Saturday, 19 March 2016

Mises and Hayek: Economic Science As Language-Game

The remainder of this chapter will study the process whereby Hayek’s and Robbins’s conception of “the science of choice’ proceeds from certain assumptions (individualism, historical institutions seen as rigid ossified structures, scarcity or ‘rarete’’, competition) which allow it to be distinguished from pure engineering and yet permit the selection of a “box of tools” that turn it into a “technique” that purports ‘to describe’ social reality but in fact prescribes social action and shapes it decisively.

It is the combination of “in-dividualism” (recall Hobbes – in von Clausewitz’s perspective, if war is the continuation of politics by other means this is only because politics is incipient war) and “scarcity”, as the expression of the antagonism of self-interested in-dividuals, that make the theory particularly powerful strategically for capital. By adopting these assumptions, Robbins’s formal categorization of “praxeology” – which (Napoleoni) is the encapsulation of the fundamental assumptions of neoclassical theory – completely overlooks the fact that these notions of “individualist competition” and of “scarcity” are not “scientific” categories but in fact are themselves determined by “political” conditions that go from the ‘Trennung’ to the selection of production technologies, consumption schedules and income distribution (Napoleoni points this last element out in reference to Pareto optimality, which cannot encompass this parameter, at p. 46) which are not “given data” (Hayek pointed this out by reference to general equilibrium and “competition” – also covered by Sraffa and Robinson later) because they are not “exogenously/independently” determined but are endogenous variables to “the science of choice”, thereby destroying their “scientificity”.

As Napoleoni notes, Robbins’s aim was to turn “economics” into a “technique” in a fashion similar to engineering, but this is not possible because of the fallacy of misplaced concreteness (invoked by Hayek against “scientism”) because “individuals” and “scarcity” are themselves social constructs. Above all, Robbins’s definition of an “economic” problem leaves out the act of “exchange”, that is, the institution of private property and the artificial calculation of “individual labours” against the division of “social labour”, which are fundamental to a “market” economy and without which it would be entirely consistent with a “planned” economy. It is the “choice” implied by “the science of choice” that, once it is seen as “conflict”, destroys the “scientific” pretensions of the Robbinsian epistemological definition of economics. It follows that the “goal-neutrality” and “means-neutrality” of “the science of choice” is anything but neutral but in fact disguises clear ideological-political choices that reveal its strategic-political character largely dependent on “prices” determined through equilibrium analysis.

We can now see (what remains a mystery to Cacciari, p44) why Schumpeter as well as Hayek had to cling “desperately” to equilibrium analysis even though they were aware of these “apories” (simultaneity and perfect competition in Hayek, endogeneity of technology and organization as well as “finance-capitalist” nature of ‘Statik’ analysis in Schumpeter where ‘Dynamik/Krisis’ become the differentia specifica of capitalism). Without equilibrium analysis, both Hayek and Schumpeter were aware that their attempts “to distil” the core of (scientific) “economic analysis” in isolation from the “Marxian” factors (relegated by Schumpeter to “economic sociology”) would come to naught. The theory was evidently un-historical (cf. Napoleoni – who also neglects to emphasise its internal inconsistency) and Schumpeter sought to improve on this score without relinquishing the Machian presuppositions and yet introducing Nietzschean notions that give it far greater political realism and “honesty”/bluntness.

Thus, “praxeology” becomes a Wittgensteinian “language-game” that limits the scope of human action forcing it into a straitjacket. We seek to outline the epistemological foundations of this construct (also discussing Nietzsche’s Frammenti Postumi) and to highlight its Kafkaesque “violence” (recall Arendt and Cacciari’s references). Interestingly, Cacciari uses the word “inexorable” to describe the functional instrumentality of the kind of “language game” erected by Hayek-Robbins.

As we noted, Wittgenstein had already reached the epistemological limits of the project of establishing the logical foundations of mathematics and then also the development of a non-metaphysical “language-game” aspiring to scientific status. This was the failure of Machism as well (recall also Lenin’s intervention discussed by Cacciari). Relativity and quantum theory will put paid to these velleities, whilst Husserl and Heidegger will perform similar tasks in philosophy/phenomenology (cf. Logische Untersuchungen and “The Problems of Phenomenology”, respectively).

The Hayek-Robbins pro-ject does not seek to go beyond Machism because its “self-understanding” is in reality/effectively to develop “tools” that can serve as the foundations of a “Science of Choice”. What Wittgenstein (and Nietzsche before him) show is that this is im-possible. Thus Hayek remains a prisoner of the Wiener-Kreis position, seeking if not a Neo-Kantian correspondence of logic with reality, at least a Machian phenomenological correspondence with truth, an “explorative” procedure a’ la Tarski or Carnap, allowing a growing approximation or refinement of logical analysis to reach scientific truth. Popper’s definition of “scientificity” of course is “empirically” antithetical to this, preferring the experimental road to science (contra Hayek).

