The Pure Logic of Choice - from Wittgenstein to Mises

This is the first instalment of a large study I have undertaken on the Austrian School's notion of "the pure logic of choice" which led to Lionel Robbins's definition of economics as "the science of choice". As we have seen from our studies on Carl Menger and Bohm-Bawerk, the Austrian School defines economic value as "Objective Value" as the resultant of conflicting Subjective Values that are then manifested in market prices. Despite their attempt to reject metaphysics, the central principles of Neoclassical Economics are pure metaphysics - and that is what we are seeking to demonstrate here by drawing the intellectual antecedents of what the Neoclassics believed was a new "positive science".

 Cheers to all!

'When I use a word,' Humpty Dumpty said, in rather a scornful tone, 'it means just what I choose it to mean — neither more nor less.'

'The question is,' said Alice, 'whether you can make words mean so many different things.'

'The question is,' said Humpty Dumpty, 'which is to be master — that's all.'

Al hacer el paralelo lingüístico del punto de partida de Wittgenstein y

de Heidegger acabo de emplear intencionalmente el término “autoenajenación”.

Con este motivo puede recordarse una tercera crítica a la

metafísica tradicional, en boga al presente, que parte asimismo de una

sospecha fundamental: a la “sospecha de falta de sentido” de Wittgenstein

y a la sospecha del “olvido del ser” de Heidegger precedió la “sospecha de

ideología” de Karl Marx dirigida contra la metafísica. Esta consideración

lateral puede servir para delinear por completo el horizonte históricoespiritual,

dentro del que esferas de la filosofía contemporánea presentan,

por más heterogéneas y recíprocamente separadas que parezcan, un

punto de referencia común.

El punto de referencia común en conexión con nuestro problema es la

puesta en cuestión de la metafísica occidental como ciencia

teórica.

Así pues, en lo que sigue yo deseo comparar entre sí a Heidegger y a

Wittgenstein desde el punto de vista de que a través de ambos, cada uno

de diversa manera, la metafísica occidental es puesta en cuestión y con

ello es desplazada por nosotros fácticamente como un fenómeno histórico.

El punto de vista de nuestra comparación puede determinarse con más

exactitud, si tenemos ante los ojos la pregunta fundamental de Heidegger

sobre el sentido del ser y la pregunta fundamental de Wittgenstein sobre

el sentido de proposiciones filosóficas como maneras de la crítica de

sentido. (K-O Apel, Wittgenstein y Heidegger, p.4)

The aim of Ernst Mach’s philosophy of science was to e-liminate philosophy from scientific inquiry – to push it, and especially meta-physics, well and truly beyond the realm of physics, beyond the ken of science. In his own words, philosophy ends where science begins and it begins where science ends (see Introduction to Knowledge and Error [Erkenntnis und Irrtum]). Science does not describe a world of “things” – literally, a “reality” – outside our own perceptions or “sensations” (Empfindungen). Human sensations are what they are: they are and can never be “erroneous”. What can be erroneous, instead, are the scientific “hypotheses” that we develop so as to account for our various sensations. When these hypotheses are changed because of new or different sensations or “evidence”, it is not that we see “reality” any more “truthfully”; it is rather that we now assemble and connect our sensations in a manner that is more systematic and “economical” than before; in a manner that is more “consistent” with our plans and intentions. The old idea of science as the search for Truth or for a Reality that lies beyond or behind our sensations is entirely irrelevant. Plato, Descartes and Kant all assumed that the task of the theoretician was to penetrate the “nature” of Reality, to arrive at an inconfutable “Truth”. But this attempt is simply “meta-physical” and therefore impossible, because all we possess, all that we are aware of and can know are “sensations” - and science is a way of connecting them through hypotheses that are constantly changing in correspondence with our needs and activities.

