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!