But Mises remained the “fundamentalist”. The misguidedness here as in Hayek to a lesser extent is in failing to understand that the “rules” to be “distilled” from the reality of capitalist social relations of production do not and cannot correspond to reality because the reality is in a different dimension, a multi-verse that is worlds removed from the one encompassed by the “rules”. This is so not only in an epistemological sense, as Godel (but also Russell and Cantor with their ‘paradoxes’) showed, because the “rules” cannot “explain” their “truth”, the “causality” of the events they “measure” and “relate”; but also because, as Wittgenstein showed, there is no (Kantian) truth.

And this is why it is possible to attribute Kantian foundations to Mises (“Kant is metaphysics!” we can hear Neurath cry out) in the “introspective/individual” rationality of “human action” representing the Ratio of the transcendental subject. Misesian appraisement stands for the “freedom” of the Kantian Subject which remains “exogenous” to the economic system: it simultaneously “re-equilibrates” the system of exchange described by marginal utility, pushing it toward an “equilibrium” thanks to the “logic” of its rationality; but then it makes the attainment of this “equilibrium” impossible because the “choice” of the transcendental subject cannot be subordinated to the “phenomenal” link of causality, of empiricism.

Here the Planlosigkeit of “choice”, the Kantian “freedom” of the Subject, is what rescues “homo agens” from the “non-action” of the “end-state”, of equilibrium. The market mechanism, therefore, whilst it is analyzable “scientifically” through “logic”, must retain for Mises the freedom of “choice” that restitutes the Subject to the centre of the system of exchange: the exchange cannot be one of “equivalents”; exchange must involve conflict, “competition”.

The “socialist” attempts to transform “the logic of choice” into a “Plan” would remove this subjective element, this “appraisement”, this conflict, as would the Hayekian emphasis on “co-ordination”. These are Neo-Kantian moralistic elements that Hayek-Robbins seek to supplant with Machian observational/empiricist ones evocative of the logical positivism of the Wiener Kreis, (tending toward equilibrium but generating the “utilization of knowledge” or “learning” that would evolve the system) – notions Mises despised because they would lead to a “scientistic determinism” incompatible with “action” and “choice”. Schumpeter will retain the Kantian moment with the notion of “Innovation”, exogenous to the system, and supplement it with Marxist antagonistic “evolutionary” notions.

Mises instead always turns “calculation” into “appraisement” by supplementing the “exchange” with “competition”. (For Kant’s influence on Mises, see Long’s, and also Boettke’s recent piece, “Witt., Austrian School and Logic of Action”. But Long ably re-establishes the Mises-Hayek link with Wittgenstein. See also Festre’; and the “Husserl vs. Schlick” article. Note also Kaufer’s article on Heidegger and Logic, re Frege-Husserl-Carnap.)

Cf. and discuss “The False Prison” which rightly teases out the “Schopenhauerian” origins of the Tractatus (ch 1 – “Wide-Angle View”.) whilst justly circumscribing the Kantian rapport.

Indeed, Wittgenstein moved further away from Machism and well toward Nietzsche after the failure of the Tractatus in that “later” he came to see the hopelessness of “founding” logic and mathematics “outside” (even phenomenologically – see Husserl’s concepts of “apodictic transcendence”) of their “self-referential” consistency, effectiveness or instrumentality which is the “inexorability” of the rules of language games. As Cacciari brilliantly expounds, the “rules” are “effective” because once they apply to a “reality” they encapsulate it or “circumscribe” it – they possess or permeate it ineluctably and totally: “the law always catches (raggiunge sempre) the guilty” …. because the law has no meaning without the guilty or guilt (Kafka) and without co-action or the State to enforce it (v. Bobbio on Kelsen). And this “always” is not just a statement of infallibility: it is a statement of im-possibility (non c’e’ possibilita’ di grazia – Cacciari). (Wittgenstein – if you think outside of the rules of chess, you are not playing the game. Therefore, pace Humpty Dumpty, I cannot choose to make a word mean whatever I choose. There is no choice in a language-game where words are governed by rules. To think outside the rules is im-possible.)