Mach’s criticism of Newtonian essentialism – of the notions of absolute Space and Time – does not contest the empirical findings of Galileo-Newtonian physics, but it does redefine the entire nature and scope of “science”. This Machian critique of essentialism and of philosophy tout court is inconceivable, of course, without Schopenhauer’s critique of Kantian metaphysics, even before one considers Berkeley’s idealism (as does Karl Popper in Conjectures and Refutations; see on this our contributions on Schopenhauer). Yet that is precisely why, contrary to what Mach and the Vienna Circle intended, “the end or com-pletion or ful-filment of metaphysics”, as diagnosed by Nietzsche, does not entail the beginning of theoretical science but its real “crisis”. The very inability of philosophy to encompass the world without reifying it, its inability to ascertain the congruence of “mind” and “thing” is the reason why science will never be able to be “scientific”. Conversely, Mach’s attempt to denigrate the ultimate Reality, the ultimate Values, that may lie beyond science leaves science open to the criticism that it is indeed only a disguised tool in the hands of the scientists who pursue it and the business interests that finance its “research”.

This, then, is the meaning of the Krisis that Husserl denounces in his seminal essay at the turn of the last century: - a crisis that is not confined solely, as Apel wrongly suggests above, to Western metaphysics as a theoretical science, but to all theoretical science as an enterprise that can capture reality itself from an objective, “scientific” viewpoint – that is, from a rationally neutral standpoint free from antagonistic human interests, free from social conflict.

For this philosophical debility cannot be interpreted solely from a purely philosophical standpoint, as the failure of meta-physics. Indeed, as Husserl himself argued in the titles of two of his last major essays, “the crisis of the European sciences”, including the natural sciences, is really “the crisis of European humanity” in the sense that the ideal role of science as the “neutral” pursuit of Truth par excellence could no longer be sustained given its growing subordination to the sphere of capitalist business interests and, thereby, its avulsion from its original “speculative” goal as theoria. Mach himself in the Introduction to Irrtum und Erkenntnis had felt impelled and took pains to distinguish the two roles, stressing how business aims could not be reconciled with the “nobler” aim of “dispassionate” scientific research, evincing thus the apprehension that science may not be epistemologically “scientific” after all. (See also, of course, M. Weber’s all-important lecture Wissenschaft als Beruf diagnosing the definitive confluence of science and capitalist enterprise under the guidance of the State apparatus or bureaucracy.)

Nor does this “crisis” concern merely the so-called “social” sciences: it concerns all science because the relation of the apparent “progress” of the natural sciences to human social progress, far from being “natural”, is entirely dependent on the specific forms of human social relations. In other words, the crisis is not merely a “social” one but one that concerns also the very nature and import of “scientific truth”.

What is obviously also completely forgotten is that natural

science (like all science generally) is a title for spiritual accomplishments,

namely, those of the natural scientists working

together; as such they belong, after all, like all spiritual occur

The Vienna Lecture / 273

rences, to the region of what is to be explained by humanistic

disciplines. Now is it not absurd and circular to want to explain

the historical event "natural science" in a natural-scientific way,

to explain it by bringing in natural science and its natural laws,

which, as spiritual accomplishment, themselves belong to the

problem?

In equal measure, the “suspicion of ideological intent” moved against metaphysics by Marx is really the suspicion of the lack of democratic content not just of philosophy but of all theoretical sciences under the rule of the bourgeoisie, chief among them that “political economy” that is the object of his “critique”: the “transcendence” of metaphysics amounts to a hypostatization and a reification of human life and reality – of “the world” – that prevents the reconciliation of human interests that only an immanentist view of human historical reality and therefore of “the world” can allow. Regardless, Husserl’s own attempts to ground his phenomenology as theoria encompassing the pre-reflexive lifeworld foundered on the impossibility of separating the lifeworld from theoretical concepts (this is an expression of Godel’s theorem and of Wittgenstein’s findings in the Tractatus):

While the theoretically known world may depend on consciousness

for its "constitution” the life-world seems to provide

the given materials with which consciousness deals. If it is in

turn to be dealt with in terms of transcendental constitution, as

Husserl also insists, then it seems to lose precisely what was

described as one of its essential features, its pre-givenness. But in

either case the second difficulty arises, namely, that the attempt

to describe the life-world, as Husserl admits, is itself a theoretical

activity, indeed, theöria of the highest order, phenomenology.

But if every theoretical activity presupposes the structures of the

life-world, this must also be true of phenomenology, which in

this case cannot be without presuppositions. (Ross, loc.cit., p. xli.)

