the laws of logic as inexorable, still more inexorable than the laws of nature. We now draw attention to the fact that the word "inexorable" is used in a variety of ways. There correspond to our laws of logic very general facts of daily experience. They are the ones that make it possible for us to keep on demonstrating those laws in a very simple way (with ink on paper for example). They are to be compared with the facts that make measurement with a yardstick easy and useful. This suggests the use of precisely these laws of inference, and now it is we that are inexorable in applying these laws. Because we 'measure'; and it is part of measuring for everybody to have the same measures. Besides this, however, inexorable, i.e. unambiguous rules of inference can be distinguished from ones that are not unambiguous, I mean from such as leave an alternative open to us.

The convention is that “everybody has the same measures”. The hypothesis is the application of the logico-mathematical tool to an aspect of reality so as to measure it. The closedness of the system means that the outcome or result is “unambiguous”, that is, an absolutely conventional hypothesis – “such that the outcome does not leave an alternative open to us”!

What we have called a Schema here is a knowledge tool, a technique that in and of itself has no economic significance: it is simply a technical mechanism (a logico-mathematical tool) that has no intrinsic aim or goal outside the purpose for which it is used – which includes the nature of the entities or “facts” that the tool and its components represent. For instance, in the equation F=MxA, the tool consists of the mathematical operation of multiplication and the equal sign and the contents of this tool - the concepts of force, mass and acceleration. Thus, the purpose of the tool is constituted by the combination of the calculating operations (convention) and the selection of concepts to which they are applied (hypothesis). The calculation itself is a pure identity and therefore tautological and meaningless. But once it is applied to its conceptual contents, it becomes purposeful; it becomes a project. If we define Force as “mass times acceleration”, then we have a closed system – a tautology. What makes this equation an open system is the simple fact that we do not know what a “force” is, what its real effects are; and we do not know what “mass” is, so we cannot define the one in terms of the other. Force and mass are abstract concepts that cannot be defined practically one in terms of the other. We only know what “acceleration” is – the displacement of a body over time over time, that is, the rate of increase of its velocity. The same is true for E=mc2 where “energy” is an indefinite concept not definable in terms of mass and light-velocity. A closed system is not “true”: it is a tautology, a verity (Arendt, The Life of the Mind). Indeed, all equations are not true because they are mere static identities that can only be said to be either “correct” or “incorrect”, equal or unequal. Truth instead is a moral judgement that applies to the correspondence of a statement or judgement to a state of affairs.

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