What Mises and Hayek (Schumpeter as well with his insistence on the Machian/Walrasian schema) do not understand is that the “efficacy” of “the logic of action” lies entirely in its first having “appropriated” reality. Logic does not describe or contain or refer to “reality”; logic has no “truth”, no “meaning”, it tells us nothing new but it renders visible: it is only ineluctable, it is only “inexorable” because it is tautological (Wittgenstein). Once we define money or rent and “utility” in a certain way – once we define “supply” and “demand” - once the “rules” of the game are set – the conclusions are inescapable and the consequences inexorable. But this is not because “reality” conforms to the “theory”: there is no theory – there is a language game! The hypothesis is not “falsifiable” – hence Hayek had to disagree with Popper about this as a condition of “scientificity”, although he also disagreed with Mises on the aprioricity of economic theory. There is only a “game” whose inexorability is hidden only by the fact that it does not “initially” encompass all reality as “given data” (Hayek)…. but it does so sequentially by approximation or “perfection” (Tarski).

Indeed, Hayek was the first to perceive (no, actually Walras and Pareto did too) that general equilibrium was flawed in the sense that it encompassed “simultaneously” the “totality” of events: it was, in Loasby’s words, a “closed system” that was completely and utterly “totalitarian” – Kafkaesque. But Hayek failed to see that this was the “destiny” of his “Pure Logic of Action”. Once the “reality” of its field of operation was “given” metaphysically (by positing scarcity-dependent ‘utility’, for instance, or ‘rarete’’), then the conclusions would follow “inexorably”. Hayek does not perceive this “inexorability” (his cousin Wittgenstein did) except perhaps in the case of “the impossibility of a socialist economy”, where Hayek could intuit the “extremity” of Mises’s arguments. Yet he believed that it was possible to proceed “by approximations” (like Tarski, but without the latter’s awareness of the impossibility of establishing the truth of logical propositions, but only the effectiveness of the rules in a given game).

Similarly with the concept of “competition”: Hayek showed how hopelessly aporetic this was. Loasby (‘Econ&Ev’, pp21-2) approves of Demsetz’s recasting of the concept as “perfect decentralization” and relates how Hahn regards general equilibrium as leading to intellectual death, as does Debreu – no improvements in knowledge are possible. He then proceeds unperturbed with “evolutionary/institutional” approaches that, as we will soon see (‘Demsetz’ below), are doomed by their limits! And Metcalfe refers to Hayek’s critique of “competition” in “equilibrium” theory as “devastating” (‘Ev Econ and Cr Destr’, p.15). But he still examines the implications of Hicksian growing returns to scale – as if these did not provide a perfect illustration of the “closed system” approach, though one that at least “formally” contradicts the assumptions of equilibrium analysis in favour of an “open-ended” Schumpeterian approach in the sense of Langlois (‘Analytical Review’)!

(My argument here is, see next section, that the “open-endedness” is only “formalistic” or “contemplative” [cf Lukacs] and therefore either aporetic or re-enclosable in the “closed system” model, at its “theoretical” best, or lapsing into a vulgar “practical empiricism” at worst. Indeed, it is this last “strategic use” [or ideological, but we prefer the other term to stress the “political usefulness” of ideology as against the “idealistic/impractical” connotations of the latter] that gives these “theories” any “relevance” at all! Pareto and Schump [CS&D] have something to say about these notions of “ideology”, too – cf Bobbio in our ‘Scientism’.)

Saturday, 12 March 2016

Mach and Robbins: Economical Science and Scientific Economics

How can a Wittgensteinian language-game be fitted to human reality? Conversely put, how can human reality be made to fit into a  Procrustean language-game such as "economic science"? The idealist "separation" (Plato's chorismos denounced by Nicholas of Cusa) of Subject and Object - starting from Berkeley through to Mach and then the Wittgenstein of the Tractatus - is the fateful precursor of Neoclassical Economics. The genealogy of this forma mentis is illustrated in and exemplified by Lionel Robbins's epistemological mise en scene of economics as "the science of choice". Yet far from being scientific, the Robbinsian definition of the economic problem rapidly degenerates into logical formalism, into yet another language-game far removed from the reality of human pro-duction. Any economics worthy of the name must become a "critique of political economy", that is to say, it must acknowledge its political essence, and then seek to overcome the real antagonism of its object of study - the capitalist economy and the society of capital. Cheers.