WITTGENSTEIN

Behind Wittgenstein’s attempt to isolate a logic that corresponds to an ineluctable reality independent of all metaphysics lies this strenuous and desperate search for “scientific” neutrality, for objectivity: his ultimate desperate failure is an admission of the inevitability of metaphysics, of linguistic ambiguity and partiality, of the ineluctably conventional status of language and logic – and therefore also of the human antagonism it conveys. Wittgenstein’s lifelong “logico-philosophical investigations” drown in a sea of mysticism. (Cf. G. Piana, Interpretazione del Tractatus.) Equally, Heidegger’s notion of Dasein, of human existence as contingency and possibility, as mere “freedom toward death”, - his emphasis on authenticity as a prise de conscience against the reifications of Technik and of “gossip”- his definition of language as “the house of Being” – all this mirrors Wittgenstein’s mysticism in the sense that it is impossible to identify an order of things independently of conflicting human interests.

Wittgenstein represents the utmost attempt to give a secure philosophical grounding to the Machian/Austrian Weltanschauung that seeks to relegate metaphysics to the realm of the unknowable – but an attempt that he records as a “desperate failure” from the very outset – and the reason for which he scorned any attempt at affiliation with Rudolf Carnap’s Vienna Circle (see B. McGuinness, Wittgenstein and the Vienna Circle). Indeed, Wittgenstein’s logical investigations into the interface of language and reality only serve to reaffirm the inevitability of metaphysics and therefore his philosophical investigations (in the wake of Husserl’s Logical Investigations) turn into an illustration of the necessity of his failure – the failure of these investigations is their con-clusion, ful-filment, their outcome, their suc-cess, their Erfolg (multiple meaning in German of “event” and “success” or “outcome”).

But Wittgenstein acknowledges this failure only philosophisch in the sense that he reaffirms the necessity of the inter-connection of language with the world, the inevitability of their symbiosis, only from the transcendental viewpoint, not from an immanent one. His conclusion that language is as dependent on the world as the world is dependent on language – his dire refusal to fall either into Platonic rationalism or conventionalism or into Aristotelian realism or empiricism – still fails to overcome the contemplative stance of philosophy, its chorismos or scission of Subject and Object as Gegen-stande, as the op-posing positions of “mind” and “thing”, of “facts” and “concepts”:

We have a colour system as we have a number system.

Do the systems lie in our nature or in the nature of things? How are we to put it? — Not in the nature of numbers or colours.

Then is there something arbitrary about this system? Yes and no. It is akin both to the arbitrary and to the non-arbitrary.

It is immediately obvious that we aren't willing to acknowledge anything as a colour intermediate between red and green.

. . . but has nature nothing to say here? Indeed she has—but she makes herself audible in a different way.

‘You'll surely run up against existence and non-existence somewhere!’ But that means against facts, not concepts.16 (from Pears)

Wittgenstein here neglects the symbiosis of fact and concept in the immanent development of human perception or intuition (cf. Merleau-Ponty, Phenomenology of Perception). It is in this regard that the Marxist critique of the bourgeois antinomies on the part of Gyorgy Lukacs can be inserted in what Apel aptly calls the “self-alienation” of philosophy from the world in the theories of both Wittgenstein and Heidegger. By abandoning its enigma, by reducing itself to a system of identities, by aiming for Truth, all science seeks to com-plete its object and thereby to abolish itself: this completion (German, Voll-endung) and therefore “full-ending” of science has always been the self-alienating goal of Western thought, of metaphysics itself – its Selbst-aufhebung - in the sense that Western thought in its philosophical and scientific moments has always sought to circum-scribe language and human experience by privileging contemplation over praxis, transcendence over immanence, separation (chorismos) over participation (methexis) (Cusanus in Cassirer), domination and subjugation over discourse and democracy (cf. Colli, Nascita della Filosofia). (This tendency of Western societies to circumscribe thought and language, to limit them to the sphere of passivity, inaction and contemplation, is the target of the revival of the distinction between “constituted power” and “constituent power” by Hannah Arendt in On Revolution [for a fuller discussion, v. A. Negri, Insurgencies].)

