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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