Even the wildest dream is a fact as much as

any other. If our dreams were more regular, more connected,

more stable, they would also have more practical

importance for us. In our waking hours the relations of

the elements to one another are immensely amplified in

comparison with what they were in our dreams. (p.11)

The ego is not

sharply marked off, its limits are very indefinite and

arbitrarily displaceable. Only by failing to observe this

fact, and by unconsciously narrowing those limits, while

at the same time we enlarge them, arise, in the conflict

of points of view, the metaphysical difficulties met with

in this connexion. (p.13) (Mach, “Antimetaphysik” in The Analysis of Sensations)

Mach’s theory of sensations is pure Schopenhauer. It contains therefore an implicit and stinging critique of Kantian metaphysics. To be sure, already the Kantian “thing in itself” had removed the relation between Subject and Object to one of mere “transcendence”, to the realm of “idealism” – however “critical” Kant intended these to be. And yet Kant’s notion of “intuition”, although it made human objective reality “unknowable”, still retained that indissoluble material link between human thought and “its” object – between fact and concept, between Object and Subject. The Kantian universe is still Galileo-Newtonian in the sense that it is something that can be com-prehended and en-compassed by human beings through the faculty of Reason by means of which the universe acquires an “order” and a “reason” that can be “uni-versally” recognized by all human beings – that can lead to a convergence or con-sensus over ultimate human goals and values. It is not that dreams are neglected because they have less “practical importance to us as scientists!” than waking reality: rather, it is because they have less importance “for the business of scientists!” The con-nection – empirical! – between the rise of capitalism and that of science is undeniable.

For us, therefore, the world does not consist of

mysterious entities, which by their interaction with

another, equally mysterious entity, the ego, produce

sensations, which alone are accessible. For us, colors,

sounds, spaces, times, . . are provisionally the ultimate


Elements [sensations], whose given connexion it is our business to

investigate. 1

Such empirical formalism simply obliterates the role of human goals in the pursuit of science, the search for a shared reality of human values.

With Mach and then Wittgenstein, Kantian rationalism gives way to pure empiricist positivism. There is no “substance” behind concepts; there are no “things” behind facts; there is no “reality” behind sensations. The task of science is merely to con-nect these sensations or facts by means of hypotheses whose guiding principle must be that of “economy”.

But anyone who takes his stand as I

do on the economic function of science, according to which nothing is

important except what can be observed or is a datum for us, and

everything hypothetical, metaphysical and superfluous, is to be

eliminated, must reach the same conclusion. (fn1 at pp.27-8)

But what is a “datum”? Mach is deceived by the “given-ness” of facts as data, which are not “given” at all but “found” in the sense of “searched for” by the scientist, in-vestigated like “vestigia” (tracks), hunted for. The tragedy of positivism is to forget the “activity” (auctor, auctoritas), the exercise of decision and power behind the data or facts (from facere, human action) that are “found” or ascertained. Certainly, anything “superfluous” can be neglected – because it is “superfluous”. But what is superfluous relates to a particular line of research – and then we must ask, “Who decides what to research?” Similarly, the hypothetical cannot be abandoned – because all science starts with “hypotheses”. And the drives, the human needs that lead to hypotheses can reflect meta-physical goals. What, then, can be “the economic function of science”?


But when time and the means for achieving ends

are limited and capable of alternative application,

then behaviour necessarily assumes the form of choice.

Every act which involves time and scarce means for

the achievement of one end involves the relinquishment

of their use for the achievement of another. It


has an economic aspect.1

But economic science cannot prescribe what particular choice an individual must make “scientifically” for it to be “economic”, because from an individual’s point of view the “choice” cannot be dictated by considerations other than the “choice” itself. Given a “choice”, its implementation is a matter for engineering, not for “economics”. Clearly then, economics intervenes only when individual choices are in conflict (scarcity) with the choices of other individuals (Hayek on Walrasian equilibrium). There must be the possibility of “exchange” of “goods”. But this presumes the prior existence of “goods” as individual pro-ducts – hence, the division of social labour into “individual labours” – and then the prior existence of property rights.

There is a tautology of choice here in that choice is reduced to science, and an oxymoron in the sense that “choice” cannot be scientific and “science” is “objective”, that is, it is independent of “choice”. This applies to societies as well – because it is impossible to determine what the “scientific” way of maximizing choices is without first knowing what these “choices” have “in common” – their “interest”, perhaps a “market mechanism” to reach “equilibrium” (Hobbes’s paradox – how can self-interested individuals agree to form a society or set up a market?)

Choice necessarily involves “scarcity” – that is why a “choice” must be made. But this “choice” is not “economic” because there are no parameters by which the “choice” can be graded apart from, outside of, the “choice” itself! If I specify what my parameters for my “choice” are…. then I do not have a “choice”! My choice becomes a mere “calculus”. Both logic and mathematics are just calculi that do not involve “choice”. Choice is ineluctably “political”, it involves many “individuals”. But then economics must become “political economy” and can never be a “science of choice”.