Husserl follows Plato and Aristotle in attributing the

origin of philosophy to Thaumazein simple wonder at things being

the way they are. But while such wonder constitutes at most a recurring,

fleeting pause in the natural course of life, the theoretical

attitude reverses the priorities: the concern with "the way things

are" which was intrusive and nonessential to natural life becomes

the primary concern, while the non-theoretical life, which still

remains, is subordinated to the theoretical life. "In other words,"

Husserl says, "man becomes a non-participating spectator, surveyor

of the world; he becomes a philosopher" (Appendix I, p.

285, below).

Yet contained in this description of the emergence of the

theoretical attitude, and developed at length in the Crisis, is a

theory of its dependence upon the naive attitude that precedes it.

The naive, pre-theoretical life is engaged in the world, the milieu

and horizon of its activity. The world with which the philosopher,

the scientist, attempts to deal is this very world-horizon in

which the naive life runs its course. This is the life-world, which

is always "already there," "pre-given," when theory begins its

work. But the world's very pre-givenness, the structure through

which it envelops conscious life and provides the ground (Boden)

on which it moves, is always presupposed by any theoretical

activity.

The pre-theoretical attitude of naive world-life, and the lifeworld

which is its horizon, are thus found to be prior to all

theory, and not merely in the historical sense. (D. Carr, Intro. to E. Husserl, Krisis, p. xl.)

In keeping with Mach’s empirio-criticism, the very first proposition of the Tractatus, that the world is all that either is or is not the case, already “banishes” the world itself from the compass of philosophical analysis intended as meta-physics – because the world is not a proposition and it is not a “case” (Fall), a mere “possibility”. By circumscribing the task of philosophy to that of identifying what may and what may not be the case, Wittgenstein already relinquishes the aim of philosophy, indeed of language tout court, to describe the world as a totality encompassing its individual “cases”: “the world is the reach of my language”.

Nella metafora dello spazio logico si annuncia gia’ nelle prime frasi del Tractatus il tema della connessione tra logica e mondo. La logica non tratta del mondo, di cio’ che in esso accade, ma di cio’ che puo’ accadere. I suoi “fatti” sono tutte le possibilita’. Percio’ possiamo dire che la forma logica e’ la forma della realta’; oppure che la logica e’ logica del mondo (Piana p.47)

The “logic” of the Tractatus is purely formal in that it applies to “objects” that cannot be further described on the purely “logical” assumption that for every describable fact there must be an object that can no longer be described as a fact. But this is a purely formal assumption that does not correspond to reality because language can never be logical except to the extent that it is governed by logical rules – and in turn logical rules can never be proved ab-solutely, that is, independently of linguistic senses or meanings that are il-logical. Language, like the lifeworld, encompasses logic but it is not itself logical. Similarly, the world encompasses language but is not itself linguistic.

E come nel razionalismo il richiamo all’evidenza era niente altro che la posizione dell’istanza di una sfera di verita’ fondate in se stesse, cosi’ anche qui’ [con Wittgenstein] arriviamo a concludere che “la logica deve bastare a se stessa” [5.473]. Ma in questo contesto l’idea dell’autonomia della logica non e’ altro che l’idea dell’autosufficienza [della logica], della conclusione e perfezione dek suo linguaggio (Piana, 83)

Wittgenstein proves that, just like metaphysics, the aim of logic is to ful-fill, to com-plete, to per-fect, and therefore to abolish itself. The Tractatus still held out the promise of an internally-coherent “language” with demonstrable truth value referring to sense data that could clarify thought processes prone to philosophical delusions – on the ground that reality cannot be contradictory, but language can be. But logic is the rigorous, non-contradictory form of language. And language can never define the world because its definitions are indefinite – they always engender fresh definitions (cf. Godel’s Theorem) - and because the world is not Being but rather being-as-becoming, physis (cf. Heidegger’s fundamental essay on physis in Holzwege). This is the enigma of theoria – one that can be solved only by human resolve, only through praxis.

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.

All language must then become a language-game that can never encompass the world and yet is indissolubly bound to the world when it exits its own logical content. 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 “Kant’s 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”.