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!
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