Economics is the science which studies human behaviour

as a relationship between ends and scarce

means which have alternative uses.1

1 Cp. Menger, Orundsätze der Vólkswirtschaftslehre, lte aufl·, pp. 51-70;

Mises, Die Gemeinwirtschaft, pp. 98 seq.; Fetter, Economic Principles, ch. i.;

Strigl, Die ò'lconomischen Katagorien und die Organisation der Wirtschaft,

passim; Mayer, op. cit. (Robbins, p.15)

By rejecting the “classificatory” definition of economics, which refers to “material welfare”, Robbins espouses the “analytical” formalism of Mach and Wittgenstein (p.16). But by so doing he completely dis-embodies economics, divorcing it even from its most fundamental political element – one that even Menger could not ignore: - the exchange of goods (p.16-7).

One may realise completely the implications

for oneself of a decision to spend money in this way

rather than in that way. But it is not so easy to trace

the effects of this decision on the whole complex

of "scarcity relationships"—on wages, on profits, on

prices, on rates of capitalisation, and the organisation

of production. On the contrary, the utmost effort of

abstract thought is required to devise generalisations

which enable us to grasp them. For this reason

economic analysis has most utility in the exchange

economy. It is unnecessary in the isolated economy.

It is debarred from any but the simplest generalisations

by the very raison d'etre of a communist society. (Robbins cites Mises’s Gemeinwirtschaft, p.18)

[I]t is clear that the phenomena

of the exchange economy itself can only be explained

by going behind such relationships and invoking the

operation of those laws of choice which are best seen

when contemplating the behaviour of the isolated


For it is not

the materiality of even material means of gratification

which gives them their status as economic goods;

it is their relation to valuations. It is their form

rather than their substance which is significant. The

"Materialist" conception of economics therefore misrepresents

the science as we know it. (p.20)

Economics is not concerned at

all with any ends as such. It is concerned with ends

in so far as they affect the disposition of means. It

takes the ends as given in scales of relative valuation,

and enquires what consequences follow in regard to

certain aspects of behaviour. (P.29)

It is obvious that this ends-means definition of economics can stand its ground if it breaches the condition of universality that Robbins seeks to ascribe to it: if it is empirically and positivistically confined to the effects of human behavior under specific conditions of exchange – but not to the totality of exchanges - then economics becomes pure engineering or “technique” as Robbins calls it in this chapter on “Ends and Means”. But if it seeks to extend to all combinations of ends and means, then it is clear that “economic science” must also be able to prescribe the ends that are “economic” or “affordable” – which contradicts his categorical exclusion of “ends” from economic analysis earlier in the chapter: Robbins is then forced to amend his definition to include not just the choice of scarce means with regard to known or given ends, but rather also the choice of combinations of all ends and means:

[Th]e problem

of technique arises when there is one end and a

multiplicity of means, the problem of economy when

both the ends and the means are multiple.1(p.31)

In fact, the problem arises when the ends are “given”, not when there is only one end! If the ends being pursued by agents are known or “given” (as in Walrasian equilibrium where utility schedules are common knowledge), then the economic problem does not exist and the “solution” is pure engineering – “technical”. But where the ends are not discernible, then the problem becomes at once political and economic – it becomes political economy, never “economic science”!

Robbins is confusing a technical problem – the choice of appropriate means to given ends - with the essentially political nature of “economics”: the social relations behind capitalist production. This is why, from the piecemeal viewpoint of exchange transactions only, where it remains a “technical” tool, his definition of economic science misses out on the essential political characteristic of capitalism – the accumulation of social power as value, as command over living labour by means of its “exchange” with dead labour. It is the impossibility of this “exchange” that inspired Marx’s critique. Thus, “value” in economics – what lies behind market “prices” and is embodied in “money” – is an entity that cannot have a “scientific” or technical meaning, but one that is intrinsically political. His failure to understand this vital point is why Robbins entirely misunderstands the function of money, leaving out entirely its role as a “store of value” in a capitalist economy:

Money-making in the normal sense of the term is

merely the intermediate stage between a sale and a

purchase. The procuring of a flow of money from the

sale of one's services or the hiring out of one's property

is not an end per se. The money is clearly a means to

ultimate purchase. It is sought, not for itself, but for

the things on which it may be spent—whether these

be the constituents of real income now or of real

income in the future. Money-making in this sense

means securing the means for the achievement of all

those ends which are capable of achievement by the

aid of purchasable commodities. Money as such is

obviously merely a means—a medium of exchange,

an instrument of calculation. For society, from the

static point of view, the presence of more or less money

is irrelevant. For the individual it is relevant only

in so far as it serves his ultimate objectives. Only the

miser, the psychological monstrosity, desires an infinite

accumulation of money. (P.30)

Money is much more than just a means of exchange and a unit of account – “a means of calculation” as Robbins clumsily puts it. Money is above all a store of value: it is the necessary expression of political relations pertaining to the exchange of living with dead labour (pro-ducts or goods or commodities). And the aim of capitalism is precisely “the infinite accumulation of money” as the embodiment of political power through the “exchange” of dead labour with dead labour! The miser Robbins has in mind – “the psychological monstrosity” – intends precisely to reach the Nirvana that is “the satisfaction of all needs” through the renunciation (Schopenhauer’s Entsagung) of present consumption! This is the crucial point behind the theory of capital in both Menger and then Bohm-Bawerk.

Friday, 4 March 2016

The Pure Logic of Choice - Part Two

Language can only be logical by being “internally” coherent, on its own terms (Godel), only by axiomatic definitions that cannot be proved “externally”; it can describe the world only by inscribing it, by de-limiting it through tautologies and their obverse, contradictions, set as its outer limits. A tautology is the outer limit of logic – the point at which, according to the principle of non-contradiction, logic has exhausted its possibilities and language has become circuitous or meaningless. The principle of non-contradiction is founded on the conventional application of tautologies to propositions. Logic can only certify the internal consistency of the use of symbols within “closed” or circuitous language-games: it can tell us whether a game is being played according to its internal “rules”. But logic, and therefore language, can never assure us of the intrinsic reality of the objects (intended in Wittgenstein’s sense of the word) to which language-games apply. This Wittgensteinian discovery – which, as we showed in the Nietzschebuch, belongs to Nietzsche - applies to all language-games, including theoretical science.

Does this mean that logical languages such as mathematics are entirely irrelevant to the world because they can only "say" something practically relevant when they "exit" the circuitous world of logic? Not at all! What we are arguing here is that by the very fact that logical propositions can be mistaken for substantive judgements about the world, as if they had a content or a meaning, - by that very fact logical propositions or language-games such as mathematical physics and economic theory can have a devastatingly brutal political "effectuality"!

All logical languages must then become language-games that can never encompass the world and yet are indissolubly bound to the world when they exit their own logicality. Only by abandoning logic can language hope to act upon the world. Logic is a negative tool that can tell us what is impossible, what is contradictory, but can never capture the possible entirely - because to do so its language, its signs, would need to be identical with their content – be factual in the sense of objective – and in that case this identity of object and predicate would annihilate itself as tautology.

(On conventionality and Poincare’, ‘S&H’, p66, see Cacciari, p72.)

Tragic were therefore both Wittgenstein’s stance and the attempts by the WKreis to give the lifeworld a “logical” foundation together with mathematics. W knew this and advised his readers to read the Preface and the Conclusion. But the PI relinquish even this goal. The turnaround in the PI represent a further concession of defeat in that they now confine the entire task of philosophy to the formal exercise of describing “language games” without even the hope of internal truth-hood coherence – the real reference of words to objects or perceptions - that the Tractatus had held out.

The inexorable instrumentality of the formal logico-mathematical “rules” ensures that the “theory” (which is the mere “id-entity” of the relations between “entities” that make up the rules) has a functionality that confuses “inexorability” with “predictability” and therefore makes those rules effective. But not true, because “truth” would require the ab-solute identity of the “rules”, of the language-game, with reality, the ab-solute congruence of thought and thing, mentis et rei – which is impossible, because no “rule” can be ab-solute, that is a legibus solutus - independent of other rules or of the matters over which it rules. (This is a version of Russell’s Paradox: logic depends on the rule or principle of non-contradiction; if this rule is independent of all other rules, if it is ab-solute, then it is not a rule because by definition a “rule” is dependent on the matters over which it rules; and if it is dependent on the matters over which it rules, then it cannot be an ab-solute rule. Thus, even the rule of non-contradiction is relative to the particular set of logical rules or matters to which it applies. Put differently, non-contradiction relies on difference, on the possibility of non-identity or non-tautology:

La proposizione negante deve avere qualcosa in comune con la proposizione negata, eppure non deve avere nulla in comune (Piana, p. 42.)

Yet difference can be tested only by reference to identity, which is a paradox because identity is mere tautology that can tell us nothing about the identical entities – which means that identity [like mathematical equations] can tell us nothing about difference.)

Durante le lezioni tenute a Cambridge negli anni 1930-33, Wittgenstein riprende questo tema con una sorta di reductio ad absurdum della stessa nozione di regola deduttiva.

Vi sia una regola r in base alla quale posso concludere p da q. Potremmo dire che p deriva da q e da r. Vi sara’ allora bisogno di una nuova regola che giustifichi questa inferenza. Sic ad infinitum (p.88. Piana’s attempt to explain away W’s reduction of deducibility is thoroughly unconvincing – because it is specious to distinguish between the “rule” r that makes a proposition deducible from another, and the “proposition” that it entails for the simple fact that the rule and its implied proposition are not logically distinguishable. If indeed a proposition has the logical “force” of deducibility, then it is equally a “rule”. And it is clear that all “rules” must be able to be “read” or interpreted, however “intuitively”, as propositions – because there can be no distinction between logic and its translation into language [ although, as we have said, language is broader than logic]. Cf. Piana’s discussion of W’s meanings for “intuitive” from p.79.)

Se vi e’ una regola che consente di concludere p da q, allora p deve essere gia’ una consequenza di q. In nessun modo una regola inferenziale puo’ giustificare dall’esterno il sussistere di un rapport di consequenza logica tra proposizioni. Percio’ la regola – e qui l’argomento erroneo di Wittgenstein mostra il suo rovescio – non puo’ essere intesa come come una nuova premessa che va ad aggiungersi alle premesse di una deduzione. Non vi e’ una molteplicazione infinita delle regole ma, al contrario, vi potrebbe essere una loro totale eliminazione (p.90)

But, if Piana were right, then one could argue, as he does, that there is a total elimination of rules of deducibility! How, then, would we be able to determine that p is deducible from q? Deducibility is not a fact: it is an argument, it is a proposition that tells us about the necessity of the deduction. Even assuming that the rule of deducibility is a command (Do this!) and not a proposition, it is still true that a command is a proposition of the type “All propositions of the type q necessarily must result in p”. Indeed, all tautologies contain such a “command” which is really a “de-finition”. Deductions or inferences or tautologies do not follow “intuitively” – this is the point! There is no intuitus originarius (pace Leibniz and Kant) behind tautological deductions: they are just “rules of the game”, axioms and definitions set up conventionally before they are applied to propositions. (This realization or objection was behind Heidegger’s critique of Kant’s notion of “imagination” and “intuition” in “Kants Metaphysik”.)

If the correspondence of proposition and reality were “unregulated”, then no “deduction” would be possible because there could be no awareness of a tautological state: quite simply, the tautology would not, could not, ec-sist. This, if nothing else, is the basis of Kant’s distinction between synthetic and analytic a priori! But Kant could not see just this point: that the “synthesis” is purely tautological, just as the analysis – because of the “rule”!!! Even a phrase such as “the bald man is bald” requires a rule of deducibility because there is nothing in “the bald man” that requires this phrase to be tautological, unless we state that “the bald man” on either side of “is” are one and the same “object”! If all “rules” could be abolished, then there could never be a tautology or a contradiction (which relies on tautologies – because nothing is contradictory unless it is defined by a rule as the direct opposite of a tautology) in the first place! Otherwise, if deductions were “possible” without “rules” of deducibility, then deductions would be a matter of merely empirical intuition, indeed of an intuitus originarius! But what makes tautologies and deductions empirically possible – what makes them “effectual” – is precisely the conventional “rule” of deducibility. Here the materiality of logico-mathematics comes prepotently to the fore!

Therefore, neither mathematics nor logic and least of all scientific “laws” based on equations can reconcile human interests – because their validity and value only become apparent at the precise point where logico-mathematics and science abolish themselves, at the point where their conventionality, their arbitrariness becomes evident – at the point of tautology. A logical tautology is more than “nothing” when it implies a practical difference between the entities whose id-entity it wishes to fix “logically”!

All that remains is the sheer “functionality-instrumentality” of symbolic frameworks that can only be “games” with inexorable rules (Foundations, 118). The ‘de-finition’ of a “language-game” can achieve only “internally logical” (self-referential, circuitous) consistency by the postulation of “arbitrary” premises or axioms that exclude/abolish any “scientific or logical” validity. Indeed, Cacciari reminds us, Wittgenstein objected (against Russell) to the very idea of a “single” language game, one with “meta-linguistic” or “essential” rules. Just as the “rules” of a language-game” subject its ‘universe’ and domain to an inexorable logic or “destiny” (recall Nietzsche’s and Heidegger’s ‘Schicksal’), so are they ‘destined’ to “scientific failure”.

Just like sovereignty (Schmitt) and freedom (Hobbes, Schopenhauer) and existence (Hegel, Heidegger) for the negatives Denken. Legality and legitimacy cannot co-exist in the same entity: a sovereign reigns but does not rule. To rule, a sovereign must receive its authority from a pre-existing rule, but then the sovereign would be subject to that rule, which removes the auctoritas of the sovereign. That is why, for Schmitt, “sovereign is he who decides on the exception [to the rule]”. Nevertheless, the authority of the sovereign relies on the acceptance of rules on the part of subjects, including acceptance of any “exception” imposed by the sovereign. But the sovereign’s ability to impose both the rules and the exception does not and cannot arise from the rules themselves – because otherwise the sovereign could not impose the exception to the rules. But if this authority is “extra-legal”, if it is beyond the law, then it is illegal and illegitimate, or it can be “legal and legitimate” only if the law prescribes who is to decide but not what is decided, what is “law”. Hence, legality and legitimacy cannot co-exist (cf. Schmitt’s homonymous work).

As Carl Schmitt acutely perceived, it is always “the outer boundary” of a science that reveals its real content – its “effectuality”, its political force. Like sovereignty for Schmitt, it is the exception to the law that defines the ruler; like the Hobbesian social contract, it is the alienation of freedom that preserves its possibility: by limiting the Ego, the State preserves but can never reconcile all individual egoisms (Schopenhauer). It is the destructive tautology – the logical identity that destroys the content of entities by erasing their difference - that shows the outer limit of language. Only beyond tautology can language begin to describe the world; but beyond tautology logic and language have no rational validity or consistency: they have only a political sense.

Una tautologia non e’ una  proposizione vera per ogni cosa, essa non dice qualcosa che vale per tutte le cose. Essa non dice, in generale, nulla (Piana, 81-2, also pp.84-5 and p.88)

To reprise and correct Humpty Dumpty, then, it is not “the master” who can fix the meaning of words (the rules) through his power; instead, it is the power of the master that determines what meaning words (rules) must acquire (including the exception) if he is to remain master! The master cannot make words mean what he chooses; rather, it is what makes him master that gives a particular meaning to words: words reflect the power of the master, they are not the master’s arbitrary imposition or expression; they are the expression of the “game” that empowers the master. Hence, the master must play by the rules of the language-game that reflects his real power if he is to retain that power.

Cio’ che un segno puo’ esprimere e’, fino a un certo punto, deciso dal segno stesso: e’ impossibile prescrivere ad un segno “che cosa gli sia lecito esprimere” (Piana, p.54)

Ad esso e’ lecito esprimere cio’ che gli e’ possibile esprimere” (what it can[!] express)

The language-game is a strait-jacket that reproduces and seeks to perpetuate the power of the master; it is not an arbitrary invention by the master. Max Weber’s notion of “responsibility” [Ver-antwortung or “answerability” or “accountability”] takes heed of this necessary constraint on “power” – that it cannot be “arbitrary” because, as Hannah Arendt points out in On Violence, arbitrary power lacks authority or legitimacy, which is why its exercise is prone to violence. This is the political significance of Wittgenstein’s insistence that logic and language are not entirely “conventional”.

What concerns us here is the “attempt” to transform the fluid human activity in the sphere of production (which therefore we do not see, pace Lowith or Hegel, as “the annihilation of nature” but rather as its “transformation”) from a “playful/creative” activity (represented by the concept of living labour) into a straitjacket of “game-rules” that define and confine, limit and constrain living labour to ensure its domination by dead labour. This attempt is thus the real practical political strategic goal of the “scientific” game or paradigm that neoclassical theory has sought to set up, culminating in Robbins’s “economics as science of choice”, Hayek’s “Pure Logic of Choice” and, more recently, in the whole enterprise of “game theory”.

To illustrate, just as the rules of any game, such as a “competitive sport”, do more than  describe the playful agon of human beings but actually and effectively serve to con-fine, to limit and con-dition the human activity and its creative aspirations or aims – so neoclassical theory constitutes (to invoke Wittgenstein, “ideas are like glasses on our nose – everything we see is through and for them”) the “glasses” through which reality or human action is not only “seen/interpreted” but also guided/channeled and confined/conditioned (seen for the theory).

But the “conventionality” of sporting games (from chess to rugby) is readily visible in part because the “rules” are fixed by convention and not, as in economic activity, through long historical transformations that make less “visible” and com-prehensible or per-spicuous the super-position or im-position of the rules to the conduct of human activity. The “activity” becomes “ossified” or reified, either “frozen in time” (and therefore “synchronic”) or “evolving” in one dimension (steady state, cf. Lachmann) into a “uni-verse” so that this latter becomes confused with and mistaken for the original activity  – which, instead, is only the variable and mutable “historical content” of the “rules” which are themselves in-variable, im-mutable and alas in-exorable – so that now the “activity” appears to be transformed into, wholly “captured” by, the “in-variance”, “im-mutability” and “inexorability” of the rules!